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Coherent Betatron Radiation from Laser-Wakefield
Accelerated Bunches of Monoenergetic Electrons
S.P.D. Mangles1, S. Kneip1, C. McGuffey2, S. S. Bulanov2, V. Chvykov2, F. Dollar2, Y. Horovitz2, C.
Huntington2, G. Kalintchenko2, A. Maksimchuk2, T. Matsuoka2, C. Palmer1, K. Ta Phuoc3, P. Rousseau2, V.
Yanovsky2, and K. Krushelnick2, Z. Najmudin2
2
1
The Blackett Laboratory, Imperial College London SW7 2AZ, UK
FOCUS Center and Center for Ultrafast Optical Science, University of Michigan, Ann Arbor, Michigan 48109
3
Laboratoire d’Optique Applique, ENSTA, Ecole Polytechnique, 91761 Palaiseau, France
Abstract: X-rays generated by 0.1 – 0.5 GeV electron beams generated using a 100 TW laser are shown to
have a low emittance, be spatially coherent and have a peak brightness comparable to 3rd generation
synchrotron sources.
1. Introduction
Multi-keV betatron radiation produced by mono-energetic bunches of electrons ranging from 0.1 to 0.5 GeV has been studied
using the 100 TW Hercules laser at the Center for Ultrashort Optical Science in Michigan, USA. Single-shot characterization of
the x-ray beam yields source sizes smaller than 5 !m and divergences smaller than 10 mrad, corresponding to an x-ray emittance
comparable to 3rd generation conventional light sources. The peak brightness of the x-ray beam is also found to be comparable to
3rd generation conventional light sources and more than three orders of magnitude brighter than previous studies of a laser driven
plasma wiggler [1,2]. Measurements based on Fresnel diffraction from a knife-edge show, for the first time, that this source can
be spatially coherent. This opens up the possibility of using laser-produced betatron sources for many applications such as lensless imaging of non-crystalline specimens, that currently require conventional synchrotron sources.
The ponderomotive force of a laser, that propagates through underdense plasma displaces electrons from regions of high laser
intensity and can set up a plasma wave. Plasma waves are ideally suited to accelerate electrons producing narrow energy-spread,
low-divergence beams. The production of quasi-monoenergetic electron beams with such a laser wakefield accelerator has first
been demonstrated in 2004 [3]. Since then, the stability of the electron beams has been improved [4] and peak energies have been
scaled to the GeV level [5-6]. GeV electron beams are integral to conventional radiation sources and laser-driven beams hold the
promise to make novel light sources more compact and economical.
Electrons that are injected into the plasma bubble off-axis or with a transverse momentum, will, during their acceleration,
undergo transverse oscillations due to the radial electrostatic fields present in the plasma structure. These oscillations are termed
betatron oscillations, and the physical mechanism is similar to electrons oscillating in a conventional wiggler or undulator type
magnetic insertion device, as found on synchrotron facilities [1-2]. Depending on the plasma parameters (electron density ne) and
electron parameters (electron energy ! and oscillation amplitude r" ) the betatron radiation can be spectrally narrow or a broad
synchrotron spectrum, of small source size, divergence and high peak brightness in the several keV range.
Here we present the first measurements of betatron x-rays from monoenergetic bunches of electrons, yielding unprecedented
small source size and divergence, spatial coherence and peak brilliance comparable to 3rd generation conventional light sources.
2. Experiment
The experiments where carried out at peak power of 100 TW on the Hercules laser facility [7] at the Center for Ultrafast Optical
Science of the University of Michigan. Laser pulses with energy of 3 Joules, pulse duration of 30 fs and central wavelength of
800 nm were focused on the front edge of supersonic gas jet nozzles with length ranging from 3 to 10 mm. The laser was focused
with an f/10 off-axis parabolic mirror assisted by a deformable mirror to a diffraction limited spot size of 8 µm at full width half
maximum, yielding a peak intensity of 7 x 1019 Wcm-2, corresponding to an a0 of 12.
Electron beams with mono and poly energetic features where observed at a range of densities depending on nozzle length,
with maximum electron energies in excess of 400 MeV. A sample electron image is displayed in fig. 1.
