Download A compendium on beam transport and beam

A compendium on beam transport
and beam diagnostic methods for
Free Electron Lasers
IRUVX-PP Expert Group Report
A. Lindblad, S. Svensson, K. Tiedtke
Partners of IRUVX-PP – the preparatory phase of EuroFEL
Imprint
Publishing and contact:
Deutsches Elektronen-Synchrotron DESY
IRUVX-PP Project Coordinator
Notkestr. 85, 22607 Hamburg, Germany
Tel.: +49 40 8998-4130
www.eurofel.eu
ISBN 978-3-935702-45-4
This compendium is neither for sale nor may be resold.
Editors:
Dr. Andreas Lindblad , Prof. Dr. Svante Svensson, Dr. Kai Tiedtke
Copy deadline: March 2011
Cover layout: Monika Illenseer
Printing: Konrad Triltsch GmbH, Ochsenfurt-Hohestadt
Editorial note:
The authors of the individual scientific contributions published
in this compendium are fully responsible for the contents.
Cover:
FLASH experimental hall at DESY in Hamburg and diffraction image.
(Photos: © Heiner Mueller-Elsner / Agentur-Focus.de; DESY)
A compendium on beam transport
and beam diagnostic methods for
Free Electron Lasers
IRUVX-PP Expert Group Report
A. Lindblad, S. Svensson, K. Tiedtke
Partners of IRUVX-PP – the preparatory phase of EuroFEL
Dr. Andréas Lindblad
MAX-lab, Lund University
P.O. Box 118,
SE-221 00 Lund
Sweden
Prof. Dr. Svante Svensson
Dept. Physics and Astronomy, Uppsala University
Box 516
SE-751 20 Uppsala
Sweden
Dr. Kai Tiedtke
Deutsches Elektronen-Synchrotron (DESY)
Notkestr. 85
D-22607 Hamburg
Germany
ISBN 978-3-935702-52-2
This book was set with LATEX using the memoir class
Foreword
Text on IRUVX-PP and the reports, participants in the different workpackages
(Svante and Kai?)
iii
Preface
Caveat Lector
This book’s humble beginning was as a summarizing report of the collective efforts
within the 7th workpackage of the Iruvx-PP programme. During the time of writing
(the last twelve months of the programme) the members of the workpackage produced
reports on their findings – often containing reviews of the various fields where the
undertakings took place.
Each such report have been, more or less, basis for sections and indeed whole
chapters in this book, notably in the second part. The reports’ titles and their authors
are mentioned in the very beginning of the chapters where material from them have
been used.
A summarizing report may be interesting in itself, but to heighten the appeal to
a broader audience and to future students and colleagues it was thought that when
adding context to the reports (who by themselves deal mainly with X-ray optics
and photon diagnostic methods) a good introductory textbook describing the various
challenges pertaining to work and development of free electron lasers could be realized.
Hence the first part of the book describes the physics and concepts that govern
free electron lasers. The various components of a free electron laser is also described
– from the electron gun to the undulators, and some X-ray optics. The second part
of the book focuses heavily on diagnostic methods that can be used to quantify the
properties of the free electron laser photon beam. In the last chapters of part two
the current running and planned facilities are described in the light of what we have
learned in the first part of the book, planned and performed experiments are described
as to give an orientation of what scientists are trying to achieve with the facilities.
The bibliography of this book contains both references to books and articles that
reflect the current state-of-the-art, at least for part two of the book, at the time of
writing (February 2011). No such list is ever complete and will soon become dated
– however through citations to those papers the reader will soon find where the field
have developed. Without any doubt many of the references will remain key references
for quite a foreseeable time.
v
vi
Preface
Acknowledgements
I would like to extend my gratitude to my editors Prof. Df. Svante Svensson and Dr.
Kai Tiedkte for giving me the opportunity to work with this book. I also thank them
for the many nice discussions and the good criticism during the authoring process.
Naturally I also like to thank the authors of the reports which constitute parts of this
book without which I would literally have started with a blank page.
Thanks to the many nice presentations on the Iruvx-workshops and free electron
laser conference last year I have been kindly introduced to the fantastic subject of
free electron laser science. Again, for the opportunity to work with it and writing a
book about it I will be forever grateful.
Andréas Lindblad, Hamburg, Xth Feb. 2011.
Contents
Foreword
iii
Preface
v
Contents
vii
I Free electron lasers – a primer
1 Introduction
1.1 Historical exposé & scientific background . .
1.2 Laboratory X-ray and UV/Vis photon sources
X-ray tube and anode sources . . . . . . . . .
Synchrotron light sources . . . . . . . . . . .
Lasers . . . . . . . . . . . . . . . . . . . . . .
High Harmonic Generation Lasers . . . . . .
1.3 Free electron Lasers . . . . . . . . . . . . . .
1.4 Development of X-ray free electron lasers . .
1.5 Seeding schemes . . . . . . . . . . . . . . . .
eSase . . . . . . . . . . . . . . . . . . . . . .
HGHG . . . . . . . . . . . . . . . . . . . . .
EEHG . . . . . . . . . . . . . . . . . . . . . .
Harmonic afterburners . . . . . . . . . . . . .
1.6 Definitions used throughout the book . . . . .
Brilliance and Brightness . . . . . . . . . . .
Emittance . . . . . . . . . . . . . . . . . . . .
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2 Synchrotron radiation and its properties
2.1 Radiation from a moving charge . . . . . . . . . . . . . .
Maxwell’s laws . . . . . . . . . . . . . . . . . . . . . . . .
Charged particle at rest or moving with constant velocity
The fields from a charge in arbitrary motion . . . . . . . .
Frequency and coherence of synchrotron radiation . . . .
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viii
Contents
2.2
2.3
2.4
2.5
Radiation from a bending magnet . . . . . . . . . . . . .
Undulator radiation . . . . . . . . . . . . . . . . . . . .
The undulator equation . . . . . . . . . . . . . . . . . .
Microbunching . . . . . . . . . . . . . . . . . . . . . . .
Interaction between the electron beam and the radiation
Exponential gain . . . . . . . . . . . . . . . . . . . . . .
Scaled free electron laser equations . . . . . . . . . . . .
Sase . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Coherence properties . . . . . . . . . . . . . . . . . . . .
3 Free electron laser ”hardware”
3.1 A prototypical FEL amplifier . . . . .
3.2 Electron guns . . . . . . . . . . . . . .
General requirements . . . . . . . . . .
Thermionic emitters . . . . . . . . . .
Photocathode emitters . . . . . . . . .
Normally conducting guns . . . . . . .
Superconducting guns . . . . . . . . .
Summary . . . . . . . . . . . . . . . .
3.3 Radio-frequency driven accelerators . .
The accelerating RF-field . . . . . . .
Energy gain in a radiofrequency driven
Warm technology: Copper . . . . . . .
Superconducting technology . . . . . .
3.4 Undulators . . . . . . . . . . . . . . .
Undulator tolerances example . . . . .
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4 X-ray optics
4.1 Demands on optics precision at free electron lasers . .
4.2 Focussing mirrors – back-reflecting geometry example
4.3 Damage . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Diffraction gratings . . . . . . . . . . . . . . . . . . . .
4.5 Monochromators . . . . . . . . . . . . . . . . . . . . .
4.6 Beam attenuators . . . . . . . . . . . . . . . . . . . . .
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5 Beam-splitting methods
5.1 Introduction . . . . . . . . . . . . .
5.2 Beam-splitter specification . . . . .
5.3 Amplitude division beam splitters
Partially transmitting materials . .
Crystal diffraction beam splitters .
Gratings . . . . . . . . . . . . . . .
Grids . . . . . . . . . . . . . . . . .
5.4 Wavefront division beamsplitters .
Beamline apertures . . . . . . . . .
Knife-edge mirrors . . . . . . . . .
Knife-edge crystals . . . . . . . . .
Fresnel bi-mirror . . . . . . . . . .
Slotted or perforated mirrors . . .
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Contents
5.5
5.6
ix
Structured arrays . . . . . . . . . . . . . . .
Time-based splitting . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . .
Techniques requiring the least development
Techniques requiring more development . .
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II Beam diagnostics
93
6 Introduction
6.1 Diagnostics categorization . . . . . . . . . . . . . . . . . . . . . . . . .
Subcategorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
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7 Spectral diagnostics: Intensity
7.1 X-ray spectrometry . . . . . .
7.2 Intensity/Beam energy . . . .
Gas monitor detectors . . . .
Calorimeters . . . . . . . . .
Solid state devices . . . . . .
7.3 Photon-energy . . . . . . . .
Ion time-of-flight . . . . . . .
Electron time-of-flight . . . .
& Energy
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106
8 Beam cross-section diagnostics
8.1 Introduction . . . . . . . . . . . . . . . . . . . .
The ideal cross-section diagnostic . . . . . . . .
Distribution of diagnostics along the beam . . .
Content of this chapter . . . . . . . . . . . . . .
8.2 Definitions . . . . . . . . . . . . . . . . . . . . .
8.3 Direct imaging of the beam . . . . . . . . . . .
Imaging a replica of the beam . . . . . . . . . .
Summary of imaging techniques . . . . . . . . .
8.4 Scanning techniques . . . . . . . . . . . . . . .
Scanning wire . . . . . . . . . . . . . . . . . . .
Scanning crossed wires . . . . . . . . . . . . . .
Scanning slit . . . . . . . . . . . . . . . . . . .
Scanning pinhole . . . . . . . . . . . . . . . . .
Scanning knife-edge . . . . . . . . . . . . . . .
Summary of scanning techniques . . . . . . . .
8.5 Ionization beamprofile detectors . . . . . . . . .
8.6 Imaging ion chambers . . . . . . . . . . . . . .
Fluorescence detection in residual gas monitors
8.7 Sampling techniques . . . . . . . . . . . . . . .
8.8 Spot size . . . . . . . . . . . . . . . . . . . . . .
Techniques useable with unattenuated beams .
Photoionisation saturation of rare gases . . . .
8.9 Techniques requiring attenuated beams . . . . .
Wire, knife-edge and slit scans . . . . . . . . .
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109
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x
Contents
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9 Pulse length, profile and jitter
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Cross-correlation techniques . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Electro-optic techniques . . . . . . . . . . . . . . . . . . . . . . . . . .
9.4 Autocorrelation techniques . . . . . . . . . . . . . . . . . . . . . . . .
Intensity autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . .
Autocorrelation techniques for complete pulse characterization . . . .
Frequency Resolved Optical Gating (FROG) . . . . . . . . . . . . . .
Polarization-gate FROG (PG FROG) . . . . . . . . . . . . . . . . . .
Self-diffraction FROG (SD FROG) . . . . . . . . . . . . . . . . . . . .
Transient-grating FROG (TG FROG) . . . . . . . . . . . . . . . . . .
Second-harmonic-generation FROG (SHG FROG) . . . . . . . . . . .
Third-harmonic-generation FROG (THG FROG) . . . . . . . . . . . .
9.5 Spectral Phase Interferometry for Direct Electric-field Reconstruction
(SPIDER) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.6 Reflectivity modulation . . . . . . . . . . . . . . . . . . . . . . . . . .
9.7 Streak cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
151
151
153
155
155
156
159
160
162
163
163
163
164
10 Free electron laser experiments
10.1 The ”holy grails” of free electron laser experiments
”Molecular movies” . . . . . . . . . . . . . . . . . .
”Single-molecule/nanostructure imaging” . . . . .
”Single-shot spectroscopy/imaging” . . . . . . . . .
10.2 Time-resolved spectroscopies . . . . . . . . . . . .
UV/Vis pump-X-ray probe spectroscopy . . . . . .
Nexafs . . . . . . . . . . . . . . . . . . . . . . . . .
10.3 Imaging and Crystallography . . . . . . . . . . . .
10.4 Non-linear X-ray science . . . . . . . . . . . . . . .
Photoionization . . . . . . . . . . . . . . . . . . . .
173
173
173
174
174
174
174
175
175
177
177
8.10
8.11
8.12
8.13
Photographic film . . . . . . .
Gas-filled detectors . . . . . .
Charge coupled device (CCD)
Multichannel plate (MCP) . .
Solid State Detectors . . . . .
Position and centroiding . . .
Sampling techniques . . . . .
Wavefront measurements . . .
THz/IR techniques . . . . . .
Thermal detection . . . . . .
Photonic detection . . . . . .
New detectors . . . . . . . . .
IR and THz beam profiling .
Summary . . . . . . . . . . .
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165
166
167
168
11 Free Electron Laser facilities
181
11.1 Operating facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
11.2 Flash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Contents
xi
Injector and accelerator . . . . . . . . . .
Undulators . . . . . . . . . . . . . . . . .
sFlash . . . . . . . . . . . . . . . . . . .
Flash-II . . . . . . . . . . . . . . . . . . .
Experimental stations: . . . . . . . . . . .
11.3 Scss – X-fel . . . . . . . . . . . . . . . .
Scss . . . . . . . . . . . . . . . . . . . . .
Injector & accelerator . . . . . . . . . . .
Undulators . . . . . . . . . . . . . . . . .
X-ray free electron laser/ Spring-8 . . . .
Injector & accelerator . . . . . . . . . . .
Undulators . . . . . . . . . . . . . . . . .
11.4 Fermi@Elettra . . . . . . . . . . . . . .
Injector & accelerator . . . . . . . . . . .
Undulators . . . . . . . . . . . . . . . . .
Experiments: . . . . . . . . . . . . . . . .
11.5 Lcls – Linac Coherent Light Source
Injector and accelerator . . . . . . . . . .
Undulators . . . . . . . . . . . . . . . . .
Lcls-II proposal . . . . . . . . . . . . . .
Experiments: . . . . . . . . . . . . . . . .
11.6 Facilities under construction . . . . . . . .
11.7 The European Xfel . . . . . . . . . . .
Injector and accelerator . . . . . . . . . .
Undulators . . . . . . . . . . . . . . . . .
Experiments: . . . . . . . . . . . . . . . .
11.8 SwissFEL . . . . . . . . . . . . . . . . . .
SwissFEL injector test facility . . . . . .
the SwissFEL proposal . . . . . . . . . .
Injector & accelerator . . . . . . . . . . .
Undulators . . . . . . . . . . . . . . . . .
Experiments . . . . . . . . . . . . . . . . .
11.9 Proposed facilities . . . . . . . . . . . . .
11.10PAL-X-fel . . . . . . . . . . . . . . . . .
Accelerator . . . . . . . . . . . . . . . . .
Undulators . . . . . . . . . . . . . . . . .
12 Outlook & Conclusions
12.1 Current trends . . . . . .
More compact sources and
Higher repetition rates . .
Polarization control . . . .
Coherence & Seeding . . .
Harder X-rays . . . . . . .
12.2 Conclusion . . . . . . . .
Bibliography
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. . . . . . . . . . . . .
alternative approaches
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197
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203
Part I
Free electron lasers – a primer
1
1. Introduction
1.1
Historical exposé & scientific background
Ever since the advent of electricity it has been possible for humankind to produce
artificial light sources not emanating from chemical processes, i.e. different from candles, bon-fires, and the like. With the discovery of X-rays by Wilhelm Röntgen in
18951 for which he subsequently got the first Nobel prize in physics 1901.
His discovery was made possible with the advent of vacuum
tube discharge sources in the end of the 19th century – in
a discharge tube (invented by William Crookes and others,
Figure 1.1) electrons travel between two electrodes in a gas
tube between which a high electric voltage have been applied,
Röntgen discovered that, even though he covered the cathode,
using cardboard, wood, books (and seemingly whatever came Figure 1.1: A Crookes tube
in handy) a phosphorous screen placed in the other end of from 1910’s.
his laboratory room still glowed. In part II of this book we
will see how such screens are still in use to characterize X-ray
sources2 .
The interaction of X-ray photons with matter can generate many answers in the
scientific inquiry – spurred by the rapid development of quantum theory – and thus
our understanding of atoms and matter, combined with the development of X-ray
lightsources with ever-increasing quality (Figure 1.3). As evident in the short list
below both scientific topics ranging from biology, chemistry and physics and industrial research and development (notably the pharmaceutical industry) have greatly
benefitted from the development of this area of science.
• X-ray imaging – medical imaging, materials’ science, safety
• X-ray diffraction – crystallography, materials’ science
1
Reported in Über eine neue Art von Strahlen – published the December 28, 1895, where
Röntgen refers his discovery as ”X-rays” (a notion which the modest Röntgen preferred, in many
languages this type of radiation is still known as Röntgen-rays). An english translation can be
found in Nature 53, 274–276 (January 23, 1986). The discovery was deemed important enough to
be translated and communicated within a month of the original publication.
2
For instance, Section 8.3, (see page 113)
3
4
1. Introduction
• X-ray absorption and emission spectroscopies – materials’ science, long range
order.
• X-ray photoelectron spectroscopies – materials’ science, chemical bonds, spinresolved
Of course the technological development of techniques for particle accelerators, sample
handling, radiation detection, vacuum have both received and given synergetic effects
in society at large.
High energy photons or particles from radioactive sources3 is an alternative as
particle sources, though they lack tunability and the energy is often too high to be
used for many of the important applications of X-rays. Applications of radioactive
radiation have been found elsewhere, notably in radiation therapy, as gene-markers,
the carbon-14 age-determination method etc.
In Ernest Rutherford’s laboratory (1909), Hans Geiger and Ernest Marsded used
a beam of alpha particles generated from a radioactive decay of the element radium
impinging on a gold foil to find out how charge was distributed within atoms. They
intended to investigate the prevailing plum pudding model4 where the positive charge
was delocalized (the pudding) and the electrons submerged (as the plums). The
gold foil was surrounded by a sheet of zinc sulfide which would fluoresce when hit
by alpha particles. From the plum model it was expected that the alpha particles
would not scatter at all, however it was observed that a significant fraction of the
alphaparticles was backscattered – something which indicated the presence of very
small concentrated positive charged objects in the gold film, this was taken as a strong
indication of the existence of an atomic nucleus – a result which was not expected.
In 1911 Rutherford explained the experiment in terms of scattering which resulted in
the Rutherford ”planetary” model of the atom.
In Rutherfords laboratory significant developments followed this, especially the
development of particle accelerators with the purpose of splitting the atom. A note
on the development of some particle accelerator techniques and concepts emanating
from Rutherford and his students relevant for this book can be found on page 52.
For a lot of medical purposes (therapeutic and otherwise) radioactive materials
are increasingly phased out to the benefit of particle accelerators where control of the
particle energy is possible and thus the interaction length and dose can be controlled.
Theories on the nature of light – a small historical primer
In the 17th century investigations into the nature of light were pursued by means
of the modern scientific method. Light was thought of as waves or particles – both
with their shortcomings. The discourse between the two, seemingly incommensurate,
standpoints were ultimately resolved by the advent of quantum mechanics in the
beginning of the 20th century – which argue that light (and matter) can behave both
as waves and particles.
3
That is: photons, electrons or their antiparticles: positrons, or 4 He nuclei – gamma, γ, beta,
β ± and alpha, α radiation respectively. The greek names for radiation were all coined by the
english physicist Ernest Rutherford. For his work on radioactivity – transmutation, the notion
of half-life, and the differentiation between alpha and beta rays – he received the Nobel prize in
chemistry 1908.
4
The plum pudding model of the atom was proposed by J. J. Thomson in 1904.
1.1. Historical exposé & scientific background
Robert Hooke and Christiaan Huygens both published theories (In the 1660s and
late 1670s respectively) on light that built on light rays being waves. The main
proposition was that light, being waves, would not be affected by gravity – thus
slowing down upon entering a denser medium. The wave theory though assumed the
existence of a medium in which the waves could propagate through: the luminiferous
æther 5 .
Isaac Newton described light as particles (corpuscles) to explain reflection of light
(Opticks, 1704 ). Perhaps owing to his work on gravity, he postulated that the corpuscles were accelerated when they entered a denser medium, because of the larger
gravitational influence on the particles from the medium, which helped explain refraction. Nowadays we know that this was a step in the wrong direction since the
speed of light is slower in a denser medium than in a dilute medium.
Investigations into the various properties of light such as refraction, reflection,
polarization and diffraction undertaken in the beginning of the 19th century tilted
the balance in favor of the wave theory. However – as both theories made different
predictions on how the speed of light changed upon entering a denser medium – the
most convincing test to be made, i.e. measuring the actual speed of light had to wait
until 1850 and Léon Focault for a precise enough experiment to be performed6 . His
results favored the wave theory of light and thus put the particle theory of light out
of the scientific limelight
In the later part of the 19th century James Clerk Maxwell formulated the governing equations of electromagnetism. His theory built on that electromagnetic waves
travelled at a constant speed – equal to the speed of light. 1862 he published the
notion that light was a form of electromagnetic wave in On the physical lines of force.
A full theory, describing mathematically the behavior of electric and magnetic fields –
the celebrated Maxwell’s equations7 – was published in 1873 by Maxwell in A treatise
on electricity and magnetism 8 . Heinrich Hertz confirmed Maxwell’s theory by generating and detecting radiowaves in a laboratory setting and proving that radiowaves
exhibited the same properties as light waves, e.g. reflection, refraction, interference
and diffraction.
5
The existence of the æther medium was cast into strong doubt by the famous MichelsonMorley experiment (this is the Michelson with the interferometer setup). They reasoned along the
following lines: when the earth revolves around the sun it should produce a substantial wind in the
æther medium – thus, the speed of light would be slightly different depending on the experiment
(at the earth surface) was facing the wind (foul wind) or facing from the wind (fair wind). The
changes in speed of light, both dayly and seasonal, was expected to be very small – hence the need
for an interferometer which would split up a beam and propagate the beams along long arms and
recombine them, which would produce a interference pattern if the beams did not propagate in
the same manner, i.e. a beam propagating parallel to the æther wind would propagate slower than
one propagating perpendicular. Michelson and Morley combined their efforts in 1887 and their
experiments cast doubt on, but did not disprove, the existence of the æther medium; their most
important contribution remains the interferometer that bears their names.
6
The Fizeau-Focault apparatus consisted of a light source and a two mirrors spaced 35 kilometers apart. The mirror closet to the lightsource was rotating at a constant angular rate. The
elapsed time for the light to pass the distance ℓ between the mirrors is 2ℓ/c (c being the speed of
light). During the flight of the light the moving mirror will have rotated away from its original
2h
position. The angle at which the returning light is observed is then α = dα
dt c . A drawing of
the original experiment can be found: here (From his collected works Volume Two - Recueil des
travaux scientifiques de Léon Foucault, 1978).
7
Stated in detail below (see page 23).
8
The basic equations was in fact published already in 1865 in a paper entitled A dynamical
theory of the electromagnetic field[1].
5
6
1. Introduction
That electromagnetic radiation can ionize atoms, was discovered by Heinrich Hertz
in 1886 in the course of the inquires described above.
The apparatus Hertz used was a high voltage induction coil to create a discharge
between two pieces of brass and a piece of copper wire with a brass sphere on one end
and on the other a sharp point directed towards the sphere. The basic idea is that
the charges in the discharge oscillate back and forth thus emitting electromagnetic
radiation; if the emitted light would create another spark between the tip of the wire
and the brass sphere light would then be proven to be electromagnetic waves.
The photoelectric effect
Ekin
During 1886, Hertz carried out a series of experiments with his apparatus showing
that electromagnetic waves were reflected through prisms, that it was polarized etc.,
just the same properties as light waves. The only snag was that it sometimes were
very hard to see the tiny spark created at the wire tip9 , to improve this Hertz enclosed
the wire in a dark casing – which reduced the intensity of the spark. He soon found
out that if the part of the casing shielding the discharge were removed the intensity
was not reduced and that glass reduced the intensity but not quartz (quartz being
transparent to ultra-violet light).
By using a quartz prism to disperse the electromagnetic waves it was also found
that the greatest intensity of the detected spark was obtained in parts of the dispersed
light which were above the visible range. Hertz reported his observations in Annalen
der Physik 10 but offered no explanations of the phenomena11 – he rather concluded
that this phenomenon was probably of no practical use whatsoever – as we will see
below this was a rather pessimistic conclusion.
In 1899, J.J. Thompson observed that negative particles were emitted when a metal surface was exposed
to ultra-violet light. Later, in 1902, P. von Lenard observed that the emitted particles’ kinetic energy12 did
depend on the color (frequency) of the light and not
on the intensity of the light.
In one of his annus mirabilis (1905) papers Einstein
gave a mathematical description of the photoelectric
f0
effect[3]. The ionization was described to be caused by
frequency f
the absorption of a ‘light quantum’ and that different
materials had different onset frequencies f0 for electron Figure 1.2: A minimum frequency of
emission was explained by that the size of the energy the photons are required to ionize a
packet needed to be large enough to overcome the first material.
ionization potential of the material.
9
As one remedy it was suggested that a suitably prepared frog’s leg would serve equally well
as a detector.
10
In, Über einen Einfluss des ultravioletten Lichtes auf die electrische Entladung[2].
11
The spark in the detector was enhanced by charges knocked out from the material in the
detector by photons from the ultra-violet parts of the spectrum emitted from the discharge.
12
More exactly he measured the stopping potential of the emitted electrons. He performed the
experiment by, in essence, shining light on the positively charged plate of a parallel plate capacitor
and observing the potential that causes the, by the light, induced current to become zero.
1.2. Laboratory X-ray and UV/Vis photon sources
7
For this work he was awarded the Nobel prize of physics 1921 “for his services
to Theoretical Physics, and especially for his discovery of the law of the photoelectric
effect”.
The use of quantized energy-levels was used in 1900 by Max Planck to explain the
distribution of radiation from a black body. To avoid the ultra-violet catastrophe of
classical electrodynamics, i.e. that the radiation energy distribution tends to infinity
for short wavelengths, he assumed that the energy of the emitting oscillators was
quantized. By stating that light consists of discrete energy packets, Einstein could
formulate an equation that explained the photoelectric effect:
εkin = ~ω − φ
where the kinetic energy of the photoelectron is related to the frequency of the light
and the work needed to escape the material. ~ is Planck’s constant (divided by 2π)
and ω = 2πf is the angular frequency of the light. The slope of the line in Figure 1.2
is thus Planck’s constant
In section 3.2, we will see how the photoelectric effect is utilized as one way to
provide a high quality source of electrons to be used in accelerators. The effect also
forms the basis for electron spectroscopy which is an important experimental field as
well as a diagnostic possibility for free electron laser light sources (as elaborated upon
in Section 7.3).
Laboratory X-ray and UV/Vis photon sources
35
Peak Brilliance of X−ray sources
30
30
2
3rd gen. synchrotrons
20
10
2nd gen. synchrotrons
15
10
1st gen. synchrotrons
10
X-ray tubes
5
10
1850
X-FEL
25
10
2
25
10
10
Average brilliance of X−ray sources
10
X-FEL
10
2
2
Peak brilliance [Phot./(s⋅ mrad ⋅ mm ⋅ 0.1% bandw.)]
10
Average brilliance [Phot./(s ⋅ mrad ⋅ mm ⋅ 0.1% bandw.)]
1.2
20
10
3rd gen. synchrotrons
15
10
2nd gen. synchrotrons
1st gen. synchrotrons
10
10
X-ray tubes
5
1900
1950
Time
2000
2050
10
1850
1900
1950
Time
2000
2050
Figure 1.3: Development of the brilliance of man-made X-ray sources. The brilliance is a measurement of beam
quality that measures how directional and pointy a source in combination by how strongly it emits light within
a certain bandwidth, (see page 19).
8
1. Introduction
Vanode
V
-
+
Water out
Water in
X-rays
Figure 1.4: A schematic of an improved Crooks tube Figure 1.1.
The development of X-ray sources with respect intensity and source quality have, as
shown in Figure 1.3 developed superexponentially13 since the end of the 19th century.
A technological development like this is logical, when one considers the accumulated
knowledge of relevant physics and related areas14 .
When the X-ray tubes reached their optimum potential, that is when the effort
in terms of time and money did not yield enough payback to develop the technology
further – accelerator based synchrotron light sources took over as the developing
technology. Currently both synchrotron storage rings and free electron laser develop
in parallel since they satisfies different demands from the user community.
X-ray tube and anode sources
The X-ray tubes used by Wilhelm Röntgen and others in the
years leading up to and the first years into the 1900’s was
limited in intensity (and brightness) largely by the power that
the anode could dissipate without melting.
In Figure 1.4 a schematic of an X-ray tube of a model
dating from 1913 is shown. The electrons are produced by
1
10
thermionic emission15 from a heated tungsten filament serving
~ω [keV]
as the cathode; the electrons are accelerated towards an anode
1.5: Generic spectarget which is watercooled. This type of tube can produce Figure
trum of X-rays from a tube
powers up to 18 kW.
source.
The generic X-ray spectrum from a source which generates
X-rays by bombardment of a target with electrons is presented
in Figure 1.5. On top of a broad feature ranging over several keV of photon-energies
13
That is, for instance, faster than Moore’s law for the transistor density of integrated circuits.
The rate of publication in physics and chemistry was also growing faster than an exponential
curve during the first part of the 20th century[4].
15
Discussed further in the context of electron guns for free electron laser below in Section 3.2
(see page 47).
14
1.2. Laboratory X-ray and UV/Vis photon sources
sharp features emanating from discrete atomic transitions in the target which generates X-rays with precisely determined energies. The broad smooth feature arises
from bremsstrahlung from electrons that decelerate in the target and thereby emits
X-rays.
An improvement still upon this is the rotating anode source where the area of
illumination is increased to allow more efficient cooling of the anode by letting it
rotate in vacuum. It is desirable to keep the illuminated spot as small as possible
to increase the brilliance of the source. Since the surface temperature of the anode
can easily reach above 2000 ◦ C the cooling needs to be very efficient and the rotation
speed kept high. Modern rotating anode sources can produce up to 100 kW of X-ray
power thanks to this development.
Rotating anode sources are a mature technology which therefore is used for medical
purposes (imaging and therapy) and as laboratory sources both for scientific research
and in industry for material diagnostic purposes.
Synchrotron light sources
Intensity
First generation synchrotron light sources were particle physics electron storage rings
where the synchrotron light produced in the dipole magnets (used to bend the electron
beam in a quasicircular orbit) was used by others in a parasitic fashion. For particle
physics experiments, the production of light in the accelerating structures is a, more
or less significant, problem. The first observation of man-made synchrotron light was
published in 1947 [5].
Second generation synchrotrons were built in the early 1970s to dedicatedly supply
synchrotron radiation for a growing number of researchers from various fields; the
multitude of scientific disciplines attracted by synchrotron radiation can in part be
explained by that the emitted spectrum is from the infrared to the hard x-rays with
an well defined polarisation. The light was still produced in the bending magnets
that accelerates the electrons so that the electrons can be stored in a quasi-circular
orbit.
Third generation synchrotrons are used today and use insertion devices, such as wigglers
and undulators[6] to produce radiation with
even higher brilliance and power. The insertion
devices are periodic magnetic structures (Figure 1.8) which, stated bluntly, makes the electrons turn more often which produces a higher
radiation power than just one bending magnet.
However, since a wiggler do not need to bend
the orbit – and thus ideally should not influPhoton energy
ence it – the magnetic field can be much higher
which not only increases the radiation power Figure 1.6: Typical intensity distributions from
but also shifts the wavelength of the photons dipole (dashed), wiggler (red, solid) and unduupward (which is why wigglers are sometimes lator (filled) radiation.
called wavelength shifters). An undulator have
generally a lot more magnetic periods than a
wiggler with weaker magnetic fields which keeps the deflections from the central orbit small such that photons emitted at an earlier instant can interfere with photons
9
10
1. Introduction
emitted at future times which produces a build up of emitted power at certain frequencies. In chapter 2, we will investigate with some detail and rigor the properties
of undulator radiation – as this is a prerequisite for the understanding of the free
electron laser formalism.
Figure 1.6 presents how the general appearance of the spectra from different insertion devices can look like. In the case of the undulator there is sharp peaks where
the condition for positive interference is fulfilled distributed at multiples of the first
resonance (i.e. harmonics of the fundamental energy where the condition is first fulfilled).
Synchrotron storage rings provide almost a continuous source of radiation with
repetition rates in the 100’s of MHz something which gives rise to high average power.
The high repetition rate is often too much for time-resolved measurements which
is why synchrotrons are sometimes run in ”low filling modes” where only one or a few
bunches of electrons travel around the orbit which brings down the repetition rate to
the order of 1 MHz. The bunches are still relatively long (in the order of picoseconds);
experiments demanding short pulses can use femtosecond laser slicing of the electron
bunches before they pass through a bending magnet, or undulator, this modulates
part of the electron beam and causes that part of the beam to emit a short pulse
which is separated from the radiation fro the majority part of the bunch.
One can conclude that synchrotron radiation has many attractive properties which,
as mentioned, have made its use widespread over a broad range of scientific communities, i.e. tunable light with an (extremely) well defined polarization (which can be
linear, circular or elliptical) available over a very large range of energies. It also have
an inherent timestructure that can be manipulated to provide relatively long x-ray
pulses in the MHz repetition rate domain; in combination with lasers other timestrutures other types of time-resolved experiments are enables. A (significant) fraction of
the light is also transversely coherent, which enable imaging experiments making use
of – for instance – phase contrast at X-ray wavelengths.
Lasers
The theoretical framework for the Laser was laid down by Albert Einstein in his
Zur Quantentheorie der Strahlung [7] from 1917. In this paper he detailed how light
quanta are absorbed and emitted by atoms16 . By introducing probabilities for the
processes of absorption, spontaneous emission and stimulated emission he was able
to quantify how atomic spectral lines was formed.
The processes of absorption and emission of light works in the intuitive way; Stimulated emission describes how the presence of electromagnetic radiation causes atoms
in a higher energy state to decay into a lower one. One can then imagine a process
where, if we were to pump atoms to a higher energy state, decays from this state will
then in turn stimulate other atoms in the ensemble to decay to.
If, in a medium, the number of atoms in the higher energy state is larger than
the number in the lower energy state the amount of stimulated emission is larger
than that absorbed in the ensable – the amount of light in the medium is amplified.
By placing this medium between two mirrors, an optical resonator, the light passes
through the gain medium many times before it is extracted somehow, this gives rise to
16
Building on Max Planck’s seminal paper from 1901 Ueber das Gesetz der Energieverteilung
im Normalspectrum[8] considered to be one of the birthplaces for quantum theory.
1.2. Laboratory X-ray and UV/Vis photon sources
an even more efficient amplfication: we have a proper laser. The word (or acronym)
Laser can be spelled out to Light Amplification by Stimulated Emission of Radiation.
The first laser was built in 1960 by T. H. Maiman and consisted of an solid stateflashlamp pumped artificially grown ruby crystal (emitting red laser light at 694
nanometer wavelength)[9]. Shortly thereafter a laser with a gasmixture as a gain
medium was demonstrated.
The number of available laser media is large17 and currently covers a wavelength
range between millimeters down to below 200 nm.
There is a multitude of non-linear optical processes that can be used to manipulate
laser light. Of particular interest for the lasers to use together with free electron lasers
is harmonic generation of shorter wavelengths. This phenomenon was first discovered
in a quartz crystal in 1961[10], where integer multiples of the driving laser’s frequency
was observed.
Third harmonic generation using a gas as a medium was observed a few years
later[11]. The intensity of the generated harmonics drops very fast – the process can
be understood (in the regime of weak fields) as an atom absorbs several photons which
in turn are emitted as one; the probability of absorbing n photons drops with n.
High Harmonic Generation Lasers
If one ventures out of the weak field regime there is a possibility for another process
to occur: high harmonic generation. Laser light is shone into a gas sustaining high
enough energy density (typically in the order of 1014 W/cm2 a fraction of the laser
power can be converted into (odd) higher harmonics of the original laser pulse. This
allows for the creation of UV and even soft X-ray pulses. Typically the repetition
rates for such systems range from a few Hz to KHz (the same as the driving laser)
and even attosecond pulses can be created.
High harmonic generation can be understood via a semi-classical picture[12]: A
sufficiently strong laser field can perturb atomic potentials enough to allow the outermost electrons (illustrated as a red wave-packet in Figure 1.7).
This allows the electron wave-function to tunnel out of the atomic potential into
the continuum (2 in the figure) during the first half cycle of the laser pulse; during
the second part of the laser cycle the electron wavefunction finds itself on a strongly
attractive potential leading back to the atom where it came from – upon recombination the system will emit the excess energy as a high energy photon with significantly
higher energy than that of the driving laser. There is also the possibility of higher
harmonics of this motion to occur and thence higher photon energies.
Unlike in the weak field regime the intensity of the higher harmonics do not drop
with the harmonic number in a simple decreasing manner. Indeed, the higher harmonics have roughly the same intensities up until a cut-off energy.
This cut-off energy can be understood from the recombination model mentioned
above, with the ionization potential of the medium being Ip :
Ecut-off = Ip + 3.17 · Up
17
Diagram of laser lines from commercially available sources.
11
12
1. Introduction
Laser field
3
X-ray photon
2
1
Figure 1.7: Illusration of the high harmonic generation process.
and the pondermotive energy being the average energy of a free electron in the linearly
polarized laser field E (with angular frequency ω.
Up =
e2 E 2
4me ω 2
This process is effective (that is, it works) for linearly polarized light – elliptically
polarized light accelerates the electrons in such a way that it misses the ionized atom
on on the returning path so no recombination occur. At very high energy densities
(1016 W/cm2 ) the ”magnetic” term in the Lorentz force equation (Equation 2.5)
becomes significant, which causes the acceleration to deviate from the intended return
path.
In the context of free electron lasers, ordinary lasers and high harmonic generation
lasers are interesting both for experiments in combination with free electron laser radiation,i.e. two-color experiments as discussed in chapter 10, and as a way to increase
the quality of the free electron laser light in ways that will be elaborated upon below
(see page 16).
1.3
Free electron Lasers
In a conventional laser the average output power is limited by how much of the unused
power (which is significantly larger than the output power) that can be dissipated by
the active medium. Moreover the light from a laser is seldom diffraction limited
owing to heat effects in the lasing medium and non-linear processes taking place in
the medium.
Contrasting this is the free electron laser process which can be close to unity in
efficiency. In a free electron laser the amplification of the electromagnetic field occurs
by the interaction between an electron beam and the radiation field it creates when
moving through a periodic magnetic structure. Hence the operating wavelength is
tunable via machine parameters such as electron beam energy, and magnetic field
strength.
1.3. Free electron Lasers
13
Figure 1.8: Different ways of generating coherent laser radiation. From left to right, electrons are fed into a
long undulator either from a storage ring or in a storage ring but with mirrors that reflect part of the pulse to
modulate the electron bunch even further, or from a linear accelerator where the electron bunch gets modulated
by the light field it generates.
Figure 1.8 depicts three different ways of producing free electron laser radiation:
bunches in a storage ring passes through a long undulator; an oscillator where the
interaction where the electromagnetic radiation interacts with the electron bunches
many times; an amplifier, where the electrons pass once through an long undulator
structure – the interaction between the electromagnetic field and the electron beam
is strong enough for one pass to be sufficient.
There is a number of free electron lasers operating in the world today (chapter 11),
covering light wavelengths from the infrared to the x-ray regions. This book will cover
free electron laser that are providing light in the X-ray range which are amplfiers that
operate in the high-gain regime.
Sase
Log radiation power
The physical process that governs the function of a free electron laser is abbreviates
Sase – Self-Amplified Spontaneous Emission. In the next chapter we will discuss this
Distance
Figure 1.9: Growth of the radiated power in a Sase-mode as a function of travelled distance in the undulator.
The process saturates when the microbunching is maximal.
14
1. Introduction
Photons/s 0.03% BW
1025
1023
1021
1019
1
10
100
1000
Photon energy [eV]
Figure 1.10: Computed Photon flux into 0.03% bandwidth at 3.63 kA at the Lcls at 1.5 Å wavelength. The
two spikes are the 1st and 3rd harmonics of the fundamental Sase mode, which sits on a broad spontaneous
radiation background.
in more detail, here follows a short introduction.
The spectrum from the photons emitted from an electron bunch traveling through
an undulator will contain a large degree of incoherent radiation and a small part of
coherent radiation. The latter occurs since a small number of electrons, by chance,
happen to be radiating coherently. In the undulator spectrum thus, a number of spikes
will be seen on top of the broad spontaneous emission spectrum. As the occurrence
of the coherent radiation is random the number of coherently radiating modes per
electron bunch will follow a Poisson distribution.
The radiation field that is created from the acceleration of the electron bunch
through an undulator in a storage ring is often considered to be weak enough as to
not have an effect on the electron bunch, i.e. the electron bunches do not interact
with the radiation field. This is true if the electron density is low enough and if the
overlap between the radiation field and the electron beam is small.
However, if the electron density is high enough and the quality, that is emittance 18 ,
of the electron beam high the interaction between the electron beam and the radiated
field can become substantial.
If the interaction between the electrons in the bunch and the radiation field is strong
enough a microbunching of the electron bunch occurs. This means that as the electron
travels along the undulator structure the electron density becomes modulated with the
wavelength of the radiation field. This enhances the coherent emission further, which
in turn enhances the micro-bunching and amplifies the radiation field. The radiation
18
See the discussion on emittance below.
1.4. Development of X-ray free electron lasers
mode thus gets amplified and the degree of coherence increases. The growth of the
radiation mode’s strength is exponential until the process saturates.
Free electron laser radiation have a number of unique features owing to the amplification process outlined above. In Figure 1.10 an example of the brilliance from
the Lcls free electron laser source is shown. The peak intensity and brilliance are
many orders of magnitude larger than can be produced by other sources (Figure 1.3).
The average brilliance, which is limited by the (generally) low repetition rate of the
driving linear accelerators are still orders of magnitudes above that of synchrotron
storage rings. In the figure the two sharp spikes mark the fundamental and third
harmonics of the Sase radiation modes. Those spikes sit on top of a significant spontaneous radiation background that encompasses several orders of magnitude of photon
energies.
• Pulse lengths down to tens of femtoseconds are also orders of magnitude shorter
than those of a synchrotron. Ordinary lasers and high harmonic generation
lasers can surpass this figure but can not deliver the brilliance at X-ray wavelengths considered here.
• Free electron laser radiation has full transverse coherence (if the Sase process
have reached saturation), i.e. it is diffraction limited.
The Sase process only amplifies certain modes at the time (and possibly their harmonics) The spontaneous radiation spectrum extends very high up in photon energy,
towards 1 MeV.
1.4
Development of X-ray free electron lasers
The concept of free electron lasing was developed in the early 1970s[13]. The prediction that spontaneous emission from electron bunches traveling through a periodic
magnetic field could experience exponential gain was demonstrated 1977[14]. The first
free electron laser to reach saturation was the Leutl free electron laser located at the
Advanced Photon Source at the Argonne National Laboratory, Illinois, USA[15].
During the 1980s and 1990s a significant research effort was conducted as to develop
the theory for free electron laser as to investigate the feasibility of increasing the
photon energies into the UV and X-ray ranges[16–18]. The first lasing of a hard
X-ray free electron laser occurred in 2009[19].
Around the world there is a number of laboratories harboring free electron lasers
operating with photon energies across the electromagnetic spectrum, from the microwave region to the hard X-ray regions.
Facilities for the VUV/X-ray region demand rather high electron beam energies,
thus linear electron accelerators (retired from use for particle physics experiments)
have been fitted with undulators and hence converted to free electron laser; Flash
in Hamburg and Lcls in Stanford are from this category. Dedicated facilites for the
X-ray range are also being deployed, for instance the Fermi@Elettra in Italy and the
Scss in Japan. In chapter 11 currently operating facilites and some of those under
various stages of commissioning and planning are described in more detail.
15
16
1. Introduction
Name
Radio
Microwave
Infrared
Visible
UV
X-ray
Gamma
Wavelength [m]
Frequency [Hz]
Corresponding
temperature of
radiating blackbody
Figure 1.11: Wavelengths and frequencies in the electromagnetic spectrum.
1.5
Seeding schemes
As discussed previously, the Sase process starts up from shot-noise in the electron
beam – thus, even though the transverse coherence is very good (optimal) the longitudinal coherence is poor. This means that the photon spectrum is different for
each pulse, both regarding the number of modes that are radiating, which frequencies
dominate the spectrum and the beam energy.
This can be seen in Figure 1.12: the frequency and intensity distribution vary on a
shot-to-shot basis. Intuitively this phenomenon can be understood by considering the
stochastic start of the amplification process; in the beginning of the undulator many
modes radiate energy, those serve as seeding radiation for the duration of the traversing of the (long) remainder of the undulator. The modes that ”fit” the resonance
condition for the undulator spectrum will get progressively more amplified whereas
those modes that are not radiating resonantly do not gain in energy. The resonance
condition may be fulfilled by several modes simultaneously, more or less well which
give rise to many spikes in the final spectrum. For each new bunch the process start
over again and thus a new set of modes arise from the stochastic start-up.
Naturally there is a desire to have a more stable free electron laser photon spectrum. Both the jitter in time between pulses, the pulse energy and the spectral
content prohibit the maximum performance of both the free electron laser itself and
the possible experiments that can be performed.
To circumvent the stochastic startup of the radiation-field amplification the most
straightforward way – at least conceptually – is to pre-modulate the electron beam’s
energy with a strong laser field, then convert this energy modulation into a density
1.5. Seeding schemes
17
Figure 1.12: The Sase photon spectrum from the Flash free electron laser.
modulation. The conversion between energy and density modulation can be done in
a magnetic structure (chicane or wiggler/undulator) since the different parts of the
bunch take different paths through such a structure.
Figure 1.13: Energy modulation of an electron bunch.
eSase
If the electron bunch are modulated with a laser in a wiggler and subsequently pass
through an undulator structure significantly shorter gain length (and thus shorter
undulators) can be achieved as compared to normal Sase operation (hence EnhancedSase)[20].
ESASE
Modulator
Radiator
18
1. Introduction
HGHG
High-Gain Harmonic-Generation is a frequency upconversion scheme, designed to upconvert the fundamental frequency of the laser to a much higher frequency[21].
This scheme has been demonstrated[22] and it includes a short modulator where
the energy-density conversion starts, followed by a chicane (two bending magnets that
bends away and returns the beam along the orignal path). The chicane compresses
the bunch further which enhances the density modulation even more before the beam
enters the second undulator (the radiator) where the free electron laser process takes
place. Since the electron bunch is pre-modulated when it enters the radiator the
spectrum from this type of free electron laser is significantly more intense in the
fundamental mode (up to 106 times) and narrow (since, ideally, all the spectral intensity is put into one mode and its harmonics). The shot to shot repeatability is also
much better as the free electron laser pulse is a up-converted version of the original
laser pulse (at least the part of the spectrum arising from the part of the electron
bunch that became modulated)[22]. The Hghg scheme can of course be cascaded,
HGHG
Dispersive section
Modulator
Radiator
that is putting several stages in front of each other, to achieve increasingly shorter
wavelengths.
EEHG
The Echo-Enabled Harmonic Generation free electron laser scheme[23] have recently
been demonstrated experimentally at the Next Linear Collider Test Accelerator at
the SLAC National Accelerator Laboratory, Stanford, USA[24].
The principle is similar to that of the Hghg scheme above with the important
difference that two modulators with two different laser seedings is used before the undulator. This enables more intricate control of the path differences the particles with
different energies takes in the two different chicanes – allowing the density modulation
of the electrons to occur at a shorter frequency than the original laser pulses; at the
entrance of the radiator one can get a pre-bunched electron beam for a significantly
shorter wavelength than any of those of the seed-lasers.
Harmonic afterburners
Harmonic afterburners consist of one or more undulators placed after the main radiator. They are either used to enhance the radiated power in a harmonic of the
fundamental – thus reaching shorter wavelengths[25]. Extra undulators can also be
used to control the polarization of the emitted light to some degree[26, 27].
1.6. Definitions used throughout the book
1.6
19
Definitions used throughout the book
Brilliance and Brightness
The intensity of a source can be regarded as the flow of energy per unit time per unit
source area
dE
I=
dtdxdy
The flux of a source Φ
Φ=
Z
1 dI
dω
ω dω
is defined as the number of photons per unit time, per unit surface area of the source.
As figures of merit for a light source the intensity and flux are rather blunt tools
since they say nothing about the directionality of the source. If we differentiate the
flux with respect to the solid angle dΩ we obtain the brightness:
B=
dΦ
dΩ
with units [photons/s/mm2 /mrad].
Brilliance, or spectral brightness[28] is defined as the number of photons emitted
per unit time, per unit solid angle, per unit source area inside a bandwidth chosen to
be 0.1%
d2 Φ
Br =
dωdΩ
thus the unit [photons/s/mm2 /mrad/0.1%BW ]. This defines the brightness of a
source inside a certain frequency envelope centered around a certain frequency ω.
Spectral brightness is closely related to the emittance of the of the electron beam
source. The emittance is the product of the beam divergence and the transverse size
of the beam along each direction perpendicular to the propagation of the electrons.
Emittance
When an ensemble of charged particles propagates through an accelerator they move
along an orbit through the accelerator structure (composed of guiding magnets and
accelerating cavities etc.). Each particle in the ensamble move along a trajectory,
i.e. the orbit is described by the ensamble motion is an average of the individual
trajectories.
The instantaneous position of an particle can be described by the tripple [x, y, s]
(as defined in Figure 1.15). In a linear accelerator the ŝ direction coincides with the
ẑ coordinate. For a complete description of the particle’s state we also need to define
coordinates that are proportional to the the momentum of the particles: [x′ , y ′ , E],
with x′ = px /p, y ′ = py /p which describe the angular deviation, perpendicular to
the direction of motion, from the ideal orbit. For relativistic particles the energy is
approximately equal to the particle momentum E ≈ cp. In some instances it is more
convenient to define the energy in terms of its deviation from the ensemble average,
as this gives a measure which is independent of the total energy.
20
1. Introduction
Potential energy surface and phase plot
10
8
6
4
2
0
2
2
1
1
0
0
−1
−1
X’
−2
−2
X
Figure 1.14: Part of a quadratic potential energy surface with a phase portrait. The circles describe orbits with
constant energy, i.e. a particle would move along those circles.
A beam can thus be defined as occupying a certain volume in a 6-dimensional
phase space. This volume stays constant if the ensemble’s motion is such that the total energy of the system do not change (i.e. evolves according to Hamilton’s equations
of motion)19 . For convenience the phase space of the ensemble is usually represented
by two-dimensional projections x, x′ ; Figure 1.14 shows a phaseportrait and a potential energy surface for a particle moving in a quadratic potential (for instance a
gravitational force), the circles represent orbits with constant energy.
Horizontal emittance (for instance along the x direction) εx is the area of an ellipse
encompassing the majority of the particles (usually this is taken to be the area of a
root-mean-square (rms) sense). A measure of the average phase space area covered by
the particles in the x, x′ -plane can then be computed, assuming a distribution along
the ideal orbit such that hxi = hx′ i = 0
p
εx = hx2 ihx′2 i − hxx′ i2
This quantity is conserved as long as the motion in this direction is independent from
the motion in the other directions (something which is common in accelerators)[29].
