Download Historical Survey of FELs

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Historical survey of Free
Electron Lasers
M. E. Couprie
Synchrotron SOLEIL
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
Introduction
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Free Electron Laser
Free Electron Laser:
«simple and elegant gain medium» : an electron beam in a magnetic field
- broad wavelength tunability (vibration frequency can be adjusted by changing
the magnetic field or the speed of the electrons)
- excellent optical beam quality
- high power
free electrons
bound electrons in atoms and molecules : vibrate at specific frequencies
Synchrotron radiation
Vacuum tubes
Lasers
Free Electron Laser
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
I. The origins of the Free Electron Laser
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même phase
undulatory properties, was not considered at that time.
même phase
même polarisation
même
polarisation
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June,
2016
jeudi 2 juin 2016
I. The origins of the Free Electron Laser
www.lunex5.com
1.3 The early times of synchrotron radiation
Josepf Larmor
(1857-1942)
Alfred-Marie Liénard
(1869-1958)
J. Larmor, On the Theory
of the Magnetic
Influence on Spectra ;
And On the Radiation
from Moving Ions, Phil.
Mag. 44, 503-512
(1897)
First correct
calculation of the
emitted power by
an accelerated
charged particule
first specific
prediction of time
dilation : "...
individual electrons
describe
corresponding parts
of their orbits in
times shorter for
the [rest] system in
the ratio
(1 – v2/c2)1/2".
(E/mc2)4/R2
A. Liénard, L ‘ Eclairage
électrique, 16, 5 (1898)
George Adolphus
Schott(1868-1937)
Dmitri Ivanenko
(!"#$%&#' !"#$%&#()#*
+),-($-./) (1904-1994)
Isaak Yakovlevich
Pomeranchuk (+0,,$.
G. A. Schott, Ann. Phys. 1$./)2()#* 3/"(&,-*4$.
24, 635 (1907),
G.
A.
S c h o t t , (1913-1966)
Electromagnetic
Radiation,
: And the
mechanical reactions
arising from it, Cambridge
University Press (1912)
angular and spectral
distribution and
polarization properties
Julian Seymour
Schwinger (1918
–1994)
Physics, 1965
J . S c h w i n ge r,
Phys. Rev. 70,
798 (1946)
peaked
spectrum
Edwin Mattison McMillan
(1907-1991)
Chemistry, 1951
E. M. McMillan, PRL 68,
1434 (1945)
Synchronism and
phase stability
Vladimir Iossifovitch
Veksler (52,6#"#&
+/0#7/)#* 5(.02(&)
(1907-1966)
D. Ivanenko and I. Pomeranchuk,
Phys. Rev. 65, 343 (1944)
energy losses due to radiating electrons would
set a limit on the energy obtainable in a
betatron (around 0.5 GeV).
V. Veksler J. Phys. USSR 9, 153 (1946)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
peaked spectrum
[Phys. Rev. 'Fl, 563 (1947))
I. The origins of the Free Electron Laser
D. K. C.
MACDONALD
AND
K.
FIG. 1. Normal cadmium (above) and isotopes altered
by neutron absorption (below).
MENDELSSOHN
Clarendon Laboratory, Oxford, L'ngland
AND
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A.
J. BIRCH
Dyson Perrins Laboratory, Oxford, England
&HE Editor regrets that Fig. 2 of the first of the above
papers has been interchanged with Fig. 1 of the second paper. The captions, however, are right, as they stand.
to 1.6+0.2 percent, about one-eighth of its normal abundance, and that the isotope at mass 114 was increased to
39.5+1.5 percent. Within the limits of the accuracy attained, the increase in 114 is equal to the decrease in 113.
Any changes in the abundances of the isotopes at masses
110, 111, 112, and 116 were less than five percent. It was
noticed, however, that in both samples the isotopes at 110
and 111 had a greater difference in abundance than is
indicated by Nier's measurements (12.8 and 13.0 percent).
We may conclude that the other main isotopes have absorbing cross sections less than one-fortieth. of that of
Cd", and that if any (n, 2n) or other reactions occur,
they are comparatively rare.
1.3 The early times of synchrotron radiation
Erratum: The Quadrupole Moments and
Spins of Br, Cl, and N Nuclei
1946 : first energy loss measurement
[Phys. Rev.
Vl, 644
(1947)]
J.C.P.H.Blewett,A. Phys.
Rev.
69,
87 (1946)
N.
F. R. MERRITT
J.
Bell Telephone et
Laboratories,
Murray Hill,
!mJersey
F. K. Gloward
al., Nature
158,
413 (1946)I
TOWNES,
HOLDEN,
BARDEEN, AND
~HE Editor regrets that Figs. 1 and 2 of the above
paper have been interchanged. The captions for the
figures, however, are correct as they stand.
B. J. Moyer, B. Peters,
1947 : first observation of synchrotron radiation
Isotopic Changes in Cadmium
by Neutron Absorption
A.
Argonne Nationa/
Laboratory, Chicago, Ilbnois
N a recent letter B. J. Moyer, B. Peters, and F. H.
Schmidt' report that the absorption of thermal neutrons in cadmium that had been enriched in the isotope at
mass 113 was six times normal, and conclude that this
isotope is mainly responsible for the large absorption in
this element.