Fig. 1. Typical electron spectrum, electron energy in MeV, beam divergence in mrad
The betatron x-rays from mono-energetic electron beams were characterized on the laser axis using an x-ray ccd camera 150
cm away from the interaction region after electrons had been deflected by a magnet,. In order to fully characterize the x-ray beam
properties, measurements of the source size, the beam profile and the spectral brightness where conducted. To get an upper limit
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for the x-ray source size, microscopic objects were back-lighted. The smallest object that could be resolved was a 5 µm diameter
wire, which requires the x-ray source to be smaller than that. Fig. 2 (left) shows a radiograph image of a thin wire object with
wires of diameter 20, 50 and 100 µm.
Fig. 2 (middle) depicts a sample image of an x-ray beam profile, with a wire grid imprint. The wire grid is made from silver
with a wire diameter of 60 µm and a gap size of 250 µm. The simultaneous measurement of the electron beam energy and x-ray
beam divergence reveals a magnetic deflection parameter K between 2 and 5. For K >> 1, the radiation source is termed wiggler
and produces a broad synchrotron spectrum. For K < 1, the source is termed undulator and the spectral distribution is narrow.
The x-ray spectrum was determined by measuring the x-ray transmission through a set metal foil filters of various material
and thickness, using an x-ray ccd. Fig. 2 (right) shows such a data sample. Knowing the filter attenuation and camera sensitivity,
the x-ray sectrum and brightness can be recovered. It was found that the Hercules 100 TW betatron x-rays are best approximated
by a 10 keV synchrotron spectrum, a broad spectrum as predicted by the K-parameter > 1. The peak spectral brightness is found
to be 1022 photons/mm2/mrad2/second/0.1% bandwidth, which is more than 3 orders of magnitude brighter than previous studies
from a laser-driven plasma wiggler [1-2]. The peak brightness is comparable to currently existing, 3rd generation conventional
light sources.
Fig. 2. (left) measurement of the x-ray beam profile, (middle) x-ray radiograph of a microscopic wire object, (right) x-ray transmission through a
filter pack of different thickness metal foil filters coupled to an x-ray ccd camera
Single edge diffraction from a ‘knife-edge’ is commonly used to determine the size of x-ray sources [2]. To accurately
measure small betatron sources, a cleaved crystal was used as the knife-edge. A cleaved crystal can be regarded a much better
step function as it is of uniform thickness unlike any tapered knife-edge. Data recorded using this technique indicates betatron
source sizes smaller than 3 µm. To the knowledge of the authors, this is the smallest betatron source size measured to date.
Some shots show multiple oscillations in the lineout, which can be understood within the framework of fresnel single edge
diffraction and require a certain level of spatial coherence from the x-rays [8]. This represents the first measurement that shows
that betatron x-rays from a laser driven miniature wiggler can be spatially coherent.
3. Conclusions
We have presented the first measurements of betatron radiation from mono-energetic bunches of electrons. The betatron radiation
has been fully characterized. The x-ray source size is found to be below 3 µm, which represents the smallest betatron source
measured to date. The x-ray beam divergence can be smaller than 10 mrad and the betatron spectrum is found to be best
approximated by a 10 keV broad synchrotron spectrum, with a peak brightness of 1022 photons/mm2/mrad2/second/0.1%
bandwidth, comparable to currently existing 3rd generation conventional light sources. For the first time, it is shown that betatron
x-rays can be spatially coherent. This opens up the possibility of using laser-produced betatron sources for many applications
such as lens-less imaging of non-crystalline specimens, that currently require conventional synchrotron sources.
[1] A. Rousse, et al., Phys. Rev. Lett. 93, 135005 (2005).
[2] S. Kneip, et al., Phys. Rev. Lett. 100, 105006 (2008).
[3] S.P.D. Mangles et al., Nature (London) 431, 535 (2004); C.G.R. Geddes et al., ibid, 431, 538 (2004); J. Faure et al., ibid. 431, 541 (2004);
[4] J. Faure, et al., Nature 444, 737 (2006).
[5] W.P. Leemans, et al., Nature Phys. 2, 696 (2006).
[6] S. Kneip, et al., , Bull. Am. Phys. Soc. 53, No.14, p.125 (2008)..
[7] V. Yanovsky, et. al., Optics Express 16, 2109 (2008).
[8] M. Born, E. Wolf, Principles of Optics, 6th edition, Pergamon, Oxford (1980)
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