19
As a consequence of Liouville’s theorem, i.e. that the volume in phase space stays constant if
the system evolves under the influence of conservative forces only. Forces that depend on position
only are conservative, e.g. gravity and Coloumb forces. It is less common that forces that depend
on the momentum are conservative, an important exception to the latter is magnetic forces which
do not change the momentum magnitude, only its direction; thus magnetic forces are conservative.
1.6. Definitions used throughout the book
21
p
hx′ i2
p
ŷ
x̂
ŝ
hxi2
Figure 1.15: Definition of the rms width and angular spread of particles in a bunch.
In Figure 1.15 the quantities inside the square-root are depicted.
The emittance, as defined above, is also preserved as long as the particles are not
accelerated. It is therefore customary to use the normalized emittance which makes
the emittance comparable even if the beam has undergone acceleration[30].
The normalized emittance is related to the beam energy via the relativistic factors
β = vc and γ = √ 1 2 :
1−β
εn = βγε
which is invariant along the accelerator structure in the absence of radiation. Consequently,
the transverse size of a charged particle beam shrinks as it gets accelerated
√
as βγ. As will be seen below the emittance needs to be very low for a free electron laser as the generated radiation needs to overlap substantially with the electron
beam for the lasing process to occur. Together with the current and the beam energy
the transverse and longitudinal emittances are very important figures of merit for
accelerators.
22
1. Introduction
Summary
• X-rays can be used to investigate the electronic and geometrical structure of matter – by spectroscopic or scattering experiments respectively. Thus they are used by a broad scientific
community for experiments, i.e. for both fundamental and
applied investigations in medicince, biology, chemistry and
physics.
• The brilliance (quality) of X-ray sources have developed exponentially since the discovery of X-ray radiation.
• Today the most brilliant, man-made, X-ray source is the free
electron laser. Other X-ray sources are X-ray tubes, anodes, synchrotron storage rings and high-harmonic generation
(HHG) lasers.
• Compared to solid state lasers and HHG lasers a free electron
laser do not have any limit on the output power imposed by
the laser medium, it being an electron beam in vacuum and
not a gas or a solid.
• The basic process that governs free electron laser amplification
is abbreviated Sase – Self Amplified Spontaneous Emission.
This process describes how the radiation field is amplified by a
relativistic electron beam moving through a periodic magnetic
field (i.e. in an undulator) when the radiation field modulates
the electron beam density (microbunching). A nice introductory description of the free electron laser process can be found
in Ref. [31].
• Sase is a positive feedback process and the amplification of
the radiation field can be exponential. The process reach saturation when the electron beam is microbunched with the
periodicity of emitted radiation. The process starts up from
electron shot-noise in the beam, thus the number of radiation
modes follow a Poisson distribution.
• The spectrum of the emitted photons is broad (from incoherent spontaneous undulator radiation) with a number of
sharp spikes corresponding to the coherent radiation from
Sase-modes. The radiation in the modes have full transverse
coherence and each mode is diffraction limited.
• The energy and intensity distribution from each pulse is
unique since the process starts up from noise. Methods to manipulate the electron beam serving to enhance the shot to shot
repeatability of the spectrum utilize lasers to seed the beam
before entering the periodic magnetic structure (undulator).
In fortuitous cases this can lock the radiation into a single
Sase-mode which then becomes one million times more intense then the corresponding unmanipulated Sase-spectrum.
2. Synchrotron radiation and its properties
2.1
Radiation from a moving charge
This chapter contains certain elements of classical electrodynamics, which is needed
in the following chapters. For the underlying framework and definitions see the book
of Jackson and Schwinger’s article from 1949[32, 33].
Maxwell’s laws
Gauss’ law for the electric field states that the flux of the electric field through a
closed surface S is proportional to the enclosed total charge:
I
Q
(2.1)
E · dA =
ǫ
0
S
Analogously there is a Gauss’ law for the magnetic field B; the field lines of the
magnetic field must be closed – thus the net flux through a closed surface must be
zero, i.e.
I
S
B · dA = 0
(2.2)
This implies that there is no magnetic monopoles, if there was this equation would
also have a source term as the equation for the electric field.
For the electric and magnetic fields to be coupled
the flux of either the electric or the magnetic fields
∂S S2
E
needs to change; if the flux of the magnetic field
S1
changes over time, then the electromotive force along
I
a closed loop on the surface S is proportional to the I
flux:
I
∂ΦB
B
(2.3)
E · dℓ = −
∂t
∂S
Figure 2.1: Surfaces sharing the same
The sum of the magnetic fields through a closed bounding contour ∂S.
loop on a surface enclosing a current
is proportional
H
to that current (Ampere’s law): ∂S B · dℓ = µ0 I. However, as seen in Figure 2.1 it
is easy to construct a situation where the same bounding contour is shared by two
23
24
2. Synchrotron radiation and its properties
surfaces where only one of the surfaces contain the current in Ampère’s law, whereas
the other one contains a changing electric field – here we use a discharging parallelplate capacitor for this purpose; even though no charge flows between the capacitor
plates there is still a current ID flowing inside the capacitor (although there is a
vacuum between the plates here), by Ampère’s law we have just stated there should
be an induced magnetic field.
Using Gauss’ law for the electric field, assuming a static surface, we can get:
I
∂E
dQ
∂E
dS ·
= I = ǫ0
≈ −Sǫ0
dt
∂t
∂t
S
This current and the conduction current must be equal since they must sum to zero.
We divide by the area of the surface element S and use current densities (i.e. divide
I by the area as well, I/S = J) and we get the result: the Ampère-Maxwell equation:
Z I
∂E
J + ǫ0
B · dℓ = µ0
· dS
(2.4)
∂t
S
∂S
Equations 2.1, 2.2, 2.3, and 2.4 are the Maxwell equations that consitute the basis
for classical electrodynamics; via Gauss’ and Stoke’s theorems we can formulate them
also in differential form as
Gauss’ law
Gauss’ law for magnetic field
Maxwell-Faraday equation
Ampère-Maxwell equation
∇ · E = ǫρ0
∇·B=0
∇ × E = − ∂B
∂t
∇ × B = µ0 J + µ0 ǫ0 ∂E
∂t
The electric and magnetic fields also couple via the force the fields exert on a
charge moving in them in the expression for the Lorentz force equation:
F = −q [E + v × B]
(2.5)
The energy flux of the fields can be found via the expression for Poynting’s vector:
S=
1
1
(E × B) =
|E|2 r̂
µ0
cµ0
(2.6)
Charged particle at rest or moving with constant velocity
A charged particle at rest surrounds itself with an electric field that can be written
(Coulomb’s law ):
1 q
r̂
E=
4πǫ0 r 2
This is a special case of Gauss’ law for the electric field, Equation 2.1.
Since the electric field is static in the situation when the particle is at rest no
magnetic field is induced (Ampére-Maxwell equation 2.4. In the case of a uniformly
moving charge we have a constant current which creates a static magnetic field (Equation 2.4 again) – no electric field is induced (Equation 2.3).
In both cases considered here no change in the kinetic energy of the particle occurs,
thus no energy exists that can be transferred to the electromagnetic radiation field.
2.1. Radiation from a moving charge
25
The fields from a charge in arbitrary motion
Following Feynman[34, 35] we write the electric field from a charge in arbitrary motion
as
′
′
q
r̂
1 d2 ′
r′ d
r̂
E=
+
+
r̂
(2.7)
4πǫ0 r ′2
c dt r ′2
c2 dt2
and the magnetic field cB = r̂′ × E. The primed quantites is to remember that we
′
have to evaluate these quantites at retarded time t′ = t − rc – this is a consequence
of the finite speed of light, at the observation point p in Figure 2.2 signals observed
at time t was created when the charge was at t′ . The second term corresponds to a
linear extrapolation of the Coulomb field (velocity times the time-delay r ′ /c), such
that when the velocity tends to zero we retain the normal Coulomb field.
The first two terms are both proportional to the inverse squared distance and thus
decays fast with respect to the distance, at least compared to the third term which is
proportional to the inverse distance. Therefore, the last term in the equation above
is called the radiation field since it survives even when r → ∞.
Electric and magnetic field lines must be to be continuous; looking at the right-side
of Figure 2.2 we can consider a charge that get accelerated a very short time towards
a non-relativistic velocity (v ≪ c). The signal at X that was emitted at time t = 0
have its front at a distance c∆t from the signal that was emitted at t = ∆t; for the
electric field lines to be continuous there must exist a perpendicular component of
the electric field which is proportional to the velocity in that direction (and thus the
acelleration). The parallel component is given by the first two terms in the equation
for the electric field above.
|E⊥ /Ek | =
ẍ⊥ · ∆t · t
ẍ⊥ · t
ẍ⊥ · r
ẋ⊥ t
=
=
= {t = r/c} =
c∆t
c∆t
c
c2
The magnitude of the electric field outside the sphere is given by Gauss’ law, which
q
1
gives the parallel component: Ek = 4πǫ
2 , yielding the perpendicular component
0 r
p
r′
t
c∆
r
2
ẋ
2
ẋ⊥
ẋt
1
r′
ẋ
c
ϑ
1
E⊥
Ek
ẋk
Figure 2.2: Signals received at the observation point p at time t was created at the retarded time t’. Equation 2.7
attempts to account for the particles motion by linearly extrapolating the Coulomb-field to guess the particles
current position.
26
2. Synchrotron radiation and its properties
we seek:
E⊥ =
q ẍ⊥
q 1 d2
sin ϑr̂ =
r̂
4πǫ0 c2 r
4πǫ0 c2 dt2
(2.8)
in the relativistic case we must take care to evaluate the derivative at retarded time.
Radiated power from a charged particle in non-relativistic motion
Equipped with the expression for the Poynting vector and the expression for the
electric and magnetic fields for a charge in accelerated motion we are now equipped
to find the expression for the radiated power.
In Figure 2.2 we can see that we can write the radiation part of the electric field
(the other terms will fall off as 1/r 4 in the expression for the Poynting vector and
thus carry an insignificant energy flux compared to the radiation field)
E⊥ =
1
q
ẍ sin ϑ
4πǫ0 c2 r
(2.9)
with direction r̂ × (r̂ × x̂). the magnetic field we get straightforwardly cB = r̂ × E⊥ .
Inserting this into Equation 2.6 we get:
|S| =
q 2 ẍ2
1
sin2 ϑ
4
c (4πǫ0 )2 r 2
To get the total radiated power we integrate over all angles
ZZ
Z π
q2
P =
|S|dS =
ẍ
|S|2πr 2 sin ϑdϑ =
6πǫ0 c3
0
(2.10)
(2.11)
This is the Larmor formula[36] for the total radiation power1 .
Radiated power from a relativistic charged particle
Equation 2.10 describes the radiation field from a charge in non-relativistic motion,
with the typical sin2 ϑ look of the power distribution (which is similar to that of
a dipole-antenna); the left-side of Figure 2.3 shows the radiation lobes from a nonrelativistic charge moving along the z-axis that gets accelerated in the direction of
the x-axis. We will now try to get a look-and-feel for how the radiation power is
distributed upon acceleration at relativistic velocities.
In the rest-frame of the particle (i.e. a reference frame moving with the same speed
as the particle) S ⋆ the radiation flux will look as in the non-relativistic case described
above, that is a dipole-field; this is shown in the left side of Figure 2.3. A radiated
electromagnetic wave with wavelength λ in a certain direction in the rest-frame will,
1
The Larmor formula is the result one obtains within the framework of classical electrodynamics. If one accounts for the quantum nature of the emitted photon, and thus the resulting recoil
exerted on the electron, the radiated power is slightly less[33]:
55 ε
P = PLarmor 1 −
√
16 3 E
with ε as the classical photon energy and E the total energy.
2.1. Radiation from a moving charge
27
a⋆
a
Θ⋆
x̂
θ
ẑ
v≪c
k⋆
θ⋆
kz⋆
v.c
L
kx⋆
k
θ
kz
kx ≈ kx⋆
Figure 2.3: Nonrelativistic (left, starred quantities) and relativistic (right) dipole radiation fields. With k =
2π/λ we get from the starred reference frame to the laboratory (observers’) frame via a Lorentz transformation
L.
will have a wavevector k⋆ in that frame. To see how this wavevector looks in ”our”
laboratory frame we must do a Lorentz -transformation.
If we consider the velocity to be solely in the ẑ direction we can write the Lorentztransformation from the starred to the unstarred system as kz = 2γkz⋆ , where γ is
the relativistic factor r 1 2 = √ 1 2 . As we approach more and more relativistic
1− v2
1−β
c
velocities more and more of the radiation is focussed in the forward direction; the
opening angle of the radiation cone shrinks:
θ≈
kx
kx⋆
tan θ⋆
1
≈
=
≈
kz
2γkz⋆
2γ
2γ
This is a very important property from the point of view of light producing accelerators, the more the particles get accelerated, the more focussed the radiation gets.
It can also be seen from the bottom in the figure that smaller opening angles get
shifted to higher frequencies than those with larger opening angles – thus there will
be a spatial frequency distribution of the electromagnetic radiation with the highest
frequencies in the middle; this is a angle dependent Doppler shift of the radiation.
To find the magnitude of the radiated power one must generalize Larmor’s formula
to take into account relativistic effects (see e.g.[32]); for the treatment here it suffices
to know that for the same accelerating force leads to a factor γ 2 higher radiation power
– it is thus more economical to have light producing structures that accelerate the
particles transversely rather than accelerating them longitudinally (at least from the
light production point-of-view). This is also the reason as to why linear colliders are
historically the weapon of choice for particle physics experiments where synchrotron
radiation losses is undesirable since the particle energy is the critical parameter.
If we let rc mc2 = e2 define the classical particle radius rc and ρ the bending radius
28
2. Synchrotron radiation and its properties
of the orbit caused by the deflecting magnetic field, the total radiated power becomes:
Pγ =
2
cβ 4 γ 4
rc mc2
3
ρ2
(2.12)
In Figure 2.3 we see that most of the radiation will be radiated in the forward direction
with a polarisation perpendicular to the bending magnetic field (σ mode) – however,
some of the power will be emitted in a mode off axis with circular polarization (π
mode). It can be shown [37] that the relative power between the modes are:
Pσ =
7
Pγ ,
8
Pπ =
1
Pγ
8
Frequency and coherence of synchrotron radiation
Synchrotron radiation from a charged particle in a circular orbit at relativistic speeds
is characterized by a searchlightlike lobe of radiation of width γ1 = φ, this angular
interval is swept during the time ∆t⋆ during which the particle moves the length
∆ℓ⋆ = v ⋆ ∆t⋆ = v ⋆ ωφ0 – all in the particles frame of reference.
Due to the relativistic effects in play (length and time dilation) an observer will
measure a compressed pulse width of length:
v ⋆ ∆t⋆
v⋆
∆ℓ⋆
v⋆
φ
≈
= ∆t⋆ −
= 1−
∆t = ∆t⋆ −
∆t⋆ = 1 −
c
c
c
c ω0
"
v⋆
v⋆
⋆ 2 #
⋆
1
−
1
+
c
c
v
v
1
1
1
1
≈ 1−
=
≈ 1−
=
⋆
c γω0
γω0
c
2γω0
2γ 3 ω0
1 + vc
The spectral width of a pulse of duration ∆t is ∆ω . 1/∆t. Thus, in the case of
synchrotron radiation we can expect to observe radiation with frequencies up to about
ωMax ≈ 2γ 3 ω0
The spectrum will consist of Fourier components nω0 from n = 1 to n ≈ 2γ 3 . A
spectrum from a bending magnet in a storage ring will thus be a broad spectrum
peaked at the critical frequency (see e.g. [32, 38]).
In a storage ring, or linear accelerator there also exist collective effects since there
is a number of particles in the beam, say N ; how the particles are distributed have a
large impact on the emitted radiation. If we consider the case of a storage ring three
cases can be discerned.
• The particles are evenly distributed in a constant current along the ring – this
leads to perfect cancellation of the radiation fields since their phases are evenly
distributed.
• If every particle is closer than a typical wavelength (in a short ”bunch”) then
their individual phase differences will be small and the field from each particle
will be amplified N times – leading to a N 2 fold increase in the radiated power.
This is coherent radiation.
2.2. Radiation from a bending magnet
29
e−
∆t
1
γ
1
γ
Figure 2.4: The time during which an observer is illuminated. . .
√
• If the particles are unevenly distributed in the ring then N of the particles
√
2
will have phases that are not perfectly
√ random . Then the fields from those N
particles will amplify that of the N others which leads to that the incoherent
radiation is proportional to N .
In a synchrotron beam from a storage ring with bunches of N particles both incoherent and coherent parts of the radiation field are normally present (Equation 2.32).
2.2
Radiation from a bending magnet
As seen above in Equation 2.12, the power is inversely proportional to the radius of the
orbit squared. The upper limit for a single magnet is thus set by the strength of the
deflecting magnetic field and the beam energy. To maximize the radiated power one
thus needs to have smaller magnet gaps and higher magnetic field strengths combined
with a high beam energy. Thus there exist a limit as of how intense radiation one can
create with a bending magnet.
For a single bending magnet there exist another side-condition – that is that the
magnet should not bend the electrons away from the orbit in the storage ring, thus a
too strong magnetic field can not be utilized. To circumvent this we can imagine an
array of strong magnets that eventually returns the electron to the intended orbit.
If the array of magnets are strong, such that the deflection from the central orbit
is large so that the light pulses from different bunches do not overlap, we will get a
spectrum similar to that of a single bending magnet but more intense and – with the
now stronger magnetic field – shorter critical wavelength. Such a device is called a
wiggler or wavelength shifter. The output power exceeds that of a bending magnet
by twice the number of periods, i.e. 2 · N .
We can also imagine a device with a smaller magnetic field strength where the
deflections from the central orbit is not too large, instead we employ many more
2
Imagine that the emitted radiation is shot-noise – thus characterized by a Poisson distribution,
then for a sufficiently large number of particles
the signal to noise ratio will be the square root of the
√
number of emitters, since the variance is N for a normal distribution – which can be considered
applicable since for large N the Poisson-distribution tends towards the normal distribution.
30
2. Synchrotron radiation and its properties
poles to get the intensity stronger. In this type of scheme the emitted radiation field
can positively interfere for certain wavelengths (this condition will be specified below)
resulting in a spectrum with a fundamental radiation mode and its harmonics whose
wavelength corresponds to a given combination of magnetic field strengths and beam
energy. This type of device is called an undulator. In a free electron laser this device
is a critical component which ultimately sets the properties of the emitted radiation.
The output power exceeds that of a bending magnet by the square of the number of
periods: N 2 .
2.3
Undulator radiation
The undulator was described already in 1951 as a source for synchrotron X-ray radiation [6]. In Figure 2.5 a schematic of the alternating-magnetic pole scheme of a
permanent magnet undulator is shown – usually the number of poles is much larger
since the number of deflections for the electron bunch dictates the intensity and spectral quality of the radiation emitted (as we will derive below).
ẑ
θ
λu
Figure 2.5: A schematic of the periodic magnet structure of an undulator. In yellow the electron path is shown.
The undulator equation
The undulator strength parameter K
The magnetic field in an periodic magnet structure can be written, if we consider that
we look at the structure from above as in Figure 2.5:
2π
B(z) = B0 cos
z ŷ = B0 cos (ku z) ŷ
(2.13)
λu
Remembering the expression for the Lorentz force (Equation 2.5) and Newton’s
second law we can write
dp
= [ṗ] = e (v × B)
dt
⇒
ṗx = −evz By
where in the last step we have used v = vz ẑ; we have also used the approximation
that the electric field created is weak enough so that the interaction is negligible –
later we will see what consequences occur when this is not the case [SASE kapitlet]
2.3. Undulator radiation
31
this is the equation of motion for the electron in the periodic magnetic structure3 .
If we insert Equation 2.13 into the equation of motion we get
ṗx = −e
dz
B0 cos [ku z]
dt
which after integration with respect to time gives the
mγvx = −
eB0
sin (ku z)
ku
(the relativistic factor γ enters from the expression for relativistic momentum) which
defines the undulator strength parameter K:
vx = −
Kc
eB0
sin (ku z) = −
sin (ku z)
m e ku γ
γ
(2.14)
If the deflection from the ẑ direction can be considered small we can use tan θ ≈ θ
together with the approximation that vz = c to obtain:
vx
vx
K
tan θ =
≈
≈ θ = − sin (ku z)
vz
c
γ
Usually the non-dimensional parameter K is written as:
K=
λu eB0
2πme c
≈ 0.9337B0 λu
(2.15)
where the latter holds true if the magnetic field strength is measured in Tesla and the
undulator period in centimeters.
The condition of coherent emission
In an undulator the transverse motion is small, thus significant parts of the radiation
field emitted at different times will overlap as the electron transverse the undulator.
This will result in positive and negative interference of certain wavelengths which
are on or off resonance with the period of the magnetic field. The condition for
a wavelength to experience positive interference can be derived without too much
effort in terms of the undulator strength parameter, the relativistic factor γ and the
deflection angle.
Consider that the electron emit radiation at the wave-crest4 labelled A in Figure 2.6
and at some later instance τ emit radiation at crest B.
In Figure 2.6 the path through an undulator for an electron moving in the field
described by Equation 2.13. The relationship between the emitted wavelength λs
and the period of the undulator λu can be found by considering the condition for
constructive interference of the wavefronts emitted at A and B respectively.
If we denote the average longitudinal velocity ṽz then the time difference between
the to points of emission is τ = λu /ṽz . The path difference between the two points will
3
4
In an helical undulator. . .
The strength of the radiation is proportional to the acceleration, Equation 2.11.
32
2. Synchrotron radiation and its properties
sθ
λ u co
θ
A
θ
B
ẑ
λu
Figure 2.6: Light traveling the path AB interferes with light emitted from A at an angle θ (path AB’).
be a multiple of some wavelength λs of the emitted light; multiples of this wavelength
will experience positive interference and will dominate the spectrum.
λu
c
− λu cos θ = nλs
| {z }
ṽz
|{z}
AB’
n ∈ Z+
(2.16)
AB
We now need to seek the average longitudinal velocity. Remembering Equation 2.14, we have an expression for the velocity in the transverse direction – thus we
can write:
s
p
c2
vz = v 2 − vx2 = v 2 − K 2 2 sin2 ku z
γ
p
where, by using β = v/c and γ = 1/ 1 − β 2 , one can by breaking c out of the
square-root find:
r
r
1
1 1 2 2
vz = c 1 − 2 − 2 K sin ku z = c 1 − 2 K 2 sin2 ku z
γ
γ
γ
√
Knowing that γ >> 1 and the McLaurin series for 1 + x = 1 + 12 x − 18 x2 + . . .
1
2
2
vz ≈ c 1 − 2 1 + K sin ku z
2γ
which averaged over one half oscillation gives the sought average velocity5 :
K2
1
ṽz ≈ c 1 − 2 1 +
2γ
2
which, inserted into Equation 2.16, gives:
5 1
π
Rπ
0
sin2 xdx =
1
2
(2.17)
2.3. Undulator radiation
33

nλs = λu 
1−
1
2γ 2
1
1+

θ2 
− 1−
K2
2
2
where we have expanded the cosine for small θ, for the first term we again use the
fact that 1/γ is very small:
1
= 1 + x + x2 + . . .
1−x
which gives the final result, for n = 1:
λu
1 2
2
λs =
1
+
K
+
(γθ)
2γ 2
2
(2.18)
In a helical undulator the 21 K 2 term becomes K 2 . This equation is usually referred to
as the undulator equation which defines the wavelength which satisfies the resonance
condition upon which the radiation is experiencing positive interference.
On axis (θ = 0) the total time of travel through the magnetic structure will be
∆t = Nu ∆T , with Nu being the number of poles – this yields a linewidth of the
radiation given by,
1
∆ω
=
ω
Nu
For future reference we note that owing to the properties of the Fourier transform:
The pulse length will be increased if it is larger than λNu and the line width will be
increased if the energy spread of the beam superseeds 2N1 u .
A detailed look at the equations of motion in an undulator
To derive the frequency spectrum of undulator radiation it is convenient to know a bit
more about the trajectories of the particles in the undulator, so far we only concerned
ourselves with the transverse component of the motion as this gives us expressions
for the wiggler/undulator strength parameter K and the resonance condition for the
emitted radiation.
It is here convenient to use Hamiltonian dynamics, as this will simplify our discussion later when we consider what happens when we can no longer make the approximation that the radiated electric field is de-coupled from the motion of the electrons.
The Hamiltonian for an electron in an electromagnetic field with vector potential A
can be written:
q
(2.19)
H = (p − eA)2 c2 + (mc2 )4
From Maxwell’s equations it can be inferred that, since we know the rotation and
curl of the electric and magnetic fields one can formulate them in terms of a vector
potential A and a scalar potential φ. This is Helmholtz theorem of vector calculus;
for the B field this relation is particularly simple B = ∇ × A – thus (with the aid of
Equation 2.13)
A=
B
sin(ku z)x̂
ku
34
2. Synchrotron radiation and its properties
is the vector potential defining the undulator field. The Hamiltonian described
above do not have any explicit time dependence in the coordinates; for such a system
the Hamiltonian describes the total energy of the system, i.e. H = γmc2 . Moreover,
as the magnetic field do not perform any work on the particles, as it only changes their
trajectory – we get an added bonus in that the canonical momenta in the transverse
directions of the system is conserved, hence[39]:
ṗx
=
ṗy
=
∂H
= 0,
∂x
∂H
−
=0
∂y
−
Both momenta are thus constant and we can choose this constant to be zero if
we consider the electron’s velocity upon its entrance in the magnetic structure to be
completely axial. The trajectories are given by
ẋ
=
ẏ
=
∂H
px − eAx
=
,
∂px
γm
py − eAy
∂H
=
∂py
γm
We use the definition of the undulator strength parameter K and divide by c to
obtain expressions for the velocities
βx = −
K
sin(ku z)
γ
βy = 0
p
from the definition of the relativistic parameter γ = 1/ 1 − β 2 we can get an
expression for the axial velocity βz as well:
K2
cos (2ku β0 ct) + β0
(2.20)
4γ 2 β0
where β0 is the average longitudinal velocity (Equation 2.17). The longitudinal velocity is thus slowed down since a part of the kinetic energy is transferred to the
transverse motion.
It can be expected that the velocity in the forward direction will be much greater
than the transverse deviations, thus we can consider the longitudinal trajectory as
approximately given by βo ct + z0 in the integration of Equation 2.20
βz =
1 K2
sin (2ku β0 ct) + β0 ct + z0
8β02 ku γ 2
The transverse component can be obtained similarily as was done above:
z(t) =
x(t) =
(2.21)
1 K
cos ku β0 ct + x0
β0 ku γ
In the rest frame of the electron it will therefore describe a figure eight motion.
2.3. Undulator radiation
35
Frequency distribution of undulator radiation
Using the vector potential introduced above we are now equipped to derive the frequency spectrum from a relativistic electron in an undulator field.
Another way to express the radiated power per unit solid angle is[32]
dP (t)
= |A(t)|2
dΩ
thence the total radiated energy becomes the time-integral (assuming that the radiation field drops sufficiently fast for large times, past and future, so that the radiated
energy is finite)
Z
dW
= |A(t)|2 dt
dΩ
The relativistic fields can be derived from the vector potential A and the scalar
potential ψ, the Liénard-Wiechert potentials[32, 40] which takes care of the fact that
the radiation perceived by an observer was generated at an earlier instant (i.e. at
retarded time t′ = t − R/c).
h
i

r
r
c
c  n̂ × (n̂ − β) × β̇ 
[RErad ]ret =
A(t) =
4π
4π
(1 − β · n̂)3
ret
the electric field here have some resemblance to the one described by Equation 2.8,
however in the present case all the consequences of the relativistic velocity of the
motion have been manifested.
To analyze the frequency spectrum of the radiation it is convenient to express the
radiated energy in terms of the Fourier transform, where we can make use of the
Parseval theorem6
Z∞
dW
= |A(ω)|2 dω
dΩ
−∞
If integration is taken for positive values of the frequencies, since negative ones do
not have any physical meaning, we can write, as the integrand:
|A(ω)|2 + |A(−ω)|2 = 2|A(ω)|2
where the last equality hold if A(t) is real so that A(−ω) = A∗ (ω). We may formulate
the argument of the integral as the intensity as the double derivative of the intensity,
as perceived on the direction n̂ from the source
dW
=
dΩ
Z∞
d2 I(ω, n̂)
dω
dΩdω
0
6
Loosely stated: the integral of the square of a function is identical to the integral of the square
of its Fourier series, i.e. with appropriate units: the energy contained in a waveform is identical
to the energy contained in the sum of its various frequency components.
36
2. Synchrotron radiation and its properties
We need to find the Fourier transform of the vector potential to proceed
h
i

r
Z∞
n̂
×
(n̂
−
β)
×
β̇
2
e
 dt
A(ω) =
eiωt 
8π 2 c
(1 − β · n̂)3
−∞
ret
we should now change variables as to take explicit care of the retarded time, t′ +
R(t′ )/c = t, we also assume that the unit vector n̂ stays constant in time – that
is, our observation point is sufficiently far away from the region in space where the
acceleration takes place. The distance R(t′ ) ≈ x − n̂ · r̂(t′ ).
h
i
r
Z∞
n̂ × (n̂ − β) × β̇
′
′
e2
eiω(t −n̂·r̂(t )/c)
dt′
(2.22)
A(ω) =
8π 2 c
(1 − β · n̂)2
−∞
it can be shown that one can rewrite the integrand in terms of time derivative
h
i
n̂ × (n̂ − β) × β̇
d n̂ × (n̂ × β)
=
(1 − β · n̂)2
dt′
1 − β · n̂
with this in mind one can integrate Equation 2.22 by parts to obtain a significantly
simpler expression for the frequency distribution
2
∞
Z
e2 ω 2 iω(t′ −n̂·r̂(t′ )/c) ′ n̂ × (n̂ × β)e
dt (2.23)
4π 2 c −∞
On axis, the fundamental harmonic of the
undulator will thus have a frequency distribution given by:
2
d2 I
sin x1
e2 Nu2 γ 2 K 2
= F1 (K)
2 2
dωdΩ
x1
c 1 + K2
(2.24)
where F1 is a difference between Bessel functions such that
F1 (K) = [J0 (κ) − J1 (κ)]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2
0
−30
where the arguments are written as κ =
2
K 2 . Furthermore
K
4 1+ 2
x1 = πNu
1
0.9
ω − ωr
ωr
where ωr is the resonant frequency obtained
from the undulator equation above:
ωr =
2cku γ 2
2
1 + K2
−20
−10
0
10
20
30
Figure 2.7: Undulator-radiation in frequencyspace (amplitude scaled to unity) shows an oscillatory behaviour dominated by the sin x/x
term.
2.4. Microbunching
2.4
37
Microbunching
Interaction between the electron beam and the radiation field
Up until here we have considered the coupling between the electrons’ motion and
the radiation field to be negligable. If we consider the possibility for energy to be
transferred back and forth between the electron beam in an undulator and the radiated
electromagnetic field.
An energy-modulation to occur along an electron bunch can be accounted for via
the action of the part of the Lorentz force (Equation 2.5) containing the electric field:
dW = F · ds = −eE · ds = −E · v · ds
(2.25)
In an undulator the electron velocity have components which is parallel to the electric
field.
Ex (z, t) = E cos (kz − ωt + φ0 )
(2.26)
To find the flow of energy per time we need an expression for the electron velocity
in an undulator – this is given by Equation 2.14, hence:
cK
dW
= −eE0 cos (ks − ωt + φ0 )
sin(ku s) =
dt
γ
{z
}
|
Eq. 2.14
=
ecE0 K
{sin ([k + ku ] s − ωt + φ0 ) − sin ([k − ku ] s − ωt + φ0 )} =
2γ
=−
ecE0 K
[sin Ψ+ − sin Ψ− ]
2γ
(2.27)
For the energy transfer between the electron beam and the radiation field to be
efficient over the whole undulator structure, the phase between the sinosoidal terms
within the brackets in Equation 2.27 needs to be constant, i.e.:
K2
0=
1+ 2
dΨ±
ds
= − [k ± ku ]
− ω ≈ −kc
± ku c
dt
dt
2γ 2
The resulting wavelength can thus be calculated:
K2
K2
2π
λu
2π
1
+
1
+
=±
=
λ=
k
2ku γ 2
2
2γ 2
2
(2.28)
(2.29)
in the last step, the negative branch of solutions have been dropped since only wavelengths larger than zero make physical sense. Our hope is to make Ψ+ constant to
fulfill the resonance condition defined by Equation 2.28. This is fulfilled if the electrons lag behind the radiation field one λu per undulator period. The energy between
the electron beam and the radiation field is exchanged with the same wavelength as
spontaneous undulator radiation.
The electron velocity is parallel with the electric field twice per period – there
dW
= 0. The pondermotive phase Ψ+ , related to the negative branch as Ψ− =
dt
38
2. Synchrotron radiation and its properties
dΨ
Ψ+ − 2ku s when dt± = 0, oscillates twice per period and on average cancels out,
i.e. for a homogeneous e- -distribution half the electrons gain energy while the other
half looses it.
As a result the electrons, if bunched from the start, tend to become density modulated with the periodicity of the radiation field – this process is called microbunching.
The wavelength of the density modulation is thus given also by Equation 2.29.
With the resonant condition fulfilled the electron beam and the radiation field can
exchange energy over several (many) undulator periods which, taken together with
the microbunching, can lead to a net gain of energy in the radiation field.
So far we have considered the electron beam to be monoenergetic – it is instructive
to consider also a beam with an energy spread (which will later be seen to relate to
other figures of merit for free electron laser beam). We denote the energy spread by
∆γ, then we can write the pondermotive phase change as:
1+
dΨ+
= −kc
dt
2
K2
2
1
1
− 2
(γ + ∆γ)2
γ
∆γ
≈ 2ku c
γ
|{z}
(2.30)
=η
where in the last step the relative energy spread has been defined. Knowing this we
can formulate the energy transfer rate:
dη
dW
=
γme c2
dt
dt
(2.31)
Using the two relationships found above we can write an equation system in the two
variables Ψ and η:


 dΨ+ = 2ku cη
dt
dη
eE0 K


= − 2m
2 sin Ψ
e cγ
dt
with Ψ = Ψ+ as the phase of the radiation field compared to the electrons with
∆γ = 0 somewhere where dW
= 0. The system of differential equations can be
dt
combined to a single second order differential equation:
Ψ̈ + Ω2 sin Ψ = 0,
Ω2 =
eE0 ku K
me γ 2
For small oscillations (i.e. sin x ≈ x) this is nothing but an harmonic oscillator:
ẍ + ω 2 x = 0. Large oscillations, where one needs to keep the sine-term intact, cause
the frequency to decrease; analogous to, for instance, a swing that can make a full
loop.
For the electrons that deviate from the ”central” energy more energy is lost than
gained. This further drives the bunching since ”fast” electrons slow down and ”slow”
electrons get accelerated. This longitudinal motion of the electrons reduce the coupling (contained in K) between the electron bunch and the radiation field, a correction
need thus to be made, i.e.
K2
K2
K −→ K J0
−
J
1
4 + 2K 2
4 + 2K 2
2.4. Microbunching
39
ŷ
x̂
v
E
ẑ
ŷ
x̂
0
0
ẑ
ŷ
x̂
v
E
ẑ
ŷ
x̂
v
E
ẑ
λu
λr
Figure 2.8: The interaction between the electrons in the beam and the radiation field give rise to a density
modulation of the electron bunches. This occurs most efficiently if the the electron bunch lags behind the
radiation field with one λu per period.
For K close to unity the reduction caused by the Bessel functions within the brackets
is 0.9 and tends toward 0.7 for large K. This correction is commonly written as [JJ]
in free electron laser litterature.
40
2. Synchrotron radiation and its properties
Exponential gain
The radiated power in a spectrum emanating from spontaneous radiation is proportional to the number of emitters, i.e. no phase correlation exist. In a free electron
laser beam ideally all electrons in the beam emit in phase, as stated previously such
an ensamble’s radiated power is proportional to the square of the number of emitters.
In a storage ring, part of the electrons in a bunch emit in phase – the number of
such emitters can be enhanced by various laser slicing schemes, all striving to increase
the number of coherent emitters. In general
the power from such a mixed ensamble
can be described by P = P0 Ne + Ne2 Fe ;
2
Z
(2.32)
cos (2πz/λ) S(z)dz
Fe =
where S(z) is the longitudinal density distribution of the electrons, The number of
electrons in the storage ring case is Ne ∼ 1010 .
In a free electron laser amplifier three collective phenomena contribute towards the
quadratic dependence on the number of emitters:
1. Modulation of the electrons’ energies due to the interaction with the radiation
field.
2. Change in the electrons’ longitudinal positions from path length differences in
the combined potential created by the radiation field and the undulator field.
3. A, so far, ignored growth of the radiation field which enhance the two aforementioned effects.
If we let ei2πz/λ−iωt describe the radiation field (which develops according to the
wave equation) and E = E0 eiΦ describe the transverse oscillations of the electrons,
one may formulate the three cooperating processes in a more specific language:
∂
µ0 X eiΦj
∂
(2.33)
+
E = i aw
c∂t
∂z
2
γj
j
The right hand side of this expression clearly have a maximum when the phases Φj
are the same, i.e. when the electrons emit in phase. Furthermore, the strength of this
maximum is clearly larger with increasing number of electrons j.
aw
dγ
= eE0
sin(Φ + Ψ)
(2.34)
dt
γ
This equation describes how the energy transfer occurs between the electrons and the
radiation field. Here aw describes the coupling
on-axis in the undulator so that for
λ0
a planar undulator λu = 2γ
1 + a2w + γ 2 θ2 , for a planar undulator a2w = K 2 /2.
2
Lastly, the equation below describes the energy modulation of the electron beam
which give rise to the microbunching of the electrons. If the longitudinal velocity
βz differs from the resonant velocity β̃z the electron slips in pondermotive phase,
electrons with higher velocity move forward while slower ones are retarded.
dΦ
2πc βz
=
−1
(2.35)
dt
λ
β̃z
mc2
2.4. Microbunching
41
Scaled free electron laser equations
The equations above can be formulated compactly by utilizing the Pierce parameter :
ρ=
2
· A2jj
λu 4π 2 · j0 · Krms
3
4π
I A · λu · γ
(2.36)
where j0 is the beam’s current density, IA = mc3 /e = 17 kA (the Alfvén current). Ajj
is the coupling coefficient between the electron and photon beams – for a helical field
it is equal to unity, whereas for a planar sinusoidal magnetic field it is a combination
of Bessel functions of the first kind: Ajj = [J0 (κ) − J1 (κ)] with argument κ =
2
2
/[2 · (1 + Krms
)]. To connect it stronger with the results above we may write it
Krms
as function of the undulator parameters and properties of the electron beam:
2/3
F1 Kγ0 Ωf
ρ=
4cγr2 ku
with this we can write a detuning parameter describing how the electron beam’s
energy relates to the resonant energy of the radiated field:
δ=
∆γ
η
γ02 − γr2
≈
=
2γr2 ρ
γρ
ρ
where the approximation holds for small deviations from the resonant energy. The
resonant energy is given by the undulator equation as:
γr =
kr 1 + K 2 /2
2ku
2
q
2 2
ee c
The Ωf is the plasma frequency µ0 N
which enters as a parameter in the space
γme
charge coefficient which describes the repulsion forces between the electrons in the
beam – something which counteracts the micro-bunching. The balance between the
space charge effects and micro-bunching is one of the reasons why the amplification
eventually saturates. The space charge coefficient is defined as:
s
Ωf γ0
1
σ=
ckr ρ 1 + K 2 /2
We write our new set of variables, describing the energy-spread, field amplitude and
position-time, following[41]:
η
ρ
F1 Kkr A=
−iKr eiΨ
2
4γr ku ρ
2ckr ργr2
t
z̃ =
γ02
η′ =
where in the second equation we have introduced the complex amplitude of the vector potential. For the details on the derivation – not important for the following
42
2. Synchrotron radiation and its properties
– the reader is referred to Bonifacio et al. [41]. With the new variables above our
equations 2.35, 2.35 and 2.35 can be normalized to the system of equations:
θ̇ = δ + η ′
η̇ ′ = − A+ iσ 2 e−θ eiθ − c.c.
Ȧ = e−θ
This 1-D system of equations can be solved analytically for a few idealized cases,
otherwise we have to utilize numerical methods to solve them. Without energyspread
and using the reasonable ansatz A ∝ eiΛz̃ we find that the cubic dispersion relation:
(Λ + δ)2 − σ 2 Λ = −1
reduces to Λ3 = −1.
This equation have three solutions describing the free electron laser collective instability: the real solution, which is oscillatory, and two complex solutions which is
decaying and growing. In the start-up phase the three solutions have comparable
magnitudes, after a certain time the growing solution will dominate, and the field
amplitude grows exponentially. Within the linear one dimensional framework we can
not explain where this growth process ends (for instance via beam blow-up due to
space-charge effects) as it is a non-linear process.
Inserting z̃ = 2k uρz (using z = ct and no energy spread) into our ansatz gives the
scales solution A ∝ eiΛz/Lg , defining the one-dimensional gain-length 7 :
λu
Lg = √
2 3πρ
which is the undulator-length needed for the field to grow a factor e. As will discussed
below, different factors combine to limit the gain after a certain length in the undulator
– it can be shown that this length is[31]:
Ls ≈ 22Lg
Significant effort is put to keep the gain-length (and thus saturation-length) as short
as possible for economical reasons.
The results here is valid for a mono-energetic beam, introducing energy-spread
effects the gain negatively as it prevents the bunching of the electrons at the proper
phase.
The output power at saturation of the free electron laser can also be expressed in
terms of ρ:
hγi Ipeak mc2
Psat = ρPbeam = ρ
e
Besides maximizing ρ to shorten the undulator, a large value of the parameter also
give greater radiation output power.
7
By solving −ℜe(iΛ) =
√
3/2
2.4. Microbunching
43
Saturation – limiting factors for the gain
The Pierce parameter defined above shows up in several relations highlighting the
demands on the quality of the electron beam for the free electron laser amplification
to be efficient. Electrons transfer energy to the radiation field until they fall out of
the bandwidth of the free electron laser and the synchronism condition is no longer
fulfilled. We may thus formulate the efficiency of a free electron laser simply by
restating the last equation as ρ = Psat /Pbeam – the Pierce parameter is thus a measure
on how good a machine is when it comes to converting electron beam energy to
radiation energy.
Among the limiting factors for the gain process (and indeed the free electron
laser process as a whole) is:
• Energy spread around the resonant energy
• Deviation of the mean energy from the resonant energy
• The size and divergence of the electron beam, that is normalized emittance.
• Diffraction effects in the beam.
In Equation 2.24 we found that the frequency spectrum of undulator radiation
2
with w ∝ (γ − γr )/γr . The gain curve, showing how a
is proportional to sinww
mode with arbitrary energy will get amplified in the undulator, for the free electron
laser process can be shown to be proportional to the derivative of that function, i.e.
2
d
sin w
G(ω) ∝ −
dω
w
The proportionality constant contains parameters that define the electron beam and
radiation field properties as dictated by the list above – a detailed treatment requires
assumptions on the electron beam and the details would vary8 .
8
See for instance the books by Saldin and co-workers, or Wiedemann[42, 43], or for a more
compact account the review in Ref. [44]. Said references also serve as good general references for
this chapter for readers who want a more detailed and perhaps more stringent account of matters
than presented in this introductory text to the subject at hand.
Gain
1
−10
0.5
−5
5
−0.5
10
w
−1
Figure 2.9: The small-signal gain function for a free electron laser amplifier.
44
2. Synchrotron radiation and its properties
In Figure 2.9 the derivative of the negative cardinal sine function is plotted, this
is the functional dependence on the beam’s energy for the gain curve as given by the
equation above. It can be seen that a beam must have a certain, not too large, energy
spread and ideally a small shift towards higher energies than the resonance energy
to have a positive gain (for a nearly monochromatic beam the optimal shift is about
+1.2 on the gain curve).
An energy spread prevents efficient microbunching of all electrons with the same
pondermotive phase, this smears out the electron bunch which prevents efficient transfer of energy into thepresonant mode with (fundamental) wavelength λr . The resonant
energy being γr = (λu /2λ) · (1 + a2w ) the initial energy spread σ ′ of the electron
beam should be kept
σ′
≪ρ
γr
The undulator resonant energy needs, of course, to be tuned to the beam energy,
i.e. the energies needs to be matched:
hγi − γr ≪ρ
γr
Greater efficiency is obtained if the electron beam and the photon beam overlap
exactly. An electron oscillates around the central path through and undulator with a
period that is much longer than the undulator’s period; this motion is called a betatron
motion. Part of the electron’s kinetic energy is thence partitioned into the execution
of this betatron motion which slows down the electron, effectively acting as an energy
spread. The betatron amplitude function β ′ have a direct effect on the normalized
transverse emittance of the photon beam which dictates the following demand:
ǫn ≪
4γβ ′ hγi
ρ
λu
The beta oscillation needs to be optimized to strike a balance between a high electron
density and space charge effects which degrades the emittance – a good starting point
λ
ρ. This gives us a condition on how
is to set it equal to the gain length, β ′ ≈ Lg ≈ 4π
the emittances of the electron (ǫ) and the photon beam (diffraction limited λ/4π)
should be matched:
λ
ǫn
<
ǫ=
γ
4π
If this condition is fulfilled neither beam diverges faster than the other.
Diffraction effects in the beam softens the coupling between the radiation field and
the electron beam, to account for those properly a more intricate three-dimensional
model needs to be constructed[17]. A 3-d analogue to our one dimensional Pierce
parameter can be found where the relations states are still fulfilled.
2.5
Sase
So far our treatment of the free electron laser problem have been done without any
assumption on the nature of the radiation mode(s) that are amplified. In the previous
chapter schemes aimed to create conditions for amplification of already coherently
2.5. Sase
45
radiation modes from the start were discussed. Such schemes were not employed in
the X-ray range until recently – at the Fermi@Elettra free electron laser in Italy,
which successfully demonstrated Hghg seeding in december 2010.
The process of Sase utilizes the broadband spontaneous undulator radiation from
the first few gain-lengths of the undulator section as a seed for the remainder of the
amplification process. Owing to this the resonance condition is always fulfilled for
some modes of the radiation, thus the number of radiation modes and their energy is
sampled from a random distribution (within the bandwidth of the amplifier which is
also related to the Pierce parameter: ∆ω
= ρ) on a shot-to-shot basis.
ω
The shot-to-shot fluctuations of the radiation pulse energy follows a Gamma distribution [45] whose free parameter M can be interpreted as the number of spikes
in the final frequency spectrum. The length of the individual spikes is proportional
to the gain-length and the wavelength of the radiation as λ/λu Lg . Shorter pulses
increases the number of spikes as the energy content of such√pulse is broader. The
width of the Gamma distribution is inversly proportional to M ; the fluctuation of
the power is distributed as a negative exponential[42].
Coherence properties
Coherence means that the relative phase of waves is fixed. Spatial coherence between two radiation sources means that the photons originating from them occupy
the same volume in phase space. In practice this means that emitters within the
coherence-length/area can amplify each other by constructive interference if the phase
relationship means that they are equal.
Temporal coherence can be thought of in the same manner: waves emitted at
different times have a phase-correlation that is predictable. The time during which
the phase-relationship remains locked is referred to as the coherence-time. Waves
emitted during this time interval (e.g. from electrons along the electron bunch) can
constructively interfere with each other if the phases are equal. The coherence time
τ is intimately related to the spectral width ∆λ of the source via:
∆λ =
λ2
cτ
A long coherence time thus ensures a narrow spectral bandwidth of the source. This
is the case for a normal Laser. In a Sase free electron laser many modes are excited
with various coherence-times for each meaning that each mode give rise to a narrow
spike in the spectrum, whereas the compound spectrum is broad[45].
Sase ensures very high transverse (spatial) coherence at the saturation point[45–
47]; towards the end of the linear gain regime ideally all electrons in the beam radiate in concert. This makes the free electron laser extremely attractive for diffractive imaging[48] and other experiments relying heavily on this property of the X-ray
source[49]. As we have seen earlier the ratio between the coherent radiation part of
the radiation spectrum and the in-coherent (spontaneous) radiation can be extremely
high in a free electron laser whereas in a storage ring the relationship the coherent
part of the undulator spectrum is significantly lower[50].
46
2. Synchrotron radiation and its properties
Summary
• Synchrotron radiation is radiation emitted from accelerated
relativistic charged particles.
• This type of radiation can be produced in bending magnets in
storage rings. The number of photons emitted and the quality
of the photon beam can be optimized with magnetic arrays.
– Bending magnet – magnetic field strength limited by the
condition that the electrons should stay in orbit in the
storage ring. The number of emitted photons is proportional to the beam energy and the curvature of the bend
(denote this flux Φ).
– A wiggler can have a stronger magnetic field since it returns the electron beam to its original path – it is a sequence of bending magnets. The photon flux is proportional to the number of magnetic periods, i.e. ∝ Nw ×Φ.
– An undulator have many magnetic periods that have
smaller field strengths than the wigglers – however the
spontaneous emission can constructively interfere for certain wavelengths yielding a dependence of the flux that
is proportional to the square of the number of magnetic
periods, i.e. ∝ Nu2 × Φ.
• In a free electron laser the electron bunches become density
modulated with the period of the radiation field. The photon
flux is therefore proportional to the number of cooperating
electrons in the beam in addition to the undulator flux: ∝
Nu2 × Ne × Φ.
• An undulator has a spectrum with harmonics of a fundamental
frequency. The frequency spectrum is dominated by the sinc
function ∼ sinx x . The bandwidth of an undulator is inversely
proportional to the number of periods.
• The gain-function for a free electron laser amplifier can be described by the derivative of the sinc function: we must have an
electron beam with slightly higher energy than the resonance
energy with a small energy spread for optimal gain.
• Sase starts up from noise in the beam resulting in a random selection of radiating modes – giving rise to a broad
spectrum with many spikes with poor longitudinal coherence.
Each spike is diffraction limited.
• Short-pulses and low charge gives fewer radiating modes[51].
A monochromator between two undulator sections can be used
to select a desired mode[52].
• Seeding schemes serves to increase the micro-bunching before
the free electron laser amplification takes place which increases
the degree of longitudinal coherence.
• Simulations Genesis[53], Fast[54]. See for instance the start
to end simulations of the Lcls facility described in Ref. [55].
3. Free electron laser ”hardware”
3.1
A prototypical FEL amplifier
In this chapter we will have a closer look at what is actually inside the tunnel of a
free electron laser facility. Key technologies will be presented and at which facilities
they are utilized.
A free electron laser consists, in principle, of four parts before the user experiments
(and their optics): (1) an electron gun optimized for low emittance which injects a
short intense electron bunch into (2) a linear accelerator structure followed by (3) one
or more undulator section(s) where the free electron laser process takes place; in some
cases the three first principal sections are followed in turn by an (4) gas-attenuator
section.
e- -gun
Accelerating structure
Undulator(s)
Gas attenuator
Figure 3.1: Schematic of a free electron laser facility.
3.2
Electron guns
The electron emitter source at the start of the accelerator is commonly referred to
as an electron gun. In the ideal case it produce a monoenergetic current spike with
y
y
x
I [A]
I [A]
x
Time [t]
Time [t]
Figure 3.2: Ideal properties of an electron gun (left) compared to real life properties.
47
48
3. Free electron laser ”hardware”
minimal spatial extent. This current spike (see Figure 3.2), produced with electron
emission, is transported and focussed with an electric field (sometimes in combination
with a magnetic field) to the exit of the gun.
Since electrons carry charge they can not be compressed into an arbitrarily small
beam. Space charge effects effectively limits the minimal size of the electron beam.
As will be seen below this is one of the principal limitations when constructing guns
for free electron lasers.
Electron guns can be divided into categories by the method of electric field generation (direct current (DC) radiofrequency (RF)), by the method of electron emission,
i.e. thermionic, photocathode, cold emission or plasma source. A general division also
exist for accelerators between hot and cold technology, i.e. normally conducting vs.
superconducting – both of which have their pros and cons.
A direct current electrostatic thermionic gun is arguably the simplest: a hot cathode emits electrons through thermionic emission (i.e. the cathode is hot enough so
that electrons can escape from the surface) cased by the heating from the direct current going through the cathode – the electrons from the cathode are then accelerated
away via an electrostatic field.
Of course the accelerating field need not be static. Either an RF pulse provide
the accelerating potential or a pulsed DC field can provide the same. For instance,
the Scss free electron laser at the Spring-8 site in Japan a thermionic gun is used
together with a pulsed DC field of 500 kV with a CeB6 cathode[56, 57].
Neither cold emission (also called field emission) nor plasma source electrodes are
used for free electron laser electron guns. Field emission emitters are though an area
of current research[58]. Photocathode guns on the other hand are used both at Flash,
Fermi and at the Lcls. A photocathode gun is constructed from a laser that can
photoionize a cathode.
General requirements
Generally, the beam dynamics throughout the accelerator downstream from the electron gun can be described by independent longitudinal and transverse parts. In this
approximation a few parameters are critical at the start of the undulator: charge per
bunch, the geometrical transverse emittance and the longitudinal emittance.
For lasing at X-ray wavelengts, the geometric emittance must be smaller than
λ/4π (where λ is the photon wavelength), i.e.that the electron beam must overlap
sufficiently/totally with the generated photon-beam.
The geometric emittance is proportional to the normalized emittance divided by
the beam energy[59]
εn
εg =
E
thus, a small normalized emittance allow for a lowering of the beam energy of the
accelerator – which in turn lowers the total cost for the facility.
The emittance of the electron beam is defined by the electron gun where the charge
cloud to be accelerated is created. The ultimate performance of a free electron laser is
ultimately determined by quality of the electron beam at the start of the accelerating
structure. More precisely the emittance of the electron beam needs to be low, as this
quantity can – in the best case scenario – be conserved throughout the accelerator.
3.2. Electron guns
49
Since performance (and cost efficiency) can be gained by constructing an low emittance electron gun a lot of effort have been (and still is) put into research and development in this area (for a recent overview see W. A. Ferrario[60]).
The longitudinal emittance and the bunch charge define two important parameters
for the lasing process: the energy spread and the peak current. The path difference
of the electrons (caused by, for instance energy spread) in the undulator over one
gain-length must be very small (very much smaller than the radiation wavelength)
allow microbunching to occur1 .
Table 3.1, constitutes a wish-list for electron guns suitable for X-ray free electron
lasers. As will become evident, it is hard to find guns that simultaneously fulfill all of
the mentioned points. The accelerator structure (normal conducting, superconducting) and user demands on the facility will guide the choices.
Parameter
Value & Comments
Repetition rate
Charge per bunch
Normalized emittance
Energy at gun exit
E-field at the cathode
B-field compatibility
Spatial distribution
Bunch length (rms)
Vacuum
Load-lock compatibility
High reliability
Hz to 100’s of MHz
Tens of pC to ∼ nC
∼ 0.1 to ∼ 1 µm
≥∼ 0.5 MeV
≥∼ 10 MV/m
emittance compensation
controllable
fs to 10’s of ps
10−9 − 10−11 mbar
Facilitate cathode replacement
User facility operation
Table 3.1: Some requirements for X-ray free electron laser electron guns.
The design parameters of a facility vis-à-vis average brightness and flux sets the
repetition rate and peak current; the desired radiation wavelength sets the electron
energy and undulator energy and field; photon pulse length and radiation field intensity constrain choices of seeding schemes, peak current, total charge, etc.
Choice of cathode materials range from pure metals to various semiconductor compounds (e.g. CeB6 [56], ZrC[61]). They are chosen with respect to their stability and
quantum efficiency. With low repetition rates (up to about 1 kHz) presently available lasers can in combination with a low quantum efficiency material (i.e. QE ≈
10−5 − 10−4 ) achieve a high enough photocurrent to be employed. Megahertz repetition rates require materials with higher efficiency in the order of percents.
Thermionic emitters
The normalized rms emittance of electrons emitted from a hot cathode of radius rc
can be described by[62]:
r
p
r c kB T
2
′2
εn = βγ hx ihx i = γ
2
mc2
1
see equation. . .
50
3. Free electron laser ”hardware”
-
-
-
-
-
+
-
+
-
-
-
-
+
+
-
-
-
+
-
-
-
-
-
-
+
+
-
-
-
-
-
+
Figure 3.3: Thermionic emitter (left) and photocathode emitter (right) with a static accelerating gradient.
with T being the cathode temperature and kB Boltzman’s constant. Clearly the key
to a low emittance is to have a small cathode to begin with. At the SCSS (Spring-8)
a thermionic gun using a CeB6 cathode operating at 1450 ◦ C produces a 3 A peak
current with a emittance as low as 0.4π mm mrad[56].
Photocathode emitters
The emittance from a photo-cathode depends strongly on material properties, thus
materials in combination with laser technology is therefore an active area of research[63,
64].
Photocathode guns are used at the majority of free electron laser facilities around
the world.
• LCLS: currently polycrystaline Cu, CsBr coated Cu being considered as a future
alternative[65].
• Flash: Cs2 T e.
Semi-conductor cathode materials are more sensitive to degrading processes such
as ion backscattering and surface degradation than their metal low efficiency counterparts. Nevertheless, by asserting proper vacuum conditions Cs : GaAs and Cs2 T e
are operating at user facilities .
For an comprehensive investigation on different cathode materials and a perspective of the current research efforts see[66]. The emittance can be reduced by cooling
of the cathode[62].
Normally conducting guns
Static (DC) acceleration
In this type of electron gun the particles are accelerated by a static2 (or pulsed field
that is static during the duty cycle, i.e. when an electron bunch is to be accelerated
into the accelerator structure), as depicted in Figure 3.3.
2
Cockcroft & Walton used an electrostatic linear accelerator where an alternating current source
is rectified by diodes and capacitors to achieve a voltage multiplication over several stages. They
used the machine to split lithium atoms with 400 keV protons – the results were published 1932[67];
for this achievement they were rewarded the Nobel prize in physics 1951 for ”Transmutation of
atomic nuclei by artificially accelerated atomic particles”.
3.2. Electron guns
The charges are accelerated by a force proportional to the gradient of the potential,
i.e. the voltage difference F = −q∇φ. The energy gained is ∆E = qU with the unit
often given in electron volts (eV). With this type of voltage multiplication it is possible
to reach voltages of 1-2 MV.
Radio frequency (RF) acceleration
An oscillating electromagnetic field can be used to accelerate charged particles. If the
particles motion is matched so that they interact resonantly with the rf-field a very
high amount of acceleration can be achieved (see page 52).
Guns operating in the L- and S-bands3 (∼ 1 − 2 GHz and 2 − 4 GHz) have already
been constructed and successfully employed in photoinjector schemes, notably the
Lcls gun at SLAC[68]. Normally conducting RF-guns can be considered a mature
technology that exhibit several important performance parameters in-line with what
is demanded from a free electron laser point-of-view: they are capable of producing a
high field gradient (up to 150 MV/m) which allow the extraction of high peak currents
in short bunches; they permit the use of emittance compensation through the use of
solenoidal magnetic fields; they are compatible with a large number of various cathode
materials.
The limiting factor is the power density exerted on the cavity walls when they are
submitted to a high accelerating field gradient. A high radio frequency implies that
the cavities are comparatively small which makes efficient dissipation of the generated
heat through a cooling system technically challenging. Hence the repetition rate for
is limited to a maximum somewhere between 100 Hz and about 10 kHz (depending on
the RF-frequency). The small cavities also imply that the apertures are small which
can also impair pumping which may generate vacuum quality concerns.
Below a certain frequency the heat load on the cavity walls becomes manageable
in such a way (with lower RF frequency the cavities become larger which decreases
the power density) that a continuous wave (CW) operation mode can be allowed[69].
Lower frequency implies a lower accelerating gradient which are still higher than the
alternative ”varm technology” direct current counter parts.
The interest for this type of operation is large from the user community since it
allows a higher repetition rate than stated above, even for a non-superconducting
apparatus. Owing to the correspondence to RF technology employed at storage ring
this technology is well matured which ensures reliability and simplicity hard to find
in other schemes.
Superconducting guns
A scheme where superconducting radiofrequency (SRF) accelerator cavities are combined with photocathode laser electron guns can potentially allow for the production
of electron beams of sufficient quality for usage in free electron lasers at very high
repetition rates[70].
An overview of the current research and developments have been published by A.
Arnold and co-workers[71].
3
RF sources are classified into VHF, UHF, microwave and millimetre wavebands. The microwave bands are divided into the following categories: the L band, 1.12-1.7 GHz; S band, 2.6-3.95
GHz; C band, 3.95-5.85 GHz; X band, 8.2-12.4 GHz; K band, 18.0-26.5 GHz. The millimetre wave
band is between 30 and 300 GHz.
51
52
3. Free electron laser ”hardware”
The Meissner effect (exclusion of B-field from superconducting cavity walls) makes
the inclusion of emittance reducing B-fields in the source region problematic. The
use of higher order cavity modes that generate a magnetic component achieving the
emittance reduction have been proposed and are under investigation[72, 73].
Summary
Table 3.2 presents the current best beam performance as obtained from different gun
technologies. The low emittance of the LCLS gun is achieved thanks to the low
peak current operation. The PITZ gun has a 10 Hz structure with 1 MHz pulse
substructure. The Rossendorf setup apparently suffers from a damaged cavity –
impairing the strength of their accelerating field.
Gun
Technology
Rate
[Hz]
Acc. Field
[MV/m]
E
[MeV]
εn
[µm]
C
[pC]
LCLS
NC RF
3 GHz
120
140
6
0.5
0.14
250
20
PITZ
(Flash)
NC RF
1.3 GHz
10
60
>5
1.3
1000
JLab
Scss
Rossendorf
DC
Pulsed DC
SRF
75 · 106
60
125 · 106
6
∼ 60
5
0.35
0.5
1̃
3
0.6
3
140
300
80
Table 3.2: Performances of existing guns employing different technologies. Table obtained from W. A. Barletta
et al. [74].
3.3
Radio-frequency driven accelerators
RF
RF
RF
RF
RF
RF
RF
RF
Figure 3.4: Different rf acceleration schemes. From left to right: in the betatron charged particles are accelerated
in a spiral path in a static magnetic field; in the microtron the magnetic field is static but the orbit is stretched
longer for each pass to adapt to the particles’ higher kinetic energy; in the synchrotron the magnetic field
strength is risen per turn to compensate for the higher kinetic energy (in a storage ring the rf power is matched
to the synchrotron radiation losses, hence the orbit is kept stable with a constant magnetic field strength). A
linear accelerator successively accelerate the particles without bending their orbit.
A radio-frequency (RF) accelerator use power from a single RF generator to create
an alternating electric field gradient over the gaps of the accelerating sections. Figure 3.4 different particle acceleration schemes are presented, all can be understood
from the Lorentz force equation (Equation 2.5): only an electric field can change
3.3. Radio-frequency driven accelerators
53
the kinetic energy of a particle, whereas an magnetic field can change the orbit of a
particle (since it exerts a force perpendicular to the particle’s velocity)4 .
In 1924 G. Ising suggested that time-varying electric fields could be used for the
acceleration of charged particles through a periodic structure of drift-tubes[75]. The
first successful operation of a radio frequency driven linear accelerator was demonstrated in 1928 by R. Wiederöe[76].
In Figure 3.5 an accelerator of this type is outlined. The lengths of the drift tubes
needs to be progressively longer as the particles’ velocity increases along the structure.
However, when their velocity is sufficiently close to the speed of light they mainly pick
up energy, thus after a while the length of the drift tubes need not to be increased.
Since the length of the structures in a Wiederöe linac is βλ/2 it makes economical
sense to choose higher radio frequency – since the overall accelerator would become
2
shorter. However, the structure radiates energy as P = ωrf CVrf
– the losses thus
increase with the radio-frequency ωrf , the gap capacitance C and the voltage squared.
If the drift tube is placed in a cavity the electromagnetic energy is also stored within
the structure in a magnetic field (owing to the cavities inductive properties). The
resonant frequency of the cavity can of course be tuned (via the cavity radius) to
match that of the accelerating field.
The mass of an electron is 1832 times smaller than a proton, an electron thus
achieves relativistic velocities much faster with the same accelerating force. Therefore
linear accelerators for electrons generally have structures that have equal length since
the velocity factor is β ≈ 1 already after the electron gun accelerating structure.
The governing principles for linear accelerators using resonant acceleration are
slightly more convoluted than those of the electrostatic accelerators mentioned above[77].
We will consider here only a few key features of their components necessary for understanding of accelerator parameters necessary for free electron laser.
4
At relativistic speeds v ≈ c the second term in F = −q [E + v × B] may be about 300 times
larger than the first term already at 1 T magnetic strength (which is readily achievable technologically).
+
-
+
-
+
βλ/2
Figure 3.5: Schematic of the cavity structure of a Wiederöe accelerator. To the right there is a source for the
particles to be accelerated.
54
3. Free electron laser ”hardware”
The accelerating RF-field
A good starting point to get a feeling for how the accelerating electric field within
a accelerator cavity looks is to consider the field within a capacitor. If we, initially,
assume the field to vary very slowly with the angular frequency ω we can write the
field as:
E = E0 eiωt
(3.1)
i.e. with the alternating field the charges on the plates gets depleted and accumulated
sequentially.
E
Γ
B
Figure 3.6: A capacitor connected to an alternating current source stores both an electric and a magnetic field.
The Γ contour (dashed) is an integration path.
We know that a varying electric field induces a magnetic field (from the AmpèreMaxwell equation, eq. 2.4). Inside the capacitor we have no stored current and thus
(Figure 3.6):
Z
I
∂
E · dS
(3.2)
c2
B · dℓ =
∂t S
Γ
where S is the area enclosed within Γ. The contour is a circle with radius r.
c2 B2πr =
∂
Eπr 2 ,
∂t
thus B =
iωr
E0 eiωt
2c2
(3.3)
Where we have made use of our definition of the oscillating electric field.
If the time derivative of the electric field is identically zero (i.e. a static electric field) all energy in the capacitor was stored in the electric field. Now with a
time-varying field there is the additional possibility of storing energy in the induced
magnetic field.
In the center of the capacitor (r = 0) there is no magnetic field, elsewhere there is
an induced field that varies with the distance from the center. Since such a magnetic
field is present there is a increasing perturbation of the electric field with increasing
3.3. Radio-frequency driven accelerators
55
r. It is now possible to construct a correction to the electric field that takes this into
account using Faraday’s law eq. 2.3:
E = E1 + E2
(3.4)
Γ2
S0
Figure 3.7: The capacitor viewed from the side, depicting the surface and integration path used for Faraday’s
law.
The second term in the superposition is required to be zero in the center, it is also
the only term contributing to the line integral in (Figure 3.7):
I
∂ΦB
E · dℓ = −
∂t
Γ2
The flux of the magnetic field in a vertical strip of width dr is B(r)hdr (imagine that
we split the surface S0 into strips). The right hand side boils down to −E2 (r)h:
Z
−hE2 (r) = −h B(r)dr
Here it can be seen that the correction field does not depend on the separation of
the fields, only on the distance from the center. The equation above gives E2 (r) =
2 2
− ω4cr2 E0 eiωt , this gives us the corrected electric field in the capacitor
ω 2 r2
E = E1 + E2 = 1 −
E0 eiωt
(3.5)
4c2
Our obtained electric field now differs significantly from the one we started out
with to obtain the magnetic field above. Since we are dealing with fields we can
repeat the same procedure for the magnetic field, i.e. use the ansatz that
B = B1 + B2
iωr
E eiωt .
2c2 0
With B1 =
To find the correction term we may use the Ampère-Maxwell
equation again (as we did above in eq. 3.2):
Z
∂
E · dS
c2 B2 2πr =
∂t S
3. Free electron laser ”hardware”
The flux of the electric field is taken through the circle enclosed by Γ in Figure 3.6
and we get:
iω 3 r 3
B2 (r) = −
16c4
This gives us a new correction to the electric field via
Z
∂
B2 (r)dr
E3 (r) =
∂t
We obtain a new term in the expansion of the electric field as:
1 ωr 2
1 ωr 4
E = 1− 2
+ 2 2
E0 eiωt
2
c
2 ·4
c
if we were to continue we would get an increasingly large expansion within the parenthesis which continues as (slightly rewritten):
1 ωr 4
1 ωr 6
1 ωr 2
+
−
+
.
.
.
1−
(1!)2 2c
(2!)2 2c
(3!)2 2c
This series is, by definition, the Bessel function of the first kind (J0 ) with argument
ωr/c. The oscillating electric field in the capacitor can thus be written in the very
compact form:
E = J0 (ωr/c)E0 eiωt
Bessel’s functions are solutions to the wave equation in a cylindrical geometry. The
subscript zero denotes that this solution is independent of the polar coordinate. In
Figure 3.8 we can see that the function have a zero around 2.4 (it is actually 2.405).
This implies that a pair of plates have a resonant
frequency 2.405c/r – of course there is also the possibil1
ity for harmonics of this frequency, functions that will
0. 8
have additional nodes inside the cavity – meaning that,
the electric field and magnetic fields will exchange en0. 6
ergy in an oscillating manner indefinitely (as a capac0. 4
itor and an inductance coupled together). If the fields
were enclosed in a cylinder with conducting walls this
0. 2
would hold if the walls were perfect conductors.
0
0
1
2
3
Imperfect conducting walls implies that the oscilr[c/ω]
lating fields gradually gets drained of their energy due
to resistive losses.
Figure 3.8: The Bessel function of
To describe a resonating cavity, we may imagine the first kind.
that the oscillating field occur in a hollow cylinder
containing the same oscillating field as above (the solutions are basically the same). The lowest mode in such a cylinder is usually denoted
TM010 which can be written:
J0 (x)
56
Ez = E0 J0 (kc r) cos(ωt − kz z)
The wave number kz describes the dependence of the field upon the cut-off wavelength
λc of the cavity – only electromagnetic waves with wavelengths shorter than the
3.3. Radio-frequency driven accelerators
57
√
cylinder diameter can propagate through the structure: kz = k2 − kc2 , where kc =
2π/λc and the free space wavenumber k = ω/c. We require that the field vanish at
the surface of the cylinder, letting the radius of the cylinder be ρ, thus kc = 2.405/ρ
must hold (2.405 being the first zero of the Bessel function J0 ).
If an electron would have the same speed as the phase velocity of the wave described
above it would be accelerated, however the phase velocity of the wave is:
ω
c
>c
vphase =
= q
2
kz
1− λ
λ2
c
The condition of acceleration is thus possible to fulfill for a very short distance only
after which the wave would reverse the field orientation and decelerate the electron
again – on average no net gain in energy would be possible.
To overcome this, i.e. to make a working accelerating structure, the phase velocity
of the wave can be slowed down for a certain frequency to match the speed of light
by introducing irises along the cavity. Such a structure will naturally perturb the
fields of the perfect cylinder, a working accelerating structure is obtained when the
wavelength is chosen such that it is a multiple of the distances between the iris-discs,
λ = nd (see Figure 3.9). The modes inside the disc-loaded cavities are usually named
after the phase advance kz d = 2π/n of the wave per sub-cavity.
π mode
2π/3 mode
d
Beam
Figure 3.9: Two common modes used in disc-loaded cavities.
Energy gain in a radiofrequency driven accelerating cavity
If U0 ≫ me c2 the electron speed is close to the speed of light. Let z = −d/2 be the
entrance of the cavity (corresponding to a time ωt = −π/2), a particle entering the
cavity may experience the electric field at a phase φ relative to the peak field (defining
zero phase).
Then the field on axis (in the ẑ direction with r = 0 in cylindrical coordinates)
can be written:
Ez = E0 cos(ωt(z) − φ)
since, on axis the Bessel
function J0 is equal to unity. If the particle is at z the time
Rz
is given by t(z) = 0 dzv(z). The energy gain is then:
Zd/2
E0 cos(ωt(z) − φ)dz
∆U = −qE · z = q
−d/2
We know that during the passage the change in velocity is small – we may set t(z) ≈
z/v. With the use of a trigonometric identity we can have the phase angle outside
the integration. Defining the accelerating gradient V = E0 d and transit time T
∆U = qE0 dT cos φ = qV T cos φ
58
3. Free electron laser ”hardware”
the transit time T = sin(ωd/(2v))
is a correction to the particle acceleration owing to
ωd/(2v)
the time variation of the field while the particles transverse the cavity.
is the energy gain of an electron passing an accelerator of length L. The phase φ
is measured relative to that of the traveling wave.
Often one do not operate the accelerators at the point of maximum acceleration
since one wants to introduce a energy chirp (gradient) along the particle bunch to
achieve a shorter bunch.
Warm technology: Copper
Accelerating structures built in Copper have been used for decades in both storage
rings and linear accelerators, thus this technology can be considered to be very mature
and solutions are often available commercially. Copper is chosen for its good electric
conductivity coupled with a high thermal conductivity.
The cheap cost per GeV (about 15 Million USD) must though be put against the
limited average brightness that can be delivered to the users.
Cavity structures for the L, S, C and X bands are currently being used for different
purposes. Thanks to the cheap cost the technique is being developed for 100-150
MV/m for the X-band, mainly for the TeV lepton linear collider but with obvious
synergetic effects for linear accelerators for X-ray production[78].
C-band normally conducting copper structures operating at accelerating gradients
of 35 MV/m are used at the Scss free electron laser.
Superconducting technology
Superconducting technology is vastly more expensive than the warm counterpart;
however, the high average brightness required for larger facilities (especially those
where it is envisioned that many experimental stations are served simultaneously,
e.g. the European X-FEL) this might be the only way forward.
Since the short duration and low emittance of the electron bunches would not be
preserved in a synchrotron, Sase free electron lasers are based on linear accelerators,
either employing normal- conducting or superconducting rf structures as sketched in
Figure 4. In contrast to the case of a constant current, the resistance of a superconductor does not completely vanish in the presence of an rf field, see e.g. [79]. It is
nevertheless much smaller in superconducting niobium at e.g. 2 K than for copper at
room temperature.
Therefore, the quality factor Q of a superconducting cavity (where Q/2π is the
ratio of the energy stored in the system and the energy dissipated per oscillation cycle)
is of the order of 101 0, compared to below 105 for copper cavities. On the other hand,
for 1 W of power lost in a superconducting cavity at 2 K, the cryogenic system requires
almost 1 kW to keep the temperature constant. This together with the technological
complexity and a fundamental limitation given by the critical magnetic field makes
the choice not so obvious.
It required a committee of international experts in 2004 to identify the superconducting TESLA technology as the best solution for the International Linear Collider
[80].
At Flash, six acceleration stages, each accommodating eight nine-cell
TESLA cavities used to accelerate the electron beam to 1 GeV[81]. The average
3.4. Undulators
59
y
D
h
z
x
Figure 3.10: Schematic of an Apple-I variable polarization undulator. The short magnet in the start have λu /8.
electric field is about 20 MV/m with one meter cavity lengths. By optimizing cavity
design and with the advent of new techniques to clean the cavity surfaces, fields larger
than 50 MV/m have been demonstrated[82].
The European X-ray free electron laser will employ TESLA cavities with a field of
21 MV/m. Lcls at Stanford, on the other hand, is based on the normal-conducting
SLAC linac, and some other projects, like the Scss XFEL in Japan for example, have
opted for normal-conducting rf structures as well.
Continuos wave operation with TESLA cavities have recently been demonstrated[83]
3.4
Undulators
Most free electron lasers use planar undulators with a fixed undulator period, which
then provide linearly polarized light containing a fundamental wavelength and its
harmonics. If one desires to suppress the higher harmonics, for some reason, a
quasiperiodic scheme can be employed[84]. A quasiperiodic undulator scheme generally degrade the performance of the undulator for the fundamental which makes
such devices unattractive for the use in, at least, Sase free electron laser, since the
cost is highly dependent on the undulator length and an decrease in photon density
necessitates a longer gain length.
However, often polarizations other than the linear is desired by the user community.
By introducing a magnetic field parallel to the central path through the undulator
(superimposing the vertical field) it is, in principle, possible to generate arbitrary
polarization directions[85].
In Figure 3.10 (adapted from Ref. [86]) a schematic of an Apple-1 (Advanced Planar
Polarized Light Emitter) undulator. Two magnetic fields (sinusoidal and helical) are
superimposed on each other with variable strength and phase. The type II and III
varieties looks similar but have different pole geometries[87, 88].
By placing a variable polarization device after the Sase undulator or using it
directly as the primary undulator in the free electron laser elliptically polarized light
can be delivered to the user experiments.
The resonance wavelength in this type (Apple-1) of undulator looks slightly differ-
60
3. Free electron laser ”hardware”
ent than our expression found earlier as we now have two fields in the undulator:
Kx2 + Ky2
λu
λr = 2 1 +
E
2
Here we obtain the resonance wavlength in Ångström if the undulator period is given
in millimeters and the beam’s energy in GeV. The coupling parameter between the
undulator field and the radiation fields is also different with the [JJ] Bessel-function
factor reducing to unity[17].
Undulator tolerances example
Using the Pierce parameter ρ (Equation 2.36) one can estimate the accuracy needed
to be achieved, with errors from different sources: temperature, alignment, undulator
gap accuracy and flatness change upon undulator gap changes.
The fundamental wavelength have to be tuned within
ρ≥
∆λ
λ
(3.6)
For an error to have a large impact on the amplification process it has to be in
effect for at least one gain length. As an example we can use the European Xfel
which has a gain length of 10 meters and undulator sections that are 5 meters long –
the ρ = 3 · 10−3 at 0.1 nm for this facility. If all error sources are equally severe, then
one can obtain an idea of the tolerances required for an free electron laser undulator
system[89]. We can express the bandwidth as a function of different errors impacting
the magnetic field in the undulators:
∂λ q
2
2
2
∆Btemp.
+ ∆Bgap
+ ∆Bflat
(3.7)
∆λ = ∂B from this one obtains that – for Equation 3.6 to be fulfilled – the alignment between
undulator sections needs to be within ±100 µm; the temperature stability of the
whole undulator system within ±0.08 K – and that the gap adjustment accuracy and
the flatness preservation upon gap changes needs to be better than ±1 µm.
3.4. Undulators
Summary
• The basic components of a free electron laser before the user’s
experiments are:
– An electron-gun. Which can be of thermionic, photocathode or field emission type. The electron gun defines the emittance and the number of electrons in the
bunches.
– A linear accelerator. Defines the repetition rate of the
system. Superconducting accelerators have higher repetition rates (kHz-MHz) than normally conducting (100’s
of Hz).
– Undulator(s) sets the wavelength and polarization of the
X-rays.
– (Gas attenuator) - can be used to limit the intensity at
the experiments.
61
4. X-ray optics
The material presented here in this chapter is partly adapted from ”Survey of
in situ metrology for the measurement of damage to FEL photon transport
optics” by A. J. Gleeson, Iruvx WP7, 2010
It is a challenge to construct any optical system for X-rays. The requirements on
optical elements at free electron laser is often different than those imposed at synchrotron X-ray sources because of the high peak-power rather than the high average
power. The demands on precision is also higher since the photon beam from the free
electron laser undulator(s) have a very high brilliance that one wishes to preserve to
as high degree as possible. In the following sections we will investigate how stringent
those demands are and the techniques that can be used to achieve this.
Also connected to the high brilliance and fluence is damage to optical elements and
methods to minimize/prevent it. This will be discussed below before the chapter end,
containing descriptions of dispersive optics, monochromators and beam attenuators.
If we write the index of refraction for X-rays in matter as:
n = 1 − δ − iβ
with δ and β as the refraction and absorption coefficients respectively a number of
conclusions can be drawn. In the X-ray regime the reflection coefficient δ is in the
order of 10-5 to 10-7 , generally thus a refractive optic would not be very effective. The
absorption coefficient is very high in the UV-soft X-ray region for all elements which
present yet another tamper, however for materials constituted of elements with low
mass (and thus small nuclear charge) this coefficient is small above 1.5 keV – since
the photoionization cross-sections become very low there. For instance, the deepest
laying single-ionization threshold for carbon is around 300 eV.
Absorption can be further traded into reflection by having a grazing incidence of
the X-rays onto the optical elements[90]. In the soft X-ray region this is the general
approach utilized. For hard X-rays reflection planes in crystals of low Z materials can
be used.
4.1
Demands on optics precision at free electron lasers
A real-life mirror is not perfect and imperfections of various kinds distort and degrades the mirror’s performance. To analyze the impact of various errors one usually
63
64
4. X-ray optics
compares with an idealized surface which perfectly transfer the source point to the
image point.
It can be shown that low frequency surface errors, between millimeters and λ,
distort the wavefront but still image the incident wave into the image plane (often
taken to be within the 1/e intensity points in a Gaussian spot). Higher frequency
errors scatter the incident waves outside the image plane[91].
The authors of Ref. [91] have developed a model classifying an optical systems
performance in terms of the slope error (deviation from ideal shape) and surface
roughness – the system coherence length describes the limit between ’high’ and ’low’
frequencies in a natural way:
√
λ
W = 2
Θ cos ϑi
treating Θ as the given angular radius for the image and ϑi the incident angle relative
to the surface parallel we have, as a function of the operating wavelength λ the
wavelength W which is the surface spatial wavelength that diffracts intensity into the
1/e radius of a Gaussian spot.
For a diffraction limited source (as is free electron laser and modern synchrotron
storage rings) the W is roughly equal to the illuminated length (ℓ) of the optical
element. For the X-ray optics considered here this wavelength thus lies between λ
and ℓ.
The degradation of transmission and image quality in the optical system due to
mirror errors may be described by the deviation from the ideal case, the so-called
Strehl-factor :
2
8 2
4π
I(0)
≈ 1− 2δ −
cos ϑi σ 2
I0 (0)
Θ
λ
with δ and σ are the rms values of the slope error and surface roughness within the
band-pass of the optical component[91].
Both the slope error and the surface roughness are integral properties of the surface,
i.e. the accumulated error is what affects the beam:
2
δ = 4π
2
1/W
Z
1/L
dfx S1 (fx )fx2 ;
2
σ =
Z1/λ
dfx S1 (fx )
1/W
Owing to this property of the imaging system one is faced with an array of different
problems when it comes to manufacturing and commissioning a device with such
stringent demands on surface quality:
• Manufacturing
– Polishing a surface down to a few nanometers peak-to-peak roughness over
a large area (typically the mirrors are above 25 cm long)
– Process such a large substrate to a determined shape.
• Metrology of the manufactured surface with high (sub-nm) accuracy[92, 93]. A
detailed account of techniques and metrology methods for the manufacturing
of X-ray optical elements is given in the book ”Modern developments in X-ray
and Neutron Optics” edited by A. Erko et al.[94].
4.2. Focussing mirrors – back-reflecting geometry example
• Moving and mounting the finished element into its position in the optical system of the facility without degrading the surface. One way to circumvent this
problem is to make mirrors that have an mount where the surface can be mechanically distorted to compensate for the errors – so called adaptive optics (see
e.g. Ref. [95]).
As an example we here take the offset mirrors at the Lcls, they have figure errors
on the order of 2 nm (rms)[96] and because of the reflectivity condition on the grazing
incidence they need to be of different lengths for the soft and hard X-ray regions:
• soft X-rays, 25 cm long, boron-carbide-coated a total of four.
• hard X-rays, pair of 45 cm long mirrors with SiC-coating and 25 keV cut-off.
Allows the throughput of the 3rd harmonic of the 8.3 keV fundamental.
4.2
Focussing mirrors – back-reflecting geometry example
So far we have only discussed plane mirrors, there is naturally a demand for focussing
mirrors for experiments that utilize high photon-density. Figure 4.1 shows a princi-
Figure 4.1: Spherical/Parabolic mirror used to focus the free electron laser beam. the focuspoint do not overlap
with the incoming beam because of the beamstopper (black).
ple for an experiment that uses a backscattering geometry with a focussing mirror
that focus the photonbeam to a point. Such set-ups are utilized, for instance, when
investigating multiphoton ionization of gases. One such experiment utilized a Mo-Si
multilayer spherical mirror with 68% reflectance (this number is made possible by
progress in EUV-litography[97]) – which could then be focussed down to 3 to 5 µm
focus diameters[98].
4.3
Damage
Because of the high peak powers and short pulses routinely achieved at free electron
laser it is entirely possible that new kinds of damage mechanisms that degrade optical
components in X-ray beamlines have to be considered. Often our knowledge for such
mechanisms emanate from the world of storage ring synchrotrons where rather a high
average power load provides the source for potential damage to optical elements and
coatings.
At a free electron laser the high peak power could potentially render an (costly)
optical component useless within fractions of a second[99]. The research of various
damage mechanisms caused by this kind of sources is therefore an active field[100, 101].
The empirical data for damage thresholds that exist are often very specific to a certain (synchrotron) beamline and are thus unique to the flux and operating wavelength
65
66
4. X-ray optics
under consideration. Recently materials for optics and their coatings employed at Xray free electron laser around the world have begun to be studied in a more systematic
fashion[101, 102], notably the low Z materials B4 C and SiC[103].
Damage to opical elements at a free electron laser can be thought of as direct and
in-direct: direct damage could be ablation cratering of the surface, distortion due to
the heat-load caused by the pulse, etc. In-direct damage mechanisms are more subtle
and include damage to multilayers by diffusion or chemical modification of surfaces
and layers, changes to the refractive index.
Careful monitoring of the beamline performance is thus important and the methods
described in the second part of this book inherently give information that can be used
to diagnose the optics.
4.4
Diffraction gratings
A diffraction grating (henceforth taken to be synonymous to ’grating’ only) is a periodically structured surface that divides and diffracts a lightbeam into several beamlets
propagating in different directions depending on their wavelength. This can readily
be understood from the Huygens-Fresnel principle – stating that each point on a
wavefront act as an independent source and that by adding up the contribution from
such pointsources the properties of any subsequent point can be found.
Light reflected from an an ideal grating can be consideredt to equal to that from
emitted from a set of infinitely long narrow slits spaced with distance d from each
other. If we add up the beams from each slit at some point (far) away from the
grating the optical path difference between the beams will casue positive and negative
interference owing to the phase difference between the waves. If the path difference
between the slits are some multiple of the wavelength d = n · λ positive interference
occur – for a given wavelength this condition will be fulfilled at some angle ϑ away
from the normal (taken to be perpendicular to the surface)
d sin ϑ = n · λ
If we allow for the incoming light’s (considered to be a plane wave) angle to be different
from that of the outgoing we get a generalization of the equation above:
d(sin ϑout − sin ϑin ) = n · λ
(4.1)
This equation is commonly referred to as the grating equation. Since the result was
obtained using the phase differences this holds for regular structures, i.e. wavefront
distortions occur through the irregularities of the grating.
The solution corresponding to n = 0 is the zeroth order component mentioned
before (this is akin to specular reflection at a mirror); the nonzero solution corresponds
to different diffraction orders.
A grating is thus a dispersive optical component that can be used in at normal or
grazing incidence to deflect a certain wavelength part of the beam into a defined angle.
At short wavelengths (in the EUV/soft X-ray regions) it is necessary to operate with
grazing incidences since the reflectivity materials increase with decreasing angles.
The zeroth order diffraction have the same diffraction angle as the incoming angle
whereas the diffracted orders have a different angle as compared to the incoming light
(angles α and β in Figure 4.3). Since the grating splits the beam, either the diffracted
4.5. Monochromators
orders or the zeroth order can be used for beam diagnostic purposes without disturbing
the user’s experimental stations downstream – this aspect is further discussed below
in chapter 5 (see page 73),
Because of their dispersive nature gratings act as bandpass filters on the radiation
and can thus be used to define the wavelength at the experimental stations (see
below).
Gratings that are blazed produce a maximum efficiency vis-à-vis reflectivity into
a certain order (other than the zeroth) for the light that hit the grating. The higher
reflectivity decreases the potential for radiation damage to the grating.
4.5
Monochromators
Although the bandwidth of the radiation from free electron laser can be very small,
e.g. at Flash it is about 1%[104], many experiments – especially spectroscopic dittos
– have a more stringent demand on the spectral purity of the light. This is one reason
why monochromators are present at some free electron laser– other reasons include
the increase of stability of the central wavelength as discussed below.
Some experimental cevats concerning free electron laser radiation
A Sase pulse from a free electron laser can be considered as being built up from a
series of spikes arising from the radiating longitudinal modes that happended to be
amplified as that pulse passed through the undulator structure. Each spike in the
spectrum is transform limited1 whereas the spectral distribution in the pulse is chaotic
in the sense that each pulse have a unique spectral composition. Thus a Sase pulse
consists of many independently radiating modes whose intensity varies from pulse to
pulse – hence the median wavelength of the pulses change, as well as the spectral
intensity distribution, on a pulse to pulse basis. Additionally, as seen in Figure 1.10,
the radiation emitted in the Sase part of the spectrum sits on top of a large broad
background of spontaneous undulator radiation.
If the undulators are not perfectly helical (that is the electrons emits non-circularly
polarized radiation) the spectrum will contain harmonics of the fundamental wavelength emitted. In certain instances this can be viewed as fortuitous since the harmonics will have shorter wavelengths (but then the intense fundamental becomes a
problem at the experiment) or as a serious drawback if it is the fundamental wavelength that is to be used – and the harmonics becomes a problem at the experiment
side.
Seeded free electron laser schemes (section 1.5, see page 16) improves upon the
basic Sase scheme in various ways – all striving to improve the quality of the emitted
radiation by enhancing the microbunching of the electrons in various ways. To avoid
timing errors between the seed pulse(s) and the electron bunch (timing jitter) the
seed pulse is often significantly shorter than the electron bunch. Hence, only a part
of the electrons experiences the additional density modulation owing to the seeding
process, in addition to the seeded free electron laser radiation one thus obtains a
Sase background from the rest of the electron bunch (as well as the background from
spontaneous undulator radiation mentioned before). Eventhough the Sase part of
1
i.e. the spectral width is minimal for a given pulse-length. For a Gaussian pulse this implies
that the time-bandwidth product is 0.44.
67
68
4. X-ray optics
the beam do not reach saturation it can still carry significant power. The unseeded
part of the beam can thus disturb downstream experiments both with the background
itself and that it arrives before, and extends after, the main pulse.
Benefits and drawbacks of from a monochromator
A monochromator is a device that filters a photon beam with regard to wavelength
– acting essentially as a wavelength band-pass filter. Considering only the wavelength variation issue first, it is obviously beneficial to filter the photon beam with a
monochromator since it resolves many of the issues mentioned above. A monochromator provides:
• Suppression of the spontaneous emission background.
• Selection of a narrow(er) wavelength range – essentially translating central wavelength jitter to intensity jitter. The latter is significantly easier to measure on
a pulse by pulse basis2 to be used in the analysis of other experimental data.
• Selection of a single harmonic. Either filtering away the fundamental if higher
harmonics and thus shorter wavelengths are desired, or suppressing the contribution from higher orders if the fundamental wavelength is to be used.
• Selecting the seeded part of the spectrum – suppressing the spontaneous undulator emission and the Sase background. The spontaneous and Sase background
which lies directly underneath the seeded part will not be filtered away and thus
contribute to a intensity jitter of the monochromatized pulse.
From a wavelength stability aspect it is thus very advantageous to insert a monochromator before the experiments. This is provided that the intensity jitter between pulses
can be measured on a pulse by pulse basis which can be included in the data analysis
of the experiments. Ways of measuring the intensity are discussed in chapter 7 (see
page 99).
The price to pay for the wavelength stability is that the transmitted power through
the optical system gets smaller (per each new optical element) and that the pulses
get temporally stretched. The time-stretch can be controlled or compensated at the
cost of transmission as will be seen below.
For high energy photons (larger than about 2 keV) it is not possible to use gratings
because their cut-off energy prohibits transmission. Instead crystal monochromators
can be employed which is constructed from channel cut crystals (often Si) optimized
to transmit one photon energy optimally. At Lcls one such monochromator is built
into the beam transport system that is optimized for 8.3 keV[96].
Time-stretching
In the soft X-ray ranges the incidence angle on any optical element needs to be small
(i.e. the beam impinges at the optic at grazing incidence). Thus there will be a time
difference between the parts of the beam that hits the surface first and the parts
2
Otherwise the full spectrum of the pulse (i.e. both wavelength and intensity distribution)
needs to be measured on a pulse by pulse basis. This is slightly more involved than measuring the
intensity in this manner, as discussed in chapter 7 (see page 99).
4.6. Beam attenuators
69
that hit at a later time, as illustrated in Figure 4.2. The time-stretching can be
reversed by letting the beam bounce off a second surface – at the cost of reduced
transmission, it can also be controlled as it is proportional to the number of grooves
that are illuminated by the beam[105]. By illuminating the grating parallel to the
grooves (off-plane mounting) the time-stretching can be reduced also[106, 107].
Figure 4.2: Time stretching of a pulse arising from the grazing incidence.
α
β
β
0th order
α
Figure 4.3: A time-stretch compensating double grating setup. The beam moves from left to right in a Z-shaped
path and the outgoing beam is parallel to the incoming.
4.6
Beam attenuators
Although not a proper optical element per se, gas attenuators are a integral component of the beam transport system of free electron laser providing a robust mean of
controlling the intensity of the radiation at the experiments. The intensity can be
controlled in a continuous manner over several orders of magnitude with the limit set
essentially by vacuum considerations, i.e. how good the differential pumping is.
Beam attenuators and filters based on metal foils and metal/ceramic windows free
electron laser beam can be used at higher energies provided that they can withstand
the fluence of the X.rays.
There is strong indications that, at least, gas attenuators do not distort the wavefront [104] thus conserving the coherence properties of the x-ray beam.
Figure 4.4 describes a generic attenuator, at the Lcls there are solid attenuators
included whereas at Flash and Scss only the gas attenuator is needed (owing to
70
4. X-ray optics
Intensity detector
Pumping
Solid attenuators
Gas input
Intensity detector
Pumping
Figure 4.4: Schematic of a gas attenuator with intensity monitors before and after.
their wavelength ranges). Intensity monitors are usually put before and after the
attenuators3 .
The gas attenuator at Flash is 15 m long and sandwiched between intensity monitors. It is operated either with nitrogen for the wavelength ranges 60-19 nm, and
for smaller wavelengths xenon or krypton can be employed. The differential pumping
system is fast and changes of transmission of up to four orders of magnitude can be
provided by the attenuator within minutes[104, 108].
At the Scss a smaller gas-cell is used with argon as attenuator gas[109, 110].
Lcls employs a 4.5 meters long gas attenuator using nitrogen for operation between
800 and 2000 eV photon energies. The pressure range is up to about 10 mbar and
thus provide an attenuation span of four orders of magnitude. A set of solid beryllium
attenuators (0.1 to 32 mm thickness) provide the attenuation for the harder X-rays
up to 8 keV.
3
Intensity diagnostic devices will be discussed further in section 7.2 (see page 100).
4.6. Beam attenuators
Summary
• The demands on X-ray optical elements for free electron lasers
are more stringent than those utilized for e.g. storage ring
lightsources – owing to the, in most instances, higher peak
power of free electron lasers compared to the high average
power exerted from storage ring synchrotrons.
item Damage on optical elements changes the properties of
the radiation at the user stations vis-á-vis spectral content,
intensity, coherence and temporal structure.
• Optical elements used at free electron lasers generally suffers
damage primarily from ablation caused by the high peak brilliance of the source.
• In the VUV and soft X-ray regions diffraction gratings are universally adopted as the dispersive optic necessary to provide
wavelength selection in monochromators.
• Simulation codes: Shadow[111], Xtrace[112], Spectra.
71
5. Beam-splitting methods
The material presented here in this chapter is partly adapted from ”Survey of
beam splitters” by M. A. Bowler, A. J. Gleeson, D Laundy, and M. D. Roper.
Iruvx WP7, 2010
5.1
Introduction
The number of beamlines, where experiments can be carried out, at Free Electron
Laser (FEL) facilities is much less than on synchrotrons, and may not be enough to
meet user demand. One possibility of increasing the number of users being able to
carry out experiments on free electron lasers is to split the radiation in a beamline
into two or more separate paths allowing more than one experiment to be carried out
simultaneously. This could be achieved by splitting the photon beam, or if the pulse
repetition rate is slow enough, by kicking the electron bunches into different paths.
This chapter is mainly concerned with the former technique, and gives a survey of
techniques for splitting a photon beam.
The type of beam splitter used will depend on the wavelength range over which it
is required to operate. This chapter concentrates on the wavelengths from the vacuum
ultra-violet (VUV) to the soft X-ray (SXR) regions. However, mention will be made
of techniques employed at other wavelengths, at harder X-ray energies of relevance for
example to XFEL, and at much longer wavelengths in the infrared regime of relevance
to existing free electron lasers and possible future far infrared (FIR) sources.
Beam splitters are also used to partition the radiation for pump-probe experiments,
for sending a small fraction of the radiation for diagnostic purposes, and for input to
interferometers. Beam splitters designed for these and other uses have been included
as they may be able to be adapted to fullfil the requirements for allowing multiple
end-stations to be used simultaneously.
Beam splitters can be divided into two main categories. Firstly, there are those
that divide the amplitude of the radiation, such as:
• partially transmitting mirrors - metallic foils, multilayers, pellicles, beam splitter
plates
• beam splitter cubes
• thin crystals
73
74
5. Beam-splitting methods
• diffraction gratings
• wire grids
Secondly, there are those that divide the wavefront, such as
•
•
•
•
knife edge mirrors or crystals
Fresnel bi-mirror
slotted or perforated mirrors
structured arrays
In the case of a pulsed source, it is also possible to divide the beam in time by
using moving mirrors (translating, rotating, vibrating) to deflect pulses in different
directions.
Each type of beam splitter is discussed in turn, and in section 5.6 a list is drawn up
of those which may be suitable candidates for splitting a main free electron laser beam
for multiple experiments for different wavelength regimes. General points for the
specification of a beam splitter are given in section 2 before the survey of the different
types.
5.2
Beam-splitter specification
A sample specification is given in Table 5.1 for a beam splitter on an XUV-FEL.
The full specification of a beam splitter will include the maximum power loading,
overall efficiency, relative intensity of the split beams, minimum angular separation,
polarisation and wavefront preservation. The required power handling and efficiency
to a large extent will determine the incident angle and the material(s) used. The
incidence angle will have a large impact on the size of the optic. Cost and ease of
manufacture of the component are also important considerations.
FEL radiation has a high degree of polarisation and coherence. In considering
the suitability of different types of beam splitter, the starting assumption is that the
quality of the incident beam is to be preserved in the split beams, i.e. polarisation,
wavefront shape and pulse duration are preserved as far as possible. However, it may
be that in order to increase the efficiency these assumptions have to be relaxed, at
least in one if not both of the beams. Obviously the exact beam qualities required
will depend on the experiment and preserving all properties may not be important
in all cases and such a relaxation may not matter. Different splitting techniques will
compromise different aspects of the beam and the correct choice will depend on the
experiment; there is unlikely to be a universal beam splitter.
The minimum required efficiency will be set by the ability of the optics to handle
the power load or beam fluence. The efficiency requirement as determined by the flux
needs of the experiments falls outside the scope of this survey. It is however assumed
that the experiments on each branch will be equally demanding of photon flux and
so the beam should be split roughly into equal parts. It is however noted that for
some applications the free electron laser be may be too powerful, and it may be that
a beam splitter could be used as an attenuator on one beam path.
A further point to note is that he space available for the beamlines may well also
limit the maximum angular separation and in general it may not be practical to have
very large angular separations between the beams.
5.2. Beam-splitter specification
Parameter
Value
Photon energy
Average power
Beam fluence
8-100 eV
10-100 W
≤ 50 mJ/cm2
Grazing angle
< 5◦ , preferable ∼ 3◦
Size
Overall efficeny
100-200 mm by 50 mm
> 50%
Intensity split
Roughly equal in each
branch
Ideally small/negligable
Polarisation
Wavefront distortion
Minimum
angular
separation of beams
Vacuum compatibility
75
Comments
Depends on rep. rate
Value at 100 eV, normal incidence
Determined by reflectivity
requirements and ablation
threshold
Depends on grazing angle
This may increase if power
loading becomes problematic
This will be difficult for
lower energies
Ideally the modal structure
of the beam should be preserved
5 mrad (0.3◦ )
UVH bakable
hydrocarbon free for operation near the carbon edge
Table 5.1: Sample specification for a beam-splitter for XUV radiation.
76
5. Beam-splitting methods
5.3
Amplitude division beam splitters
Partially transmitting materials
Partially transmitting mirrors can be made from metallic foils or multilayers. When
these are deposited on glass they are termed plate beam splitters, or on a thin (of
the order of µm thickness) stretched polymer membranes, they are termed pellicles.
Thin crystals are also used as beam splitters in the harder X-ray regime.
Plate beam splitters, by their nature of being deposited on glass, operate mainly
the visible and near infrared (NIR) but their range can be extended to 200 nm using
UV grade fused silica as the substrate. They will normally have the beam splitter
coating on the front face of the plate and an anti-reflection coating on the back to
prevent ghosting and the substrate will be slightly wedged to eliminate interference
fringes. They can be either polarising or non-polarising. Polarising beam splitters
use bi-refringent materials and/or are operated near the Brewster Angle. Plate beam
splitters can be made for high power applications, but those that are readily available
are mainly single wavelength, single angle devices, made for specific laser lines. As an
example, ESCO[113] make a range of beam splitters with a 10% bandpass, damage
threshold 300 - 500 W/cm2 , designed to work at 45◦ incidence for a range of laser
lines from the UV to IR.
Broadband dielectric plate beam splitters are available in the visible and NIR, e.g.
Newport[114] provide beam splitters covering the wavelength ranges 480 - 700 nm,
700 - 950 nm, 1290 - 1500 nm. These operate at 45◦ angle of incidence and all are
slightly polarising. The damage threshold is quoted as typically 500 W/cm2 CW, 0.5
J/cm2 with 10 ns pulses.
Conventional plate beam splitters may not be applicable for ultra-fast use due to
dispersion in the transmitted beams. Newport provide thin (3mm) ”ultra-fast” plate
splitters made from UV quality fused-silica operating over 700 - 950 nm for s-polarised
light and 680 - 1060 nm for p-polarised light. Again these operate at 45◦ angle of
incidence and split the radiation nearly 50:50 and are usable for pulses in the 100’s
of fs regime.
Pellicles
Pellicles operate in the wavelength range 400 - 2500 nm. They have the advantage
over plates in that there is no ghost image due to their extreme thinness (except for
extremely short pulses which would only be a few cycles long at these wavelengths).
For uncoated pellicles the reflectivity is about 10%, transmission about 90%, but
coatings have been made which increase the reflectance up to the order of 50 %.
Typical damage thresholds are 2 W/cm2 CW and 1 J/cm2 with 10 ns pulses for
uncoated membranes, which makes them unsuitable for free electron laser beamlines.
The thin membranes are also susceptible to vibration and interference fringes. For
further details see for example: [114, 115].
As an extension to what is normally considered to be a pellicle, a beam splitter for
an FTIR spectrometer has been made for the THz free electron laser at KAERI by
coating a polyester film with silver [116]. At 3 THz, the absorption of the polyester
film is about 2%, and the balance between reflection and transmission was obtained by
coating the film with several tens of nanometers of silver to create the beam splitter.
5.3. Amplitude division beam splitters
In an analogous manner, thin foils of a low-Z material might be used at soft x-ray
and shorter wavelengths.
For example, Lcls propose to use 30 µm thick polished beryllium foils at a grazing
angle (∼ 1◦ for energies around 8 keV) above the critical angle to reflect a small
( 0.01%) part of the beam to a diagnostic instrument, while transmitting 99% of the
radiation[117]. Because low-Z materials give a sharp reflection cut-off, achieving a
more balanced split will require the grazing angle to be adjusted to suit the photon
energy and hence the angle of beam separation would be a function of photon energy.
At lower photon energies high transmission will not be possible e.g. it is effectively
zero below 1 keV for a 30 µm Be foil.
Extension of this technique into the XUV would require exceptionally thin foils
where the challenge of manufacturing and supporting a surface of sufficient quality
for good reflection would be very severe indeed. Where absorption is high, there is
also the concern of radiation damage.
Multi-layer beam splitters
Multi-layer beam splitters can be made for the XUV and shorter wavelengths, however
in general they only operate for a given wavelength and incident angle. Multi-layers
are usually formed on SiC, SiN or Si3 N4 membranes but obviously for the transmission
multi-layers required for beam splitters, absorption in the membrane is a problem at
XUV wavelengths. Much work has been done in the 13–16 nm wavelength range
for applications in lithography using multi-layers on Si3 N4 membranes, however in
general the overall efficiencies are not very high. Some examples found on the web
with overall efficiency greater than 20% include:
• Near-normal incidence (10◦ ) Mo/Si multilayer - reflectivity 28%, transmission
32% [118]
• Ru/SiN bilayer operating at 17.5◦ incidence - reflectivity and transmission about
11% [118]
• Mo/Si multilayer on silicon nitride at 7.2◦ incidence - reflectivity 20%, transmission 22% [119]
Some work has been done on manufacturing free-standing multi-layers. For example, Haga, et al. [120] report the manufacture of a 10 by 10 mm2 Mo/Si multilayer
where the silicon nitride membrane is etched away. The outer Mo layers were replaced
by Ru which was much more resistant to the etching process. They also investigated
the effect of the substrate smoothness on the efficiency of the multi-layer. Measurements using synchrotron radiation revealed that the multilayer worked as a one-to-one
beam splitter whose reflectivity and transmittance for s-polarised radiation at 13.4 nm
are both 27% at an angle of incidence of 45◦ , i.e. the efficiency is similar to supported
multilayers. More recent work on free-standing multilayers has not been identified.
By varying the thickness of the multi-layers with depth, the wavelength and/or
angle range can be increased, e.g. for reflecting multi-layers a reflectivity of larger
than 40% is expected over the energy range 4 - 9 keV using 20 Mo/Si bi-layers with
five different spacings on an SiO2 substrate[94]. If these multi-layers could be made
on transparent substrates, their use as beam-splitters could be investigated. Note
again there may be a problem of dispersion which may preclude their use for very
high time resolution application[121].
77
78
5. Beam-splitting methods
Radiation damage is an area for concern for the use of multilayers in free electron
laser beamlines. Recently Bajt, et al. [122] reported that a normal incidence parabolic
Mo/Si multilayer mirror with a reflectivity of about 60%, used to focus 13.5 nm
radiation at Flash did not show signs of damage. This efficiency is similar to the
overall efficiency of some of the beam splitters mentioned above. Obviously more
work needs to be done in this area. However, it is unlikely that a multilayer beam
splitter would be used for the current application due to the wavelength specificity as
well as possible power handling issues.
Beam splitter cubes
Beam splitter cubes onsist of 2 right-angled prisms, made of fused silica for UV
applications, normally cemented together with an epoxy. Broadband cubes, with
bandwidths of 300 - 400 nm, are available over the wavelength range 400 - 1600 nm,
and may alter the polarization of the light by about 10%. There are nonpolarizing
cubes designed for specific laser lines in the UV, for moderate power laser operation.
The epoxy absorbs radiation and hence cannot be used in high power applications.
However, cubes which do not use adhesives to cement the prisms together have been
recently designed for high power laser applications, e.g. Showa Optronics[123] market
a cube for the UV over the range 193nm - 355 nm with a damage threshold at 248
nm of 1 J/cm2 and Precision Photonics Corporation[124] make cubes for high power
applications (damage threshold of 10 J/cm2 at 1100 nm) in the visible and IR.
Crystal diffraction beam splitters
Perfect crystals are commonly used as monochromating elements for hard X-rays
(working at X-ray energies above about 2 keV). An X-ray entering a perfect crystal scatters from the regularly space atomic planes - a process known as dynamical
diffraction[125]. This leads to a very sharp reflectivity curve with a bandpass (∆E/E)
for a given angle of incidence (Bragg angle) that is typically less than 10−4 . The bandpass depends on the crystal material (diamond is narrower than silicon which in turn
is narrower than germanium), on the crystal planes used (planes with lower order
indices generally give narrower reflections) and on whether Bragg or Laue geometry
is employed. In Bragg reflecting geometry, the X-rays enter and exit from the same
surface of the crystal while in Laue geometry, the X-rays enter and exit from different
surfaces. In Bragg geometry, the X-rays penetrate a short distance into the crystal
and the reflectivity curve is given by a Darwin curve, which approximates to the
ideal top hat shape. A general consequence of the narrow bandpass associated with
dynamical diffraction is that the temporal profile of a short X-ray pulse is affected.
When the radiation source bandpass is larger than the crystal reflection bandpass,
as is the case with X-ray FEL radiation, a crystal monochromator can be used as a
beam splitter. This method uses a crystal to deflect a small energy band from the
broader band source to one experiment while the remaining transmitted radiation
is passed onto a second experiment. Thin crystals are normally used to minimise
absorption. Crystal reflections are sensitive to heating from the radiation which can
result in changes in lattice parameter and lattice orientation which may degrade the
deflected beam. The ideal beam splitter crystal should have low X-ray absorption to
minimise losses to the X-ray beam and to reduce X-ray beam power absorbed inside
the crystal.
5.3. Amplitude division beam splitters
This method of splitting beams for multiple experiments is used on some undulator
and high-energy wiggler X-ray beams at synchrotron radiation sources. In the lower
X-ray energy range, diamond is often used as the beam splitter as it has low Xray absorption and also good thermal conductivity that allows the heat to dissipate
efficiently, reducing thermal distortion of the crystal. The difficulty of obtaining
diamond crystals with high enough perfection for use as monochromators is a problem
that has been recognised[126]. A second monochromator crystal may be used to
deflect the beam back into the incident beam direction and if the first reflection is
a diamond (111) reflection it is possible to use a germanium (220) reflection as the
second reflection as the d-spacings of the two reflections are very similar. Using a
germanium reflection for the second crystal has the advantage that the reflection
has a broad width making alignment easier and reducing loss of X-ray flux caused
by strain within the diamond crystal. The addition of a second crystal may also
allow the X-ray energy to be changed while maintaining almost constant X-ray beam
direction. This method of X-ray beam splitting is used at the ESRF on the Troika
beamline ID10, which has three undulator segments and has available a selection of
monochromator crystals - diamond (111), diamond (220), and silicon (111) - allowing
a variation in bandwidth on two side stations. Another example at the ESRF is the
macromolecular crystallography beamline ID14 which has three diamond (111) and
germanium (220) monochromator pairs, in line, to give three 13.3 keV fixed energy
stations and a single variable energy station using the straight through transmitted
beam.
In the higher X-ray energy range, X-ray absorption is lower and silicon or germanium may be used as the beam splitting crystal. This allows the bandpass of the
reflection to be varied by applying a bend to the crystal. An example of this application at the ESRF is the high-energy beamline ID15 which can use two bent crystals
to deflect beam from the wiggler source to two side stations at X-ray energies from
30 keV up to 300 keV.
Where beam splitting is required for X-ray interferometry, perfect crystals are
used. Laue interferometers[127] use the forward transmitted and reflected beams at
the crystal exit surface to split the beam. Interferometric beam splitters using multiple
reflections[128] or the beams reflected from and transmitted through a crystal whose
thickness is less than the extinction depth can also be used. These techniques might
be useful where multiple low-bandpass (∆E/E ∼ 10−5 ) beams are required, though
there could be thermal problems since the radiation out of this bandpass will be
absorbed in the crystal.
A similar application to that of X-ray interferometry is the use of crystal beam
splitters in optical delay lines. A splitter/delay line at 8 keV has been designed
for the Lcls using Si (400) crystals[129]. A 10 µm thick Si (400) crystal has 80%
reflectivity in a bandpass of ∆E/E ∼ 1.4·10−5 with a transmission outside this region
of 75%. The reflected and transmitted beams are sent via different sets of crystals
to be ultimately recombined on a common path but with a variable delay created
by translating one set of crystals. Two pulses are created by tuning the crystal sets
to wavelengths that differ by more than the bandpass of the crystal reflection but
with both contained within the bandwidth of the free electron laser pulse. A similar
device working at 8.39 keV with Si (511) crystals and 12.4 keV with Si (553) has been
constructed at HASYLAB and tested on beamlines at DORIS-III, PETRA-II and the
ESRF[130, 131].
79
80
5. Beam-splitting methods
Gratings
Gratings provide a very simple way of splitting a beam, though there are a number
of practical limitations and consequences. A grating divides an incoming beam of a
given wavelength into a series of orders spaced around the ”zeroth” order beam, which
has a diffraction angle equal to the incidence angle. Inside orders have a diffraction
angle (measured from the grating normal) smaller in magnitude than the incidence
angle and outside orders have a diffraction angle that is larger in magnitude than the
incidence angle. By convention, diffraction angles that are on the opposite side of the
normal are negative.
For a beam splitter, one could choose to use either one of the first order and the
zeroth order beams, or the first inside and the first outside order beams. Higher
diffraction orders are unlikely to be used as they have lower efficiency.
A possible advantage of using the first inside and outside orders is that the grating
acts as a monochromator for both. Conversely, the zeroth order contains all the
spectral content of the incident beam up to the cut-off determined by the reflectivity of
the grating coating and so a second grating would be needed to give a monochromatic
beam. However, this would allow independent choice of wavelengths for the two
beams. The relative intensity of the first diffracted to the zeroth order depends on
the shape of the diffraction grating grooves. A careful choice of the groove profile
based on modelling the efficiency with a code such as Gradif1 can give a certain
degree of tuning of the relative intensity, but one cannot expect perfect control if the
grating is to operate over a wide range of wavelengths.
One should also remember that the required zero order efficiency could be, and
probably will be, at a wavelength that is unrelated to the first order wavelength.
Therefore, a comprehensive set of calculations would have to be performed to give
not only the first order efficiency as a function of wavelength, but also the zeroth
order efficiency as a function of both wavelength and incidence angle. There is thus
no unique value to the efficiency at a particular wavelength into the zeroth order beam
as it depends on wavelength of the first order beam and hence angle of the grating.
Any requirement to tune the grating leads to the most significant practical problem
with using a grating as a beam splitter. As the grating is rotated to select a different
wavelength, the angle between the first and zeroth orders will change. Similarly, the
angle between the first inside and first outside orders that have the same wavelength
will also change. (Conversely, the wavelength into a fixed outside order direction will
change in the opposite direction and at a different rate to the wavelength in a fixed
inside order direction). This is very inconvenient for a beam splitter that is to feed
fixed end stations from a fixed source. One solution is to place a plane mirror, which
can both translate and rotate, after the grating. This mirror intercepts the zeroth
order beam and steers it always to a fixed output path. The disadvantages of this are
that the path length will change (so changing the overall beam timing) and that the
mechanism is complicated and so prone to introducing small errors giving temporal
and spatial jitter to the beam.
An alternative approach is to use the SX700 type of variable included angle grating
mount. In this, a plane mirror rotates about an axis not in the mirror surface and
allows the included angle at the grating to be varied by just a single rotation. The
1
Gradif is an update of the LUMNAB code of M. Nevière, et al. [132]
5.3. Amplitude division beam splitters
81
mechanically simpler mount will work with less mechanical error, but there is still a
path length change, and so the overall beam timing is a function of wavelength.
Providing the grating is working in collimated light, there can a free choice of
included angle without changing the focusing properties of the monochromator. This
free choice of included angle can be used to either keep a fixed angle between the
first diffracted order and the zeroth order, or to keep the first inside and first outside
orders at a the same wavelength with a fixed angle between them.
In the case where the angle between the first and zeroth order is to be fixed, one
also finds that this is the same constraint for scanning a blazed grating ’on-blaze’ and
thus has a potential advantage in optimising the first order efficiency. This would
naturally be at the expense of the zeroth order efficiency at that wavelength, but this
will not be a problem if the two branches are to operate at different wavelengths.
If the angle between the first inside and zeroth order beam is ψ, then the grating
equation under the constraint that ψ is fixed becomes
ψ
ψ
N mλ = 2 sin
cos
−β
(5.1)
2
2
where β is the diffraction angle. For a blazed grating operating on-blaze, the blaze
angle should be ψ/2.
A similar expression is obtained if the angle between the first inside and outside
orders is to be kept constant and both orders are to pass the same wavelength. If
β + is the diffraction angle of the first inside order and β − the diffraction angle of the
first outside order, then the angle between them is
ξ = β+ − β−
and the grating equation for constant ξ becomes
ξ
ξ
cos
− β+
N λ = 2 sin
2
2
(5.2)
(5.3)
which gives the diffraction angle of the inside order for a given wavelength, from which
the incidence angle and diffraction angle of the outside order can be calculated.
In both these modes of operation, the tuning range will be limited if the grazing
angles at the grating are not to become large (and hence the efficiencies low). In
general, the angles between the orders (ψ or ξ) will have to be <∼ 3◦ , and low line
density (a few hundred lines per mm maximum) gratings used.
A disadvantage of using a grating as a beam splitter with very short pulses is
that the pulse is temporally stretched in the diffracted orders due to the path length
difference across the beam in the dispersive direction – as discussed in chapter 4 (see
page 63). Since the pulse stretch is λ/c for each groove illuminated, one way to
mitigate this effect is to use very low line density gratings. At shorter wavelengths
and relatively long pulses, this may be sufficient to prevent the pulse stretch becoming
significant.
At longer wavelengths and shorter pulses, it may not be possible to illuminate
sufficiently few grooves and a second grating must be used to reverse the stretch of
the first. The second grating must work with incident angle equal to the diffraction
angle of the first and in the opposite order of diffraction. Therefore, if a variable
included angle mounting is being used for the first grating, it must be replicated
82
5. Beam-splitting methods
for the second grating with consequent impact on the cost and further path length
variations. The system with a translating and rotating plane mirror that intercepts
with just the zeroth order beam after the grating would be simpler in this respect as
both the grating mounts could simply be fixed included angle type.
Alternatively, conical diffraction mounting can be used to reduce the pulse stretch
(since the effective number of illuminated groves is reduced when compared with the
classical mount). The further advantage of the conical mount is that the diffraction
efficiency should be much higher. However, in the context of a beam splitter, the
conical mounting leads to difficulties. It is normal to operate the grating in fixed
altitude mode as this allows the grating to be tuned with just a simple rotation
(about an axis parallel to the grooves). Unfortunately, in this mode, the zeroth order
(for example) changes direction in both the horizontal and vertical planes. Capturing
and steering the zeroth order beam into a fixed direction will be very difficult. Fixed
azimuth mode would make capturing the zeroth order beam easier, but scanning the
grating requires translating and rotating mirrors.
A scheme for using diffraction gratings as a beam splitter has been proposed for
FERMI@Elettra for wavelengths around 40 nm. Light from the 0 and +1 orders
is used. For the 1st order radiation, a second grating followed by a translatable
plane mirror allows the pulse stretch to be compensated and gives a fixed position
for the output beam[133]. An efficiency of about 30% has been estimated for both
the zero and first orders using at 100 lines/mm grating, 84◦ incidence angle, over the
wavelength range of 34 - 46 nm. This design requires the manufacture of a long (60
mm) grating to a very high specification, as well as a translating mirror hence it is
technically challenging.
The above applications are all for reflection gratings. Transmission gratings can
also be used to split the beam with the advantage that, since the gratings are used
at (or near) normal incidence, the geometry of the split beams is much simpler.
Manufacturing transmission gratings that can work in the XUV to x-ray region is of
course a major technical challenge. Achieving adequate dispersion (and hence beam
separation) at short wavelengths requires the grating period to very small. The aspect
ratio (depth/width) of the grating bars is inevitably quite high if the gratings are to
be robust and they are therefore not suitable for strongly divergent light. The risk of
ablation of the grating in a free electron laser pulse is also a major concern.
In the XUV, a transmission grating will almost certainly behave as an amplitude
grating, since it will be difficult to make the grating bars anything other than 100%
absorbing. Strong absorption means the grating must also be made unsupported,
which is very difficult. Assuming a perfect amplitude grating can be made, the maximum first order efficiency occurs when the groove width is half the grating period
and is just 10% and the zeroth order efficiency is 25%.
Conversely, for hard x-rays, it is difficult to make the aspect ratio of the grating
bars high enough to be perfectly absorbing and the grating will function as a phase
grating. The efficiency depends on the grating material and bar profile, and this offers
scope for tuning the grating performance.
Weitkamp, et al. [134] used a Ronchi phase grating to make an x-ray shearing
interferometer. The grating is made by electron-beam lithography from silicon and
has a groove period of 2 µm and depth of 9 µm. They operated the grating at 12.4
keV (1 Å), but were only producing a small shear in the beam. The phase shift of the
grating was tuned by tilting the grating about an axis perpendicular to the grooves
and the beam axis so as to vary the effective thickness of the grating. This allowed
5.4. Wavefront division beamsplitters
the phase shift to be increased to π and hence the zeroth diffraction order eliminated
and first order efficiencies maximised. Naturally, this technique can only be employed
when the grating bars have sufficient transmission, and is thus only applicable for
harder x-rays due to the difficulty in manufacturing very thin gratings with such a
fine structure.
Gratings can also be used to send a small part of the beam (in first order) to a
spectrometer for measuring the spectral content of the beam, while most of the beam
is in the zeroth order and is passed down the beamline to the experiments. The groove
profile of the grating is tuned to give just sufficient intensity in the diffracted order
for the spectrometer to work (thus maximising the beam intensity to the experiment)
and the line spacing is varied to give a flat field for the dispersed spectrum on the
detector. Such an instrument is being installed at Flash [135].
A point of concern for operating gratings in free electron laser beams is the effect
of the structured surface on the likelihood of ablation since parts of the surface may
make very steep angles to the incoming beam. The effect of the groove shape on
the ablation threshold is not understood. If this were to be a problem it would be
exacerbated with classical grating mounts where the grating is likely to operate at
quite a steep angle to the beam at long wavelength part of the spectrum. In this
regard, conical diffraction in constant altitude mode has an advantage as the beam
strikes the grating at effectively the same grazing angle even as the grating is tuned.
Grids
Wire grids can be used as polarising beam splitters for FIR radiation and are used
in Fourier Transform Infra-Red (FTIR) spectrometers. Radiation with polarisation
parallel to the wires is reflected, whereas the component polarised perpendicular to
the wires is transmitted. As an example, the Millimetre-Wave Technology group[136]
in the Space Science and Technology Department of the UK Science and Technology
Facilities Council (STFC) has manufactured wire grids for a FTIR spectrometer to be
used on the THz beamline on ALICE, the energy-recovery-linac-based developmental
light source at Daresbury Laboratory.
5.4
Wavefront division beamsplitters
Beamline apertures
The simplest method of splitting a beam by wavefront division is to use apertures to
divide the beam into two spatially separated parts, as is often done on synchrotron
sources where there is a large fan of radiation (e.g. from dipoles or wavelength shifters).
The disadvantage of this is that the angular separation of the two beams is determined
by the natural divergence of the source, which will be rather small for a free electron
laser. Nevertheless, the technique might be suitable for separating off a small part
from the extremity of the beam to pass to a beam monitor or some beam diagnostics,
or for coherent scattering experiments from small samples. If greater separation is
required, a mirror could be used to deflect one beam downstream of the aperture,
though this is effectively the same situation as the knife-edge mirror described below.
As with other methods that divide the wavefront, edge diffraction effects are likely to
83
84
5. Beam-splitting methods
be significant. The design of the aperture would have to eliminate the risk of radiation
damage.
Knife-edge mirrors
The radiation can be split by inserting a mirror part way into the beam to deflect a
portion of it. As an example, a grazing incidence (3◦ ) knife-edge mirror is used as
part of an autocorrelator system designed at BESSY for use in soft X-ray pump-probe
experiments at Flash[137]. The autocorrelator was designed to work up to 200 eV,
and the slope error on the mirror is required to be less than 0.5 mikro-rad. This slope
error must be maintained up to the cutting edge of the mirror and this is very difficult
to achieve with conventional polishing techniques as there is always some ”roll-off”
at the mirror edges. The required quality was achieved by cutting away the end of
the mirror after polishing to remove the roll-off region. Alternatively, the edge of the
mirror could be masked with an aperture (see above).
6°
r 3°
litte
Beam sp
Figure 5.1: Schematic of knife-edge grazing incidence mirror beam splitter for soft X-rays.
For harder X-rays, the grazing angle needs to be smaller to maintain a high reflectivity. The required minimum beam separation of 0.3◦ in the sample specification
above means that the grazing angle must be greater than 0.15◦ . For carbon, the
reflectivity is greater than 98% for energies from 1 keV to 10 keV at this incidence
angle, but the mirror could become very long. For slightly larger angles the cut-off in
reflectivity with increasing energy will be the main limiting factor in the usable wavelength range, e.g. the reflectivity of carbon decreases rapidly above about 3 keV for a
grazing angle of 0.5◦ . Using a coating with higher atomic number (nickel, rhodium)
will give a reflectivity cut-off at higher energy for a given angle, but such materials
do not have as high a damage threshold as carbon. The main concern about using
a mirror as a beam splitter is that edge diffraction could have a significant effect on
the wavefront, especially as the beam is being cut in the middle where the amplitude
is likely to be highest. This type of beam splitter cannot therefore be expected to
produce two beams that are lower intensity replicas of the original beam.
Knife-edge crystals
To achieve higher angular separation at shorter wavelengths, the knife-edge mirror
could be replaced by a knife-edge crystal. For example, the Bragg angle of the silicon
(111) reflection at 8 keV is 14.3◦ , which gives a beam deflection angle of 28.6◦ . Doublecrystal arrangements could be used to give a deflected beam with a fixed exit direction
as the crystal is rotated to tune the photon energy. The splitting crystal would have
5.4. Wavefront division beamsplitters
85
to be translated orthogonally to the beam direction or rotated about its cutting edge
if the fraction of the beam it intercepts is to remain constant. Edge diffraction and
the impact on the wavefront would still be an issue, especially as it may be difficult
to maintain a perfect crystalline structure to its edge. There would also be a change
in the pulse length of the beam deflected by the crystal due to the monochromating
action of the crystal, and the reduced bandwidth will also limit the overall efficiency
for the reflected beam.
Fresnel bi-mirror
Fresnel bi-mirrors consist of two flat mirrors, normally joined along one edge and
inclined at an angle to each other – see Figure 5.2. In general they are used in
interferometers where the radiation reflected from the two parts of the mirror is
inclined towards each other, resulting in interference. An example is their use in an
interferometer on SU7 at SUPERACO[138], where silica mirrors at a grazing angle of
3 − 6◦ were used for 4.4 nm. While bi-mirrors could be used to cross the beams over
each other and separate them, it is hard to see any advantage over the use of a single
grazing incidence knife-edge mirror
a’
p
a
Fresnel’s bi-mirror
Figure 5.2: Basic design of the Fresnel mirror interferometer. Rays a and a′ create an interference pattern
when they add up.
Slotted or perforated mirrors
In this method, the incident wavefront is coherently split on a microscopic scale with
the use of holes or slots cut in a mirror. This method is easier for longer wavelengths,
but has been realised in the XUV regime, e.g. a slotted mirror has been used in an
interferometer on beamline 9.3.2 on the ALS[139]. This is similar to the proposal
for a prototype beam splitter to be made for IRUVX by AZM at BESSY[140], in
which arrays of small holes will be machined in a grazing incidence mirror. An area
of concern is the ability to manufacture high aspect ratio holes to a great enough
precision and surface quality. The effect on the coherence of the radiation must also
be considered.
86
5. Beam-splitting methods
Losses in reflection due to diffraction as well as filling factor have to be taken
into account for mirrors with holes in them. One such example in the field of microelectromechanical systems (MEMS), an area of considerable research effort, has been
found. A key component for future nanoscale optical devises is the freestanding
micro-machined mirror – as shown in Figure 5.3.
Figure 5.3: A MEMS free-space optical reflector. Taken from Zou, et al. [141] .Note the scale at the top of
the figure – the line is 200 µm long.
The holes in the mirror surface serve no useful purpose regarding the function
of the reflective surface. They are commonly referred to as release holes and allow
release etchant to flow behind the mirror once the micromachining process is finished,
releasing the component from the bulk material. In[141], the losses in the reflectivity
due to the filling factor and diffraction are calculated for light of wavelength 632.8
nm as a function of hole size from 5 - 23 µm and spacings of 10 - 30 µm. For the
case of 21 µm square holes spaced at 30 µm, the filling factor is 50%, and the loss in
reflected light due to diffraction was estimated to be 14%. For the same spacing, as
5.4. Wavefront division beamsplitters
the hole size decreases, the diffraction loss increases, so that for a 10 µm hole size the
filling factor loss is 11%, and the diffraction loss 15%.
Much bigger holes relative to the wavelength were used in the beam splitter for
the ALS interferometer, designed to operate between 60 eV and 100 eV. Slots were
cut in a highly polished (rms roughness ∼ 3 Å) single crystal silicon wafer. Based on
the coherence properties of the incident X-ray beam, the width and spacing of the
slots were set to 50 µm and 100 µm respectively. The slots were 15 mm in length
and created by chemical etching. The completed assembly was then coated with
molybdenum. A major concern in the manufacturing was to keep the mirror flat to
within 1 µrad, and to maintain the surface smoothness.
Structured arrays
A ’1-D capillary beam splitter’ has been designed to work around 13.9 nm (89 eV) on
a plasma-based XUV source[142]. It consists of a stack of 20 µm thick plates, 7.9 mm
long and separated by 130 µm. The plates are tilted at a small angle (grazing angle
of 0 − 0.8◦ ) with respect to the incoming radiation. Light can either pass unhindered
between the plates, or else undergo a single reflection, causing two beams to emerge
at different angles. At 0.8◦ angle of incidence, all the light has to be reflected to get
through the device. The transmittance (efficiency of the direct path) varies from 85%
to 0% depending on the angle of incidence. The efficiency of the reflected light varies
from 0% to 75% and 15% of the light is lost by absorption on the front edges of the
plates. If a similar design were to be used for splitting free electron laser beams, the
stack would need to be designed to absorb a smaller fraction of the radiation. The
effect on the wavefront would also need to be investigated.
Capillary arrays have been used in the keV regime to suppress higher order harmonics passed by a monochromator on a bending magnet beamline at BESSY[143].
This device uses a double reflection in the array, the grazing angle of 3.6 mrad giving
an 89% efficiency at each reflection, so the reflected light is in the same direction as
the incident; however this example shows that single reflection capillary plates could
be used at this wavelength.
An alternative construction scheme could be to adopt the same technology used to
form Multilayer Laue Lenses (MLLs)[144]. The x-ray lens technology developed by
Argonne National Laboratory consists of many individual layers precisely sputtered
onto a silicon wafer. The multilayer stack is then ”sliced” to form a thin transmission
element in which the stacked diffracting surfaces are oriented almost parallel with the
optical axis. Although developed as a Fresnel lens structure for micro-focus applications, it is foreseeable that the same technology could be used to create a beam
splitter, either by employing a similar geometry to that used in the capillary beam
splitter stack or as a knife edge diffractive element redirecting a proportion of the
beam.
Possible drawbacks for this unproven technology include radiation damage to the
multilayer structure and achieving the necessary manufacturing tolerances for both
the microstructure fabrication and material slicing.
87
88
5. Beam-splitting methods
5.5
Time-based splitting
An alternative to splitting the wavefront in space is to send alternate pulses or trains
of pulses to different beamlines. One scenario is to send hours/minutes worth of pulses
to one experiment while the other endstation is changing samples, checking data etc.
This could be done simply using a switching mirror. At the other end of the time
scale, is may be possible to use vibrating mirrors or alternating mirrors and slots on a
rotating disc to send alternate pulses to two end-stations. The feasibility of this will
depend on the repetition rate of the free electron laser.
An early example utilising a disc rotating at 25 Hz was designed and used at
on a synchrotron radiation source at DESY. A grazing incidence mirror occupied a
segment of roughly a quarter of the disc area, with an equally sized slot occupying
about another quarter. The system operated for wavelengths 20 - 280 eV, the grazing
angle of the mirror being 4◦ [145].
In order to increase the repetition rate, one could use the fact that the free electron laser beam is much smaller than those from a synchrotron radiation source and
consider a system of several mirrors and slots on a disc, and also increase the rotational speed of the disc. High-speed slotted discs have been designed for use as beam
choppers. For example, a beam chopper for operation at photon energies below 50
eV has been built by Forschungszentrum Jülich GmbH for use on the synchrotron
radiation source at BESSY. The disc is aluminium alloy with a diameter of 338 mm
and has 1252 slots cut in the edge. It uses magnetic bearings and is designed to spin
at about 1 kHz. It was reported at the SRI meeting in 2008 that the chopper had
been successfully tested at 1 kHz and will be commissioned with photon pulses in the
autumn of 2008[146].
A second example, in this case using air bearings, is the chopper which was designed
to chop the 4.3 MHz pulsed beam from the VUV-FEL on proposed 4GLS facility to
100 kHz. The disc would have to have withstood a high heat load from the 400
W of beam power as well as high mechanical stresses from the high speed rotation.
Consequently, martensitic stainless steel was chosen for the disk material. The disc
had a polished chamfered edge to reflect the unwanted light at 2.5◦ grazing angle. A
prototype chopper with just 2 slots has been built and tested by Fluid Film Devices
Ltd[147]. The disc has a diameter of 134 mm and was tested up to 500 Hz, half the
design frequency, before the project was discontinued due to 4GLS being replaced by
the NLS project.
If one wanted to use the chamfered edge to reflect the light into a beamline for
use by an experiment, the edge would need to be polished to an optical quality
surface. An alternative would be to attach mirrors to the disc. Both options require
further feasibility studies. For the martensitic steel prototype described above, the
manufacturer was not able to polish to the edge to optical quality, though the main
aim was simply to reflect as much of the incident power as possible to prevent it
from being absorbed in the disc. Distortions at the edge of the disc could also be
a problem. For the second option, the feasibility of having mirrors bonded onto a
high-speed rotating disc would need to be investigated. Furthermore, this technique
would be difficult to apply to X-rays since the very grazing angle required for good
reflectivity would lead to a thick disc and very high mechanical loads.
5.6. Summary
5.6
Summary
As the preceding sections have shown, there is a wide variety of techniques that can
be used divide a photon beam. Some of these techniques are very well established,
whilst some are more developmental. A key issue for free electron laser sources is that
the properties of the radiation produced extend into new ground when compared
with conventional laboratory or synchrotron sources. The short wavelengths, high
transverse coherence, short pulse duration and high pulse energy all mean that there
is some element of development required for any splitting technique.
Two lists of techniques are presented for further consideration for use mainly in the
soft x-ray regime. The first list gives those techniques that would seem amenable to
rapid development into practical beam splitters. The second list gives the techniques
that show potential but will require more extensive development to over come the
technical challenges. In all cases, the properties of a beam splitter derived from a
particular technique will be somewhat specialised and so there will be no ”universal”
beam splitter. The technique chosen will depend on the nature of the photon beam
being split and the particular needs of the experiment.
Techniques requiring the least development
Diffraction gratings
Reflection gratings give amplitude division and since they can be made to very high
tolerances, splitting with good wavefront control should be possible. Polarization
effects will be present but should only be significant at VUV and XUV wavelengths.
At least one of the beams will be monochromatic. Additional optics are required to
keep the output beam directions constant if tuning of the photon energy is required.
Pulse stretch is inevitable for ultra-short pulses, but can be corrected with a second
grating. In general, flexibility is high, but the systems are likely to be complex and
optimizations will give a more restricted operating envelope. The likely operating
range is from the VUV to the soft X-rays. Infrared gratings are also feasible, though
there are arguably easier splitting techniques for this part of the spectrum.
Knife-edge mirrors
A knife-edge mirror is one of the simplest techniques and also offers a very flexible
splitting with minimal constraints. Both beams are essentially spectrally unmodified,
though the reflected beam will be filtered at wavelengths shorter than the mirror
reflection cut-off. Very low grazing angles will thus be required for hard X-ray operation, and so the splitting angle will become very small. (Bragg reflection from a
crystal will give larger angles but with the disadvantages of reduced bandwidth and
the need to rotate the crystal for wavelength tuning). The splitting is achieved by
wavefront division and so the main disadvantage is that neither beam is a replica at
reduced intensity the incident beam since diffraction effects at the edge will distort
the wavefront. However, pulse lengths should be preserved. A key technical challenge
is achieving a mirror with an edge that does not badly degrade the beam at the division region. Knife-edged mirrors could be designed to operate over the entire spectral
range from infrared to X-ray wavelengths (though not necessarily in one device).
89
90
5. Beam-splitting methods
Slotted mirrors
A slotted (or perforated) mirror may overcome the key disadvantage of the knifeedge mirror by dividing the wavefront periodically in space (thus making each beam
closer to a less intense replica of the incident beam) whilst maintaining the advantages
of transparency (to the pulse properties) and flexibility. The technical challenge of
making the mirror is however much more severe. There is no inherent restriction on
spectral range, though the technical challenges will become more severe at shorter
wavelengths and the devices may be limited to the soft X-ray regime and below.
Crystal diffraction beam splitters
These are mainly applicable to use at shorter wavelengths (< 6 Å), but have the
advantage in this range over mirror type splitters of allowing much greater angular
separations. Wavelength tuning requires a rotation of the crystal and hence additional
optics to maintain a constant output beam position. Laue and Bragg reflections
are always highly monochromatic (unless one distorts the crystal lattice) and so the
full bandwidth of the free electron laser is not preserved. Accompanying this is
a stretching in the pulse length and whilst this stretching should be small (a few
femtoseconds), it cannot be reversed as is the case with a grating. Only in the case
of very thin crystals can a broadband transmission be achieved, though there will be
a missing component matching the bandwidth of Laue/Bragg reflection of the split
beam. The most important area for technical development is in achieving higher
quality diamond crystals, which are attractive due to their high thermal conductivity
and resistance to radiation damage.
Techniques requiring more development
Multilayers
A transmission multilayer is the most likely way that a plate beam splitter can be
realized at short wavelengths. In fact, the multilayer beam splitter will be more akin
to a pellicle. The technical challenges are thus making a membrane that is robust
and flat but has adequate transmission. If the membrane is small, this will be easier
but then the beam fluence will be high if the beam must be focussed onto it in order
to fit through it. A larger membrane would allow operation in the diverged light but
may be challenging to keep flat and vibration free.
Structured arrays
These devices have similar properties to slotted mirrors but differ in the approach
to fabrication. Operational range will depend on the fabrication technique (e.g. the
overall thickness of the structure is linked to the angular acceptance). Wavefront
quality will be very dependent on the manufacturing and thus development is required.
Time-based splitters
Mechanical switching to direct alternate pulses (or trains of pulses) to different beamlines is a logical approach for an inherently pulsed source. The potential advantage to
the experiment is that all received pulses contain the full free electron laser output and
5.6. Summary
can (in principle) be unchanged in all other properties. The difference is a lowering of
the repetition rate or pulse structure (e.g. the change from a uniform pulse train to a
macropulsed train). For some experiments this may offset the advantage of the intact
pulse single pulse energy. In any case, there is a considerable engineering challenge
of achieving a mechanical based system that can deflect alternating pulses or pulse
trains at rates of the order of a kHz or higher. High speed operation will probably
be restricted to the VUV/XUV to ease the challenge of making a fast moving mirror
that can deflect a complete pulse.
91
92
5. Beam-splitting methods
Summary
• Splitting the photon beam can be done to serve several experiments in parallel, it also enables the use of part of the beam
for diagnostic purposes. The trade off is that less (in some
sense) of the beam gets handed out for the various purposes.
• A beam can be split in the amplitude (using e.g. a semitransparent mirror), frequency (a dispersive optic is needed)
and temporal (using for instance a moving mirror) domains.
• Of the techniques listed in this chapter not all are suitable
for the use at free electron laser. Often the limiting factor is
the intended splitting techniques robustness when it comes to
withstanding the high peak power at X-ray wavelengths.
• In some instances the following techniques are already in use
at free electron laser whereas some need some kind of adaptation for the purpouse:
– Diffraction gratings (dispersive).
Induces a pulsestretching whose length depends on how many grooves
are illuminated. Pulse-stretch gets reversed if two gratings are used, at the expense of lower transmission.
– Crystal diffraction splitter – effective below ∼ 6Å wavelengths. An attractive material is diamond crystals, owing to their high thermal conductivity combined with
good radiation hardness[148]. The diffraction in the crystal causes a non-reversible pulse stretch of a few femtoseconds.
– Knife-edge mirrors
– Slotted mirrors
• Other techniques have been employed for specific purposes
and proven to be applicable in the free electron laser regime
of experimental conditions. Introducing them for general utilization require further development and research:
– Multilayers
– Structured arrays
– Time-based splitters
Part II
Beam diagnostics
93
6. Introduction
Since the Sase-process starts up from white noise – i.e. the initial shot-noise in the
beam is uniformly distributed, each light-pulse will have different temporal, spatial
and spectral properties. Over the course of many shots said properties average out and
the machine attains its ”average” properties in terms of intensity, pulse-length and
spectral purity; it is therefore natural that beam diagnostic methods are an integral
part of any free electron laser-project (see, for instance Ref. [89]).
Diagnostics of the photons (and electrons) also provide valuable feedback to the
accelerator part of the machine. This feedback is essential to ensure stable operation
and long up-time for the users.
The various schemes that exist to enhance the overall shot-to-shot repeatability,
e.g. HGHG, EEHG1 , may seem to loosen the demand on diagnostics – however the
delicate problem of overlapping a laser pulse (which can be of HHG type – also requiring its own diagnostics) with the electron beam still requires a strict characterization
of the light as in the Sase case.
In this chapter the various categories of diagnostics are presented, as well as the
different subcategories that we can sort them into.
6.1
Diagnostics categorization
Figure 6.1 gives an indication of how we can categorize the different diagnostic methods that needs to be employed to characterize the free electron laser photon beam.
• Beam cross-section
– Transverse (also along the beam path to discern the focus-size)
– Longitudinal
• Pulse arrival time
• The jitter between pulses
• Intensity / Pulse energy
• Spectral content
1
Sections 1.5, see page 18 and 1.5, see page 18.
95
96
6. Introduction
y
x
I
t
z
Figure 6.1: Photon pulses needs to be diagnosed vis-à-vis spatial and temporal extents. Spectral properties
can be inferred from the temporal distribution.
• Median energy
The beam’s size in space, and how it varies along the optical system is important
to characterize since those properties needs to be known to know the focus points
along the beam – both for simulation purposes and experiments.
The longitudinal cross-section of the beam gives the pulse length and shape. This
is connected both to the spectral content and the pulse to pulse arrival time jitter.
For experiments that are considering temporal properties of matter (pump-and-probe)
this is crucial information.
The pulse energy (or intensity) follows a gamma-distribution depending on how
many radiating modes that are present[104] – hence a shot-to-shot measurement of
the intensity is necessary to have at a free electron laser facility.
The centroid of the photon energy fluctuates about 0.5% at Flash[149], obviously
a shot-to-shot measurement of this needs to be provided, both to the users and to the
staff handling the accelerator itself.
Spectral diagnostics (Intensity and energy) are discussed in chapter 7 below.
Various methods concerning the measurements of the transverse spatial extent of
the photon beam are described in chapter 8 (see page 109).
A survey of pulse length, profile and jitter diagnostics can be found in chapter 9
(see page 151).
Subcategorizations
Shot-to-shot / Average
Many properties of the free electron laser photon beam needs to be known at a shotto-shot basis. A spectroscopic experiment, for instance, needs to know the incoming photons’ energy and intensity per pulse as to allow sorting of the experimental
data. Knowing just the average intensity and photon energy does not allow this
post-experiment analysis of the data.
Average properties, on the other hand says a lot about the long term stability
of the free electron laser and may also serve as a measurement of the condition of
transport optics. Averaging measurements are usually more stable than their shotto-shot counterparts – and can thus be used to calibrate other diagnostics.
6.2. Conclusion
Transparent/Opaque/Blocking
A diagnostic can be, more or less, invasive, i.e. how much it affects the photon beam’s
properties for experiments and other diagnostics downstream. An position measurement based on the photo-current generated on a slit will cut away parts of the beam,
thus reducing the available intensity downstream from the diagnostic.
As can be inferred from the title, we can divide the degree of invasiveness of a
diagnostic tool into transparent, opaque and blocking. As on-line diagnostics it is
preferable to have transparent diagnostics since they have least effect on the beam.
For commissioning of diagnostics, beam-transport elements, calibrating of diagnostics
and accelerator conditioning opaque and blocking diagnostics can be used.
As discussed previously (chapter 5) it is possible to split off part of the beam
to be diagnosed in parallel to the downstream experiments/diagnostics. Hence even
a blocking diagnostic that otherwise have the needed specifications can be used to
provide information to the downstream activities.
Photon-energy range
Physical processes that may be used as basis for a diagnostic can be challenging to
find. For infrared and THz beams it is not possible to photo-ionize a gas, whereas for
UV and soft X-rays the cross-section for this processes is very large – and in turn, for
hard X-rays the cross-sections for photo-ionization become very small.
Hence, the photon-energy range(s) of interest needs to be taken into account in
designing the diagnostic array for a facility.
6.2
Conclusion
There is no such thing as an perfect diagnostic, i.e. a device that measure a property
on a shot-to-shot basis in a transparent manner for any photon-energy with negligible
error. Thus we have to rely on a combination of diagnostics to measure the desired unknowns of the photon beam. To ensure the integrity of the resulting diagnostics array
one needs to calibrate them against each other (and possibly additional diagnostics).
97
98
6. Introduction
Summary
• A diagnostic needs to be more robust and more user friendly
than an experiment, as the information provided is used to
analyze experimental data – for users, as feedback to the running of the accelerator and for commissioning of the transport
optics.
• Diagnostics can be divided into:
–
–
–
–
–
Beam cross-section – transverse and longitudinal
Arrival time, jitter
Intensity and Pulse energy
Spectral content
Median energy
• Any diagnostic method can also be further characterized by:
– its ability to measure on a shot-to-shot basis or if it provides an average measurement of the property.
– if it is transparent, opaque or beam stopping/blocking for
a downstream experiment.
– what photon-energy range it can be used in, i.e. infrared/THz, UV, soft X-ray and hard X-rays.
• No perfect diagnostic exists (neither an universal that measures everything, nor optimal for all photon ranges). Thus
a judicious combination of diagnostics needs to be composed
into a diagnostics array distributed along the beam-path that
can be used to
– Measure – during the course of other experiments
– Calibrate – other diagnostics during commissioning
– Cross-check – the integrity of the diagnostics array
• Beam-splitters allows the use of opaque/blocking diagnostics
in parallel to other experiments and diagnostics.
7. Spectral diagnostics: Intensity & Energy
In this chapter some ways to infer the spectral properties (or some spectral property)
of the free electron laser light. During the course of Part I of the book we have gotten
the indication that both seeded and Sase free electron laser provide light that need
to be diagnosed on a shot to shot basis.
The Sase process start up from current shot noise in the beam that is subsequently
amplified with a few radiation modes contributing to the final spectrum at/after
saturation. Each pulse is therefore unique and for an experiment to be meaningful
the mean intensity and mean-energy of the pulses can be considered to be the minimal
information to be provided to the user. In various seeding schemes the quality of the
pulses needs to be monitored to ensure stability. The harmonic content of the pulses
and the spontaneous emission background levels needs to be diagnosed as well.
Ideally the full spectrum of the pulse should be measured on a pulse to pulse basis
in a manner that is transparent to the users of the beam. This is often not practically
possible, as will be seen in the following, but this can be overcome by dividing the
beam between the experiment and the diagnostics utilizing, e.g. a beamsplitting device
as discussed above in chapter 5.
7.1
X-ray spectrometry
The obvious spectral diagnostic of the fel beam is to measure it, or parts of it directly
with an X-ray spectrometer. With one or more gratings it is possible to disperse the
photon beam converting energy spread into a spatial distribution. In most instances
variable line spacing gratings is used to focus a higher order diffracted beam onto a
focal plane, passing the 0th order reflected beam for the experiment (Figure 7.1).
Rewriting the grating equation (Equation 4.1) in terms of line density
sinα − sinβ = n · λσ0
one can vary the groove depth according to a third degree polynomial (with x along
the grating) as:
σ(x) = σ0 + σ1 x + σ2 x2 + σ3 x3
Then one can choose σ(x) so that the abberation and spectral defocusing effects are
minimized. With proper materials chosen between one and ten percent of the radiation is dispersed onto the focal plane (this percentage also depend on the wavelength).
99
100
7. Spectral diagnostics: Intensity & Energy
focal plane
β
Incoming FEL pulse
α
Oth order
Figure 7.1: A variable line space grating disperses different wavelengths along the same focal plane.
λ range
central line spacing
fraction in 1st order
diffraction angle
Res. power (CCD)
incident angle
coating
6-40 nm
900 l/mm
8-0.5%
83.8-74.5◦
> 7000
88◦
C, Ni
20-60 nm
300 l/mm
11-1.5%
83.5-79◦
> 4000
88◦
C
Table 7.1: Design parameters of the flash VLS grating spectrometer – as given in Ref. [104].
This kind of spectrometers provide the full spectrum around a certain photon
energy – harmonics are usually filtered away by the grating. The detection can be
done either by CCD camera or strip detectors. At Flash the spectrum is recorded
by a Ce:YAG screen imaged by a CCD camera. The camera can record images at a
rate of 5 Hz[104].
Similar set-ups are used at LCLS[150] and at Fermi@Elettra[151].
7.2
Intensity/Beam energy
Earlier we discussed the use of monochromators in combination with the free electron
laserbeam – in section 4.5 (see page 67) – as a means to convert the spectral jitter
(wavelength and intensity fluctuations per pulse) into intensity jitter.
Intensity can be measured on a per pulse basis or as an average property over many
pulses, of course a fast enough detection scheme can be made to integrate over many
pulses if one needs to measure the average intensity. As free electron laser pulses are
often in the order of tenths of femtoseconds (or shorter) a measuring on a pulse by
pulse basis poses quite a challenge as will be seen below.
As for most diagnostics we can roughly divide intensity measurements into opaque
and transparent – as seen from an imagined experimental station downstream from the
diagnostic. Diagnostics which are, more or less, transparent are possible to distribute
along a beam path leading up to an experimental station, whereas opaque diagnostics
needs to use either a part of the free electron laser beam using a beamsplitter, or be
placed after the experiment (provided that the experiment is somewhat transparent).
Besides the gas monitor detectors and solid state devices described below a way of
discerning the average energy of the free electron laser beam have been invented at
7.2. Intensity/Beam energy
101
the Lcls[96]. By determining the energy loss for different trajectories of the electron
beam through the undulators a measure of the average pulse energy can be determined
within 1 and 5%.
Gas monitor detectors
Ion/electron detection
To provide a transparent diagnostic of the intensity at the Flash free electron laser a
an intensity monitor based on photoionization of gases and detection of ions and
electrons have been developed [152] at Flash. These detectors are placed before and
after the gas attenuator[104]. The latter is places immediately before entering the
experimental hall.
By measuring the yield (electron or ion) from a known density of a gas it is possible
to conclude the intensity of the photon beam via:
N = Nγ · ρ · σ(E) · ℓ
(7.1)
relates the number of particles ionized (N ) with the number of photons Nγ ; the target
density (ρ); the photoionization cross-section at the photon energy in question σ(E)
and the length of the interaction volume ℓ.
-V
+
+V
Figure 7.2: A Faraday cup counts the ions and electrons produced by photoionization of a target gas to produce
a measure of the intensity of the FEL photon beam via Equation 7.1.
The gas monitor detector scheme is shown in Figure 7.2. The charged particles
(electrons and ions) created by the ionization of the gas is separated and accelerated
by a homogeneous electric field, and can thus be detected separately. The gas pressure
is typically held at 10-6 mbar, as to disturb the downstream experiments minimally.
The charged particles are detected by Faraday cups.
With this type of detector it is possible to measure the pulse intensity with an
error less than 10% with a jitter between pulses of 1%. The latter is dominated by
the signal statistics and holds for more than 1010 photons per pulse.
102
7. Spectral diagnostics: Intensity & Energy
It is important to note that, since the detected intensity depends on the crosssection1 for photo-ionization the sensitivity of the detection scheme varies strongly
with photon energy. This is an issue to consider when this type of detector is to
be used for hard X-rays, where cross-sections are several orders of magnitude lower
than in the VUV/soft X-ray region. The sensitivity of the scheme when it comes to
the detection of intensities of higher harmonics in the free electron laser pulses are
therefore also impaired.
Photoluminescence detection
At the Lcls a gas monitor detector have been developed that detects the fluorescence
of nitrogen with two photomultiplier tubes[96, 153].
Magnetic coils around a 30 cm long and 8 cm wide pressure chamber (with 0.0150.9 mbar of gas pressure) confine the photoelectrons produced by the free electron
laser beam, these electrons excite the surrounding nitrogen gas. The de-excitation of
the molecules occur by the emission of photons in the UV range between 300 to 400
nm. During the course of detection of cosmic rays it have been concluded that the
yield in this spectrum depends weakly on the exciting electron energy.
Calorimeters
A calorimeter (also called radiometer in the present context and will henceforth be
denoted thusly) measure, in principle, the integral spectral power impinging on it.
Hence, the sensitivity is equal for the harmonic content in the pulses. Standard
for measuring radiated power from UV/X-ray lightsources around the world (i.e. at
PTB[154] in Germany, NIST[155] in the USA, and NMIJ[156, 157] in Japan).
The device consists of a cryogenically cooled temperature sensor in front of a target
upon which the radiation impinges on (Figure 7.3). The pulse energy is given by:
E=
∆T
s·f
(7.2)
where the temperature difference (∆T ) is the temperature raise in the absorbing
cavity, f is the repetition rate of the source and s is the thermal response of the
system. The radiated power is then simply P = E · f .
The thermal response of the system can have more or less inertia, but the time
constant for transition from one equilibrium of the system to another upon changing
absorbed power is measured in minutes. Hence, average energies per pulse can be obtained, however with small systematic errors (dominated by the intensity fluctuations
of the radiation).
A radiometer of this kind is also effectively a beam stopper and needs to be placed
at the very end of the beam transport system, i.e. after the experiment(s) or operate
at a split of branch of the beam. This type of diagnostic can therefore be used as a
standard which to calibrate other intensity diagnostics against, for instance the gas
monitor detectors mentioned above, or during commissioning runs and as a machine
diagnostic.
1
Cross-sections for the noble gases have been tabulated by K. Tiedtke and co-workers for the
noble gases up to 300 eV photon energy[152].
7.2. Intensity/Beam energy
103
Liquid He
Liquid N2
Photon beam
Heater
Temp. sensor
Figure 7.3: Illustration of a cryogenic calorimeter setup.
Solid state devices
Photodiodes
Photodiodes, commonly employed at synchrotron laboratories for intensity diagnostic
purposes have shown to exhibit quite large errors when employed at free electron
laser, at Scss in Japan one such measurements yielded an error of about 30% of the
intensity.
Bolometers
A solid state bolometric sensor that can withstand the power from a free electron
laser laser beam can be realized from a device where the resistance change of a colossal magneto-resistance thermistor film upon absorption of electromagnetic radiation.
With a sufficiently efficient coupling to a cooling substrate the operation can be fast
enough to allow very precise measurement of the beam energy on a pulse to pulse
basis – since they can be operated close to their metal-insulator transition where the
resistance changes are very large. At low temperatures the contributions from thermal
noise in the circuit is also lower.
The resistivity and the temperature of such thermistor films can be varied depending on their composition[158]. The sensitivity of the resistance upon temperature
1 ∂R
) can be as large as 10%/K.
changes (understood as R
∂T
Assuming that the sensor is efficiently coupled to the cooling substrate then the
current signal S from a voltage biased sensor is proportional to the total X-ray energy
and inversely proportional to the heat capacity of the substrate C:
∆T ∝
Efel
C
(7.3)
104
7. Spectral diagnostics: Intensity & Energy
Assuming that the noise in the circuit mainly arises from thermal noise (i.e. Johnson
noise) of the sensor and the readout (in , en ) we can write the signal to noise ratio
(S/N ) during an integration time τ [158]:
∂R
√
S√
Vbias
∂T
p
∆(t) τ
τ=
2
N
R
4kB T /R + i2n + (en /R)2
(7.4)
For low resistances and low temperatures this
√ expression is maximized. Low√noise
operational amplifers have en as low as 1 nV / Hz and in in the orders of pA/ Hz.
Signal to noise ratios of 100 000 can be obtained for integration times of milliseconds.
Neodynium strontium manganese oxide (NSMO) sensors grown on a silicone substrate can be used to measure the total energy on a pulse to pulse basis with very
small errors[96, 159].
Even-though this diagnostic interrupts the beam (which can be worked around as
seen earlier) the devices can be absolutely calibrated with an ordinary pulsed laser.
Lastly this kind of detectors have a sensitivity that is linear over three orders of
magnitude of incoming beam energy. This kind of detectors are currently in use (and
being further developed) at the Lcls free electron laserwhere they also serve as to
calibrate the photoluminescence detectors described above.
At 8.3 keV the average energy is determined with a pulse to pulse jitter of about
8%[96].
7.3
Photon-energy
Measuring the photon-pulse directly, as outlined above in section 7.1, needs the beam
to be split (in amplitude or in frequency) or to be placed at the very end after an
experiment – that, in turn, needs to be transparent to the diagnostic. In various
circumstances this is not desirable or even possible – either because the experiment
is photon-hungry and can not afford to use the loss of transmission from a beam
splitting device, and/or the experiment is opaque (i.e. effectively a beam-stopper).
One way to circumvent this is to measure the time-of-flight of the ions and/or electrons in a manner similar to the intensity measurement with the gas-monitor detectors
described above (section 7.2). Since the arrival time of the pulses at the diagnostic is
known (or can be inferred from other diagnostics) we can measure different aspects
of the ionization processes occurring in, for instance, a rare gas via the time-of-flight
of the produced charged particles in a homogeneous electric (and/or magnetic) field.
Ion time-of-flight
The time of flight of ions through an electric field is proportional to their mass and
charge – for a small source region the flight times for different charge to mass ratios
are deterministic and depends only on electric field strengths and the geometry of the
apparatus, usually referred to as a Wiley-MacLaren spectrometer[160]. Ion time-offlight is thus a mass-spectroscopic measurement, in essence.
The resolution of a Wiley-Maclaren setup (spatial and temporal) can be analyzed,
let us spell it out in detail: define
Ut =
qsEs + dEd
,
sEs
k=
Ut
qsEs
7.3. Photon-energy
105
s
d 0 , E1
d 1 , E2
D
Figure 7.4: The field in the drift tube is zero. The ratio between the fields is uniquely determined by the
geometry given by s, d1 and D.
With T as the total flight time, zero initial kinetic energy and starting position s,
the position where ions having s ± 12 δs pass each other can be found where
dT 1
d
3/2
√
=
0
⇒
D
=
2sk
1
−
ds 0,s
k+ ks
This focus condition is the same for all ions and is independent of the systems total
energy. Hence, if s, d, and D is given, the ratio Ed /Es since k can only have one
physically reasonable value.
= 0,
T(U,s) has either a maximum, minimum, or an inflection point where dT
ds 0,s
the latter can be found with:
d2 T k−3 D
d
=
=
0,
⇒
ds2 0,s
s
k
2s
For the parameter values chosen for best resolution, two-field systems are operated
at the maxiumum, i.e. with the ds smaller than the righthand-side.
Spatial resolution
Let Ms be the largest mass for which the flight times are discernibly different,
Tm+1 − Tm = τ ≈
s 2
Tm
⇒ Ms ≈ 16k
2m
∆s
The latter is true whenever k ≫ 1 and k ≫ d/s.
This shows that the distance to the sourcepoint s must be larger than the spread
∆s for space resolution to be made adequate – this, in turn, is dependent on D
being large since D/s determines k. Increasing d (thus increasing k) improves space
resolution.
106
7. Spectral diagnostics: Intensity & Energy
Energy resolution
Consider two ions at the same initial position s but with opposite velocities along the
spectrometer axis, equal in magnitude, then the turn-around time is
√
2 2mU0
∆T = 1.02
qEs
Then the maximum resolvable mass becomes, with D/s given by the focusing condition:
!
r
√
k+1d
1 Ut k + 1
√
√ −
ME =
4 U0
k
k+ ks
To find the overall resolution a compromise between Ms and ME has to be found.
Higher order focussing can be achieved by having additional drift-sections and fields[161]
– for those the flight times, etc. can still be calculated analytically[162].
Ion time-of-flight as a diagnostic
A precise way of determining the charge to mass ratio of photo-ions allows us to
measure the photon-energy. The photoionization cross-section depends on photon
energy, i.e. one can measure it directly via the intensity of one charged state; a much
more stable measurement of the photon energy is obtained via the ratio between singly
and doubly charged ions (or higher charge states). All this assumes that the crosssections as functions of energy and charge state are known beforehand. Moreover, the
photon-density must be low enough to ensure that only single-photon events occur –
something which is usually fulfilled for an unfocussed free electron laser beam[152].
Juranić et al. have used a Wiley-MacLaren spectrometer to measure the photon
energy at Flash with uncertainties staying below 1% up to 150 eV photon energy[163].
Ion time-of-flight measurements can be shielded from perturbing magnetic fields
easier, and provides higher countrates than the electron measurements described below. The time-of-flight times are also longer since the particles have higher mass
which makes the measurement less demanding with respect to the data-acquisition.
Electron time-of-flight
The time-of-flight for the electrons can be converted into kinetic energy with the aid
of known ionization energies of atomic states – hence this is a spectroscopic measurement. If performed at high enough resolution electron time-of-flight can thus give
information on the spectral content of the pulse as well as the mean energy. Potentially this spectrum also give access to the pulse length[164] as discussed in chapter 9.
This allows for measurement of the photon-energy and the fluctuations of it, as
have been done near 93 eV at Flash[149]. The resolution in the spectra for the He
1s photoelectron line was about 100 meV.
The limitation of this photo-electron spectroscopic measurement is the relatively
low countrate (in the order of thousands of electrons per pulse). The kinetic energy
of the electrons is also not invariant with changing intensity of the free electron
laser beam, where the attractive forced from the positively charged ions cases the
kinetic energy to be lowered for the electrons – which, if not accounted for, induces
an apparent decrease in photon-energy with increasing photon-densities.
7.3. Photon-energy
However, the lower cross-section at higher energies lowers the Coulomb attraction
between ions and electrons, since the number of electron-ion pairs (for single-ionziation
events) is:
Nparis = Nphotons · ngas · σgas · ℓ
(7.5)
where ℓ is the length of the interaction region and n = p/kB T for an ideal gas. The
non-ideality of the gas can be accounted for via a correction using the mean-free
path[149].
For higher photon-energies thus, electron time-of-flight measurements can be a
viable option for determining the photon-energy and its fluctuations.
107
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7. Spectral diagnostics: Intensity & Energy
Summary
• The beam energy (or intensity) is a critical parameter for user
experiments and other diagnostics.
• Gas monitor detectors analyze the total yield occurring from
photoionization (which is proportional to the beam energy) of
a target gas by accelerating them in an electric (and possibly
an magnetic field). This is a diagnostic that is transparent.
• Another transparent diagnostic is photoluminescence measurements of, for instance, nitrogen gas.
• Calorimeters (Radiometers) is a measurement that gives the
average intensity of the pulses in a very exact manner. This
is an opaque diagnostic which can also be used to calibrate
other intensity diagnostics.
• Bolometers provides a measurement of the beam energy over
a large photon range – for instance with 8% error at 8.3 keV
photon energy at the Lcls.
• Diodes have shown to have rather large errors when used at
free electron laser, e.g. 30% at the Scss.
• Bolometers and diodes are opaque diagnostics and thus require splitting or a transparent user experiment.
• X-ray spectrometry measures the dispersed fel beam from a
(VLS) diffractive grating. Thus obtaining the full spectrum
of the free electron laser beam on a shot to shot basis.
• Ion time-of-flight measurements diagnoses the photon-energy
of the beam with relatively small errors – assuming that the
cross-sections for the ionized gas is known as a function of
energy and the various charged states.
• Electron time-of-flight can provide a measurement of the spectrum of the pulse and provides a way of discerning the fluctuations in photon-energy.
• Electron and ion time-of-flight measurements that are transparent to the user’s experiments.
• Time-of-flight measurements utilize photoionization for which
the cross-sections drops fast after 100-200 eV – i.e. for higher
photon-energies they may be impractical due to low countrates.
8. Beam cross-section diagnostics
The material presented here in this chapter is adapted from ”Survey of diagnostic techniques for measuring the beam cross-section of ultra-short photon
pulses” by M. A. Bowler, A. J. Gleeson and M. D. Roper. Iruvx WP7, 2010
8.1
Introduction
By measuring the profile of the generated photon-beam many important parameters
important for the beam transport towards the experiments can be learned. The
beam-profile is also an important diagnostic for the machine and as an parameter for
experiments (e.g. the spot-size determines the energy density at the experiment).
The specific information that is required is:
• The transverse intensity distribution of the pulse – allowing the source size,
position and quality factor (M 2 ) to be calculated from the second moment1 .
• The centroid (first moment) of the transverse pulse profile – giving beam position and (in combination with a second measurement of the same pulse at
different longitudinal distance) the beam angle.
• The pulse wavefront – giving a complete description of the spatial properties of
the beam.
• The focused spot size of the beam – critical for optimizing adaptive mirrors to
give the best focusand for achieving high fluences for non-linear studies.
The ideal cross-section diagnostic
Any measurement that gives a full beam profile can be used to calculate the beam
centroid but a measurement that gives only centroid information gives no profile
information. Centroiding measurementsare nevertheless useful where they are less
invasive or can give pulse by pulse information. For a free electron laser source, the
ideal diagnostic would have the following properties:
1
The quality factor for a diffraction limited gaussian photon beam at wavelength lambda is
λ/π. For a real beam the product of the minimum waist-size of the beam with the divergence of
the beam in the far field is called the beam parameter product (BPP). The ratio between the BPP
and λ/π is the quality measure M 2 . For a diffraction limited beam this ratio is unity; for real
beams this measure is larger than unity.
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110
8. Beam cross-section diagnostics
• A sub-µm spatial resolution to allow the focused beam to be measured.
• A field of view of ∼ 1 cm to allow the unfocused beam to be measured.
• Non-invasive – give negligible disruption to the beam.
• Sensitive – to allow a single pulse to be measured.
• Wide dynamic range with linear response – to measure attenuated and fullpower beams, focused and unfocused, fundamental and harmonics without damage, or excessive noise.
• Large bandwidth – to measure every pulse up to MHz repetition rates in real
time.
• Broadband – work at THz/IR or from the VUV to hard X-rays.
• Spectrally discriminating – to separate signals from e.g. fundamental and harmonics.
The number of these properties that a given practical monitor will need will depend
on the particular application or location in the photon transport system. For example,
sub-µm resolution is only required to measure the size of the beam at a focus, it will
not be necessary for a monitor to be able to wavelength-discriminate if it is situated
after a monochromator, and diagnostics situated after the experiment do not need to
be non-invasive.
Distribution of diagnostics along the beam
feedback
to source
On-line centroid monitors for
beam position and angle
Centroid monitors for
mirror alignment
Wavefront
sensor
Beamline optics
Source
Focus spot-size
monitor
Profilin monitors for
quality factor analysis
Profiling monitor for
commisioning
Figure 8.1: A schematic on how to distribute various diagnostics to determin transverse beam properties.
Figure 8.1 shows schematically how the various diagnostics might be distributed
along a beamline. Before any optics it will be necessary to have non-invasive (or
minimally invasive) ”on-line” diagnostics that give at least beam position and angle
information continuously and individually for every pulse. These monitors could
be used in feedback control of the machine to ensure the photon beam is stable in
position and angle. There should also be diagnostics that can give a full pulse profile
at three or more positions such that the source position and size and beam quality
factor M 2 and can be determined[165]. The main application here would be during
commissioning and so the monitors could be invasive, though if that were case it
would not be possible to calculate the quality factor for a single pulse. Therefore a
non-invasive measurement is preferred, but it need not work at the full rep rate of
8.1. Introduction
the free electron laser since statistical methods can be used to infer the overall beam
quality.
After each optical element a beam position monitor is required to ensure the beam
alignment is correct. These might just give centroid information and may average
over a number of pulses. Ideally, they would be on-line so the beam stability can be
constantly monitored, though this may be unnecessary. Additional profiling monitors
will also be available specifically for commissioning and diagnosing problems; these
can be invasive.
At the experiment it is necessary to determine the position and quality of the beam
focus to:
• Ensure multiple beams can be overlapped spatially
• Optimise adaptive mirrors
• Achieve the highest beam fluence
• Position the sample at the focus
It would generally be acceptable for these measurements to be invasive since, with
a stable source, they would normally only be needed during commissioning and experimental set-up. Depending on need, the measurements could either be averaged
over many pulses (e.g. for positioning) or measure just a single pulse (e.g. focus quality). If a measure of every pulse is needed outside the realm of commissioning then
a noninvasive detector or a detector remote from the sample position is needed. The
latter is quite easy with gas-phase experiments (which are almost transparent to the
beam) since the detector can be placed after the experiment. It would not be possible to measure the focus directly, so the wavefront would have to be measured and
reverse-propagated to reconstruct the beam focus.
Direct measurement of the wavefront would be the optimal way to measure the
beam as it allows for simulated propagation to arbitrary positions along the transport
path, e.g. back to the source. However, wavefront measurement is invasive and so
cannot be a general ”on-line” diagnostic. Furthermore, accurate propagation across
an optical element requires detailed information on the element surface shape at a
large range of spatial frequencies and thus the accuracy of any prediction will fall as
the simulation traverses more optical elements.
Content of this chapter
In this chapter, a broad survey of the range of techniques that have been used to
profile non-visible photon beams is presented. In the VUV to X-ray range, most
existing diagnostics have been developed for use on synchrotron radiation sources.
The challenges there tend to be rather different, and the techniques may not be easy
to modify for free electron laser use. Specific problems for FEL beams include:
• Damage from ablation rather than high average power.
• The need for pulse resolved rather than time averaged measurements.
• The need to avoid beam disruption through coherent diffraction effects.
It is worthwhile to describe briefly several common techniques that are used in the
diagnostics as follows:
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8. Beam cross-section diagnostics
• Scanning – in which a scan through the beam section is made, recording the
intensity in a step-wise manner to build up the profile
• Imaging – in which the entire intensity profile, in one or two dimensions, is
measured in one shot
• Sampling – in which a small part of the beam is extracted and the required
information deduced from this whilst the bulk of the beam passes on to the
experiment
• Replicating – in which the beam profile information is transferred to another
medium and that measured to give the actual profile.
In some cases a mixture of these techniques is used, for example in imaging a
replica of the beam.
In the THz and IR ranges, diagnostics at existing free electron laser sources tend to
be limited to characterizing the beam at the experiment rather than having distributed
diagnostics along the transport system. The available means of detecting IR and THz
radiation restrict the range of diagnostic techniques that can be applied, in particular
because the long wavelength radiation cannot directly ionize materials. For the near
and mid-IR, techniques can be adapted from the visible regime.
In section 8.4 will be described those techniques that can give a profile of the
beam intensity. In some cases this will be along a single axis (or two axes with two
instruments situated orthogonally), and in others a complete 2-dimensional map of
the beam intensity will be recorded. Section 8.10 will describe those techniques that
give only information about the position of the beam centroid (”centre of gravity”,
or first moment, of the intensity). How the complete wavefront can be measured is
described in section 8.11 and specific applications of beam profiling to determine the
size and quality of the focused beam are described in section 8.8. Diagnostics for IR
and THz wavelengths will be described collectively in section 8.12.
8.2
Definitions
In this chapter we will look into various schemes as how to determine the transverse
(x, y) distribution of photons in the beam2 . Most of the methods also carry over to
more applications of particle beams in general.
Let us define the problem more specifically, consider the particle beam to have a
Gaussian distribution in the x, y plane orthogonal to the direction of the beam (the
s direction)
1 − 12 (x2 /σx +y 2 /σy )
N (x, y) ∝
e
σx σy
Along the s-axis the distribution is ideally a step function. The measurement of this
profile will be covered more specifically in chapter 9.
Various schemes can be envisioned on how to measure the profiles concerned, each
with its own merits – as a first rough division we can divide them into invasive and
non-invasive methods:
2
Diagnostics concerning the longitudinal (s) extent of the pulses will be covered in chapter 9.
8.3. Direct imaging of the beam
113
y
I
x
x
I
s
y
Figure 8.2: Projection of the spatial density distribution in the x.y plane (left) and onto individual coordinateaxes (right).
invasive – or direct measurements
Direct imaging of the beam
Wire grids
Scanning wires, slits, knife-edges, pin-holes
non-invasive – or in-direct measurements
rest gas ionization
photo dissociation
synchrotron light
Compton scattering
8.3
Direct imaging of the beam
The simplest way to image the transverse footprint of a photon beam is to directly
illuminate an array detector such as a CCD with the beam[166, 167]. Providing the
detector is sensitive to the photon wavelength, a direct readout of the beam profile is
achieved.
If the array is two-dimensional, then a complete transverse map of the beam can
be recorded. The spatial resolution of a CCD detector is determined, in principle,
by the photo-site size and spacing in the detector array. In practice this limit cannot
be achieved due to diffusion, where electrons created in one pixel are collected in an
adjacent pixel.
To record an image of every free electron laser pulse individually, the frame rate
of the camera must of course match the pulse repetition rate. Extremely high-speed
cameras are available for optical imaging (e.g. 600,000 fps with the NAC Memrecam
GX-83 ) and commercial high-speed X-ray imaging services are available (e.g. Speed
Vision Technologies Inc. offer frame rates of 1000 fps4 ). Speeds for scientific applications are typically much lower.
3
4
www.nacinc.com
www.speedvisiontech.com/speedvision-x-ray.php
114
8. Beam cross-section diagnostics
For example, Princeton Instruments5 manufacture
CCD cameras for both direct and indirect (q.v.) X-ray
imaging that have readout rates of 2 MHz or 100 kHz
depending on the sensitivity and signal to noise ratio.
This rate equates to roughly the rate at which a single
pixel can be read out since all the data passes through
a single serial register. Thus the frame rate depends
on the number of pixels. They offer a 512 x 512 pixel
camera (with 13 µm pixel spacing) which could thus
be read out at only ∼ 7.5 fps.
Nevertheless, it is clear that higher speeds are
achievable, though the balance of sensitivity and noise
needs to be considered. We might therefore reasonably
expect to be able to record every pulse at repetition
rates of about 1 kHz. For single pulse imaging at repe- Figure 8.3: A typical scintillator
screen setup.
tition rates above the detector frame rate, the camera
would need to be gated to record just one pulse in the
frame cycle. Gating at the nanosecond level is available with optical cameras, but is
presumably achieved using electro-optical shutters which are not available for X-rays.
A mechanical shutter would be needed to pick just one pulse and this would be also
be challenging to design and synchronize.
The high fluence of a free electron laser pulse also raises significant concerns over
ablation, radiation damage, and linearity / saturation effects. The saturation level
is a compromise with spatial resolution since if the pixels are made smaller then
they can hold less charge and will saturate earlier. In fact, CCD detectors are not
often used to measure the direct beam on synchrotron sources because they saturate
too easily. Fedotov in 2000[168] reported that an ”old” 1200LC1 type CCD would
saturate with 500 photons at 10 keV compared with 5-50 photons for ”more modern”
CCDs. Therefore, a conventional CCD is limited to the direct measurement of only
attenuated or spatially dilute beams. Direct detection with solid-state arrays offers the
potential of energy discrimination, which might allow the fundamental and harmonics
to be distinguished. However, this may only be possible if each pixel collects no more
than one photon[166].
Another factor to consider is the wavelength sensitivity of the CCD. A standard
front illuminated CCD detector will be insensitive to VUV photons as they cannot
penetrate through the inactive layer on the detector surface. Conversely, the sensitivity can drop with harder x-rays as they can pass straight through the depletion
layer of the detector. Different types of CCD are thus needed for different parts of the
spectrum,for example ’back thinned’ for soft X-rays less than 2 keV, ordinary ’front
illuminated’ from 2 to 10 keV, and ’deep depletion’ type for X-rays above 10 keV.
Imaging a replica of the beam
A common approach for imaging techniques is to measure indirectly via the production of a replica of the beam. One way of achieving this is by illuminating a luminescent screen with the beam and then imaging the luminescence through a viewport
on the vacuum vessel with an optical camera[169]. This allows for higher ultimate
5
www.princetoninstruments.com/products/xraycam/
8.3. Direct imaging of the beam
115
Viewport
M
Source
or
irr
pinhole array
Beam profile
YAG
Camera
Figure 8.4: The use of a YAG screen together with a pinhole array for X-ray beam profiling as described by
Boland and co-workers.
spatial resolution than with direct CCD imaging. The resolution is determined by the
quality and thickness of the screen, the magnification and aberrations of the camera
optics, and the camera sensor resolution. The ultimate limit is set by diffraction of
the visible light through the camera optics, and is thus ∼ 0.5 µm. The viewport must
be of high optical quality if it is not to degrade the image. On the Australian Light
Source diagnostic beamline, Boland et al. [169] placed a pinhole array before a YAG
screen (Figure 8.4) so that several fully resolved images are recorded and this allows
the beam divergence as well as the profile to be measured. This approach could be
useful with a free electron laser since it would simplify single-pulse measurement of
the beam divergence.
With traditional powder phosphors a grain size of c. 1 µm is available and the resolution as defined by the line-spread function is approximately equal to the thickness
of the phosphor layer[170]. But if the phosphor layer is made too thin (less than a
few µm) then the light yield decreases dramatically and performance is compromised.
Optically transparent luminescent screens, or scintillators, are a better choice for
achieving high spatial resolution. Since the camera is now focussed on a transparent
screen, the screen thickness and depth of field of the camera optics play an important
part in the resolution. The scintillators must therefore be thin, have a surface of high
optical quality, and contain high Z elements to increase absorption. Cerium doped
aluminum garnets are most often used. Koch et al. [170] used 5 µm YAG:Ce on 170
µm undoped YAG crystal in combination with diffraction-limited microscope objectives and achieved spatial resolutions of less than 1 µm in micro-imaging experiments
at the ESRF. Tous et al. [171] achieved resolution of about 1 µm with an anode X-ray
source using YAG:Ce and LuAG:Ce, both of 20 µm thickness.
The bandwidth of such a system will be limited by the camera read-out rate and
ultimately by the decay time of the luminescent material. The decay time of some
luminescent materials can be roughly 1 µs, but the visible luminescence from YAG:Ce
is very fast at ∼ 70 ns[172] and is thus fast enough to resolve single pulses at even 1
MHz. As discussed above, cameras with frame rates up to 600,000 Hz are available,
though not with continuous output at that rate. It would need to be checked that
they would have the sensitivity to record the luminescence from a single free electron
laser pulse (the monochrome sensitivity of the Memrecam GX-8 referred to is 20,000
ISO). With slower frame rates, it should be possible to select just one pulse in the
frame cycle by gating the luminescence with a high-speed electro-optical shutter such
as a Pockels cell. Clearly, the total number of photons collected from the screen in
this mode will be low and so an image intensified camera may be required. These are
116
8. Beam cross-section diagnostics
available commercially, for example the Lambert Instruments LI2CAM6 ,which has a
frame rate of just 15 fps but can be gated down to 2 ns.
It is also possible to create an electron replica of the photon beam profile by directly
illuminating a multichannel plate with the free electron laser beam. A phosphor
screen placed near the plate converts the electrons to visible light whilst preserving
the spatial origin of the electrons, and the luminescence from the screen is imaged
by a CCD camera. This approach was used by Yang et al. to image the profile of
the X-ray pulses from a Compton back-scattering source[173] (though the image was
integrated over many pulses due to the very low intensity). The spatial resolution
will be determined by the channel pore size, which at 10 µm would give a similar
resolution to direct CCD imaging. The sensitivity would be determined by the photoemissivity of the channel plate, which is dependent on wavelength. Coatings can be
added to enhance the photoemission at long wavelengths. At shorter wavelengths,
the efficiency drops as the X-rays are absorbed more in the bulk of the channel plate
material. At very short wavelengths, the X-rays may penetrate through the pore walls
and this will reduce the spatial resolution.
The bandwidth will still be limited by the camera frame rate, but the ultimate
limit will also be influenced by the time of the avalanching process in the pores,
as well as the luminescence decay. The bandwidth could be greatly increased by
replacing the phosphor screen and camera with an anode array. Assuming parallel
readout of each anode, the detector response could be reduced to the multichannel
plate response time, which could be in the nanosecond region. This would allow every
pulse to be measured, but the spatial resolution would be limited by the anode array
size. Alternatively, the charge pulse from the multichannel plate as the photon pulse
strikes it could be used to trigger the gating of the camera to select a single pulse.
This would obviate the need for synchronization to the X-ray beam itself. If this is
not possible, the timing trigger from the free electron laser pulse could be used to
gate the multichannel plate.
A refinement of this approach would be to illuminate a photo-emissive material
(e.g. a metal foil) and image the emitted photoelectrons. A key requirement for this
to work is preserving the spatial information encoded into the photoelectrons whilst
they transported to the multichannel plate. Similar problems face the techniques
described in sections 8.6 and 8.7.
An imaging detector based on the photoconductive effect in Type IIa CVD diamond has been developed at the APS by Shu et al. [174]. This detector is an extension
of work done on quadrant detectors (q.v.). A 127 µm thick diamond disc was patterned on both sides with sixteen 0.2 µm thick and 175 µm wide aluminum strips.
The patterns on the two sides are orthogonal such that a 16 by 16 pixel array is
created with 175 µm by 175 µm pixel size. The strips on one side are connected to a
bias supply via a 16-channel switch, whilst those on the other side are connected to
sixteen discrete current amplifiers.
The disc has a high transmission for hard X-rays (around 10 keV) and thus the
monitor can be used on-line for constant beam monitoring. When the X-ray beam
passes through the diamond, the localized conductivity rises in proportion to the
absorbed X-ray power. Thus, the current passing through the diamond when the bias
is applied is highest where the incident X-ray beam is most intense. In order to build
up a two dimensional picture of the beam intensity profile, the bias is applied to each
6
www.lambert-instruments.com
8.4. Scanning techniques
strip on one side in turn and the current from the sixteen strips on the other side
recorded.
The spatial resolution is naturally fairly low, but sufficient to give a true beam
profile assuming the beam is not highly structured and overlaps with enough of the
electrode strips. The bandwidth is limited by the need to apply the bias voltage to
each strip in turn. Nevertheless, the data acquisition system was able to scan at 300
to 3000 columns per second (from 19 to 190 Hz). Of course, this still means that
the system will give only aline profile and not a full image of a single free electron
laser pulse; the electrode structure would have to be modified to give simultaneous
readout of all 256 channels for single pulse image.
Summary of imaging techniques
All the imaging techniques described above are invasive. Direct imaging with a CCD
and direct illumination of a micro-channel plate will stop the entire beam and so
could only be used during commissioning or if the experiment is transparent (e.g. gas
phase) so that the detector can be placed after the experiment. The other techniques
could be made partially transparent. For example, hard X-rays could pass through a
sufficiently thin luminescent screen without excessive loss. The luminescent intensity
is proportional to the number of photons absorbed and so some losses are required for
the detector to work. On the other hand, since photoemission is essentially a surface
phenomenon, a very thin and thus highly transmitting foil would give the same signal
as a thick one. In any case, the disruption to a coherent free electron laser beam
as it passes through a screen or foil would probably be unacceptable. There are also
concerns over radiation damage, ablation,linearity and saturation with high-fluence,
ultra-short free electron laser pulses. The risk of ablation would need to be controlled
by using these techniques only where the beam is spatially dilute, and this might also
be sufficient to prevent saturation and non-linear effects.
The wavelength response of the detectors needs to be considered. It is obviously
desirable for the detector to work over as wide a range of photon energies as possible.
However, a broad-band response can cause problems if it is very non-linear. For
example, photo-emission yield is much greater at VUV than X-ray wavelengths and
this can distort an X-ray beam profile if there is low level VUV light with a different
spatial pattern to the X-ray profile.
8.4
Scanning techniques
Scanning wire
This is perhaps, at a glance, the simplest solution to the present problem: scan a
wire through the beam. A thin metal wire (such as tungsten) is step-scanned through
the beam and the beam intensity deduced from, for example, the drain current in
the wire[175], the intensity of electrons emitted from the wire, or the intensity of
scattered or fluorescent light from the wire, all of which should be proportional to the
beam intensity hitting the wire. The signal at each position in the scan is the result
of an integration of the beam intensity along the illuminated length of the wire, i.e.
in the direction orthogonal to the scan. The measured profile is thus a convolution
of the actual beam profile and the illuminated length of the wire. This means the
117
118
8. Beam cross-section diagnostics
s
ep
s.
ire
xw
ng
ni
an
sc
Figure 8.5: Working principle of a scanning crossed-wire monitor, after Ref. [177].
measured profile will be distorted when the orthogonal beam section is not uniform
such that the illuminated length varies through the scan[176]. This will occur, for
example when the wire is tilted relative to an elliptical beam.
The resolution of the wire type monitor depends on the step resolution of the
scanning mechanism, the diameter of the wire relative to the beam width, and the
straightness and uniformity of the wire. Radiation scattering from the edges of the
wire will degrade the resolution. Thin wires give higher resolution, but are harder to
cool. If a wire gets too hot, thermionic emission can occur even before melting and
this will distort the profile when electron detection is used to infer the beam intensity.
Scanning crossed wires
Two wires are crossed at 90◦ and scanned through the beam along a direction at 45◦
to each wire – see Figure 8.5. In this way, two orthogonal profiles can be derived in
one scan, but detection is limited to drain current to allow the signals to be distinguished. Each profile is still an integration in the orthogonal direction.The instrument
developed by Fajardo and Ferrer[177] has a reported resolution of better than 5 µm,
limited by mechanical reproducibility and vibration in the scanning mechanism. The
finite response time of the amplifiers results in a difference in apparent position on
forward and backward scans if the scan speed is too high; this effect was not observed
at a speed below ∼ 1 mm/sec.
Scanning slit
A fine slit is scanned through the beam and the transmitted intensity measured by
a detector (e.g. a photodiode, a micro channel plate, or a luminescent screen and
video camera combination)[178].Again, the intensity in the orthogonal direction is
integrated by the length of the slit. The result is analogous to the scanning wire
but the technique is more invasive, though easier to cool. Scanning slits are however
8.4. Scanning techniques
useful for probing aperture related aberrations in optical systems, though the beam
spread after the slit caused by diffraction can confuse the results.
Scanning pinhole
A refinement of the scanning slit in which the beam profile is not integrated along the
direction orthogonal to the scan direction and so true line profiles through the beam
can be made. With two-axis control of the pin-hole motion, line profiles in arbitrary
directions through the beam can be made. The pin-hole is commonly achieved by
using either two slits crossed at 90◦ to make a rectangular pinhole or with four jaws
making the two orthogonal slits. The advantage of the latter is that the size of the
pin-hole can be easily changed, though a 4-axis drive is needed and very small pinholes
are not realizable because of diffraction at each jaw and the necessary longitudinal
separation between them.
Scanning knife-edge
A blade is scanned through the beam such that it successively obscures (or reveals)
more and more of the beam. The intensity passing the blade is recorded by a detector
such as a photodiode or mictro-channel plate[179]. The recorded signal is the integral
of the profile in the scan direction and the deduced profile is integrated in the orthogonal direction. If the profile is being measured at a focus, a wire of diameter greater
than the beam size can be used instead of an edge[180]. This has the advantage that
it is easy to achieve a smooth edge with a wire than with a blade.
Summary of scanning techniques
The most important drawback when applying these techniques to a free electron
lasersource is that they cannot be used to measure a single pulse due to the step-wise
nature of the measurement. In addition, the techniques are invasive (i.e. disruptive
to the beam), especially as the coherent nature of the photon beam will mean the
disruption will be enhanced due to diffraction effects. Therefore, in the context of a
free electron laser source, these techniques are useful neither during commissioning
(when the invasive nature would not be an issue but the inability to resolve single
pulses is), nor during operation (as the invasive nature makes them unsuitable as online monitors). In addition, the high pulse intensity of an unattenuated free electron
laser fundamental gives serious concern over the damage to the scanning elements.
With a free electron laser source, there are two modes of damage, viz. melting and
ablation. At low repetition rates (less than 1 kHz) melting is unlikely as the average
power is less than in a synchrotron beam, but ablation is likely unless the pulses
are attenuated (for example with a gas absorber, as discussed above in chapter 4 see
page 69). Without attenuation, there is also the possibility of reaching non-linear
regimes where the measured signal is no longer proportional to the incident intensity,
e.g. through space charge effects.
119
120
8. Beam cross-section diagnostics
8.5
Ionization beamprofile detectors
The beam-profile from a high-energy beam of particles (photons, electrons, neutrons. . . ) can be measured by detecting the ions (or electrons) resultant from ionization events occurring in a residual gas intersecting the beam. By accelerating the
ions in a homogeneous electric field towards a multichannel plate detector (see Figure 8.6) combined with a position sensitive read-out anode an image of the beam can
be recorded.
From Equation 2.5 one would expect the ions to get accelerated in straight lines
towards the detector since the force on the charged particle is directly proportional
to the electric field strength; the ionized particles, however, will have velocity components in other directions besides normal to the detector – this will give rise to a
broadening of the profile which can be minimized by applying a stronger electric field.
A microchannel plate detector also have a finite resolution since the actual channels
are in the order of 10 µm in diameter. There is also a possibility that several channels
detect a single event which will blur the image further.
Ion
MCP 1
MCP 2
Output signal
Anode
Figure 8.6: Microchannel plates mounted in a chevron geometry with voltages coupled to detect ions. When an
ion hit a microchannel plate it gives rise to several secondary ionizations – the electrons from those ionizations,
in turn, gives rise to other secondary electrons, thus an amplification occurs. The resulting charge cloud hits
the anode and gives rise to an electric current which can be read out. An alternative to this scheme exist where
a phosphor plate is mounted behind the anode which can be read out optically with, for instance, an CCD
camera.
At Flash this type of beam position monitor, using a phosphor screen together
with a camera, gives a reported spatial resolution of c. 50 µm[181]. Obviously this
type of detector also gives the position of the beam.
8.6
Imaging ion chambers
An established technique for profiling particle beams in high-energy accelerators is to
image the beam path through the residual gas (or gas added at a very low pressure
gas, i.e. less than 10-5 mbar) in the beam transport system. As the beam passes
through the gas, it will ionize it and the ion density is proportional to the particle
density in the beam. Thus, if the ions can be channelled linearly to a luminescent
screen with a uniform electric field, the intensity of luminescence is also proportional
to particle density and the beam profile can be recorded with a video camera. The ion
8.6. Imaging ion chambers
signal is usually amplified by generating multiple electrons for each incident ion with
a micro-channel plate placed in front of the screen. The benefit of this system is that,
when using just the residual gas, the monitor is completely non-invasive. However,
the achievable resolution has tended to be rather poor, of the 1 mm. This is mainly
due to perturbation of the drifting ions by the electric field of the particle beam, which
causes them to spread away from the regions of high ion density, and so broadening the
recorded image. Ions, rather than electrons, are usually detected since their greater
mass means they are less susceptible to these perturbations. Nevertheless, Fischer
and Koopman were able to improve the resolution by measuring the electrons[182].
They achieved this by placing the ion chamber in a uniform magnetic field parallel to
the electron trajectories. The emitted electrons will precess about the field and so can
be channelled more linearly. The resolution was improved such that an actual beam
width of 1 mm RMS could be measured without instrumental broadening (implying
a resolution not worse than a few hundred µm).
The same measurement principle can be applied to an X-ray beam, with which
there is the advantage that the beam will not perturb the electrons and ions directly
once created. However, preserving accurately their spatial point of origin is still
difficult. The approach used by Ioudin et al. [183] is to encode the point of the spatial
origin of the ions onto their kinetic energy by accelerating them with an extraction
field – see Figure 8.7.
The further the ions are from the cathode when created, the greater the kinetic energy they gain during the acceleration. The ions are accelerated towards the entrance
slit of an electrostatic energy analyzer, which disperses them in kinetic energy onto a
micro-channel plate. Thus position along the plate corresponds to spatial coordinate
of ion generation. The multi-channel plate amplifies the ion signal, which is imaged
using a phosphor screen and video camera.
This instrument, called the Beam Cross-section Image Detector (BCID), gives a
profile of the beam in two axes – the section along x is mapped along the microchannel plate as shown in the figure, X1 = 2XEe /Ea , whilst the section along y is
mapped in the orthogonal direction on the plate. The spatial resolution is determined
by a number of factors.Ions generated at longitudinally adjacent positions a and b to
q2 in Figure 8.7 are mapped to different positions on the channel plate despite having
the same kinetic energy. The slit width determines the longitudinal acceptance and
hence the positional spread on the plate and must thus be kept small to control
this blurring. The analyzer resolution is determined by the energy dispersion and
the camera spatial resolution. Aberrations in the analyzer will distort the measured
profile. The accuracy in the y-direction is determined by how linearly the ion chamber
/ encoder can preserve the transverse position along the length of the slit and the
linearity of the analyzer response in the plane orthogonal to the dispersion plane. The
ultimate resolution is limited by the extent to which the ions acquire extra momentum
in the y- and z-directions as the result of inter-ion scattering and the influence of stray
external (especially magnetic) fields. These effects will be reduced by increasing the
gradient of the extracting field to increase the kinetic energy of the ions. But, if the
kinetic energy is too high, then the analyzer performance will be degraded.
The sensitivity of the technique is limited by the number of ions generated in the
residual gas and the detection efficiency. Ion generation is more likely at VUV than Xray wavelengths and thus the spectral content of the beam will influence the recorded
profile. To measure the X-ray profile in, for example, the beam from a synchrotron
dipole source would require the long wavelength components to be removed by a filter
121
122
8. Beam cross-section diagnostics
Extraction field Ee
y
z
+
x
q1
X-ray beam
X
q2
-
Phosphor screen
MCP
X
1
Analyzer field Ea
+
Figure 8.7: The beam cross-section image detector (BCID) as described by Ioudin et al. [183].
such as a beryllium window[184]. This would however facilitate the addition of a gas
such as argon or xenon at a low pressure to improve the ion count. In all cases,
the necessity for a small analyzer slit limits the total count rate and all reported
measurements of X-ray beams have been done with a gas pressure of 10-5 to 10-3
mbar and by integrating up to 256 frames with frame rate of 12.5 Hz [184, 185]. It
is thus debatable whether the technique could have sufficient efficiency to record a
single shot of a free electron laser beam. There is little information in the references
on the spatial resolution achieved with the BCID.
A residual gas beam position monitor is also being developed for use as an X-ray
beam position monitor at PETRA III at HASYLAB. The RGBPM as described by
Ilinski et al. [186] uses a layout similar to the original particle beam monitors, i.e. the
kinetic energy encoding approach of Ioudin is not used and the spatial coordinate of
the beam is mapped directly onto the detector. The generated ions or electrons are
drifted in an applied electric field to a micro-channel plate (MCP) which produces
an intensified image on a phosphor screen – Figure 8.8. The beam profile is recorded
in one axis only, this being in the direction perpendicular to both the drift field and
beam direction. The profile is recorded for a finite length in the propagation direction
8.6. Imaging ion chambers
123
Guide electrode
X-ray beam
Repeller electrode
Phosphor
Profile axis
MCP
Guide electrode
Field axis
Prop
agat
ion
ax i s
Figure 8.8: Schematic of PETRA-III RGBPM; a vertical profile of the beam is measured.
of the beam determined by the longitudinal aperture of the detection system.
Improvements in the resolution come from close attention to the quality of the
electric field, initial kinetic energy of the ions or electrons, resolution of the detector
system, and data processing. To quote: ”The electrical field has to be uniform in
order to provide aberration free beam profile. Broadening of the beam profile occurs
due to electrical field non-uniformity and presence of the transverse component of the
electrical field. This broadening should not exceed the broadening of the beam profile
which is caused by the initial transverse kinetic energy of the ions or electrons. The
resolution of detection system is defined by the MCP, the phosphor screen, optical
coupling and signal background ratio. A proper data processing allows for sub-pixel
resolution.” The guide electrodes shown in Figure 8.8 are designed to improve the
repeller field uniformity.
A prototype RGXBPM was tested on ID6 at the ESRF at 29 m from the centre
of a straight containing three undulators. The monitor was located after a diamond
window of 300 µm thickness. Two readout systems were tried, viz. optical by imaging
the phosphor screen with a CCD camera, and current by using a multi-channel plate
with a split saw-tooth electrode. The channel plate had a channel diameter of 12 µm
and the CCD camera had a resolution of 15 µm/pixel. With the optical readout, each
CCD frame had an integration period of 300 ms and the beam centre of gravity could
be calculated for each frame with a ring current of 68 mA and a residual gas pressure
of ∼10-7 mbar. A 5 µm step in the RGBPM position could clearly be resolved. The
noise was not quoted, but looked to be 2 to 3 µm. The resolution with the splitelectrode detection was about twice that with the optical detection, with a 10 µm
124
8. Beam cross-section diagnostics
step being resolved.
An important limitation of these devices for measuring X-ray beams is that the
cross-section for creating ions is much greater at VUV than at X-ray wavelengths and
thus the sensitivity of monitor is strongly dependent on the beam spectral content.
This is a real issue on synchrotron sources where the long wavelength halo around an
undulator beam will give a false broadening of the measured profile even thoughit is
at a low intensity compared to the on-axis X-rays[186]. In both the measurements
of Ioudin and Ilinski, windows in the X-ray beam acted as high-pass filters. Such
filtering is unlikely to be possible on a free electron laser source (because of the
ablation risk and beam disruption) but the spectral content in such a source should
not contain the long wavelength components anyway. Nevertheless, it is important to
consider any possible sources of stray light (from dipoles, steering magnets etc and
the spontaneous radiation from the undulators) that might propagate with the free
electron laser beam.
It should also be noted that the RGBPM is principally being designed to measure
the centroid of the beam, this being achieved through measuring and analyzing the
beam profile. Thus, a small amount of profile broadening can be accounted for. Of
course, bi-axial profiling requires a second monitor. There is also the need to further
improve the resolution and speed of the monitor if it is to meet the requirements of
a free electron laser beam position monitor.
Fluorescence detection in residual gas monitors
When atoms in a gas are excited or ionized by VUV to soft X-ray photons, the
dominant decay process is Auger emission. However, at hard X-ray wavelengths,
decay by fluorescence becomes a significant process.There is therefore the option of
recording the beam profile by imaging the fluorescent light. The principle is the same
as with imaging the ion or electron emission. The density of fluorescent photons is
proportional to the density in X-rays in the beam. With fluorescence, there is the
advantage that the photons will not be perturbed once emitted since the probability
of scatter in a low-pressure gas will be negligible. However, the photon emission is
not instantaneous with the atom being excited by the x-ray. Thus, by the time the
atom emits, it will have moved under the influence of the space charge of all the ions.
The average motion will therefore be away from the beam centre and this will result
in a broadening of the fluorescence profile.
This broadening effect is much more significant when measuring charged particle
beam profiles since the ions are also under the influence of the beam space charge.
This effect has been observed when measuring the profile of proton beams[187]. When
measuring an X-ray beam in a low pressure gas, the effect of inter-ion repulsion is
probably negligible. The ions will still move randomly before emitting the photons,
and statistically more will move away from the beam centre than towards it. Thus,
there can still be some broadening effect that will depend on the lifetime of the excited
state, which will in turn depend on the gas being ionized.
This type of monitor is in use at the Cornell synchrotron CHESS, where the monitors are called video beam position monitors (VBPM). The layout is shown schematically in Figure 8.9. The beam tube is filled with helium at atmospheric pressure.
Whilst this undoubtedly increases the fluorescence intensity, it would seem the main
reason for this is that the entire beamline is gas filled after a window of unspecified
material which isolates it from the machine vacuum. (These are of course hard X-ray
8.6. Imaging ion chambers
125
Horiz. profile camera
Vert. profile camera
He gas
X-ray beam
Figure 8.9: Schema of the CHESS VBPM system.
beamlines). The video cameras image the fluorescence via plane mirrors to prevent
them being damaged by scattered radiation coming through the viewports.
One issue that affects the resolution of the VBPM is the depth of field of the
video camera lens. The depth of field of the vertical profile camera is smaller than
the horizontal beam size and so edges of the beam are not in focus. The blurring of
the image leads to a broadening of the recorded beam profile. This is not an issue
when the main purpose of the monitor is to determine the beam centroid, as in this
application, but would be if accurate profiling were required. The spatial resolution
is also dependent of the lens magnification and camera CCD pixel size, which need
to be chosen with the size of the beam to be measured in mind, and the number of
digitization levels and overall signal to noise ratio. The camera system was tested to
have an accuracy of 0.4 µm fwhm.
The imaging system of the VBPM runs at 15 frames per second and the intensity
map is usually averaged over 10 frames. This low data rate is not an issue with an
essentially continuous source like a synchrotron, but would be unacceptable for a free
electron laser source. A faster camera could of course be used; the main concern is
whether enough fluorescence can be generated with a single free electron laser pulse to
be measurable. Enhancement of the signal by adding a gas at a low pressure should be
feasible; most X-ray free electron lasers have a windowless gas attenuator anyway (c.f.
chapter 4, p. 69). But the pressure limit will be determined by absorption, vacuum
126
8. Beam cross-section diagnostics
contamination (the gas cell cannot be isolated with windows) and self-modulation of
the intense photon pulse as it passes through the gas.
8.7
Sampling techniques
The ideal sampling process would be to extract a time slice from the beam so that
the full spatial profile can be measured of the slice whilst allowing the majority of
the beam to pass onto the experiment. Unfortunately, extracting a time slice of a
femtosecond duration X-ray pulse is not practical. Therefore,sampling in the spatial
domain has to be used, for which there are two approaches. One can remove just a
small part of the spatial extent of the beam, which leads to only centroid information
(see section 8.10), or the beam can be sampled by uniformly removing part of the
overall intensity, which allows a profile to be measured. Clearly, the main objective is
to remove as little of the overall beam intensity as possible to maximize the intensity
reaching the experiment. Profiling by sampling requires an intensity beam splitter,
which is difficult to achieve in the VUV to soft X-ray range. Thus most demonstrations
of this approach have been at shorter wavelengths.
In an effort to make an effectively non-invasive profiling measurement, van Silfhout
developed a replicating technique in which the bulk of the X-ray beam passes through
a thin ”featureless” foil angled in one plane to the beam whilst a small fraction of
the X-rays are scattered from the foil and are imaged by a linear photodiode array
to give line profile of the beam[188]. Because the x-rays are scattered rather than
reflected, a Soller slit is used to give accurate mapping of each scattering point on
the foil to a single diode in the array -see Figure 8.10. Nevertheless, the measured
profile must be deconvoluted from an instrumental function determined from the
profile measured with a very small beam footprint on the foil. The limiting spatial
resolution is determined by the spatial sampling of the projected beam footprint on
the foil and can thus be improved by angling the foil at a more grazing angle to
the beam. A beam position accuracy of 1 µm was claimed. The technique can be
extended to 3-D imaging by tilting the foil in two planes and using a crossed-Soller slit
and diode array. A more recent paper[189] shows how the technique can give a fast
output of the beam profile (still at in one dimension). The ultimate limit was 10 kHz,
determined by the readout speed of the electronics, though the actual measurements
were performed at 2400 Hz. The obvious concerns for free electron laser use are: 1)
ablation damage to the foil, 2) disruption to the beam through coherent diffraction
if the foil is not perfectly featureless and 3) the limitation to hard x-rays to get high
transmission through the foil.
Another approach, tested on an undulator beamline at SPring-8, is described in
Kudo et al. [190]. A 30 µm thick CVD diamond film was grown on a silicon substrate
and the silicon was etched away from a central region of 10 mm diameter. The exposed
diamond has silicon doping from the substrate that causes it to photo-luminesce
at 739 nm when exposed to an X-ray beam. The luminescence was imaged by a
CCD camera giving a 2-D picture of the beam profile. The diamond film is almost
transparent to hard X-rays (50% transmission at 3300 eV, 90% at 6200 eV, for a
density of 3.5 g/cm3 ) and so most of the beam passes through it to the experiment.
The luminescence response to beam intensity was shown to be linear over at least
four orders of magnitude. However, the luminescence is stimulated by a wide range
of X-ray wavelengths and so the method is unable to distinguish between the on axis
8.7. Sampling techniques
127
X-ray beam
Thin foil
Scattered X-rays
Soller slit
Diode array
Figure 8.10: The profiling system of van Silfhout, based on a Soller slit collimating the scattered X-rays from
a thin foil.
emission at the resonant wavelength and the lower energy radiation outside the central
emission cone of the undulator, leading to an artificially broadened beam profile.
However, this should not be an issue with a free electron laser beam. No specific
data for spatial resolution is given, but this will be determined by the combination
of the camera resolution and the beam footprint on the diamond. Bandwidth will be
determined by the readout rate of the camera and the persistence of the luminescence
in the diamond. Diamond has high thermal conductivity and the film, mounted in
a water-cooled assembly, was able to withstand the full pink beam on BL46XU at
Spring-8. Power loading is less of an issue with a free electron laser beam but there
is a significant risk of ablation if the diamond is exposed to the full intensity of the
fundamental. A further concern is that the CVD diamond is polycrystalline and thus
there may be significant disruption to a coherent X-ray beam on passing through the
film.
An alternative approach to intensity sampling is to Bragg reflect part of the beam
from a thin crystal onto a 2-D CCD detector whilst most of the beam intensity passes
through the crystal. This also allows the beam to be fully imaged and so profile
information to be extracted, Fajardo and Ferrer used a 500 µm thick beryllium crystal
in a white beam from an undulator at the ESRF[191]. The crystal was set a 45◦ and
so measured X-rays at 4.45 keV. The quality of the image is degraded by the effects
of mosaic spread and the finite extinction depth of the crystal. This does not affect
128
8. Beam cross-section diagnostics
centroiding resolution but does affect any profile measurement.
The major disadvantage is the spectral dependence of the reflected and transmitted
beams.Varying the Bragg angle to work at different wavelengths would make a very
complicated system. Furthermore, in the context of a narrow-bandwidth free electron
laser source, the impact on the transmitted beam will be significant. The crystal acts
as a band-cut filter and, because a significant fraction of the radiation could lie inside
the crystal rocking curve width, the notch in the transmitted spectrum would be large.
The mosaic spread of the crystal is also likely to cause strong diffractive disruption to
the transmitted beam. Finally, the technique is only applicable to hard X-rays where
adequate transmission through the crystal is possible.
At lower photon energies, a diffraction grating can be used to split the beam in
intensity (as discussed previously in chapter 5). This can be utilized in one of two
ways; either the first-order diffracted beam is sent to the diagnostic and the zeroth
order to the experiment or vice versa.
For a beamline that requires a monochromator, it makes sense to use the zeroth
order beam for the diagnostic. In such a case, it is necessary to ensure the zeroth
order beam direction is fixed as the grating is turned to tune the wavelength, otherwise
the diagnostic system will have to move considerably to follow it.In a normal fixed
included angle monochromator, this can only be achieved by using additional steering
mirror(s) to catch the zeroth order beam and redirect it to the diagnostic. Such a
mechanism could be both large and complicated since translation as well as rotation of
the steering mirrors is likely to be necessary. An alternative approach is possible with
a variable included angle monochromator such as the SX700 mount when operated in
collimated light. In this monochromator it is possible to operate in the so-called ’onblaze’ mode and this maintains a fixed angle between zeroth and first order beams.
In this mode, when the angle between the first and zeroth order beams is ψ, the
wavelength λ is related to the diffraction angle β by
ψ
ψ
−β
(8.1)
cos
N · n · λ = 2 · sin
2
2
Whilst this mode also conveniently maximizes the first order efficiency when a blazed
grating with a blaze angle of ψ/2 is used, there is a significant reduction in tuning
range for a grating of a given line density and thus more gratings are required to cover
a wide photon energy range.
In the alternative approach when the zeroth order is sent to the experiment, the
grating should ideally be kept at a fixed angle to minimize the reflections in the
main beam path. The diffracted order will thus be reflected at a different angle
as the free electron laser wavelength is tuned and the profile monitor will need to
follow it. This will be easier than in the case where the grating is turned since
the angular range over which the diffracted order moves will be smaller. Thus it
should be possible to arrange the imaging detector to move on a rail to follow the
beam. It must be remembered that the diffracted order will need to be imaged
onto the detector. This is best achieved by using a varied-line-spacing grating that
also allows aberrations to be corrected. This is basically the approach used in the
diagnostic spectrometer at Flash[192], discussed elsewhere. When applied to spatial
imaging,there are two important considerations when interpreting the measurement.
Firstly, residual aberrations could still be present and secondly, the image will be
blurred due to the dispersion of the pulse spectrum. A detailed design study would
8.8. Spot size
need to be performed to investigate whether this technique could give a useful pulse
profile diagnostic.
Another factor that should be remembered is that the position of the beam at the
diagnostic will be dependent on the grating angle and thus the technique is not ideal
for getting information on absolute positions and how the beam is moving.
8.8
Spot size
From the users’ perspective, one of the critical factors determining the performance
of a free electron laser is the size and quality of the focused beam spot. For many
experiments, the requirement is for as small a focused spot as possible to maximize
the flux density or fluence and to restrict interaction to a specific, targeted sample
area.Transverse intensity profiling is also critical when aligning the focusing optics
to optimize the spot shape by minimizing any asymmetry and eliminating tails and
flares. A precise measurement of the spot size is crucial to determining the absolute
flux density, which must be known for some experiments.
The most desirable solution for spot size determination would have the ability
to directly image the spot with a suitable two-dimensional, high resolution, high
repetition rate detector which is suitably robust to accept the unattenuated beam.
However, extensive experience on synchrotron sources has demonstrated that the
current generation of CCD and proportional gas-filled detectors can be permanently
damaged by momentary exposure to the unattenuated X-ray beam of a relatively large
(several millimeters) diameter. Whilst such devices should not be excluded from a
survey of possible techniques it is reasonable to suggest that the majority of 2-D
imaging systems will require significant attenuation and shielding to provide a usable
service life on a free electron laser source. It should be noted that attenuating the
beam using solid filters or foils has been demonstrated to affect the beam wavefront
at Flash although the effect of using a gas attenuators is negligible7 .
The remainder of this section is therefore subdivided into two sections covering
those techniques that can be used with the unattenuated beam, and those for which
significant attenuation will be required.
Techniques useable with unattenuated beams
Ablation crater analysis
One of the most established methods of determining the beam cross section in conventional high power UV-Vis-IR lasers is by analysis of the laser ablation crater imprinted
into a well characterized sample, predominantly PMMA (polymethyl methacrylate).
PMMA is used extensively because of its well characterized ablation characteristics
across a wide wavelength spectrum, its short heat diffusion length and the predominance of non-thermal processes when exposed to ultra-short laser pulses. The low
ablation threshold of PMMA also allows characterization to be performed on less
efficient or highly attenuated beamlines.
Techniques exist to comprehensively reconstruct the beam profile from the ablative imprint[193]. The beam can be characterized at any point along the beamline or
7
P. Juranić et al. Desy internal presentation.
129
130
8. Beam cross-section diagnostics
TOF
GMD
Faraday cup
Open multiplier
Diff. pumping
Ions
Ions
-
FEL beam
-
e+
±2 cm
+
Faraday cup
Figure 8.11: Setup for the ion yield saturation measurement at a beam focus.
end station where it is possible to place a sample of PMMA. The material is readily available, inexpensive and can be easily shaped. It is particularly suitable for
characterizing the beam profile in user-supplied sample holders and environmental
chambers.
Despite all these advantages, there are very significant practical barriers to using
crater analysis beyond the initial commissioning stage. Measurements can only be
taken of a single pulse (although some form of carousel or sample changer could
theoretically be used for very low repetition rates). The technique is clearly disruptive
to any experimental data collection and requires significant time to mount and remove
the ablation sample. Although it may be possible to make a limited determination
of the beam cross-section using in-situ optical microscopy, detailed analysis of the
beam quality will be conducted offline. The measurements to determine the crater
profile typically incorporate both optical and atomic force microscopy,so results are
far from instantaneous. It is possible to envisage a certain degree of automation being
employed if the number of routine measurements justified the investment. Even so,
it is difficult to imagine the time between sample exposure and accurate beam cross
section determination being reduced below the level of ”several hours”.
Photoionisation saturation of rare gases
An advanced, non-disruptive technique for spot size minimization has been developed
at Flash by A.A. Sorokin et al. [194]. This is based on the saturation effect of the
photoionisation of rare gases. At lower irradiance levels there exists a linear relationship between the number of incident photons and the number of ions generated.
However as the irradiance increases (e.g. due to the reduction of the spot size at the
ideal focus position) the fraction of the atoms in the interaction region that are ionized approaches unity. The ion yield thus diminishes with respect to the number of
incident photons as the interaction region and focus coincide. This saturation effect
can be measured with an apertured time-of-flight (TOF) spectrometer mounted perpendicular to the beam direction (see section 7.3, see page 104), whilst measurement
of the absolute number of photons per pulse is made using a gas monitor detector
(the GMD presented in section 7.2, see page 100) – Figure 8.11. Careful selection of
the target gas type and pressure relative to the energy of the photon beam is required
to restrict the photoionisation process to one-photon single ionization[195].
8.9. Techniques requiring attenuated beams
The technique is not quantitative; rather the maximum level of saturation of the
photoionisation signal indicates the optimum focus position. Further diagnostics are
required to quantify the resultant beam size,although photoionisation saturation could
be calibrated using a quantitative process (e.g. ablation crater analysis) for a given
lateral position and gas pressure. One benefit of the technique is that it is nondisruptive, since both the TOF spectrometer and the GMD do not impinge directly
on the incident photons.The system has currently been tested using macropulses of
Flash free electron laser at a photon energy of 38 eV.
8.9
Techniques requiring attenuated beams
Wire, knife-edge and slit scans
For the majority of existing synchrotron-based micro-focus experiments, slit scanning
methods are used to characterize the beam size and profile[196]. In general, diffraction
or scattering effects from the scanning object are not taken into consideration when
calculating the beam size. These techniques are covered in more detail in relation to
general beam profiling in section 8.4. For synchrotron radiation sources, any thermal
loading issues are overcome by implementing water cooling to the slit jaws or apertures. However,the fluence levels at the focus of a pulsed free electron laser source will
accentuate the difficulties associated with ablation, for which significant attenuation
will be the only solution.
Photographic film
This is included for the sake of completeness, and as a demonstration that a relatively
low technology solution can prove extremely useful. Film was used extensively on
second-generation synchrotrons e.g. SRS, Daresbury UK, to produce a permanent
record of the size and shape of the focused X-ray beam. In this example the film used
was Polaroid 55 large-format self-developing film which was chosen for its ease of use,
speed, limited cost (at the time) and small grain size which led to comparatively high
resolution images.Its thinness also made it practical in an experimental set-up as it
could be placed practically anywhere in the hard X-ray beam path without disruption
to user equipment.
One could suggest that photographic film is still viable for free electron laser applications since the grain size of high quality film stock can be as small as 0.5 µm,
which is far smaller than the photo site spacing of even the best CCD sensors. Some
form of pulse selection would be required to give single-pulse imaging and high levels of attenuation would be required to avoid ablation damage and over-exposure of
the film. Since the film is by its nature disposable, damage would at least not be a
catastrophe. In practical terms though, this is of little relevance since suitable film
is now difficult to obtain in appropriate quantities and requires lengthy processing,
digitization and subsequent image analysis. Polaroid self-developing film is no longer
in production.
For information, there is a closely related material which can also be used for beam
size determination; namely self-developing X-ray dosimetry film8 . Similar products
8
E. g. http://www.gafchromic.com.
131
132
8. Beam cross-section diagnostics
have been used on synchrotrons for beam profiling and have broadly similar advantages and drawbacks as self-developing photographic film. However, the resolution
of dosimetry film (ca. 100 µm) is significantly worse than that for high quality photographic film and will be too low for many focused beam measurements on a free
electron laser source.
Gas-filled detectors
Gas proportional detection systems for X-rays are commonly based on either wire
grids[197] or, more recently, on metal strips lithographically printed onto either traditional circuit boards or glass substrates[198]. Existing large-field commercial detectors
typically have pixel sizes of the order of tens of microns, although it should be possible to lithographically produce dedicated beam imaging detectors with smaller pixel
sizes,and resolution could be further improved using pixel interpolation algorithms.
However, although these detectors are sought after for their potential for measuring
high global count rates and energy discrimination,they suffer from severe non-linearity
due to space charge effects. Thus high count-rates that are very localized, as would
be experienced with free electron laser beam imaging, would cause problems. Additionally, at high count rates there are also problems with rapid contamination of
the gas and detector wires/elements,requiring very high gas flow rates and therefore
high maintenance costs. These issues make them highly unsuitable for direct beam
imaging purposes.
Charge coupled device (CCD)
Direct-detection CCD cameras for X-ray energies are commercially available with
pixel sizes down to 8 x 8 µm9 . This is not sufficient for the strongest focusing that
will be used on free electron laser, where spot sizes around 1 µm or less will achieved.
Depending on the energy range to be covered, a selection can be made between back
thinned, front illuminated and deep depletion CCD types. However, these sensors are
specifically not designed for high flux density applications; saturation and damage
occur at low irradiance.
Significant effort has been channelled into developing radiation hard CCD cameras,
the initial driver coming from improving the longevity of space-borne astronomical
instruments and remote observation systems in the nuclear industry. Defects can be
generated in the bulk silicon through exposure to radiation, and these defects can then
become electrically active, leading to further space-charge, charge leakage and charge
trapping issues in CCDs[199]. Three key approaches have been taken to minimize the
degradation effects inCCDs; i) engineering solutions such as guard structures, voltage
biasing and a reduction in the thickness of charge channels, ii) material developments
such as reducing the contamination defects in silicon or replacement of silicon with
alternative insulator materials and iii) alternative structures such as p-channel CCDs
or charge injection devices (CIDs).
CIDs individually address each pixel in the detector and do not suffer from leakage
of stored charge from one pixel to another. Commercial nuclear inspection CID
systems are available for X-rays, infrared and the ultra-violett with a stated pixel
9
See, for example, www.hamamatsu.com.
8.10. Position and centroiding
size of 11.5 x 11.5 µm and a frame rate of up to 25 Hz10 . A Thermo Scientific CID
camera has been employed as part of the transverse beam profiler for the IFMIFEVEDA prototype deuteron accelerator[200].
As discussed in section 8.3, luminescent screens in conjunction with CCD cameras
can be used for indirect detection. Using a scintillation screen, imaging of the Xray beam from SRS dipole beamline 8.2 has been demonstrated using an attenuated
Photonic Science CCD system. At the intensity levels experienced there,the main
risk of damage was assumed to be thermal damage to the screen. For free electron
laser the highest risk of damage will be ablation of the screen, and hence attenuation
of the beam will be essential.
Multichannel plate (MCP)
A number of commercially available beam imaging systems exist based on fibrecoupled MCP technology11 and a large range of conversion media exist to enable
the imaging of neutron and electron beams in addition to IR, UV and X-ray radiation. However, these systems are of limited application to free electron laser beams
since the inherent amplification due to the MCP is at odds with the requirement to
strongly attenuate the beam.
Solid State Detectors
For many applications on existing synchrotron sources, silicon pixel detectors (often
referred to as Monolithic Active Pixel Sensors, MAPS) or hybrid pixel detectors,
typified by the PILATUS system[201], are seen as a significant emergent technology.
They combine volume manufacture with small pixel sizes,large dynamic range, high
count-rates and fast readout. However, in common with CCD-based systems the
irreliance on silicon based lithographic plates makes them susceptible to radiation
damage at modest beam intensities.
8.10
Position and centroiding
Sampling techniques
Beam centroiding is typically performed by sampling part of the beam, either spatially
or in intensity. The basic objective in measuring the centroid is to measure the beam
position and angle mainly for the purposes of beam stabilization through feedback
control.
Solid state photo-emission monitors
Blade monitors are an example of spatial sampling and are widely used on synchrotrons. Mortazavi et al. [202] describe an early implementation at the NSLS
(Brookhaven) giving a sensitivity of a few microns. Thin tungsten blades positioned
edge-on to the beam intercept the periphery of the beam and the induced photocurrent is proportional to the amount of beam they intercept. If two identical blades are
10
11
www.thermo.com/com/cda/product/.
www.sciner.com/MCP/index.htm and www.beamimaging.com.
133
134
8. Beam cross-section diagnostics
positioned either side of the beam, then the relative intensity they see is a measure
of the beam position relative to the centre of the gap between the blades. These
devices are thus centroid monitors giving beam position relative to the blade gap –
but there is an underlying assumption that the beam intensity profile is symmetric.
Johnson and Oversluizen[203] also assert that ”the apparent deviation of the photon
beam from the monitor centroid depends on the on the size of the [. . . ] beam relative to the blade gap”, though it is not clear why this should be if the detector and
photon beam are symmetric (there are however problems created by stray light from
adjacent magnets, q.v.). It is however clearly important that the blades be identical
both physically and also in terms of photoelectric yield. The latter is a condition
that is hard to ensure given that photoemission is a predominantly surface effect and
so susceptible to contamination from the residual vacuum. Aging of the blades in a
white synchrotron beam is likely and if the blades age differently then this would lead
to long-term change in the null position of the beam relative to the gap.
A similar approach uses two parallel horizontal wires or rods with a fixed gap[204].
The advantage of the blade approach is that blades are easier to cool than wires and
less invasive than rods. Alkire et al. [205] report a relative accuracy of ±5 µm for
their monitor which uses 1.5 mm diameter tungsten rods of 12 cm length and with a
centre to centre spacing of 7.9 mm.
Tungsten or molybdenum are often used as the blade material since their high
melting point and hardness makes them resistant to the high powers produced by
3rd generation synchrotron sources. However, when high-K undulators are used on
high-energy synchrotrons the total power can be such that accidental exposure of
such materials to the central part of the beam could be damaging. At the APS,
CVD diamond was chosen since it has 10 times higher thermal conductivity than
molybdenum, and lower thermal expansion allied to high strength and stiffness[206].
These monitors have sub-micron sensitivity. For initial tests, the diamond was coated
with tungsten to give high photo-emissivity and electrical conductivity. Later, a 1
µm gold coating on 150 µm diamond blades was used[207]. This approach raises the
prospect that it may be possible to coat the blades with a low-Z material (e.g. carbon
or beryllium) that would resist ablation from a free electron laser beam, which would
otherwise be a major concern when using this type of monitor on a such a beam.
An advantage of the blade type monitor is that extra blades can be added in various
configurations such as a vertical cross[208], diagonal cross [209], etc. – see Figure
13. Thus, a single monitor allows bi-axial positional information to be calculated.
Two such monitors longitudinally separated give beam angle information,though each
should use a different blade arrangement to prevent the blades of the second monitor
from lying in the shadow of the blades of the first monitor[206]. For the centroid
measurement to give an absolute position and angle, the monitors must be accurately
mapped to an external reference frame. However, if there is an asymmetry in the
response of the blades (e.g. due to surface contamination) then, when the monitor
is nulled, the beam centroid will not be centered on the gap. There is thus an error
in the inferred absolute position relative to the external reference frame. Thus the
absolute positional accuracy of a blade type monitor is not always easy to define.
In the case of synchrotron light from dipoles, these detectors can be made effectively
transparent to the X-ray beam by being designed to intercept only the UV light that
has a much larger opening angle than the X-rays, which thus pass undisturbed through
the blade gap (Figure 8.13). The same approach can also be used with undulator
sources since the emission outside the central cone is at a longer wavelength than the
8.10. Position and centroiding
(a)
135
(b)
(c)
(d)
Figure 8.12: Possible arrangements for bi-axial blade monitors. (a) simple vertical cross; (b) a diagonal cross
allows better horizontal sensitivity when the horizontal opening angle changes considerably if an undulator is
tuned from low to high K; (c) and (d) upstream and downstream arrangements used at the APS to prevent
shadowing effects [40] (the tilted horizontal blades reduce the sensitivity to dipole radiation).
UV
X-rays
Monitor blades
Figure 8.13: Figure 9 -A blade monitor can be transparent at short wavelengths on a synchrotron source due
to the reduction in opening angle as the wavelength decreases.
fundamental.However, free electron laser radiation does not have the same properties
and so this approach cannot be used. There will be spontaneous radiation from the
undulator, but this will be at a low intensity due to the low average current and may
not be of sufficient intensity to measure. Furthermore, this approach has its drawbacks
since the photons being detected are not the ones being used in the experiment and
one must assume there is a unique and consistent spatial correlation between the
spectral components in the beam.
Whilst the range of wavelengths present in a synchrotron beam can be used to advantage as described above, it can lead to problems when using photo-emissive type
monitors with insertion devices on synchrotron sources. The electron yield is much
greater at VUV wavelengths and thus these monitors are disproportionately sensitive
to the low-level long-wavelength radiation coming from the dipoles and steering magnets that surround the insertion device. Extreme lengths have been used to overcome
this problem at the APS where the machine lattice has been modified to separate the
insertion device light from the stray light in order to facilitate sub-micron level orbit
correction[210]. Galimberti et al. [211] describe a different approach that makes the
136
8. Beam cross-section diagnostics
beam position monitor only sensitive to the X-rays that are being used in the experiment. They have improved the blade monitor by adding electron energy analyzers
to measure the blade signals. Thus they can select only the electrons emitted by the
fundamental radiation and so isolate it from any low energy background and even
electrons emitted by higher harmonics from the undulator. This is a much more sophisticated approach to that suggested by Warwick et al. [209] in which the blades are
reverse-biased to prevent the low energy electrons leaving the surface. Whether such
precautions would be needed on a free electron laser source would clearly depend on
the nature of the electron beam transport, but it would be natural to assume the effect would be much reduced since the electron path is straight and the long undulator
length should limit the acceptance aperture of radiation from other sources.
In general, blade type monitors when used on undulator sources are sensitive to
the undulator tuning due to the changing radiation pattern as the undulator K-value
is changed. This makes position control to sub-micron levels difficult. A smart XBPM
system (SBPM) has been developed at the APS in which the response of the XPBM is
automatically characterized under all possible operating conditions of the undulator
so that these effects can be automatically corrected for[207].
The effect of any change in beam footprint with wavelength must be considered
carefully for free electron laser beams.This source approximates to a coherent Gaussian source and thus the divergence will be roughly proportional to wavelength. We
can therefore expect a considerable change in beam footprint at the monitor as the
wavelength of it tuned. This will certainly change the sensitivity and resolution of the
monitor at different wavelengths and there is also the issue of the inferred position
being dependent on beamsize. Possibly more important are the risk of ablation and
the disruption to the beam. Providing the blades sit only in the wings of the beam,
ablation and diffractive disruption to the downstream beam may not be an issue.
But if the expands significantly, the blades will cut the beam at a position of greater
intensity and so both the risk of ablation and diffractive disruption will increase. It
may thus be necessary for a blade type monitor to have blades that move depending
on the source’s wavelength.
In order to eliminate the sensitivity of a blade monitor to beam size, schemes using
two triangular wedge swith a gap between them running at 45◦ to the horizontal have
been developed[203] (see Figure 8.14(a)). The gap must be designed to intercept
enough of the beam to get a decent signal with the smallest expected beamsize (i.e. at
the shortest wavelength). This means that any significant increase in beam size will
result in a significant loss in throughput. A variable gap will therefore be essential with
a free electron laser source. Even then, this type of monitor will be more disruptive to
the beam and be at greater risk of ablation then blade monitors and so is unlikely to
be useful with a free electron laser source. A refinement of this scheme was reported
by Mitsuhashi and tested at Spring-8[212]. Here, two wedge monitors are placed
to just intercept the periphery of the beam, thus reducing the fraction of the beam
intercepted and allowing bi-axial monitoring. Initially, the monitors were composed
of triangular wedges but this design was found to be sensitive undulator gap. Thus a
revised symmetrical scheme was developed and tested – see Figure 8.14(b) – and this
reduced the sensitivity to the gap around ten times. Note the wedges are angled to
the beam to reduce the power loading.
The wedge type monitor can be extended to give bi-axial position detection by
using a classic quadrant detector. These can be made using metal-foil photodiodes
but are also available commercially using semiconductor junction photodiodes[213].
8.10. Position and centroiding
137
Wedge plates
Upper electrodes
X-ray beam
Signal out
(a)
Lower electrodes
(b)
Figure 8.14: (a) The Wedge position monitor eliminates the sensitivity to beam footprint of the blade counterpart but is more invasive; (b) the symmetric design of Mitsuhashi et al. reduces the beam loss and has low
sensitivity to undulator tuning.
One problem with using semi-conductor devices is that they tend to be insensitive
at the edges and thus the amount of beam overlap needed to give a signal is increased
to the detriment of the transmitted beam. Kenney et al. [214] describe how activeedge silicon detectors, which are active to within a few microns of the detector edge,
can be used in various geometries for position, profile and intensity monitoring. For
example, a quadrant detector with a small hole at the centre can be used to monitor
the stability of a tightly focused beam. The beam is focused through the hole and
only the periphery of the beam is stopped by the detector. The focus position is
stabilized using feedback control based on the quadrant signals. An example device
with 100 µm diameter hole is pictured whilst test were made on a simpler single
element torus with 200 µm hole. This device showed excellent response uniformity
to 12.5 keV X-rays. The effect of diffraction at the hole with a coherent free electron
laser beam is a potential problem with this approach, as is the high risk of damaging
the detector if the central part of the beam is inadvertently steered onto it.
A significant disadvantage of the classic quadrant detector is that the fraction of
the radiation transmitted, i.e. that which can pass through the hole in the middle,
may not be large enough. Shu et al. at the APS[215, 216] have developed a quadrant
detector that has a high transmission to hard X-rays. The detector is based on a
25 mm diameter CVD diamond disc of 150 µm thickness. This has a transmission
of 78% at 10 keV. The quadrant pattern is formed with a 0.2 µm aluminum coating
on the disc. In its simplest form, the photocurrent from the aluminum sectors is
independently monitored and gives the positional information.The diamond in this
scheme simply acts as a support for the aluminum electrodes that can withstand the
intense synchrotron beam.
A more sophisticated approach uses the photoconductive properties of insulatingtype (IIa) CVD diamond in which the diamond becomes conductive when exposed to
the X-rays. The aluminium pattern is replicated on both sides of the diamond disc and
a bias applied across the front and back electrodes – Figure 8.15. On exposure to Xrays, the diamond becomes conductive and a current flows. Since the conductivity is
dependent on the absorbed X-ray power, the current is proportional to the intercepted
X-ray intensity. Also,the sensitivity increases with photon energy and the detector
less sensitive to stray light from bending magnets etc.
138
8. Beam cross-section diagnostics
Diamond disc
Output signals
X-ray beam
Bias
Al quadrant electrodes
Figure 8.15: Quadrant detector based on the photoconductivity of diamond.
There are other ways of spatially sampling the beam such as using a pin-hole
array[217] but these are significantly more invasive and ablation damage is highly
likely.
Solid state fluorescence monitors
Measurement of the incident photon intensity on the monitor by recording the photoemission in some way is widely used because the electron yields are high and photoemission is the dominant de-excitation process until the Ga K-edge at ∼ 10 keV.
Nevertheless, the radiative yield is appreciable above c. 5 keV and thus fluorescence
presents an alternative detection route. Alkire et al. [218] describe a simple position
monitor consisting of a 0.5 µm of Cr or Ti through which the beam (5 to 25 keV)
passes with little attenuation. An array of four PIN photodiodes surround the beam
axis in a vertical cross arrangement just upstream of the foil – Figure 12. The diodes
record the fluorescence signal and give the same effect as the four blades of a normal
bi-axial beam position monitor. The advantage is that the beam is measured over its
full cross-section and so the true centre of intensity of the beam is measured. The
measured position sensitivity was 1 – 2 µm. As with other techniques that involve
passing the beam through a foil, the concerns with a free electron laser beam are
ablation of the foil a diffractive disruption to the transmitted beam.
8.10. Position and centroiding
139
D
Foil
X-ray beam
Figure 8.16: Photodiode array BPM used to collect fluorescence from a thin foil.
Gas phase photo-ionisation monitors
Split-plate ion chambers are examples of intensity sampling. This approach is more
sophisticated than blade monitors as it samples the whole spatial extent of the beam
and should thus give a more reliable measure of the beam centre of intensity if the
beam is asymmetric or inhomogeneous. The beam passes through a gas at a low
pressure between electrode plates with a high voltage bias between them, and the ion
yield is recorded as a current from the plates. By splitting one of the plates diagonally
(Figure 8.17), each half of the split plate receives a different signal depending on the
beam position relative to the middle of the slit and the ion chamber records position
parallel to the plane of the plates. The diagonal split improves the linearity of the
monitor at the expense of sensitivity near the null position[219].
A split ion-chamber that can measure the vertical position of two partially over-
140
8. Beam cross-section diagnostics
Wedge plates
X-ray beam
+
Signal out
Bias plate
Figure 8.17: Arrangement of beam and plates for a split plate ion chamber.
lapping beams simultaneously has been developed at the Cornell High Energy Synchrotron Source CHESS with a reported accuracy better than 10 µm and a bandwidth
greater than 100 Hz over a linear range of 5 mm[220]. The accuracy was limited mainly
by drift in the analogue signal electronics and the ion chamber was actually able to
resolve movements at the micron level. Differentiation of the two beams was achieved
by designing the collecting field produced by the bias electrodes such that the collecting electrodes collect only ions from the non-overlapping edges of the two beams.
Thus, the ion path is short and this also improves linearity and bandwidth.
Two make a bi-axial measurement, two ion-chambers are placed sequentially with
their plate-pairs orthogonal. Schildkamp and Pradervand[221] describe a system
tested at CHESS which achieved a resolution below 1 µm with a bandwidth of 1000
Hz.
Important considerations when using ion chambers are:
• different gases may be needed to cover different photon energy ranges;
• the effect of saturation and recombination on the measured current;
• the transit time of the electrons and ions.
A noble gas is preferred as it eliminates asymmetries that result when using polar
molecules and lighter gases reduce the transit time of the ions to the plates and so
help reduce the build up of space charge in the chamber. Whilst the ion chamber
cannot be damaged by high intensities, the probability of recombination before the
ions reach the plates increases in proportion to the beam intensity and the square of
the distance travelled. If care is not taken, false position changes can be deduced as
the beam intensity is changed. The upper limit on the detection bandwidth is set be
8.11. Wavefront measurements
141
the transit time of the ions to the plates; increasing the bandwidth requires reducing
the plate gap and increasing the bias potential[222].
The other main limitation is the need for a gas. With a transversely coherent
beam, it is not desirable to use windows to isolate the gas and so the chamber must be
isolated by means of differential pumping. In the context of a free electron laser this is
not such a major issue as gas attenuators will be a common feature and the significant
advantage of the ionization chamber is that it can be considered non-invasive if the
gas pressure is low enough. The ion chamber can thus be used as an on-line diagnostic
giving pulse-by-pulse beam centroid position.
8.11
Wavefront measurements
A wavefront is defined by the surface on which the radiation field has the same phase
(assuming a monochromatic source). The direction of propagation of the radiation is
perpendicular to this surface, hence measurements of the propagation direction can
be used to find the wavefront – this is the principle of the Hartmann sensor described
below.
A complete characterization of the radiation field at a particular wavelength requires a measurement of the magnitude and relative phase of the field. These results
could then be input into simulations to deduce the radiation field at other locations in
the beamline. Such measurements could in principle be made using a Hartmann-type
wavefront sensor for a monochromatic source. For narrow-band sources such as free
electron lasers, the wavefront sensor can be used to measure the tilt of the wavefront
and ray tracing used to find the shape of the beam at other locations, assuming that
diffraction effects are not important.
The Hartmann sensor works by splitting the beam to be diagnosed into an array
of ”mini-beams” either by passing the beam through grid of holes (Hartmann plate)
or an array of lenslets (Shack-Hartmann array) and comparing the resultant pinhole
images or microlens focal positions on a 2D detector with those from a reference
wavefront. Variations in the position of each resultant spot can then be used to
determine the local slope in the wavefront. Let Sxij denote the measured slope in the
x-direction at the spot i, j on the detector, then
Sxij =
dWij
λ dφ
=
dx
2π dx
(8.2)
where W is the optical path difference and φ is the phase. A similar equation can
be written for the y-direction. The field strength can be derived from the intensity
of the spots. The actual wavefront W has to be reconstructed from the measured
slopes – there are two main methods of doing this, either by assuming the wavefront
can be written as a low (normally second) order polynomial in the local co-ordinates
(zonal method) or by expanding the wavefront in terms orthogonal functions, e.g. 2D
Legendre polynomials (modal method)[223]. The modal reconstruction is useful in
being able to identify the contribution of different aberrations to the wavefront shape.
For X-ray applications a Hartmann plate is used due to the lack of microlens arrays
capable of focussing the beam. For IR and UV energies suitable microlens arrays
are available, their commercial design and manufacture having been stimulated by
common use in ophthalmology and corrective laser eye surgery.
142
8. Beam cross-section diagnostics
The use of wavefront measurements in commissioning a free electron laser beamline
was demonstrated at Flash using a Hartmann sensor from Imagine Optics[224]. The
sensor contained a Hartmann plate with a 51x51 pinhole array, each pinhole being a
110 µm square tilted 25◦ to aid close packing and prevent interference with adjacent
holes. A direct CCD camera was used as the detector. The reference spherical
wavefront was generated by inserting a pinhole into the beamline.
From the wavefront measurements on beamline 2 (BL2)12 , the depth of focus of
the ellipsoidal mirror was calculated using ray tracing and a small astigmatism was
found which was cured by remounting a switching mirror. The design focal spot size
was still not obtained, but analysis of the wavefront measurements on BL2 and on
the unfocussed BL3 showed that this was not due to any remaining aberrations but
to the source being larger than expected during that phase of operation. The critical
yaw angle of the toroidal mirror on BL1 was also set using the wavefront sensor.
Based on this experience, an optimized wavefront measurement system, using a
320 µm hole pitch, has subsequently been designed in conjunction with the Laser
Laboratorium Göttingen for use as an end-station diagnostic on Flash. At beamline
2 this wavefront sensor have been used to align a grazing incidence ellipsoidal mirror
– decreasing the wavefront distortion from 52.6 nm (peak-to-valley) and 9.2 nm (rms)
to 12 nm and 2.6 nm respectively. This by correcting the mirror’s pitch -0.29 mrad
and its yaw by -0.06 mrad[225]. At BL1 the focal spot size and the position of the
beam-waist (and its fluctuation on a shot to shot basis) have been found with the
same sensor system[226].
At the Scss a Hartman wavefront sensor have been used to do single-shot measurements to characterize the spatial propertis of the Sase radiation[227].
8.12
THz/IR techniques
A major difficulty in IR and THz diagnostics is that of a suitable means of detection
of the long wavelength radiation. The low quantum energy of IR and THz radiation
means it is only able to stimulate vibrational and rotational modes in molecules and
cannot directly cause ionisation. Therefore, measurement techniques that depend on
the measurement of emitted electrons cannot be used in the IR and THz. There are
two basic techniques for detecting IR and THz radiation that are well established and
commercially available, namely:
• Thermal
• Photonic (quantum)
The detectors can either be photovoltaic (an induced voltage drives a current in the
detector circuit) or photoconductive (an induced resistivity change results in a voltage
change in the detector circuit).
In all cases, background radiation is the ultimate limiting factor and detectors may
require (cryogenic) cooling and / or thermal shielding depending on the radiation
levels and wavelengths to be measured and the required signal to noise ratio.
Important factors to consider when selecting and IR detector are:
12
For a layout of the Flash beamlines, see Ref. [104]
8.12. THz/IR techniques
• Photo-sensitivity (Responsivity) – The output voltage (or current) per watt
of incident radiation power. Units: A / W or V / W.
• Noise equivalent power (NEP) – The amount of incident radiation that gives
a signal equal to √
the inherent noise level, i.e. that gives a signal to noise ratio
of 1. Units: W / Hz.
• Detectivity D∗ – The photo sensitivity per unit active area of the detector.
The specific conditions under which the detectivity was measured are usually
given as a function of: temperature (K)
√or radiation wavelength (µm), chopping
frequency and bandwidth. Units: cm. Hz / W
• Spectral response – How the output varies with incident wavelength.
• Response time – How quickly the output rises and falls in response to an
input pulse. Gating may be needed to measure individual pulses if the response
is slow.
• Background Limited Infrared Photodetection (BLIP) – The ultimate
detection limit determined by fluctuations in the background radiation flux in
the ideal case of zero noise generated in the detector and processing circuits.
This is inversely proportional to the square root of the background radiation
flux.
Thermal detection
Thermal detectors involve the measurement of a temperature dependent phenomenon
such as:
•
•
•
•
Temperature dependent resistance (bolometers),
Thermoelectric effect (thermocouples and thermopiles),
Thermal expansion (Golay cells), and
Pyroelectric effect (thermally induced change in the surface charge of polarised crystals)
Thermal detectors use the radiation as heat and thus the photo-sensitivity is independent of wavelength. Of course, as the wavelength increases, more photons are
needed to give the same incident power. Therefore the quantum yield is inversely
proportional to wavelength. Since the environment is a strong source of long wavelength radiation, achieving the required signal to noise at longer wavelengths becomes
increasingly difficult.
The spectral response of thermal detectors can be tailored by placing a window
with a suitable transmission band over the detector. It is also highly desirable to use
windows that, as far as possible, block the parts of the black body spectrum from the
environment that are outside the output spectrum of the free electron laser source.
Thermal detectors tend to have a slow response and are more suitable for timeaveraged measurements or measurements on continuous wave sources. For example,
the response of pyroelectric detectors is at the millisecond level, though cryogenically
cooled bolometers can respond much faster than this.
The pyroelectric effect does not produce a permanent voltage on the crystal because
the induced charge on the crystal surface dissipates through internal leakage and ions
143
144
8. Beam cross-section diagnostics
in the air. Thus, pyroelectric detectors produce a signal only when the temperature
of the crystal changes and they only respond to pulsed sources. Use with a continuous
wave source requires the input light to be chopped, giving a signal of opposite sign at
each opening and closing of the chopper.
Photonic detection
Photonic detectors are semiconductors with band-gaps that are narrow enough for
the small energy quanta of IR photons to excite electrons across it. They are more
sensitive and have a higher response bandwidth (i.e. are faster) than thermal detectors. Background thermal excitation will result in a significant dark output and some
sort of cooling is normally required.
Photonic detectors operate over specific wavelength ranges determined by the
band-gap. The band-gap and response time also tend to vary with temperature,
so cooling a detector to a level at which the intrinsic noise is low enough may shift
its spectral response out of the required wavelength range.
Most commercial photonic detectors work in the near to far-IR wavelength range
from 0.75 to 15 µm (1.65 eV to 80 meV). Table 8.1 below13 lists various photonic IR
detectors.
√
Detector
Spectral
response [µm]
Temp
[K]
D∗ [cm,
PbS
1 to 3.6
300
D∗ (500, 600, 1) = 109
PbSe
InAs
InSb
Ge
1.5 to 5.8
2 to 5
2 to 16
0.8 to 1.8
300
213
77
300
D∗ (500, 600, 1) = 108
D∗ (500, 1200, 1) = 2 · 109
D∗ (500, 1000, 1) = 2 · 1010
D∗ (λp) = 1011
InGaAs
InAs
InSb
HgCdTe
Ge:Au
Ge:Hg
Ge:Cu
Ge:Zn
Si:Ga
Si:As
0.7 to 1.7
1 to 3.1
1 to 5.5
2 to 16
1 to 10
2 to 14
2 to 30
2 to 40
1 to 17
1 to 23
300
77
77
77
77
4.2
4.2
4.2
4.2
4.2
D∗ (λp) = 5 · 1015
D∗ (500, 1200, 1) = 1010
D∗ (500, 1200, 1) = 2 · 1010
D∗ (500, 1000, 1) = 1010
D∗ (500, 900, 1) = 1011
D∗ (500, 900, 1) = 8 · 109
D∗ (500, 900, 1) = 5 · 109
D∗ (500, 900, 1) = 5 · 109
D∗ (500, 900, 1) = 5 · 109
D∗ (500, 900, 1) = 5 · 109
Hz/W]
Type
Intrinsic,
Photoconductive
Intrinsic,
Photovoltaic
Extrinsic
Table 8.1: List of photonic IR detectors and operating ranges
13
taken from Hamamatsu Technical Information SD-12 ”Characteristics an use of infrared detectors”. www.hamamatsu.com
8.12. THz/IR techniques
A widely used photonic detector in existing IR-FEL facilities is the mercurycadmium-telluride or MCT detector. This is because the band-gap and hence longwavelength cut-off can be tailored by adjusting the relative proportions of CdTe and
HgTe. The long wavelength limit of commercially available detectors is ∼ 24 µm14 .
The website of the Felix IR Laser facility records that a Ge:Ga detector works
from 10 to 200 µm15 . Liquid helium cooling is of course essential at such a long
wavelength.
New detectors
The increasing exploitation of IR radiation on synchrotron radiation sources has stimulated development into new types of IR and THz detectors that aim to give
• Faster response
• Wider spectral response
• Higher quantum yield
• Lower noise
• Larger arrays
• Faster array read-out
• Higher spatial resolution
Developing and future technologies include:
• Niobium nitride (NbN) superconducting bolometers (50 ps response time, size
0.1 x 1 µm)
• Transition Edge Superconducting (TES) detectors (a superconductor is held
near the transition temperature and thus a small amount of added heat gives
an exaggerated conductivity change, improving sensitivity and response time).
• Quantum Well Infrared Photodetectors (QWIPs)
• Zero-bias Schottky diodes
Schottky diodes made at the Space Science Centre at Rutherford Appleton Laboratory have been tested on the ALICE accelerator at Daresbury. The fastest has
a measured response time of 20 ns (1/e). They are able to distinguish (though not
completely resolve) the individual THz pulses from the electron bunch train with 81
MHz repletion rate (12 ns period).
IR and THz beam profiling
Scanning
The simplest way to generate a profile in one or two dimensions is to raster scan a
detector element (thermal or photonic) through the beam. The spatial resolution is
14
15
InfraRed Associates Inc., www.irassociates.com
Felix IR Laser facility: www.rijnhuizen.nl/en/felix/facilities
145
146
8. Beam cross-section diagnostics
limited by the size of the detector or the defining slit in front of it. Diffraction at a
defining slit will limit the resolution if the slit size is comparable to the wavelength.
Because IR beams are relatively easy to manipulate, it is also possible to optically
raster the beam over the fixed detector. This is likely to be faster than moving the
detector since the optical raster will use angular shifts of a lens or mirror whilst the
detector raster will use linear motions of the detector.
Scanning a linear array detector is more efficient, though the spatial sampling of
the scan in the direction along the array is fixed by the array spacing. The array
must also be matched to the beam size, whilst a single element scan can used on an
arbitrary beam size.
imaging
Infrared imaging is of course widespread. Even a standard CCD based digital camera
can image in the near infrared, whilst security applications have driven a huge development of sub-optical imaging systems. Here we will therefore consider the more
challenging area of longer wavelength imaging and imaging which is tailored to the
nature of free electron laser sources.
It is conceivable that any of the basic types of single element IR detector can
be built into an imaging array, either 1-dimensional or 2-dimensional. The specific
technical questions that need to be addressed are:
•
•
•
•
The size of the detector elements
The spacing of the detector elements
The read-out time
Sensitivity and spectral response
Achieving high spatial resolution requires small and closely spaced detector elements, but this can lead to problems with sensitivity at long wavelengths since the
low quantum efficiency means the signal generated in each element is too small to
detect. For example, a commercial pyroelectric array detector was found to be unable
to detect the THz output of the quantum cascade laser at Leeds University, UK.
Consideration must also be given to diffractive effects at these long wavelengths.
Diffraction at defining apertures could lead to a decrease the spatial resolution. Does
a sensor element that is smaller than the wavelength of the radiation accurately record
the incident intensity?
Beam splitters
The detectors described in here are opaque to the beam and thus cannot be used as
part of a noninvasive detector. However, it is relatively easy to split an IR and THz
beam in amplitude such that only a small part of it passes to the detector and the
rest passes to the experiment16 . The most suitable techniques for IR and THz are:
• Plates and pellicles – can be made of various materials depending on the
transmission band required. Pellicles can be coated to enhance the reflectivity
at the expense of transmission.
16
See chapter 5 (see page 73).
8.12. THz/IR techniques
• Wire grids – these are polarising beam splitters, suitable for the longest wavelengths only (determined by the wire spacing).
Wavefront sensing
The Shack-Hartmann sensor is a standard instrument for measuring wavefronts in
the optical and IR region. Commercial instruments tend to be limited to operation
in the near-IR (∼ 2 µm wavelength), probably because of the types of IR sensitive
array detectors that are available with sufficient pixel count, density and sensitivity.
CCD cameras would seem to be the standard detector, giving megapixel array size
with spacing in the 20 µm range. High pixel count and small spatial separation is
required to allow accurate centroid determination of a large number of micro-beams,
both of which are necessary for accurate wavefront reconstruction.
Extending operation to the far-infrared would require, for example, an MCT array
detector. It is not clear that an MCT array with sufficient pixel count and density
is technically feasible, let alone cost effective. Alternatively, and for operation in the
THz region, the array would have to be made of thermal detectors. As mentioned
before, pyroelectric array detectors are commercially available. These currently have
rather low pixel counts compared with CCD cameras and a detailed technical assessment would have to be made to decide on the minimum pixel count that would be
required. This assessment would also need to consider the effects of the much stronger
diffraction and the Hartmann plate of micro-lens array.
Electro-Optical Imaging
Electro-optical sampling of THz radiation uses the Pockels effect in electro-optic crystals. A THz pulse acts like a transient bias that induces a transient polarisation in
the crystal. The polarisation induces a birefringence in the crystal that is probed by
a synchronous optical laser beam, the probe beam undergoing a polarisation change
as it passes through the crystal.
Wu et al.[228] describe how to exploit the EO effect to produce a 2-dimensional
image of the THz beam cross-section, see Figure 8.18. The THz beam was focused
at a ZnTe EO crystal and was overlapped with a co-propagating optical laser beam.
The optical field probes the spatial distribution of the electric field in the crystal that
the THz radiation induces. Crossed-polarisers either side of the EO crystal convert
the resulting polarisation modulation of the optical beam as it passes through the
crystal into an intensity modulation that is recorded by a CCD camera, which thus
gives a 2-dimensional intensity image of the THz beam.
This technique can be directly applied to determining the focus size of THz beams.
Obviously, a very fast optical laser that is synchronised to the THz pulse is also
required. The Pockels effect is very fast and imaging rate is limited by the camera.
Gating of the camera should allow single pulse measurement provided there is enough
modulation in the optical beam to produce a measurable signal at the camera.
Measurement of unfocussed beams is likely to be limited by the photon density of
the THz and optical probe beams, since the optical beam must spatially overlap the
THz beam for a complete 2-D image to be recorded in one shot. The available size
of EO crystals will be another factor limiting the largest beam footprint that can be
measured. These limitations could be overcome by using an optical system such as a
telescope to compress the beam diameter without modifying the wavefront.
147
148
8. Beam cross-section diagnostics
Pellicle
ZnTe crystal
Analyser
THz beam
CCD
Camera
ob
Pr
eb
m
ea
Polariser
Figure 8.18: Layout of the EO imaging system of Wu.
8.13
Summary
The ideal or ”universal” diagnostic for a free electron laser source would be able to:
•
•
•
•
Give a full spatial image of the photon beam.
Do this for every pulse produced.
Not change the photon pulse in any significant manner.
Operate over a wide spectral range (at least sufficient to cover the full output
range of the source)
At the moment, such a universal diagnostic is not possible.
•
•
•
•
Techniques that give full spatial profiles tend to be slow and invasive
Faster techniques often only give information such as beam centroid
Non-invasive techniques are too insensitive to measure a single pulse
Operating wavelength range is strongly limited by the detection technique employed
For radiation with wavelengths from the VUV to X-rays, there is a considerable
range of diagnostics employed on synchrotron radiation sources that could be developed for use on free electron laser sources. Many of these techniques involve transferring the spatial information to electrons that are detected and analysed to extract the
spatial information. Imaging detection is often achieved by converting the electrons
to visible photons with the aid of luminescent screens. For harder X-rays, fluorescence
is the dominant process and detection of the fluorescent photons, probably indirectly
by conversion to visible photons, is a better approach.
For the IR and THz, these approaches cannot be used and the choice of detection
method is much more limited. Photonic detectors are fast and efficient but are mainly
limited to detecting in the near to far infrared, up to ∼ 24 µm with HgCdTe (though
∼ 200 µm is possible with Ge:Ga). Thermal detectors must be used at frequencies
below a few THz and these tend to be slow. However, output at these extremely long
wavelengths is not generally in the realm of free electron laser sources. Electro-optical
techniques are probably a better solution for the very long wavelengths.
It is thus inevitable that a range of diagnostics and detectors will be employed
depending on the information required and the use to which it is to be put, for
example:
8.13. Summary
• Centroiding techniques for pulse by pulse beam position monitoring and feedback
• Invasive imaging for optimising the source and photon transport during commissioning
• Fast imaging arrays or wavefront sensors situated behind gas-phase experiments
The use of beam splitters to separate a part of the beam for the more sophisticated
diagnostics whilst the bulk of the beam is passed to the experiment are also likely to
be a common feature of the photon transport systems due to the lack of truly noninvasive diagnostics. These splitters can be removed from the beam path for maximum
throughput and / or if the diagnostic is not required. Ideally, the beam splitters should
divide the beam in amplitude so the diagnostic beam has the same beam profile as
the measured beam (but at lower intensity). This should be straightforward in the
IR and THz, but more challenging in the VUV and Soft Xray, where knife-edged
mirrors that divide the wavefront are the easiest splitter to implement. Multilayer
and slotted-mirror type beam splitters would be required to give amplitude beam
division.
Despite the considerable challenges that must be faced when making good spatial diagnostics for free electron laser beams, there are a wide range of techniques
that can be employed. A judicious combination of techniques will allow the required
information to be measured.
149
150
8. Beam cross-section diagnostics
Summary
• Cross-section diagnostics measures the transverse intensity
distribution of the beam. For both optimization, commissioning of experiments and instruments it is important to know
where the beam is and how large it is.
• Measuring the focus size can be done either via ablation crater
analysis (the size of a hole in a thin film) or by the saturation
of an ionization process in a gas.
• Techniques developed for synchrotron sources may not be immediately used at free electron lasers or not at all.
• Examples of invasive techniques are:
– Direct imaging
– Wire grids
– Scanning wires, slits, knife-edges, pin-holes. All have the
drawback that they are not single shot.
• Non-invasive techniques can be used while other experiments
are running.
–
–
–
–
Rest gas ionization
Photo dissociation
Synchrotron light
Compton scattering
• A combination of techniques is needed, in practice, to diagnose
the beam:
– Centroiding techniques for pulse by pulse beam position
monitoring
– Invasive imaging for optimizing and commisioning
– Fast imaging devices or wavefront sensors situated behind gas-phase experiments.
• In the THz range photodiodes in the infrared or thermal detectors for longer wavelengths can be used. The latter only
for averaging measurements.
• Beamsplitters offers the possibility to use invasive diagnostics
in parallel to other experiments.
9. Pulse length, profile and jitter
The material presented here in this chapter is partly adapted from ”Survey
of diagnostics techniques for measuring the temporal properties of ultra-short
photon pulses” by M. A. Bowler, A. J. Gleeson and M. D. Roper. Iruvx
WP7, 2009
9.1
Introduction
In chapter 8 methods to discern the transverse extent of a photon-beam were discussed. Here we will review methods as to determine the length and profile of a
pulse; the jitter between the pulses is also an important temporal parameter which is
necessary to measure.
A key measure of the performance of a freeelectron laser is the temporal properties of the
∆t
photon-beam. The pulse length is required for
the integral pulse power at the experiment; the
pulse profile determines the ”quality” of the
pulse in terms of length and height of, and deviation from, the ideal pedestal shape in Figure 9.1 (i.e. deviation from the transform limit
for the spectral content of the pulse) – this is
δt
also related to the jitter, since if the pulse shape
lacks repeating structure the centroid will be Figure 9.1: Ideal pulses have square profiles of
shifted on a pulse to pulse basis which is equiv- length δt, occurring with frequency ∆t−1 ; the
alent to a shift in relative occurrence times; the pulse shape can be significantly deviated from
pulse jitter is a random fluctuation in the ar- the ideal square and occur within a frequency
envelope defined by a time-jitter.
rival time of a pulse, by necessity this needs
to be correlated to another timing event. For
pump-probe experiments this is obviously a crucial parameter.
The profile and timing of a free electron laser pulse is certainly going to change on
a pulse by pulse basis by an amount that will cause difficulty to at least some experiments. This is especially true for Sase operation because the pulses are generated
from random noise. Therefore, there is a general need for the temporal diagnostics to
be permanently ”on-line” so that the profile and timing of every pulse can be measured. Such a diagnostic should obviously impose a negligible change on the pulse
151
152
9. Pulse length, profile and jitter
being measured. The diagnostic thus needs to be either effectively transparent to the
pulse, or at the very least interrupt only a small part and pass the major part of the
pulse undisturbed to the experiment.
Hence, there is a very demanding specification on an ideal pulse timing diagnostic
apparatus:
• Measure all pulses at the repetition rate of the machine, i.e. in the kHz and
MHz regimes.
• Meaure the intensity profiles of the pulses with a temporal resolution of about
1 femtosecond – carrying in mind that this resolution needs to be maintained
over pulse lengths that can have a duration of hundreds of femtoseconds.
• Measure the arrival time of the pulse with a resolution in the femtosecond
domain.
• Be transparent to the pulse, or sample a minuscule part of the pulse.
• Work in a spectral range from the VUV to the hard X-rays.
A diagnostic tool that fulfils all of the above demands can not be found. Below
we will survey the techniques available in the VUV and X-ray regime together with
their limitations vis-à-vis the ideal outlined above.
Many of the techniques that are currently being used and developed are based
around cross-correlation with an external optical laser (a high-power IR Ti:Sapphire)
and can give both pulse length and pulse jitter (relative to the optical laser). These
techniques have started out as multi-shot measurements since they initially required
scanning the IR pulse delay. But there is a lot of activity in developing the techniques for single-shot use and in improving the temporal resolution to the femtosecond
level (see page 153).
Electro-optical sampling also uses cross-correlation with an optical laser and is
used mainly for electron bunch measurements but can also be used for measuring the
lengths of THz pulses directly (see page 155). An alternative approach to pulse length
measurement is auto-correlation, (see page 155).
Simple intensity autocorrelation only gives a pulse length and not the profile. However, more sophisticated autocorrelation techniques have been developed in the visible
and UV that can give the full pulse profile of pulses as short as a few femtoseconds.
There is some possibility to extend these techniques to shorter wavelengths, though
the limit here is not clear.
Reflectivity modulation of a semiconductor by a free electron laser pulse has been
used to give single shot measurements with a temporal resolution of 40 fs. Streak
cameras are a well established technology for measuring pulses with picosecond lengths
and they are being developed to achieve resolutions of a few hundred femtoseconds.
Streak cameras can give single pulse measurements but only at limited repetition
rates.
Recently an elegant way of achieving few femtoseconds resolution in the timedomain was demonstrated at Flash by Tavella and co-workers. Their technique
utilized the terahertz radiation generated in the undulator, which is then phasecorrelated to the X-ray pulse. The optical laser system of the facility can then be diagnosed together with he terahertz radiation without disturbing the X-ray pulse[229].
9.2. Cross-correlation techniques
9.2
Cross-correlation techniques
Cross-correlation techniques are currently the most widely used techniques at XUV
wavelengths as they give pulse length and jitter information. A wide range of techniques based on the photo-ionisation of gases are being developed as they have the
potential to be transparent to the photon beam.
With a known reference laser pulse, cross-correlation between this and a X-ray
pulse can be used to measure the relative jitter of the free electron laser pulse with
respect to the laser pulse; in some circumstances said measurement can be used to
estimate the length of the X-ray pulse.
The pondermotive energy is given by
Up (t) = e2 Ea2 (t) cos (ωℓ t + φ)
where Ea is the amplitude of the laser field, ωℓ the laser frequency and φ the phase
respectively[230].
In most experimental configurations, the presence of side-bands would be the dominant effect, but this can be suppressed by measuring the photo-electrons ejected in
a direction perpendicular to the polarisation axis of the laser radiation, allowing the
shift due to the ponderomotive energy to be observed.
The intensity of the side-bands is proportional to magnitude of the photoelectron
wave-vector[231]
1p
2m (~ωfel − Ip )
k=
~
Deconvolution of the side-band intensity as a function of delay is obviously not a
single shot measurement. In order to determine the pulse length, the jitter between
the two pulses and the X-ray pulse length must be small enough not to dominate
the cross-correlation curve. Such a technique can be successfully applied to measure
the pulse length of soft X-ray radiation generated by HHG where the jitter between
the generating infrared pulse and the resulting HHG radiation is very small. In the
case of radiation from a Sase free electron laser, the cross-correlation curve will most
likely to be dominated by the jitter between the pulses, and can in fact be used to
measure the distribution of the jitter. It may be possible that this technique could
be used for seeded free electron lasers where the pulses will be more stable and the
jitter smaller.
An example of being able to estimate the time delay from a single shot measurement is given in Radcliffe et al. [231], where they used 13.8 nm pulses from Flash
of about 20 fs long to ionise Xe and measured the sideband intensity in the presence
of 120 fs pulses from a Ti:Sapphire laser. This case is favourable for the formation
of side-bands due to the relatively large photo-electron wave-vector and up to four
high energy side-bands were obtained. From theoretical simulations of the side-band
intensity, the number of side-bands gives a measure of the laser field intensity during
the FEL pulse, and hence the overlap of the pulses. In this experiment, a precision
of better than 50 fs was achieved for the relative delay, but note that the sign of
the relative delay cannot be obtained. The cross-correlation curve has a FWHM of
about 600 ± 50 fs, which is dominated by the jitter, and gives the FWHM of the jitter
distribution of 590 fs. It should be possible to determine the sign of the jitter by
using a chirped laser pulse (as also suggested in the XFEL TDR [89] for the Auger
electron measurements mentioned below) but this idea has yet to be tested.
153
154
9. Pulse length, profile and jitter
If this work were to be extended to very short X-rays pulses, then it would be found
that the spectral width of the X-ray pulse would smear out the side-bands. This can be
overcome by observing the photo-electron spectra for electrons ejected at right angles
to the polarisation of the laser. In this case, as noted above, sideband formation is
suppressed, and one can measure the red-shift in the energy of the electrons due to the
ponderomotive force exerted by the laser field. This has been done successfully using
an HHG source of SXR (90 eV) photons co-focussed with the generating 770 nm laser
pulses [230]. A delay scan yielded an X-ray pulse width of the order of 2 fs FWHM;
again, extending this to free electron lasers would require the relative jitter to be of a
similar size to the pulse width. For a seeded free electron laser, this may be possible
if the X-ray pulse timing is dictated by the laser seed. A significant disadvantage of
these techniques is the need to co-propagate the FEL and IR pulses to a common
focus. For on-line use, this requires a permanent extra focus to be included in the
beam transport system, which is not always convenient or desirable. A perpendicular
geometry would be more flexible - this has been used in the configuration adapted by
Cunovic et al. [232] where they have used the second method of obtaining the pulse
length by mapping the temporal co-ordinate of the pulse to spatial co-ordinates. In the
proof of principle experiment, outlined below, 32 nm radiation from Flash was used
to photo-ionize Kr in the presence of a pulse from a Ti:Sapphire laser. In principle
this is a single shot technique, but for this first experiment the data were too noisy
and had to be summed over several shots.
The unfocussed free electron laser beam, of FWHM 7 mm, entered the experimental chamber containing low pressure Kr through an aperture 500 µm wide. The FEL
beam was crossed at right angles with a focussed beam from a short pulse Ti:Sapphire
laser. The width of the X-ray beam in the chamber is equivalent to 1.7 ps, much longer
than the laser pulse length of 150 fs, and one has to assume that the intensity variation over the width of the central part of the X-ray beam accepted by the aperture
is not great. Hence as the laser beam traverses the pulse, the intensity of the side
bands in the photo-electron spectra will map out the intensity of the free electron
laser beam as a function of time. The interaction region is imaged by an electron
lens system containing a retarding grid which only allows the passage of electrons
whose energy has been upshifted by the laser beam. A line will be formed in the 2D
electron detector, corresponding to the different emission time of electrons, which in
turn yields information about the intensity variation of the X-ray pulse.
In order to be able to use this technique for single shot measurement, the signal
would need to be increased by about two orders of magnitude from that obtained in
[232]. This could be achieved by increasing the target gas density in conjunction with
the free electron laser pulse energy, but there is a limit to the increase before space
charge effects become important. In the measurement reported in [232] the total
pulse energy was 2 - 15 µJ before the entrance aperture to the chamber. If photoelectrons with higher energies were produced, the signal would also be increased as
the side-band production increases with increasing energy as noted above.
For use as an online diagnostic, the experimental set-up would need to be redesigned without the entrance aperture as this will disrupt the beam through edge
diffraction effects. There does not seem to be an intrinsic need for aperturing the
beam on entry to the experimental chamber.
An alternative to detecting electrons from direct ionisation is to use electrons
generated by Auger decay of an inner shell hole. The energy of the electrons can also
be modified by the presence of a strong laser field, creating side-bands. An advantage
9.3. Electro-optic techniques
of using Auger electrons is that their energy spectrum is fixed and does not depend
on the energy width of the exciting X-ray pulse, and the Auger decay times are short
compared with the typical duration of free electron laser pulses. If the laser pulse were
chirped so that the side bands are broadened, then some measure of the X-ray pulse
length can be obtained as well as the jitter – e.g. in the European X-Fel technical
design report it is said that a linear chirp of 1 eV in a laser pulse of width of 300 fs
would lead to a broadening of 0.25 eV of the sideband for an 80 fs X-ray pulse[89].
9.3
Electro-optic techniques
The electro-optic technique uses birefringence induced in an electro-optic crystal by
the electric field of THz pulses or electron pulses. The amount of birefringence depends
on the electric field and is probed by monitoring the change of polarization of a
short optical laser pulse. The limitation to the THz regime for direct photon pulse
measurements is due the availability of crystals with a suitable electro-optic response
function.
For electron bunches, the electro-optic detection method makes use of the fact
that the local electric field of a highly relativistic electron bunch moving in a straight
line is almost entirely concentrated perpendicular to its direction of motion. The
limitations to temporal resolution are discussed in Berden et al. [233] and include the
EO material selection, crystal thickness, wavelength dependence and beam – probe
displacement. Philips et al. [234] have demonstrated measurement of electron bunch
lengths of 118 fs FWHM using a 35 fs probe laser at the Flash facility.
The method can be used to monitor the relative timing of an external laser with
the electron bunch, and using this information to improve the resolution of crosscorrelation data. A proof-of-principle experiment has been carried out at Flash by
Azima et al. [235] where they have measured the relative arrival time of the electron
bunch and the laser pulse at the entrance to the free electron laser as well as measuring
the side-band formation in the photo-electron spectra from Xe in the presence of the
laser field. A plot of side-band intensity against the delay between the laser and the
free electron laser has a rms width of 410 fs which is mainly due to jitter in the free
electron laser pulse. When the electro-optical data are used to correct for the jitter,
the rms width of the curve is reduced to 100 fs. They call this technique TEO –
timing by electro-optic sampling.
9.4
Autocorrelation techniques
The advent of ultra-short (< 100 fs) optical pulses from lasers has driven a significant
amount of development into measuring the temporal profile of such pulses. Since
there are no detectors with a fast enough temporal response to directly measure the
intensity profile of pulses with lengths shorter than a few hundred femtoseconds,
the approach taken has been to probe the pulse with another short photon pulse. Of
course, this leads to the immediate problem of producing a suitably short probe pulse.
In autocorrelation measurements, the probe is created by splitting the original pulse
into two (or in some cases more) parts that are each a replica of the original and one
part is used to probe the other. Since the pulse being measured is its own reference,
autocorrelation is thus used to study shape of pulses rather than timing jitter (though
155
156
9. Pulse length, profile and jitter
a technique such as Spider (q.v.) can be used to derive the time correlation function
of a train of pulses).
Intensity autocorrelation
When optical lasers producing ultra-short pulses were first developed, the instrument
that was most likely to be employed to measure the pulses was a simple intensity
autocorrelator. This was not because the autocorrelator was especially good at this
job, but rather because autocorrelation was about the only technique that could be
used to measure pulses with durations below 100 fs since the fastest alternative
instruments, such as streak cameras, were limited to temporal resolutions of several
hundred femtoseconds at best and more generally picoseconds.
A second-order intensity autocorrelator is relatively easy to produce. The key
components are a beam splitter to divide the beam into two (in principle identical)
replicas of the input pulse, a means of altering the path length travelled by one of the
replicas so as to vary the relative temporal delay between them in precise increments,
and a means of recombining them so that they overlap spatially. There must also be
some means of measuring the temporal overlap as a function of the delay. Typically,
this is achieved by spatially overlapping the two beams in some instantaneouslyresponding, non-linear medium so that a signal is produced that is proportional to
the overlap intensity I(t)I(t − τ ).
A detector records the intensity of this signal, after separating it by some means
from the transmitted replica pulses. Since the detector will inevitably have a response
that is very slow compared with the ultra-short pulse length, it automatically performs
a time integration of the signal. The signal as a function of the relative temporal delay
τ is thus the autocorrelation function of the temporal intensity profile of the original
pulse.
Z∞
A(τ ) =
dtI(t)I(t − τ )
(9.1)
−∞
Because the phase information is lost in this measurement, the Fourier transform of
the autocorrelation function is just the power spectrum of the original pulse. Autocorrelation thus gives the pulse length but not the pulse profile. Indeed, one has to
assume a pulse profile even to extract a pulse length. The autocorrelation also tends
to smear out any structure (such as satellite pulses) and in general any number of
pulse shapes can give the same autocorrelation function. Thus, changing the assumed
pulse profile can give significant changes to the extracted pulse length. In general,
autocorrelation measurements are prone to systematic errors (for example caused by
misalignment) since the only constraints on the trace are that it should have a maximum at zero relative delay, be zero at delays much larger than the pulse width, and
be symmetric with respect to zero delay. In fact, the autocorrelation of complicated
pulses always tends to a sharp spike sitting on a smooth pedestal1 .
In the visible and UV regions the non-linear medium is usually a second harmonic
generation (SHG) crystal which has a second-order non-linearity in its electric susceptibility and produces light at twice the frequency of the input light and with and
intensity that is proportional to the product of the intensities of the two input pulses.
1
See, for instance, http://www.swampoptics.com/tutorials autocorrelation.htm
9.4. Autocorrelation techniques
The SHG signal thus rises quadratically with intensity of the original pulse. The SHG
signal is generally detected through a spectrometer to isolate it from the fundamental
light.
The short wavelength limit for SHG production is determined by the transmission
of the non-linear crystals. The crystal must be transparent at half the wavelength
of the incident light for the SHG signal to be detectable. Petrov et al. [236] have
demonstrated autocorrelation measurements to 250 nm (5 eV) using SrB4 O7 (SBO),
which is transparent to 125 nm. A further limitation of SHG is the finite bandwidth
over which the crystal will function. It is important that the SHG signal be phasematched to the original pulses since otherwise there can be a spectral filtering effect
that can significantly distort the autocorrelation function[237]. For very short pulses,
this means the crystals have to be very thin. The crystals also need to be thin to
limit dispersion that will change the pulse being measured. To overcome some of the
limitations of SHG from crystals, Dai et al. [238] have demonstrated using SHG from
metal surfaces. This will work from the far-infrared to the plasma frequency of the
metal being used (e.g. about 10 eV for gold).
Autocorrelation measurements have also been demonstrated using two-photon absorption inside a semiconductor-based photon detector [239]. The advantage here is
that the non-linear medium and detector are combined and so the experimental set-up
is simplified. However, a detector with a bandgap that is between the photon energy
and twice the photon energy is required and so different materials will be required for
different wavelengths. Extending the technique to the XUV is also unlikely to be possible. Worth noting is that Liu et al. [240, 241] have shown that autocorrelation can
give the full pulse profile if the pulse is split into three beams. In this triple-optical
autocorrelation for direct pulse shape measurement (Toad), the delay between all the
pulses must be varied and the beams are focused into a third-harmonic generation
(THG) crystal. Thus, although the technique requires only time-domain measurements, the extension to wavelengths shorter than the optical will be significantly
more challenging than extending two-beam autocorrelation.
Making a two-beam autocorrelator that works at VUV and shorter wavelengths is
challenging but not impossible. A successful instrument has been built for Flash by
BESSY[137] and a simpler system has been made by the University of Hamburg[242]
(cross-correlators between X-ray and optical pulses have also been achieved[243]).
A significant challenge is achieving the initial beam splitting. Amplitude division
whilst preserving the quality of the original pulse-front is probably impossible at
VUV to SXR wavelengths. In the BESSY instrument, the beam is divided spatially
(i.e. wavefront division) using a knife-edged mirror and one must thus assume that
the temporal profile of the beam is the same over the beam cross-section. Diffraction
effects from the wavefront division are a concern but are said to be minor in the focal
plane[137]. A second knife-edged mirror after the delay line is used to overlap the
two beams by angling one of them slightly with respect to the other. The delay of
one beam with respect to the other is achieved through an optical delay line using
translating mirrors. The relative delay range available is -3/+25 ps and is limited
by the overall mechanical design and the size of the delay line mirrors, since the
beam moves along these as the delay is varied. The mechanical specifications (e.g.
mirror quality, angular precision, translation accuracy and overall stability) are very
challenging for short wavelength operation.
The shortest wavelength that can be measured is determined by the reflectivity
of the mirrors since there are four mirrors per beam path. Making the instrument
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158
9. Pulse length, profile and jitter
relatively compact prevents the use of extremely grazing angles of incidence; the fixed
path arm uses 3◦ grazing whilst the variable path arm uses 6◦ grazing and therefore
the intensity of the two pulses is not the same. With carbon coatings, good reflectivity
is possible from 30 to 200 eV. Different coatings (e.g. nickel) could be used to extend
this range to higher photon energies.
A mechanically much simpler instrument has been developed at Synchrotron Soleil
for use as a VUV Fourier Transform interferometer[244]. This also uses wavefront
division to split the beam but in this design two roof-mirrors are used so that the
optical assembly for each beam path is monolithic. However, this means there are
two 90◦ deflections in each path and so the longest operating wavelength is in the
VUV.
Autocorrelation measurements on pulses from an HHG source using another splitmirror approach have been reported by Tzallas et al. [245]. In their work, a focusing
wavefront divider is made by splitting a spherical mirror into two halves. A translation
of one half-mirror along the surface normal gives a relative delay between the parts of
the beam reflected from each half whilst the mirror also focuses the split beams to a
common position in the detection medium. Two-photon ionized He gas is used as the
non-linear medium and the He ion yield measured by a time-of-flight spectrometer.
Stigmatic imaging with a spherical mirror requires the system to operate at nearnormal incidence. The upper photon energy is thus limited if a simple metallic coating
is used. Multilayer coatings could be used to allow operation at shorter wavelengths,
though the operating bandwidth would be quite narrow for a given multilayer.
The final challenge in the XUV autocorrelator is a means of measuring the autocorrelation signal. In the measurements reported in [246] using the BESSY/Flash
instrument, the temporal coherence was deduced from the fringe visibility of the spatial interference pattern as a function of relative delay. In these measurements, the
mutual coherence function, which is closely related to the auto-correlation function,
is measured. The mutual coherence function is defined by[247]:
Z
Γ12 (τ ) = u1 (t + τ )u∗2 (t)dt
where ui :s are the field values at the two slits.
An alternative detection technique that gives a second-order signal like SHG is
two-photon ionisation [248–250]. The strength of the two-photon ionisation signal
produced when one photon is contributed from each beam is clearly proportional the
temporal intensity overlap of the two beams. The wavelength range over which such
schemes will work depends on the ionisation potential of the gas. For first ionisation
potentials, this ranges from 12-24 eV for helium to 4.5 to 9 eV for toluene.
Two-photon single-ionisation above 24 eV is unlikely to be practical due to the
need to discriminate against single-photon ionisation events which will give an increasingly strong background of first order signal as the photon energy increases.
Nakajima and Nikolopoulos [251, 252] have made a theoretical study of using twophoton doubleionisation of helium, which would cover the range 40 to 54 eV. This
scheme could be extended to shorter wavelengths by using heavier elements (Li, Be,
B etc) and their higher ionisation stages [253]. Nevertheless, continuous coverage of
a wide photon energy range will not be possible with ionisation based techniques. In
summary, autocorrelation is a feasible pulse length measuring technique in the VUV
and XUV, though only the pulse length is measured and the technique is usually
9.4. Autocorrelation techniques
multi-shot, though adaption to single shot should be possible (see for example the
description of single shot Frog in section 3.2.1). The pulse length extraction is also
not particularly robust due to the need to assume a pulse profile and the susceptibility
to systematic errors. Autocorrelators do not give information of pulse timing (jitter).
The mechanical demands of the instrument are high but can be surmounted. Finding
a suitable non-linear detection technique to measure the auto-correlation signal is
even more demanding and unlikely to give continuous wavelength coverage. Autocorrelators are invasive in that they modify the beam passing through them, but they
can be designed so that they can be inserted into or removed from the beam path
without affecting the operation of downstream optical elements.
Autocorrelation techniques for complete pulse characterization
Complete characterisation of the pulse intensity profile requires the measurement of
both the spectral and phase information so that the electric field can be computed
as a function of time. There are three distinct approaches to this that have been
used in the visible and near-visible spectral regions, viz. spectrographic, tomographic
and interferometric. In all cases, filtering of the pulses is required. It is the practical
realization of some of these filters that make extending the techniques to shorter
wavelengths so difficult.
The two classes of filter that are important in current pulse length analysis techniques are time-stationary filters (in which the time of incidence of the input pulse
does not affect the output) and frequency stationary filters (where the output is not
changed by arbitrary shifts in frequency of the input). Frequency-stationary filters
are time non-stationary. These filters can be further classified as amplitude-only or
phase-only i.e. they modulate only the amplitude or only the phase of the input.
Finally, the filter may have a linear or non-linear response (with frequency or time as
appropriate).
A non-dispersive delay line is a simple filter that adds the same time delay to all
the frequency components in the pulse. A delay line is thus a linear spectral phase
modulator, since a linear (with frequency) shift in the spectral phase is equivalent to
a time shift. A spectrometer is an example of spectral amplitude filter.
These are both time-stationary filters. Both these types of filter are relatively easy
to implement across a wide range of wavelengths, though some thought must be given
to the frequency response function (e.g. bandwidth, resolution) of practical devices.
The simplest time-non-stationary filters are a time-gate and a frequency shifter.
A time gate is a time-nonstationary amplitude filter and is used to take time slices
of a pulse. A linear temporal phase modulator gives a linear variation of phase with
time, which is the same as a translation or shift of the frequency axis, and thus gives
a spectral shift or shear to the pulse. Time-non-stationary filters are more difficult to
implement, especially for ultra-short pulses.
Spectrographic techniques are probably the most widely used pulse profiling techniques. They work by measuring a two-dimensional representation of the one-dimensional
field, i.e. they are phase-space measurements. This is the critical step since it allows a
generally unambiguous retrieval of the phase information in a way that is not possible
with a one-dimensional measurement. The only ambiguities are the absolute phase
and absolute arrival time.
159
160
9. Pulse length, profile and jitter
Frequency Resolved Optical Gating (FROG)
An example of a spectrographic technique is Frog or Frequency-Resolved Optical
Gating. This uses a sequential spectral filter and a time-gate, in either order, followed
by an intensity detector. Depending on the order of the filters, the recorded signal
is a measure either of the spectrum of a series of time slices or a measure of the
time of arrival of a series of spectral slices. The technique is thus operating in the
timefrequency domain (phase-space) and is both temporally and spectrally resolved.
The technique is not limited to just autocorrelation measurements (i.e. it will work
with external gate pulses), but in all practical applications the pulse is used to analyse
itself in manner that is an extension of intensity autocorrelation.
input-pulse
Beam-splitter
Probe, E(t)
Non-linear medium
Gate, E(t − τ )
Spectrometer
τ
Figure 9.2: The basic layout of a Frog experiment; τ marks the variable time-delay between the probe and
gate pulses.
In the first description of Frog by Kane and Trebino [254], a replica of the pulse
to be measured is used as the time gate. Thus, the initial pulse is split into two pulses
(gate g(t) and probe E(t)) and the gate pulse has a variable temporal delay applied
to it – see Figure 9.2. The two pulses are focused and overlapped spatially in an
instantaneous non-linear medium (in this case, self-diffraction due to the electronic
Kerr effect in glass is the non-linear process). The diffracted light is then passed to a
spectrometer and a complete spectrum recorded, i.e. the spectrogram:
2
∞
Z
E(t)g(t − τ )e−iωt dt
SE (ω, τ ) = −∞
The spectrogram is recorded for a range of relative delays of the probe and gate that
is sufficiently wide to give zero temporal overlap of the gate as it is shifted from before
to after the probe pulse. Frog is thus essentially a spectrally resolved autocorrelation
(as seen from the similarity of the equation above and Equation 9.1).
9.4. Autocorrelation techniques
161
If self-diffraction is used as the non-linear effect the signal pulse is given by
ES (t, τ ) ∝ [E(t)]2 E ∗ (t − τ ), which yields
2
∞
Z
2
∗
−iωt
[E(t)] E (t − τ )e
dt
Ifrog (ω, τ ) = −∞
It does not matter (i.e. it does not degrade the temporal resolution) that the gate
has the same time-width as the pulse being measured, though a shorter pulse would be
preferable. However, the gate pulse should not be too short as an infinitely short gate
yields only intensity information, (whilst a CW gate would yield only the spectrum).
The use of the pulse to gate itself does however complicate the inversion process since
one cannot input any knowledge of the gate pulse into the analysis.
Another point to note is that, if the Frog measurement records an equal number N
temporal slices and spectral slices, then N 2 measurements are made in total. But the
analysis will yield only N intensity and N phase values, i.e. 2N derived values. There
is thus a lot of data redundancy in the measurement, though this does contribute
to making the data inversion give unambiguous results. In fact, the unambiguous
nature of Frog is a one of its most important features (and is quite contrary to
simple autocorrelation). Although the technique as described above is multi-shot
due to the need to scan the time delay, the technique can be adapted for single shot
measurements [254, 255]. This is achieved by focusing the pulses to lines in a common
plane and crossing the lines at an angle. The position along either of the line foci
is now a linear function of relative delay between the two pulses. If the line foci are
orthogonal to the dispersion plane of the spectrometer, then an imaging spectrometer
with 2-D detector will be able to record spectrum in one plane simultaneously with
delay in the orthogonal plane. Thus the spectrum can be recorded as a function of
delay and frequency in one shot. The length of the line foci and relative angle will
determine the range of delays that is recorded, which must be sufficient to give zero
overlap of the pulses at each end for the Frog measurement to be successful. The size
of the delay step is determined by the spatial resolution of the spectrometer detector.
The experimental configuration as described in [254] is quite simple since both
the delay line and spectrometer are straightforward. Though the technique has the
disadvantage of being invasive, it would seem to be extensible to wavelengths shorter
than the visible and UV. The key limitations are the need to find a suitable beam
splitter, and in particular the need for a non-linear process to mix the two beams
and give a signal proportional to the combined intensity. As with autocorrelation,
two-photon ionisation would be possible non-linear process, at least at lower photon
energies.
Norin et al. [256] used two-photo ionisation from Xenon to study the chirp of the
5th harmonic (15.5 eV) radiation produced by HHG in a method that is described
as similar to Frog. The HHG is produced from xenon from frequency doubled IR
radiation (Ti:Sapph) whilst the probe pulse is split off from the main IR beam. A magnetic bottle spectrometer is used to collect the photoelectron spectrum as a function
of probe beam delay. The intensity of the sideband corresponding to the absorption
of one 15.5 eV and one IR photon is measured as a function of relative delay. This
allowed the extraction of the linear chirp in the HHG pulse and its length, but not
the actual pulse shape.
162
9. Pulse length, profile and jitter
Sekikawa et al. [257] were able to fully characterize the 5th harmonic pulse of a
Ti:Sapphire laser using twophoton ionisation in Frog (TPI Frog). This is because
they show that the TPI spectrum is equivalent to the spectrally resolved SHG used
in ”conventional” Frog. They also claim the technique is scaleable to XUV and SXR
pulses through the detection of two-photon absorption from the K-shell to a free state
in boron.
Frog is probably the most widely used technique for measuring the pulse profile of
ultra-short optical pulses. There are a number of different geometries for measuring
Frog as described by Trebino et al. [255]. They are summarized briefly below.
Polarization-gate FROG (PG FROG)
The basic layout of PG Frog is shown in Figure 9.3. The input pulse is split into two
equal replicas. One replica (the probe) is sent through crossed polarisers and the other
(the gate) through a half-wave plate to give a ±45◦ linear polarisation with respect
to the first. The two replicas are then spatially overlapped in a material with a fast
third-order susceptibility such as fused silica. The gate pulse induces birefringence
in the silica through the electronic Kerr effect and so the silica acts as a wave plate
and rotates the polarisation of the probe beam slightly which allows some light to be
transmitted through a polarisation analyser. Because this occurs only when the gate
pulse is present in the silica, the transmitted intensity as a function of relative delay
is an autocorrelation measurement of the pulse. Spectrally resolving the transmitted
light thus gives the Frog measurement.
input-pulse
Beam-splitter
Polariser
Probe, E(t)
Fused Silica
Gate, E(t − τ )
λ -plate
2
Filter
Photodetector
τ
Polariser
Figure 9.3: The basic layout of PG Frog.
The biggest advantage of PG Frog is that there are no ambiguities on inversion
so that the pulse characterisation is complete in all cases. Another advantage is that
the non-linear process is automatically phase matched so alignment is easy. The main
disadvantage is that the polarisers must be of high quality; an extinction coefficient
9.4. Autocorrelation techniques
of better than 10−5 is recommended. This makes the polarisers expensive and more
importantly fairly thick, which can introduce dispersion to the pulse and so change the
pulse being measured, a particular problem for the shortest of pulses. Also, because
a third-order non-linearity is used, the sensitivity of the technique is reduced.
The fact that PG Frog polarises the beam is the biggest impediment to extending
the technique to wavelengths shorter than the UV. Polarisers and half-wave plates
with the required performance are impossible to make for the XUV and X-ray regimes.
Achieving a large phase shift in this spectral range is only possible using anomalous
dispersion near an absorption edge and so polarisers would be limited to narrow
spectral ranges. Even then, absorption is strong and the performance would not meet
the exacting requirements for PG Frog. Finally, a third-order non-linear process
would be needed to extract the Frog signal. There seems little possibility of extending
PG FROG to wavelengths shorter than 250 nm (5 eV).
Self-diffraction FROG (SD FROG)
Self-diffraction Frog is the technique as originally described by Kane and Trebino[254]
– see Figure 9.2. As with PG Frog, the electronic Kerr effect is used as a third-order
non-linear process. In SD Frog however, the intensity oscillations of the interfering beams induce a refractive-index grating in the silica and this diffracts each of
the beams in a different direction. The first order diffraction of one of the beams is
spectrally resolved to make the Frog measurement.
The advantage of SD Frog therefore, is that the beams can have the same polarisation and polarisers are not required. Application to beyond the UV is therefore
potentially more straightforward than with PG Frog.
However, a third-order non-linear process is still required. Self-diffraction is not actually ideal even in the visible since it is not a phase-matched process. The non-linear
medium must therefore be kept thin (<∽ 200 µm) and the angle between the beams
small (<∼ 2◦ ) in order to minimize the phase mismatch. Since the phase-mismatch
is wavelength dependent, the problem is of particular concern when measuring the
shortest pulses. SD Frog is thus best suited to pulses of length >∼ 100 fs.
Transient-grating FROG (TG FROG)
Transient grating Frog overcomes the phase-matching problem of SD Frog by splitting the beam into three parts. Two of the beams are overlapped in space and with
fixed (ideally zero) relative delay in the optical Kerr medium to create the refractive index grating. The third pulse is diffracted from the induced grating and the
diffracted beam spectrally resolved as the delay relative to the other two pulses is
varied. TG Frog thus has the phase-matching of PG Frog without the need for
polarisers. Operation into the deep UV is thus possible. Operation at shorter wavelengths still requires an equivalent third-order non-linear process. Producing three
beams by wavefront division will also be quite challenging.
Second-harmonic-generation FROG (SHG FROG)
SHG Frog differs from the three techniques described above by using a secondorder non-linear process. This gives a significant advantage in terms of sensitivity
163
164
9. Pulse length, profile and jitter
as second-order processes are inherently more efficient than third-order ones. The
probe and gate beams are overlapped spatially in an SHG crystal and a signal at
twice their frequency is produced with intensity that is proportional to the product
of the individual intensities. The SHG signal is spectrally resolved as function of the
relative pulse delay. Since each frequency in the original pulse is up-converted by the
crystal, the SHG spectrum is directly correlated to the original pulse spectrum. It
is thus important to ensure that the crystal works over a wide enough bandwidth to
up-convert the entire bandwidth of the original pulse.
Failure to record the entire pulse bandwidth will prevent the Frog inversion from
working. Since the crystal bandwidth is inversely proportional to crystal thickness,
short pulses require very thin crystals, e.g. for measuring 100 fs pulse at 800 nm,
the maximum crystal thickness should be ∼ 300 µm for KDP (potassium dihydrogen
phosphate) and ∽ 100 µm for BBO (β-barium borate).
Of course, operation at VUV to X-ray wavelengths will require the crystal to be
replaced by another non-linear medium in any case. The options for this are discussed
in Section 9.4. SHG Frog has the most potential to be extended to operation at
wavelengths shorter than the visible/UV part of the spectrum. A final point that
should be noted with SHG Frog is that it is ambiguous with respect to the direction
of time since SHG Frog traces are always symmetric with delay. Thus it is not
possible to tell if a pulse with a satellite has the satellite before or after the main
pulse.
Third-harmonic-generation FROG (THG FROG)
THG Frog is very similar to SHG Frog except that third-harmonic generation is
used as the non-linear process. The advantage of this is that the third-order nonlinear process removes the time-direction ambiguity inherent in SHG Frog (except
in the particular case of a Gaussian pulse profile with a purely linear chirp).
A potentially important variation of THG Frog is where surface third-harmonic
generation is used (STHG)[258]. Not only is STHG a relatively efficient process
(compared to other third-order processes) but by interacting only at the surface the
phase-matching bandwidth is very large. This is of particular value when measuring
pulses of only a few fs in duration which require SHG crystals of only a few tens of
µm in thickness.
Table 9.1: Different FROG Schemes
Type
SHG
Pol. Gate
Self. diff.
THG
Esig (t, τ )
E(t)E(t − τ )
E(t)|E(t − τ )|2
E(t)2 E(t − τ )∗
E(t)2 E(t − τ )
9.5. Spectral Phase Interferometry for Direct Electric-field Reconstruction (SPIDER)
9.5
Spectral Phase Interferometry for Direct Electric-field
Reconstruction (SPIDER)
An example of an interferometric pulse profiling technique is Spectral Phase Interferometry for Direct Electric-field Reconstruction or Spider[259]. The concept of the
technique is to have a linear spectral phase filter in parallel with a linear temporal
phase filter. These are followed by a spectral amplitude filter before an intensity
detector. The input pulse is divided into two replicas and one replica passes through
each of the phase filters before being recombined and passing through the amplitude
filter before reaching the detector. If the linear temporal phase filter is adjusted from
null, then one of the replicas is given a spectral shift relative to the other. On recombining the pulses they interfere spectrally (beat) and the apparatus becomes a
spectral shearing interferometer. The spectral interferogram is recorded on the detector as the spectral amplitude filter is tuned over the bandwidth of the pulse, i.e. the
spectrometer resolves the frequency mixed signal. This information together with
knowledge of the applied spectral shear is sufficient to reconstruct the electric field of
the pulse through direct inversion.
The linear spectral phase filter can be used to introduce a temporal delay between
the two replica pulses. This additional degree of freedom allows the correlation of
pulses in a train of non-identical pulses to be calculated[259], but otherwise can, in
principle, be set to an arbitrary value. In practice however, the time delay is important
as it adds an extra phase to the frequency spectrum of one pulse replica relative
to the other and this is used to ensure several fringes per independent frequency
component. This makes an unambiguous reading of the spectral phases from the
spectral interferogram possible (because the ac and dc terms of the Fourier transform
are well separated) and thus ensures that the inversion can successfully recover the
electric field.
In terms of the practical implementation of Spider, the all-important temporal
phase filter is the hardest to implement. The spectral phase filter is just a nondispersive delay line and the spectral amplitude filter is a spectrometer with sufficient
bandwidth and resolution to record the pulse bandwidth and resolve the spectral
interference fringes. Because the final measurement is spectral, Spider can be applied
to single pulses (assuming there is enough signal to noise to extract the interferogram
accurately).
Returning to the temporal phase filter, it is necessary to achieve an appropriate
amount of spectral shear. In [259], the use of electro-optic phase modulator (EOPM) is
considered to give insufficient spectral shear. Therefore, a method using up-conversion
of the two replica pulses is described. A broadband non-linear material is required and
each of the replica pulses is up-converted through mixing with a quasi-continuous wave
of different centre frequency. The up-converted pulses are thus centred at a different
frequency and the required spectral shift is achieved.
In [260], up-conversion is again used, but the two replica pulses are temporally
displaced and mixed with a strongly chirped pulse in the non-linear material. The
temporal delay results in mixing with a different frequency range of the chirped pulse
and again the spectral shift is achieved. The fringe separation in the interferogram is
now inversely proportional to the temporal separation. Note that the spectral phase
filter (delay line) of the original concept is now linked to the role of the temporal phase
filter and cannot thus be adjusted independently. Indeed, the temporal delay and
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166
9. Pulse length, profile and jitter
spectral shear are linked through the chirp of the pulse used to drive the upconversion.
The spectral and temporal shifts must be chosen to suit the length of the input
pulse and the spectrometer resolution, and this places constraints on the length of
pulses that can be measured. The most important factor is to ensure that the delay
is small enough to ensure the fringes can be resolved whilst not so small that the inversion process cannot unambiguously determine the phases. It is thus apparent that
extending the Spider technique to shorter (XUV, SXR) wavelengths is dependent on
a satisfactory method of achieving the required spectral shear. (We will assume that
splitting the beam by means of a knife-edged mirror will prove to be satisfactory since
true amplitude division is likely to be impossible). The use of non-linear materials
is prevented by strong absorption. Another approach that has been suggested for
the XUV is to use two-colour, two-photon atomic ionisation to transfer the frequency
spectrum of the photon to the photoelectron energy spectrum[261]. This however
brings additional problems since an electron spectrometer is now needed to resolve
the photoelectron spectrum, which contains the interferogram. Matching the fringe
spacing and interferogram bandwidth to the performance of available electron spectrometers will place limits on the range of pulses that can be analysed. For example,
an electron spectrometer with a challenging high resolution of 1 meV can only probe
a temporal range of 660 fs from the uncertainty relation.
In [262], Smirnova et al. describe an approach for measuring fast processes with
photon pulses that are long relative to the process. The approach is to spectrally
shear, by dressing with a weak IR field, a correlated two-electron spectrum of photoionisation and Auger electrons created when an XUV pulse interacts with the sample.
The spectrally shifted electron spectrum interferes with the original spectrum and the
phase is mapped to an amplitude modulation in the spectral intensity and thus can be
measured. The technique is thus Spider with electrons. The relevance here is that
there is no reason in principal why the same approach cannot be used to measure
the field of the X-ray pulse since the spectral content of the pulse will be encoded
into the electron spectrum. The key requirement for the technique is that very tight
synchronisation (sub-fs) between the XUV pulse profile and the phase of the IR pulse
is required. The technique will also be flux intensive since the correlated two-electron
spectrum must be measured, but given sufficient photons per pulse a single shot
measurement can be made.
In summary, the extension of optical techniques like Frog and Spider to the XUV
and shorter wavelengths looks challenging. Progress in this area has no doubt been
limited by the lack of sources giving ultra-short pulses in this spectral range, and one
might therefore reasonably expect more progress in the future. The advantage of these
techniques is that they give the exact pulse profile by calculating the electric field and
thus provide complete information. But the techniques are also invasive. The input
pulse must be divided and manipulated and as such they are not the obvious choice
for a pulse-by pulse diagnostic even when single pulse characterisation is possible.
9.6
Reflectivity modulation
Maltezopoulos et al. [263] describe how the free electron laser beam incident at a
glancing angle on the surface of a GaAs substrate modifies the reflectivity of the
GaAs to visible light in proportion to the intensity of the X-rays. Thus, a visible laser
(frequency doubled from near-infrared 800 nm) is used to simultaneously illuminate
9.7. Streak cameras
the area of the GaAs illuminated by the X-ray pulse and the reflected visible light
imaged onto a CCD. The intensity distribution and position of the visible image give
the free electron laser pulse profile and timing.
The technique is inherently pulse-by-pulse, and does not use co-propagation, but
is not transparent. Also, the visible light must overlap the entire area of illumination
from the free electron laser and so some sort of focus of the X-rays may be required.
The technique is thus not an on-line diagnostic but could be used for checking the
beam at the experimental end-station (where there is likely to be a focus anyway).
Alternatively, since this technique does not require such high beam intensities as the
cross-correlation methods described in Section 9.3, it may be possible to split off a
small part of the FEL beam and use that to monitor the arrival time of the pulse. In
any case, the temporal resolution is limited by the length of the visible pulse and the
space-to-time correlation of the visible imaging system. The work presented gives a
resolution of about 40 fs rms.
Gahl et al. [243] suggest that the key limitation to the temporal resolution is
the visible probe pulse length, of the order 120 – 150 fs in this example. They
also suggest that the time required for the GaAs surface to recover to its original
level of reflectivity could be of the order of hundreds of picoseconds, but this would
only be a limit in multi-shot measurements at repetition rates in the GHz region.
A further consideration is the potential for radiation damage of the GaAs surface.
Maltezopoulos et al. [263] used an optimised beam fluence of 13 ± 5 mJ/cm2 rms
for their measurements, commenting that permanent damage was observed at an
unstated higher fluence, thus requiring the GaAs surface to be renewed. Conversely,
measurements at a lower average fluence led to very weak contrast in the images,
making temporal determination unreliable.
A related technique has been recently proposed by Krejcik [264]. In his scheme,
the X-rays strike a magnetised film and cause a change in the magnetisation which
is probed using MOKE (Magneto- Optical Kerr Effect). An IR laser illuminates
the magnetic film and undergoes a small relative polarisation rotation (∼ 1◦ ) in the
part that is reflected from the area the X-rays illuminated. The polarisation of the
reflected IR beam is analysed and mapped over the beam profile. Thus, a time to
space mapping of the arrival time of the X-ray pulse is achieved. The advantage of
the MOKE analysis is that the magnetisation change is extremely rapid and so there
is no issue with the response time of the process reducing the temporal resolution
achieved. The disadvantage is that the magnetic material needs a resonance at a
magnetically active orbital at the X-ray wavelength of interest. Thus the technique
is not applicable to arbitrary wavelengths.
9.7
Streak cameras
Streak cameras work on similar principles to oscilloscopes and cathode-ray tubes and
work by mapping time to a spatial coordinate in the detector. The incident photon
beam is focused onto a slit and then passes through a photocathode. The photoemitted electrons are drawn between two parallel plates that are also parallel to the
slit. A high-speed sweep voltage, synchronised to the pulse arrival, is applied across
the plates. This gives an angular deflection of the electrons that is directly related to
their time of arrival and thus to the duration of the pulse. The deflected electrons are
then multiplied with a micro-channel plate (MCP) before impacting on a phosphor
167
168
9. Pulse length, profile and jitter
screen. The streak pattern on the screen is imaged by a CCD or other suitable
detector, using a light intensifier tube if required. The advantages of streak cameras
are the applicability across a wide wavelength range (X-rays to near-IR, although not
with a single camera), single-shot time resolution in the picosecond range for off-theshelf systems, and the ability to work at high repetition rate, albeit with reduced
temporal resolution. They can also provide information on intensity and position in
addition to the temporal information in a single measurement.
Historically, the resolution of streak cameras has been restricted to several picoseconds in single-shot mode. In multiple-shot averaging systems, the use of a synchronised sine-wave sweep voltage adversely affects temporal resolution by making these
systems highly susceptible to source jitter. However, there have been recent improvements in off the shelf systems and the fastest commercially available streak cameras
claim a time resolution of <300 fs for single-shot measurements and 500 fs for multiple shots [265] although it is unclear at what wavelengths these speeds are attainable.
Although the multi-shot system can operate at MHz repetition rates, the single-shot
system is limited to operating below 100 Hz due to limited sweep voltage cycling.
Several fundamental limitations of the systems are now being addressed. In order
to limit the affects of source arrival jitter, photoconductive switches are being utilised
in conjunction with a beamsplitter to accurately trigger the voltage sweep. Bonté et
al. [266] employ photoswitches supplied by Fastlite[267], whilst the camera under
development at the Advanced Light Source (ALS) uses in-house photoconductive
GaAs switches.
Feng et al. [268] at the ALS state that one of the most significant fundamental
limitations to the temporal resolution is set by the energy spread in the electrons
from the photocathode. By adding a four-dipole, timeof- flight dispersion corrector
they have simulated 50 fs resolution. The current best temporal resolution achieved
by the ALS system is 233 fs using 266 nm UV light [268].
Researchers led by J. Larsson at MAX-lab are developing ultrafast streak camera
systems where the standard CCD detector is replaced with a ”smart camera” [269].
This combines the CCD detector with an on-chip processor that undertakes signal
processing prior to readout, reducing the amount of data output and thereby improving the potential readout speed. The development system is currently capable of
4000 frames/second and has demonstrated a resolution of better than 300 fs at X-ray
wavelengths in multi-shot experiments. In a separate development at the Thomas
Jefferson National Accelerator Facility (J-Lab), tests have been made with an ultrafast streak camera in which the voltage sweep plates are replaced with a dedicated
RF frequency deflection system, although the temporal resolution is currently in the
several picosecond range2 .
9.8
Summary
In this chapter we have surveyed the techniques that have been employed or could be
developed to measure the temporal properties sub-picosecond pulses at VUV/XUV
and shorter wavelengths. The ability to measure pulse length, pulse profile and pulse
timing are critical to the success of many experiments on free electron laser sources.
2
A. Margaryan, J-Lab seminar June 28, 2007
http://casa.jlab.org/seminars/2007/slides/margaryan 07June28.pdf
9.8. Summary
Because such sources show significant shot-to-shot fluctuations in the pulse properties, we ideally need to be able to measure each and every pulse that is used in the
experiment.
The temporal diagnostics techniques thus need to be automatic, reliable, noninvasive and capable of handling large amounts of data. And yet a key point to note
is that many of the techniques are currently at the level of experiments in themselves. This is not unexpected since sources of ultra-short pulses at VUV and shorter
wavelengths are a relatively new phenomenon, and it is only through availability of
such sources that the diagnostic techniques can be developed. In the early days of
ultra-short optical wavelength pulses, the principal diagnostic was the relatively uninformative autocorrelator, and yet sophisticated diagnostics that fully characterize
the pulse profile can now be bought ”off the shelf”.
We should not however be complacent that developments to shorter wavelengths
will rapidly follow the availability of the sources. Certainly, basic second-order autocorrelation as been successfully demonstrated into the soft X-ray, but this gives
only information about the pulse length, and even then assumptions have to be made
about the pulse profile.
At optical wavelengths, autocorrelation was extended through the addition of spectral analysis (e.g. FROG) and this allowed complete pulse profile retrieval. But a key
requirement in autocorrelation techniques is a non-linear process that can mix the
two pulses and produce a signal that is proportional to the autocorrelation function.
Here we are limited not only by the availability of suitable physical processes but
also by detectors since the non-linear signal may be accompanied by a strong background that is hard to discriminate from the signal of interest. This is particularly
true when the physical process produces electrons rather than light, as will generally
be the case at short wavelengths where ionization is a dominant process. Two-photon
ionization is the most widely cited physical process that might fulfill the requirements
and auto-correlation measurements have been successfully performed into the XUV.
The wavelength range over which two-photon ionisation will work is limited by
the ionisation potentials of available gases and so different gases are needed to cover
different wavelength ranges. Furthermore, once the energy of a single photon is above
the gas IP, then the large background of single-photon ionisation events is likely to
swamp the two-photon signal. Thus two-photon ionisation is only viable at photon
energies between half of and the full IP of the gas. Two-photon double ionisation
may then be the way forward into the soft X-ray, but at the moment such schemes
are untested.
A fundamental limitation of autocorrelation techniques is that they cannot provide
information about the timing of the pulse since it is measured against itself. Thus,
there has been a lot of development in crosscorrelation techniques in which the free
electron laser pulse is measured against a known pulse from an IR laser. As well
as pulse length information, we can gain information on timing jitter relative to the
laser, which is often very convenient, for example when the laser is also used in pumpprobe experiments. A significant amount of work has been undertaken in this area
and many possible approaches to cross-correlation have been demonstrated or at least
suggested.
A well-established approach is to measure the intensity and/or number of sidebands that appear on the photo-ionisation spectrum of a gas as the infrared laser falls
in and out of temporal overlap with the free electron laser pulse. This requires the
infrared laser and X-ray pulse to be spatially overlapped in the ionisation chamber,
169
170
9. Pulse length, profile and jitter
and thus has some implications for the optical layout of the beamline. Nevertheless,
the gas absorbs so little that the X-ray pulse is unaltered and the diagnostic meets our
requirement for being non-invasive. In the first implementations of this sort of crosscorrelator, complete pulse characterisation required measurement over a succession
of free electron laser pulses with differing infrared pulse delays. The pulse profile
measure was thus an average profile and not shot-by-shot. This limitation can be
overcome by converting the temporal information to spatial information and recording
the photo-electron spectrum with an imaging detector. Proof of principle experiments
have been done but more development is needed to improve sensitivity and temporal
resolution.
There are other approaches to cross-correlation that have been proposed, using
for example Auger electrons and chirped infrared pulses. This is an active area of
research at the moment. The common theme is detection through the ionisation of
gases, thus all these schemes rely on electron detectors, which adds significantly to
the complexity of the measurement.
A different approach to cross-correlation is that of reflectivity modulation. Although this is an invasive measurement, it is more sensitive than gas based measurements and so not all the beam is needed. Thus, a small part of the beam can be
split off and sent to the cross-correlator whilst the rest of the beam is passed to the
experiment. Since the technique is relatively simple and is inherently pulse resolved
(but limited to the external laser repetition rate), it is quite attractive. Some work is
needed to improve the temporal resolution however.
Streak cameras are a long established instrument for measuring short pulses. However, current instruments are too limited in terms of temporal resolution and repetition rate. There are a number of active development programs aimed at addressing
these points and it seems likely that temporal resolution of 100 fs will be possible
whilst the use of ’smart’ detectors will give operation to several kHz.
Electro-optical techniques are not useful for directly measuring the profile of the
free electron laser pulses since they only function at THz frequencies. But they can
be usefully employed for monitoring the timing of the electron bunch relative to an
external laser. This is likely to give important information on the overall timing of
the X-ray pulses.
9.8. Summary
Summary
• Pulse length and jitter can be diagnosed with cross-correlation
techniques. They rely on encoding the electrons emanating
from a photoionization of a gas spectrally with energy from
a known laser pulse. The main photoionization peaks will
then get side-bands (also called satellites) whose intensity is
proportional to the delay between the laser photon pulse and
that of the free electron laser. With a chirped laser pulse (the
photon-energy varies over the pulse) the pulse length may also
be extracted from such a measurement.
• Autocorrelation techniques uses the pulse itself, the pulse
length is deduced from splitting the pulse and recombining
it after the two parts of the pulse have traversed different
optical paths. The correlation between different parts of the
pulse can then be measured. Although the technique is single
shot a pulse shape has to be assumed to extract the length of
the pulse. More advanced autocorrelation techniques Frog
and Spider can also deduce the pulse shape.
• Reflectivity modulation of a GaAs surface induced by an optical laser can be used to extract the pulse length since the
free electron laser beam modifies the reflectivity of the surface. The position and intensity of the visible reflected light
can then be recorded on a pulse-by-pulse basis but not in a
manner transparent to the experiments. The resolution limit
is quoted to the 40 fs rms currently. Modulation of other processes have also been suggested, such as the Magneto-optical
Kerr effect.
• Streak cameras work on similar principles to oscilloscopes and
cathode-ray tubes and work by mapping time to a spatial coordinate in the detector. The incident photon beam is focused onto a slit and then passes through a photocathode.
The photo-emitted electrons are drawn between two parallel
plates that are also parallel to the slit. A high-speed sweep
voltage, synchronised to the pulse arrival, is applied across
the plates. This gives an angular deflection of the electrons
that is directly related to their time of arrival and thus to
the duration of the pulse. The deflected electrons are then
multiplied with a micro-channel plate before impacting on a
phosphor screen. Current time-resolution for streak cameras
are about 300 fs.
171
10. Free electron laser experiments
A free electron laser provide a tunable pulsed (transversely) coherent photon beam
with unprecedented brilliance. The beam can thus be focussed to small spots where
a very high X-ray photon density can be acquired.
The properties outlined, enable a number of experiments that are, more or less,
unique. The large number of photons per pulse (often tens of billions or more) allow
time-resolved imaging and spectroscopies – where combinations of the free electron
laser beam and laser beams make pump and probe experiments more advanced. The
high degree of coherence make single-shot imaging of nano-structures possible. The
high X-ray photon density enable the study of non-linear processes in the X-ray
regime, as well as the ability to study processes with low cross-sections or with low
target density (e.g. imaging of single unsupported nanostructures/molecules).
In this chapter some of the experiments carried out at free electron laser will be
highlighted – our treatment here will not by any means be all encompassing but is
rather intended to give an introduction to which kinds of experiments successfully
exploits the unique properties of this kind of X-ray source.
One may condense the experimental efforts into: imaging and measuring atoms
and atomic processes on the nanometer and femtosecond scales. Adding that the
development is towards Ångström and attosecond time-scales.
10.1
The ”holy grails” of free electron laser experiments
”Molecular movies”
The short pulse length of free electron laser sources makes it possible, either via
splitting or sub-pulse structure, to get a X-ray pump - X-ray probe experiment. With
the addition of external lasers X-ray pump, UV/Vis Laser-probe or UV/Vis-pump
X-ray probe is made possible. All of this in the femtosecond regime.
This, potentially, makes it possible to follow a photo-excited process like a movie,
but with a femtosecond frame-rate.
173
174
10. Free electron laser experiments
”Single-molecule/nanostructure imaging”
Real-space imaging of nanostructures and ultimately single-molecules can be realized
by the reconstruction of the image via a recorded image in momentum space obtained
from X-ray scattering from the object.
”Single-shot spectroscopy/imaging”
Single-shot experiments are made possible by the large number of photons available
that can get focussed down to a very small point owing to the beam quality. Since the
pulses are short and intense the data for imaging and spectroscopy can be acquired
before the sample explodes. This is also a cornerstone for the success of time-resolved
measurements as outlined above.
In the following some examples from each field will be given. Both planned and
already performed experiments are presented as to show what is done today and where
different groups and facilities intends to head in the near future.
10.2
Time-resolved spectroscopies
Core-level photo-electron spectroscopies give information about the chemical state
of the constituting atoms (being in free molecules or atoms, molecules or atoms on
surfaces or in solids). By using photon-pulses time-resolved spectroscopies can be
performed. At synchrotrons and HHG laser sources the number of photons per pulse is
very low compared to those at a free electron laser (at least generally) which is why this
kind of experiments needs to be performed at X-ray free electron laser facilites[270].
Many fundamental properties of matter can be studied with this type of spectroscopy, e.g. magnetization dynamics, reflectivity changes and molecular dissociation
dynamics.
UV/Vis pump-X-ray probe spectroscopy
With an ordinary laser synchronized (with a known time-delay) to the free electron
laser X-rays it is possible to study the development of the core level photo-electron
spectrum. At Flash, the Ge 3d photoemission from a n-doped Ge crystal have been
studied in this manner[271].
Time-resolved pump-probe experiments at the Lcls[272]: N2 molecule studied
with 1.05 keV X-rays (1011 photons/pulse) with a Wiley-McLaren ion time-of-flight
spectrometer. The counting rate was about 3 Hz. Comparing to the 30 Hz repetition
rate of the X-ray source focussed on 3 µm2 and 1013 molecules/cm3 .
Time resolved core level photo-electron spectroscopy (as described also in Ref. [273])
studied of atoms and molecules (in gases, clusters, liquids and solids) combined with
lasers will be an important investigative tool at free electron laser to study how the
chemical state of an atom can change with time depending on how its neigbours are
excited.
Velocity map imaging have been used sucessfully for characterization of the overlap between free electron laser X-rays and 800 nm optical laser – for instance using
hydrogen[274] as the target.
X-ray/X-ray Auto-correlation spectroscopy at the X-Fel have been discussed by
Grübel[275].
10.3. Imaging and Crystallography
175
Sample
Free electron laser beam
Ce:YAG screen
Grating
Figure 10.1: Possible set-up for a single shot Nexafs measurement (adapted from Ref. [277]).
Nexafs
X-ray absorption near an ionization threshold (Nexafs) allow for the mapping of
unoccupied states in a sample – the absorption intensity is recorded as a function
of photon-energy. The absorption may be studied with any decay product from
the excitation, e.g. ions, electrons, photons. A possible way of doing Nexafs in a
single-shot fashion is depicted in Figure 10.1 – a grating acts as a beamsplitter which
continuously disperse the X-ray pulse over a sample, thus the need for sweeping the
photon-energy is eliminated and a single-shot measurement made possible[276, 277].
10.3
Imaging and Crystallography
The high fluence of free electron laser beams allow imaging of micro- and nanoparticles via X-ray scattering on a shot-to-shot basis. A problem that needs to be
circumvented is the radiation damage and subsequent explosion of the particles upon
the multi-ionization – this problem becomes more and more substantial with decreasing particles size. For a 50 femtosecond long pulse the resolution limit have been
176
10. Free electron laser experiments
estimated to 0.2 nm because of the blurring caused by the Coulumb-explosion of the
sample[278].
A demonstration of single nano-sized particle X-ray diffractive imaging have been
performed by Bogan and co-workers[279] where an ærodynamic lens provided nanoparticles from an electrospray source. A part of their set-up is shown in Figure 10.2.
Figure 10.2: A prototypical single particle X-ray diffractive imaging (after Ref. [279]).
There is clearly a strive towards imaging ever smaller objects[280] – and ultimately
single molecules, both in free form and in their natural environment, i.e. in water or
in cells[281]. Recently a virus particle was imaged using overlays of recorded patterns
from single particles – which shows that even if the object explodes because of the
deposited X-ray energy it survives long enough to be imaged[282].
The imaging activities at Flash have recently been reviewed[283], as well as the
specific strives towards coherent diffractive imaging [50]. At the Lcls there is an
endstation dedicated to coherent X-ray imaging[284]: the (CXI) instrument[285]. At
Fermi@Elettra the first operational beamline is intended for coherent scattering experiments.
As free electron laser promise to deliver X-rays of sufficient quality to allow singleparticle/single-molecule imaging and that phase-retrieval algorithms become ever
more sophisticated this area of research attracts a lot of effort. With phase-retrieval
information (lost in the imaging process) this will ultimately allow for single-particle
tomographic measurements of nano-particles, proteins and parts of cells.
Figure 10.3 depicts X-ray scattering through a randomly ordered sample (powder
diffraction). If the beam is incoherent and wide (Debeye-Scherrer scattering) the
scattering angle is proportional to the mean distance between the scattering centers in
the samples. If the beam is small and sufficiently coherent one still obtains information
about the mean distances in the film via the scattering angle – but on the detector
a speckle interference pattern occur instead of diffuse rings. The speckles angular
extent is inversely proportional to the beam width.
By overlaying the X-ray scattering images from two time-delayed pulses Günther
and co-workers have recently demonstrated that sequential imaging with femtosecond
resolution is indeed possible to obtain for nanometer sized objects[286]. This is a
significant step towards time-resolved imaging of objects at the atomic scale.
10.4. Non-linear X-ray science
177
∼ λ/d
d
∼ λ/a
a
Figure 10.3: X-ray diffraction using diffuse and coherent beams.
10.4
Non-linear X-ray science
Photoionization
With very high irradiance levels (towards 1016 W/cm2 ) at 93 eV photon energy, Xe21+
have been observed in ion-time of flight spectra – this corresponds to the absorption
of about 57 photons for that atom (or 5 keV absorbed X-ray energy)[287]. This
amount of energy deposited in a single atom allow the study for many processes of
fundamental nature. With shorter pulses in the attosecond regime (the ”atomic unit
of time” being 24 as) processes may even be possible to study on the same time-scale
as the electron’s travel-time around the nucleus.
Sequential ionization of atomic argon have been studied at the Scss free electron
laser. They find evidence of a sequential electron emission from the absorbing atoms
during the pulse duration[288], access to even shorter pulses would naturally benefit
the study of this kind of physical phenomena.
A summary of the findings on different rare gases is provided in Ref [98]. In this
reference a survey of different possible experimental set-ups is also provided.
Multiphoton ionization of atomic clusters have also been studied in this regard
(see, e.g. Ref. [289]) since this allows for a detailed study of the Coulomb explosion
from the interaction of nano-particles with free electron laser light.
178
10. Free electron laser experiments
TOF
Open multiplier
Diff. pumping
Ions
-
+
±2 cm
Figure 10.4: Focussed free electron laser beam set-up for the study of multi-photon ionization of gases (from
Figure 8.11).
Recently Fang and colleagues have reported on an experiment where double corehole ionization in nitrogen molecules[290] is demonstrated. This type of experiment
give insight in how fast photons are absorbed during the pulse since the single coreionized species have a lifetime in the low femtosecond regime. An experiment involving
X-ray emission following two-photon absorption have also been suggested by Sun and
coworkers[291].
10.4. Non-linear X-ray science
Summary
• Free electron lasers enable the study of atoms and atomic
processes, either via imaging or spectroscopic measurements,
on nanometer and femtosecond scales.
• Current source developments strive to refine the scales to
atomic ones, i.e. Ångströms and attoseconds.
• Naturally an free electron laser experiment should exploit one,
or several of the source’s unique properties vis-à-vis:
–
–
–
–
Coherence
Brilliance
Fluence
Time structure
• The holy grails of free electron laser experiments are:
– Single-shot imaging of single molecules
– Single-shot spectroscopy of single molecules
– Molecular-movies
179
11. Free Electron Laser facilities
In this chapter, free electron laser facilites around the world will be investigated vis-àvis the different technology choices made and how the performance of the facilites have
been affected by those choices. Naturally such an overview will be somewhat limited
and the focus lies on the currently operating facilites and the intended developments
of them – also, only free electron lasers that lase in the VUV- and X-ray regimes are
considered here.
Facility
Flash
Lcls
XFEL
XFEL/SPring-8
Fermi@Elettra
SwissFEL
Pal XFEL
Lcls-II
Flash-II
O
O
C
C
C
D
D
D
D
SC
NC
SC
NC
NC
NC
NC
NC
SC
E
1.2
14
17.5
8
1.7
6
10
14
1.2
εn
<2
1
1.4
0.8
1
0.4
1
1
1-1.5
λmin
4.45
0.12
0.1
0.1
4
0.1
0.1
0.6
4
Rate
8 · 103
120
27 · 103
60
50
100
60
120
10
Pol.
No
No
Yes
No
Yes
Yes
No
Yes
No
Table 11.1: The electron energy is given in GeV and the repetition rate in Hz; the normalized emittance is
given in µm; the minimum wavelength in nm. Information in the table is adapted from the review by McNiel
and Thompson[292].
In Table 11.1 the facilites around the world currently operational (O), under construction (C) and in advanced technical planning and design phases (D) are listed
together with the facilities’ choice on normally conducting technology (NC) or superconducting technology (SC) and some other parameters.
The locations of the facilites around the world are as follows: the Flash and
the European X-Fel[89] are located in Hamburg, Germany; the Lcls free electron
laser uses the SLAC linear accelerator, which can be found in Stanford, USA[293];
the XFEL/SPring-8 is located in the Harima area in Japan[294]; Fermi@Elettra
is in Trieste, Italy; the SwissFEL[49] can be found in Switerland and the Pal XFEL
in Korea[295].
Lcls-II and Flash-II[296] are extensions of those currently operating facilities.
181
182
11. Free Electron Laser facilities
11.1
Operating facilities
11.2
Flash
Flash is situated in Hamburg, Germany (www.flash.de). The facility deliver ultrashort femtosecond coherent radiation in the wavelength range between 47 and 6.8
nm.
With a successful upgrade, wavelengths below 5 nm are expected. Since 2005,
Flash is a user facility serving a large variety of experiments. Typical user operation
parameters during the 2nd user period from Nov 26, 2007 to Aug 16, 2009:
Wavelength range (fundamental)
Average single pulse energy
Pulse duration (FWHM)
Peak power (from av.)
Average power (at 500 pulses/s)
Spectral width (FWHM)
Peak Brilliance
6.8 – 47 nm
10 – 100 µJ
10–400 fs
1 – 5 GW
∼ 15 mW
∼1%
1029 − 1030
Flash is a high-gain Sase free electron laser. The lasing process is initiated by
the spontaneous undulator radiation, and the free electron laser works then in the socalled Self-Amplified Spontaneous Emission (Sase) mode without needing an external
input signal.The electron bunches are produced in a laser-driven photoinjector and
accelerated by a superconducting linear accelerator. The RF-gun based photoinjector
allows the generation of electron bunches with tiny emittances - mandatory for an
efficient SASE process.The superconducting techniques allows to accelerate thousands
of bunches per second, which is not possible with other technologies.
At intermediate energies of 130 and 470 MeV the electron bunches are longitudinally compressed, thereby increasing the peak current from initially 50-80 A to 1-2
kA - as required for the lasing process in the undulator. The 30 m long undulator
consists of permanent NdFeB magnets with a fixed gap of 12 mm, a period length of
27.3 mm and peak magnetic field of 0.47 T. The electrons interact with the undulator
field in such a way, that so called micro bunches are developed. These micro bunches
radiate coherently and produce intense X-ray pulses. Finally, a dipole magnet deflects
the electron beam safely into a dump, while the X-ray radiation propagates to the
experimental hall.
e- -gun
Accelerator
Sase undulator
Figure 11.1: Schematic of the Flash free electron laser facility.
Injector and accelerator
Cs2 Te photocathode inside a 1.3 GHz normally-conducting radiofrequency cavity. 0.5
to 1 nC per pulse at 10 Hz. L-band cavity (1.3 GHz). The pulse trains generated
11.2. Flash
183
can be up to 800 microseconds long and the pulse spacing is usually 1 mikrosecond
(1 MHz). The peak current of the uncompresssed bunch is around 70 A. The bunch
compression occurring during the accleration-stages in two steps up to 2 kA.
The accelerator section consists of 5 TESLA linear accelerator sections (each containing eight superconducting radiofrequency cavities) that can accelerate the electrons to 1.2 GeV.
Undulators
The Flash undulator system consists of six 4.5 meter long permanent magnet undulators having 27.3 mm period with a fixed 12 mm gap. The undulator parameter K
is 1.23 (corresponding to a peak magnetic field of 0.48 T).
Infrared/THz undulator
An electromagnetic long period undulator (400 mm period) placed after the SASEFEL undulator system provides far-infrared pulses that are synchronized to the VUV/soft
X-ray photon pulses – they are emitted from the same electron bunch[297]. The
wavelength can be tuned between 1 and 200 µm (300 THz-1.5 THz). For wavelengths
shorter than 20 µm the pulse energies of 10 µJ can be obtained.
sFlash
Undulator placed before the Sase undulator section of Flash.
Seed
sFlash out
e- -gun
Accelerator
sFlash undulator
Sase undulator
Figure 11.2: Schematic of the sFlash seeding extension to Flash.
Consists of an extra 10 m long variable gap undulator before the current Flash
undulator system. The seed laser system is a HHG setup using an argon gas jet,
the 21st harmonic of a 800 nm Ti:Sa laser is used with a pulse length of 40 fs. The
seeded free electron laser radiation is then transported to a different experimental hall
situated on top of the Flash hall.
Flash-II
Is a proposed extension of the Flash facility in Hamburg, Germany (see page 182).
http://flash.desy.de/flash ii/
Besides the operating FEL undulator at Flash, a second undulator line with a
separate tunnel and experimental hall is envisaged to extend and enhance the capacity
of the Flash facility.
The facility will use a two stage Hghg seeding scheme (see page 18) with variable
gap undulators to ensure shot-to-shot pulse reproducibility with variable femtosecond
duration, gigawatt peak power, and full transverse and longitudinal coherence. A
184
11. Free Electron Laser facilities
seeding option using HHG (High Harmonic Generation) laser generation in gases to
reach short seeding wavelengths is also contained within this project[298].
The new experimental hall will house about six new beamlines with one user
beamline housing photon diagnostics and beam manipulation facilities.
The electron beam from the linear accelerator will be shared between the two
Flash undulator chains with a fast beam switch. The project is currently in the
technical design phase[296, 298].
Seed
e- -gun
sFlash out
sFlash und.
Accelerator
Flash-1 Sase und.
seed
Flash-II undulator
Figure 11.3: Schematic of the Flash-II free electron laser.
Experimental stations:
• PG1 – a monochromatized small focus beamline with a permanent high-resolution
two-stage photon spectrometer for inelastic scattering experiments.
• PG2 – 50 µm focus after a high-resolution plane-grating monochromator.
• BL1 – 100 µm spot after a toroidal mirror.
• BL2 – 25 µm spot after an ellipsoidal mirror.
• BL3 – a beamline without focussing optics.
• THz undulator beamline – provides pulsed, coherent THz pulses that can be
used in combination with the free electron laser radiation from the Sase-undulator.
11.3. Scss – X-fel
11.3
185
Scss – X-fel
Scss
The Spring-8 compact SASE source, Japan[294] is a test-bed for technologies to be
used for the japanese X-fel. It has also been used to do accelerator research, for
instance the first seeding experiments using a HHG laser[299].
e- -gun
Accelerator
Undulators
Figure 11.4: Schematic of the Scss free electron laser test facility.
Injector & accelerator
The electron gun used in the injector is of the thermionic type, based on a singlecrystal CeB6 cathode which provides a beam current of 1 A at the initial beam
energy of 500 keV. In the accelerating structure the peak current becomes 300 A after
bunch-compression with bunch-charges of 0.3 nC. The accelerating structure after
the injector (which contains two S-band accelerating structures) is composed C-band
accelerating structures operating at 35 MV/m – yielding a final beam energy of 250
MeV.
Undulators
Two, in vacuum, 600 period permanent magnet undulators with a minimum gap of
3 mm and a period length of 15 mm. The maximum K is 1.5 and the radiation
wavelength is between 30 and 61 nm.
X-ray free electron laser/ Spring-8
This project was founded in 2006. The construction is scheduled between 2006-2010
and the start of operations is planned to 2011. The aim is to produce coherent
radiation of 1 Ångström wavelength with an 8 GeV electron beam from a normalconducting C-band (5.712 GHz) accelerator.
Injector & accelerator
The electron gun was developed at the SCSS (see above) and is of the thermionic
type. The repetition rate of the accelerator is 60 Hz for macropulses containing 50
sub-pulses. The X-ray pulse frequency is thus 3000 Hz. The peak current is 4 kA
after the acceleration up to 8 GeV (with bunch charges of 0.2 nC). The 128 C-band
accelerators operating around 35 MV/m.
186
11. Free Electron Laser facilities
Undulators
The in vacuum undulators is of hybrid type using permanent magnets and iron yokes.
The gap can be varied between 2 and 40 mm with a nominal operation point at 4 mm
gap (giving K=1.9). The resulting X-ray wavelength range is between 3 and 0.1 nm
in bunches that are 50 fs long. At 1 Ångström wavelength the output power is 0.4
mJ per pulse, the photon flux is estimated to be 2 · 1011 photons per pulse. The peak
brightness is calculated to be in the order of 1033 photons/mm2 /mrad2 /0.1%bw.
11.4
Fermi@Elettra
The Italian X-ray free electron laser is located near Trieste in Italy[300].
Fel-1
e- -gun
”Cern”-type,
”Fermi”-type acc. struct.
Fel-2
Figure 11.5: Schematic of the Fermi@Elettra free electron laser.
Injector & accelerator
The injector is of the photocathode variety with a copper target photoionized by the
3rd harmonic of a Ti:Sa laser. The photocathode is placed in an S-band radiofrequency
accelerating structure (1.6 cells).
Seven ”Cern”-type accelerating structures followed by seven S-band ”Fermi” structures provide the acceleration up to 1.5 GeV. The repetition rate is 50 Hz.
After the accelerator the electron beam can be steered either into the first or the
second undulator arrays.
Undulators
Following the linear accelerator part of the facility, there is a switch for the electron
beam – allowing the alternate usage of two different free electron laser undulator
systems; the first of which have been installed and the second one is to follow.
Fel-1
The first undulator system is a seeded Hghg cascade utilizing a tunable seed laser in
the wavelength range 240-360 nm.
The first undulator, referred to as the modulator where the microbunching density modulation occurs is a 160 mm period 3.04 m long planar permanent magnet
undulator with an undulator strength between K=3.9 to 4.9. This provided the basic
wavelength that is to be up-converted in the radiator undulator system.
Between the modulator and the second undulator system there is a 1 meter long
beam transport section (which is a small chicane). The radiator undulator system
consists of four Apple-type variable polarization undulators – tuned to a harmonic
n of the modulator wavelength (thus optimized for λ/n). They have a undulator
11.4. Fermi@Elettra
187
period of 65 mm installed in four 2.34 meter long segments separated by 1.06 meter
long transport sections, yielding a total length of the radiator system of 12.48 meters.
Their undulator strengths are between 2.4 and 4.
Including transport sections, the total length of the Fel-1 system is thus 16.5
meters. This part of the free electron laser facility provides radiation in the range
between 20 and 100 nm (see Table 11.2).
Fel-2
The second free electron laser of the Fermi will be built after the first one is completed. It is intended to be a cascaded double HGHG scheme (using two modulators
and two radiators). This scheme is flexible enough to also allow HHG seeding and
Echo-enabled harmonic generation in the future. By using Apple-II undulators the
polarization can be controlled and tuned in a range around 10% of the energy defined
by the beam energy[301].
Parameter
Wavelength range (fundamental)
Photon energy
Pulse duration (FWHM)
Repetition rate
Peak power (from av.)
Spectral width (FWHM)
Photons per pulse
Peak Brilliance
Fel-1
20 – 100 nm
62 – 12 eV
20 – 40 fs
10-50 Hz
1 – 5 GW
∼ 20 − 40 meV
2 · 1014 at 100 nm
1029 − 1030
Fel-2
3-20 nm
413–62 eV
< 100 fs
10-50 Hz
1 GW
∼ 20 − 40 meV
1013 at 10 nm
Table 11.2: Photon output parameters for Fermi@Elettra. Taken from the laboratory homepage.
Experiments:
• DIPROI – Diffraction and projection imaging
• LDM – Low density matter
• EIS – Elastic and inelastic scattering.
188
11. Free Electron Laser facilities
11.5
Lcls – Linac Coherent Light Source
The Lcls was designed to become the world’s first hard X-ray free electron laser with
the fundamental wavelength lying between 0.55 and 10 keV[96, 293, 302]. The facility
is located at the SLAC national accelerator laboratory in Menlo Park, California, USA
and went into operation during the year 2009 (Lcls homepage).
e- -gun
Accelerator
Undulator
Figure 11.6: Schematic of the Lcls free electron laser.
Injector and accelerator
The Lcls free electron laser is currently utilizing the last kilometre of the SLAC linear
electron accelerator (which is 3 km long in total). The SLAC accelerator use S-band
radiofrequency-fields (2,856 MHz) in copper cavities and can accelerate electrons up
to 50 GeV - if the whole three kilometers available is used. As the LCLS uses only
one kilometer electron energies of 3.5 to 15 GeV can be delivered to the undulators.
A photocathode radiofrequency electron gun serves as injector; the gun consists
of a copper target that is photoionized by a frequency trippled Ti:Sapphire system.
This can operate up to 120 Hz with bunch charges of 0.25 nC (with a peak current of
35 A). With bunch compression during the acceleration the peak current is amplified
up to 3.5 kA.
Undulators
The undulator section of Lcls is 132 m long in total and consists of thirty-three 3.4
m long planar permanent magnet undulators - separated by short and long transport
sections. The undulator period is 30 mm with a fixed gap of 6.8 mm. The undulator
parameter K is 3.5 (corresponding to a magnetic field of 1.25 T at the mentioned
gap).
Lcls-II proposal
Proposed extension of the Linac Coherent Light Source in Stanford, California, USA
[303] (see page 188). This proposal considers the use of the 2nd km (of 3 km in total,
the first kilometer remains untouched) of the SLAC linear accelerator. By adding
a second electron gun and injector 1 km upstream from the Lcls injector the mid
kilometer of the accelerator could be used to operate a soft X-ray free electron laser in
parallel to the existing Lcls if the electron bunches are made to travel in a bypass
line running side by side to the last kilometer (used for the acceleration of the electron
11.5. Lcls – Linac Coherent Light Source
189
bunches for the other free electron laser). Besides extending the photon-energy range
of the facility this would also allow simultaneous operation of two free electron laser in
parallel which would increase the number of users significantly.
e- -gun
Bypass
Undulators
Accelerator
Figure 11.7: Schematic of the Lcls-II proposal. The grey area marks the existing Lcls facility.
Upgrade of the existing facility
An upgrade of the current Lcls is considered to allow a larger gap (and thus higher
energies). A second harmonic afterburner optimizing the bunching at 0.62 Å wavelength will be added in 2010 to produce half the fundamental wavelength efficiently.
This will be achieved by increasing the gap of the last 8-10 undulators to give them
a K of 2.26 (as opposed to 3.5 for the 23-25 undulators).
The soft X-ray undulators
With two undulators, each 36 m long having 6-60 Å wavelength range through variable
gap, a number of possible opportunities are given: self-seeding by placing a grating
between the undulators, Eehg-seeding, etc. It is also possible to control the polarization of the light by adding Apple-II type undulators at the end of each undulator
that would offer variable polarization.
Since the accelerator for the soft X-ray free electron laser operate in the 3-7 GeV
range, the repetition rate can be increased to 320 Hz.
Experiments:
• AMO – Atomic, molecular and optical science.
• CXI – Coherent X-ray imaging.
• MEC – Matter in extreme conditions.
• SXR – Soft X-ray materials science.
• XCS – X-ray correlation spectroscopy.
• XPP – X-ray pump probe.
190
11. Free Electron Laser facilities
11.6
Facilities under construction
11.7
The European Xfel
[304] http://www.xfel.eu/
The European Xfel will be 3.4 km long, starting at the DESY-Bahrenfeld site in
Hamburg, Germany and the research campus will be situated south of the town of
Schenefeld. The start of operations is planned to be in 2014.
Injector and accelerator
The injector is of the radio-frequency accelerated photocathode variety with a Cs2 Te
target (very similar to the one used at Flash presented above). Both the injector and
the linear accelerator consists of superconducting L-band (1.3 GHz) Tesla cavities
that will operate at 23.6 MV/m. The repetition rate between macropulses is 10 Hz,
each such pulse can house 3000 pulses.
In total the accelerator will be 1.6 km long with 116 accelerator modules, each 12
m long. The peak current is projected to be 5 kA with a bunch charge of 1 nC. The
maximum beam energy attainable is 20 GeV, but normal operation will be at 17.5
Gev electron energy.
Undulators
Sase
2
U1
Sase 1
U2
e- dump
Sase
3
Figure 11.8: The electron beam distribution between different undulators in the European Xfel.
To accommodate the different demands from the experimental side – and to provide
maximum flexibility for future upgrades – the 17.5 GeV electron beam can be sent
along two different paths (Figure 11.8) servicing five different undulators.
Sase 1 is a planar permanent magnet undulator optimized to deliver 12.4 keV
hard X-rays (λ = 0.1 nm) – the magnetic period is 35.6 and the gap is 10 mm (giving
K=3.3). The total undulator length is 201.3 m.
Sase 2 provides tunable hard X-rays between 3.1 and 12.4 keV. It is a planar permanent magnet undulator that thus provides linearly polarized light. This undulator
11.7. The European Xfel
191
have a magnet period of 47.9 mm with a gap adjustable between 19 and 10 mm (K
between 2.8 and 6.1). The total length is 256.2 m.
Sase 3 is an Apple II device which can deliver circularly or linearly polarized light
in the range between 0.8-3.1 keV. If the accelerator is operated at 10 GeV electron
energy the range becomes 0.25-1.0 keV. The undulator’s period is 80 mm with gaps
between 23 and 10 mm. The total length is 128.1 m.
U 1 & U 2 provides spontaneous synchrotron radiation in the range between
20-100 keV by utilizing the ”spent” electron beam after the Sase 2 undulator. The
length is 61 m each.
To attain the accuracy and maintainability of such a large undulator system the
undulators are built up from 5 m long magnet arrays intersected by 1.1 m long
transport sections.
Ee−
λ
EPhot.
Ppeak
P̃
Phot./pulse
Flux
Peak brill.
Aver. brill.
Sase 1
17.5
0.1
12.4
20
65
1012
3.0 · 1016
5.0 · 1033
1.6 · 1025
Sase 2
17.5
0.1-0.4
12.4-3.1
20-80
65-260
0.1 − 1.6 · 1013
0.3 − 4.8 · 1017
0.5 − 2.2 · 1033
0.16 − 6.5 · 1034
Sase 3
17.5
0.4-1.6
3.1-0.8
80-130
260-420
0.16 − 1.0 · 1013
0.48 − 4.8 · 1017
0.22 − 2.3 · 1033
0.65 − 5.9 · 1024
10
4.9
0.25
150
490
3.7 · 1014
1.1 · 1019
1.0 · 1032
2.8 · 1023
Unit
GeV
nm
keV
GW
W
#
#/s
a)
a)
Table 11.3: Radiation parameters of the three free electron laser undulators at the European Xfel – from
simulations[89]. a)brilliance is given in the unit photon/0.1% bw/s/mm2 /mrad2 . The pulse duration is 100 fs
overall.
Experiments:
• FXE Femtosecond X-ray Experiments
• HED High-Energy Density matter experiments
• SPB Single Particles, Clusters & Biomolecules
• MID Materials Imaging and Dynamics
• SQS Small Quantum Systems
• SCS Spectroscopy & Coherent Scattering
192
11. Free Electron Laser facilities
11.8
SwissFEL
SwissFEL injector test facility
Currently in operation at the Paul Scherrer Institut (PSI) in Switerland is the injector
test bed[305] for the proposed SwissFEL. The intent with this facility is to develop the
electron gun and injector technology sufficiently to achieve low enough emittance for
free electron laser operation. An important parameter for the intended free electron
laser is that it will have two pulses per macrobunch with a defined delay between the
(i.e. minimal jitter) subpulses – this to allow very precise X-ray pump- X-ray probe
experiments – something which also is being developed at the PSI.
A photocathode electron gun enclosed in a radiofrequency S-band accelerating
module provides the electron bunches for the linear accelerator, at the cathode (depending on long or short pulse mode) it delivers 22 or 3 A at the cathode. The accelerator structure is based on four normally conducting S-band acceleration modules
(operating at 20 MV/m) followed by a fourth harmonic X-band cavity (which decelerates the electrons somewhat to attain a better bunch compression, giving shorter
pulses). The repetition rate of the source is 100 Hz and the beam energy is 250 MeV.
the SwissFEL proposal
Seed
d’Artagnan
Athos
e- gun
Accelerator sections
Aramis
Undulators
Figure 11.9: Schematic of the proposed SwissFEL.
The time-schedule on the project’s homepage indicates that the planned start of
operations is targeted towards in 2016. This seeded free electron laser is envisioned to
deliver transform-limited pulses in the soft X-ray range. The highest electron beam
energy at the entrance of the hard X-ray undulator section is 5.8 GeV. To facilitate
experiments examining temporal processes the macropulse duration range between
6 and 30 femtoseconds with 50 ns separation between two subpulses. To achieve
short pulses the bunch charge is kept between 10 and 200 pC. For the soft X-rays
(less than 1.6 keV) circular polarization can be employed (for instance for magnetism
measurements).
Injector & accelerator
The photocathode injector uses a S-band and X-band acceleration before the first
bunch-compression, about 24 meters long. This is followed by three C-band accelerating linear acceleration sections, in total 208 meters long. The C-band parts were
11.8. SwissFEL
193
Wavelength range
Rep. Rate
Pulse duration (FWHM)
Peak power
Peak Brilliance
7-0.1 nm
100 Hz (of 2 sub-pulses, 50 ns separation)
30 or 6 fs (high/low charge mode)
10 GW
1-10·1032
Table 11.4: Main parameters of the SwissFEL.
chosen over the S-band (used for the test facility) as they preserve the emittance
better (provided a good alignment)[306], the power consumption is lower and the
number of RF stations fewer[307]. For the soft-X-ray section only two are used before
the electron beam enter the undulator system, giving a final electron beam energy
of 2.1 or 3.4 GeV – the electron beam is accelerated to 5.8 GeV in the last section,
exclusively serving the hard X-ray undulator system. The total length of the whole
free electron laser is 715 meters. Two pulse modes are envisioned with 13 or 2.1 fs.
Undulators
The details on the undulators is from a presentation given by T. Garvey at the 32nd
free electron laser conference[307].
• Aramis – an in-vacuum planar undulator system with variable gap to produce
Sase free electron laser radiation in the 0.1 to 70 nm range. The undulator
period is 15 mm (with a gap larger than 4 mm and K=1.2) and the total length
is 60 meters in 4 meter sections.
• Athos – the undulator system is built up from 40 mm period Apple-II type
undulators with a fixed 6.5 mm gap and full polarization control. Intended
for both Sase and seeded free electron laser operation in the wavelength range
between 0.7 and 7 nm.
• d’Artagnan – intended for use as the radiator in a HHG seeded HGHG cascade
together with the Athos undulator as radiator. This extends the energy range
of this part of the SwissFEL to longer wavelengths.
Experiments
The scientific program at the SwissFEL is focussed towards the study of ultra-fast
phenomena at the nanoscale. The double pulse structure and the strive to create very
short pulses is a testament to this goal.
According to the science case for the Swissfel the scientific program will focus
upon five areas:
1. Ultrafast magnetization dynamics at the nanoscale.
2. Catalysis and solution chemistry, i.e. the lifetime and structure of short-lived
intermediate states on surfaces or in solution.
3. Coherent diffraction of nanostructures – lens-less imaging can provide atomic
resolution of biological and inorganic nanostructures.
194
11. Free Electron Laser facilities
4. Ultrafast biochemistry
5. Time-resolved spectroscopies of correlated electron materials.
11.9
Proposed facilities
Besides the proposed extensions of currently existing facilites (as the Flash-II, LclsII, SwissFEL) and projects under construction as the European and the Spring-8
X-fels included here the Korean X-fel project.
11.10
PAL-X-fel
The X-fel at the Poohang accelerator laboratory in Korea is currently in the technical design phase[308]. Here we will consider the design assuming a 10 GeV linear
accelerator. Shorter more compact designs using 3.7 GeV linear accelerators envisioning the use of only the third harmonic for free electron laser radiation have been
considered.
Accelerator
The accelerator section consists of three S-band sections (4, 28 and 96 three meter
long radiofrequency accelerating structures) and one short (0.6 m) X-band section –
the total length of the S-band section is 550 m. The accelerating gradients in the
S-band structures is 27 MV/m. Simulations of both 1 nC and and 0.2 nC charges
have been done. With 1 nC the radiated output power is 6 GW, 0.2 nC gives about
2 GW.
Undulators
The undulator considered is a 94 m long (or around 100 m) in vacuum undulator with
a period of 2.23 cm and undulator parameter K=2.22.
As this facility is in the technical design stage no information on the intended
experimental program is available in the time of writing.
11.10. PAL-X-fel
Summary
• The currently two operating soft and hard X-ray free electron laser are Flash, Hamburg, Germany and Lcls, Stanford,
USA.
• Facilities currently being built is the Fermi@Elettra, Trieste,
Italy; the european and the japanese X-fels.
• Among facilities in detailed technical design phase are the
SwissFel in Switzerland and the PAL-X-fel in Korea.
• In contrast to the other facilities the Flash free electron
laser have less permanent in house experiments (encouraging
users to bring their own set-ups).
• Both Flash and the Lcls are currently specifying upgrades
to the facilites. Flash have a seeding experiment already.
Both are considering additions to the current accelerator layout that would increase the number of experimental sections.
Notably both facilites, currently producing Sase free electron
laser radiation – aims to install seeded HGHG or EEHG cascades.
• Most facilites are trying to (or at least have the option to) run
with lower bunch charges as to shorten the pulses.
• The overall length of the newer facilites is shorter, owing to
advances made in technology to reduce the emittance of the
electron beam.
195
12. Outlook & Conclusions
12.1
Current trends
More compact sources and alternative approaches
A significant effort is currently being undertaken to find technology that reduce the
normalized emittance of the electron beam and the length of the undulators – both
factors that severely impacts the overall length and cost of a free electron laser.
The radiofrequency systems driving the cavities of the linear accelerators are also
important cost drivers.
The European X-fel and the Lcls is 3.4 km and 3 km long respectively. They use
L-band and S-band accelerator technology respectively together with photocathode
electron guns. In contrast the X-fel at Spring-8 will use C-band accelerators (with
frequencies four times that of L-band and twice that of S-band) and a thermionic gun
– both contributing to the significantly shorter accelerator part of the facility of 750
m. Also contributing to this is the in vacuum undulators with small gaps that allow
the undulator period to be shortened[309] – similar undulators are considered for the
SwissFel.
The incentives are thus many to make more compact X-ray sources, not only
motivated by cost reduction but also scientifically[310], one such source would be the
plasma wake-field accelerators[311]. In such a device electrons are accelerated in a
bubble created in a plasma by a strong laser propagating through a medium (often
a gas). A plasma wake-field accelerator can be used together with an undulator to
create spontaneous X-ray radiation[312]. A question yet to be answered is if the
electron beam in the plasma wake-field can be made with high enough quality to and
if collective effects like microbunching can occur to allow free electron lasing. The
repetition rate of the driving lasers is currently slow, in the order of 10’s of Hz.
XFELO (X-ray free electron laser oscillator) and the regenerative free electron
laser amplifier are suggested low gain amplification systems, both use cavity feedback
to achieve lasing with cavities made from highly reflecting diamond mirrors that work
in the X-ray range. Unlike the single-pass high-gain systems described in this book
both the XFELO and the regenerative FEL amplifiers demand high repetition rate
electron guns – otherwise the electronbunches do not arrive in time to meet the pulse
in the cavity.
197
198
12. Outlook & Conclusions
Higher repetition rates
Normally conducting accelerator technology limits the repetition rate to about 100
Hz, e.g. at the Lcls. Currently Flash and, in the near future, the European X-Fel
operate with photon pulses that have MHz substructures.
Achieving high average brilliance is an active area of pursuit – as it opens up
new fields of research and allows for serving many user experiments in parallel or in
series (at reduced intensity or repetition rate respectively). The technology (superconducting accelerator sections? electron guns, etc.) for driving a X-ray free electron
laser with MHz frequency exist in principle with the cost being the biggest obstacle.
With other components of the free electron laser becoming shorter and more efficient
this deterring factor may be less strong in the future. Generic concepts for what
would be the necessary components in a free electron laser facility achieving MHz
repetition rates have been studied by J. Corlett and co-workers[313].
Polarization control
We fleetingly touched upon the subject of polarizations different from the linear inplane variety produced by planar undulators with a vertical magnetic field in chapter
3 when different types of undulators were discussed.
Typically the first generation free electron laser in the VUV and X-ray ranges
utilize the aforementioned planar undulators with vertical magnetic fields to generate
the photon beam generating linearly polarized light. Many experiments, for instance
those concerning spin properties and dynamics of materials, e.g. magnetic properties
and magnetization/de-magnetization processes, require circularly (helically) polarized
light for their inquiry.
On paper there it is not harder to produce helical light than linearly polarized, in
practice helical undulators involve more moving parts and are thus more intricate to
build and utilize. This is probably the main reason why the first generation of X-ray
free electron laser have chosen to operate with planar undulators – as seen earlier the
error tolerances for the undulator systems are tight without the complexity of, e.g. an
Apple type undulator.
Above roughtly 2 keV photon energies it is possible to produce befringement transparent materials that convert linearly polarized X-rays to helical polarizations given
that the thickness and orientation of the crystals conspire to do so (e.g. diamond
crystals with the proper thickness will do this). In many cases this will be a true
one-shot experiment which destroys the crystal – the cost is though microscopical
compared to installing a new undulator section in a free electron laser.
In the soft X-ray regime it is however necessary to use an undulator to create
helical polarization, among other things the absorbance for soft X-rays in materials
is too high for experiments to be efficiently executed.
Besides the Apple type of undulators described earlier, two planar undulators with
the undulator planes rotated with respect to each other can be used to produce tilted
linear and helical polarizations. The configuration drawn in the top of Figure 12.1
will create tilted linearly polarized light if the undulators are placed at a distance
that cause them to emit in phase. If, on the other hand, a magnetic chicane section is
installed between the undulators the delay between the exit of the electron bunch from
the first and entrance of the second undulator can be varied with the magnetic field
strength (as the path becomes longer for stronger magnetic fields since the deviation
12.1. Current trends
199
becomes larger). The introduced delay case a phase-shift of the emitted photons which
give rise to a (tunable) polarization change from linear to fully circular polarized light.
Chicane
Figure 12.1: Planar undulators with the plane shifted (here 90◦ ) can produce light with tilted linear polarization
when they emit in phase – or circular polarization if the phase can be shifted with a delay introduced with a
chicane section between the undulators.
It is not necessary for the whole undulator array of the free electron laser to be
composed of helical undulators. An electron bunch which is microbunched in a planar
undulator emit coherently in a helical undulator as well if the undulators are tuned
to the same wavelength. Considerable effort can thus be saved in constructing an
undulator array that can produce all kinds of polarization of the light. Most upgrades
to currently operating facilities and new facilities have this capacity included in one
way or another since the experiments enabled are numerous and studies phenomena
of general scientific interest.
Coherence & Seeding
Throughout this book we have noted that neither longitudinal, nor transverse coherence of a free electron laser is perfect. This is reflected in the spectral bandwidth,
which is inversely proportional to the number of undulator periods. We may improve
upon this number with a monochromator before the experiment, trading intensity for
higher monochromaticity.
Different up-shifting schemes involving traditional lasers and HHG lasers, e.g. Hghg,
Eehg and other seeding schemes are an integral part of most new free electron
laser projects – notably the Fermi@Elettra, the next free electron laser to come
on-line. A significant improvement upon the coherence properties of the free electron
laser radiation can be expected from this, especially if the seed power dominates the
initial Sase power. Currently, the limit of effective seeding using an HHG laser source
is around 10 nm – mainly set by the power of the driving lasers. Up-shifting schemes
therefore often use ordinary lasers because of their higher repetition rate, which will
be needed for many new free electron laser facilites operating in the kHz/MHz regions.
At the Lcls a self-seeding option is included in the upgrade proposal, which will use
the generated radiation to seed the Sase process in the following undulator sections
– something which potentially overcomes the limits imposed on external laser seeding
schemes vis-à-vis wavelength and repetition rate.
200
12. Outlook & Conclusions
The use of low bunch charges reduce the emittance of the beam and increases the
probability of only one Sase mode radiating efficiently (which improves the pulse
length).
Harder X-rays
It is problematic to reduce the photon-wavelength further than 1 Å while maintaining
free electron laser amplification efficiently – the main limits being electron beam
emittance and for very hard X-rays the recoil upon photon emission smears out the
microbunching (having an extremely short period as is at those wavelengths). At the
Lcls a significant portion of the density modulation of the electron beam is present
at half of the fundamental wavelength, giving access to sub-Å wavelengths when the
first undulator section is followed by undulators that have the second harmonic of
the radiation as fundamental wavelength. The expected power at 16 keV is about
10% of that found in the 8 keV fundamental[302]. A proposal for a free electron
laser producing 50 keV X-rays is actively worked upon[314].
γ-rays and the quantum free electron laser
The concept of the quantum free electron laser (QFEL) have been introduced by
R. Bonifacio and others (see [315] and references therein). We may check when
the photon’s momentum becomes comparable to the electron momentum spread in
the beam using the Pierce parameter ρ (see chapter 2). Classically, the momentum
spread in the electron beam is mcγr ρ. The photon’s momentum is proportional to
the wavenumber k with ~ as the proportionality constant.
Letting the ratio between the two momenta define the ”quantum FEL parameter”
as:
mcγr
ρ̄ = ρ
~k
in the soft X-ray regime the wavenumber of the photons is small compared to the
momentum spread in the electron beam, for a normal Sase-free electron laser this
means that ρ̄ ≫ 1. For very high momenta the photon momentum will have comparable magnitude to the electron momenta. In this limit we must take into account
that the momentum recoil can only assume discrete values (i.e. multiples of ~k). If
nothing is done to synchronize the photon emission the recoils will occur randomly
and widen the momentum distribution in the beam with loss of the microbunching.
For an electron beam with small enough energy spread, the quantum free electron
laser operate by colliding this electron beam with a counterpropagating laser beam
having very high power1 . The laser beam (which can be operated at µm wavlengths)
then effectively acts as an undulator with extremely short period. If one is in the
regime where ρ̄ ≤ 1 all electrons experience the same recoil losing ~k. The radiation
from this process is temporally coherent up into γ-ray energies.
Experiments with this type of radiation may extend the applicability of free electron laser (in a broad sense) into the sub-atomic regimes with the study of processes
involving, e.g. nuclear transitions.
A X-ray free-proton laser have been suggested as a way to overcome the ”quantum
momentum limitation” of the Sase process, this by using protons rather than electrons
1
For the so inclined, the process is that of collective Compton backscattering.
12.2. Conclusion
in the particle beam – although feasible, it would require a huge scale facility such
as the LHC as a driver[316]. As noted in the reference though, this may be tested
as a parasitic undertaking at the storage ring, much as synchrotron radiation studies
started out in the late 1940’s.
12.2
Conclusion
Free electron laser operating in the VUV and X-ray ranges offer scientists a light
source with unique spectral properties. The success of Flash and Lcls and the
pioneering experiments carried out there mark the potential for a broad and deep
endeavor to investigate nature in ways hitherto not possible with X-rays using that
degree of precision: nanometers and femtoseconds with developments pushing those
limits towards Ångströms and attoseconds – the true atomic scales of space and time.
With the advent of successful improvements of the spectral characteristics of the
Sase experimental work and interpretation of data will become easier and facilitate
the utilization of this type of source for a broader user community.
As the first generation of X-ray free electron laser is augmented, upgraded and the
second generation of facilities are brought on-line in the future the number of possible
experiments will surely increase as well as the intricacy of the investigations.
201
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227
This compendium serves both as a summary of the reports
generated by the IRUVX expert group on optics and photon
diagnostics and as an introduction to Free Electron Lasers,
their function and the some of the necessary technologies
to make them work. The ambition has been to encompass the subject of Free
Electron Laser technology in an introductory manner (part I),
which supports the rather deep excursion into photon diagnostic
methods that follows (part II). The list of references is extensive
and could be used for the so inclined for more in depth studies.
Members of the IRUVX-PP workpackages 3 & 7:
Rafael Abela, Marion Bowler, Roberto Cimino, Daniele Cocco,
Anthony Gleeson, Henrik Enquist, Uwe Flechsig, Ulf Fini Jastrow,
Pavle Juranic, Barbara Keitel, Jörgen Larsson, Bernd Löchel,
Paul Morin, Paul Radcliff, Mark Roper, Svante Svensson, Frank
Siewert, Ryszard Sobierajski, Kai Tiedtke, Marco Zangrando
This work is supported by „IRUVX-PP“ an EU co-funded project
under FP7 (Grant Agreement 211285).
www.eurofel.eu