The mass spectra reproduced in Fig. 1 illustrate another
phenomenon
that also indicates the absorbing isotope,
namely, the gradual alteration of the isotopic constitution
of an element by long exposure to neutrons. The upper
mass spectrum shows the normal isotopes at masses 110,
111, 112, 11.3, and 114, with Cd"3=12.3, and Cd"4=28
percent. The faint isotopes at 106 and 108 do not show on
the prints. The lower spectrum shows the changed isotopic abundance in a sample scraped from the surface of
a piece of metal that had been used to absorb intense
neutrons from a pile over a long period of time. These
neutrons include a considerable number with energies
above the thermal range.
Photometric measurements,
made by using Nier's
measurements
of the normal cadmium abundances as
standards, showed that the isotope at mass 113 was reduced
-
ELDER, A.
M.
AND
GUREWITSCH, R.
POLLOCK
V.
LANGMUIR,
H. C.
'" 'IGH
May 7, 1947
energy electrons which are subjected to large
accelerations normal to their velocity should radiate
electromagnetic energy. ' 4 The radiation from electrons
in a betatron or synchrotron should be emitted in a narrow
cone tangent to the electron orbit, and its spectrum should
extend into the visible region. This radiation has now been
observed visually in the General Electric 70-Mev synchrotron. ' This machine has an electron orbit radius of 29.3
cm and a peak magnetic field of 8100 gausses. The radiation
is seen as a sma11 spot of brilliant white light by an observer looking into the vacuum tube tangent to the orbit
and toward the approaching electrons. The light is quite
bright when the x-ray output of the machine at 70 Mev
is 50 roentgens per minute at one meter from the target
and can still be observed in daylight at outputs as low as
0.1 roentgen.
The synchrotron x-ray beam is obtained by turning off
the r-f accelerating resonator and permitting subsequent
changes in the field of the magnet to change the electron
orbit radius so as to contract or expand the beam to suitable targets. If the electrons are contracted to a target at
successively higher energies, the intensity of the light radiation is observed to increase rapidly with electron energy.
I f, however, the electrons are kept in the beam past the
~
-
~
~
F. R. Elder et al., Physical Review, 71, 11, (1947), 829-830
J. P. Blewett, 50 years of synchrotron radiation, J. Synchrotron Rad. , 5, 135-139 (1998)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
Schmidt, Phys. Rev. 69, 666
Research Laboratory, General Blectric Company,
Schenectady, %no Fork
J. DEMPSTER
May 1, 1947
General Electric 100 MeV (1947)
F. H.
Radiation from Electrons in a Synchrotron
F. R.
~
and
(1946).
www.lunex5.com
easily obtained from electrons with speeds ranging from
a megavolt, say, to 1000 Mev.
Several applications suggest themselves. We shall
discuss them under the following headings:
(1) production of energy in rather inaccessible spectral bands, viz., millimeter to infrared radiation j*
(2) speed monitoring for electron beams produced
by linear or other accelerating devices;
(3) speed measurement for fast individual electrons
or other particles (mesons, protons).
We shall also briefly consider the radiation emitted
by an electron moving through an electromagnetic
wave traveling in the opposite direction. This occurs,
e.g., in a linear accelerator in which a wave is reflected
fields. Hence, we shall be mainly interested in the case
of transverse fields, as shown in Fig. 1. The spatial
field distribution may be fourier analyzed. Let the
fundamental wavelength be 10• It will be shown that
the frequency of the emitted radiation varies with the
angle of observation. The fundamental component of
the radiation emitted under the angle (j (see Fig. 1) has
a frequency
I. The origins of the Free Electron Laser
1.3 The early times of synchrotron radiation
w=\l,e=21T/3c/lo(1-f3 cos8).
The undulator
• Calculation of the field created by a relativistic particle in the
magnetic sinusoidal field (i.e. such
as produced by undulators)
* Notes added in proof: According to reports of the Electronics
(1)
Beam
M.I.T., P.
D. Coleman
working
Research
Motz H. : Applications of the radiation from
fastLaboratory
electronatbeams,
Journ.
Appl.isPhys.
22,on
such a scheme. Prior reference to the problem treated in this
paper by V. L. Ginsburg, Radiation
paper has also been
527--535 (1951)
of microwaves and their absorption in air, Bull. Acad. Sci.
U.R.S.S. Ser. Phys. 9 (1947), No.2, 165 (in Russian).
FIG. 1. Schematic arrangement of undulator magnets.
527
830
• Influence of the bunching
of
the
electrons
on
ÉLECTRONIQUE.
–toProduction
d'ondes millimétriques par un
ondulateur
[This article is copyrighted as indicated in the article. Reuse
of AIP content is subject
the terms at: http://scitation.aip.org/termsconditions.
Downloaded
to ] IP: 195.221.0.34
On: Sat, Note
01 Aug 2015
the coherence of the produced radiation
magnétique.
de 20:55:40
M. RENÉ COMBE et Mme Thérèse FRELOT,
• observation of the polarized visible radiation présentée par M. Louis de Broglie.
from an undulator installed on the 100 MeV Après avoir décrit un dispositif destiné à produire, par application de l'effet Doppler
relativiste, un rayonnement de courte longueur d'onde, on donne les résultats concerStanford accelerator.
nant la puissance et le spectre de fréquences.
A buncher set-up after a 3.5 MeV accelerator
Nous avons construit un ondulateur (*), composé d'un aimant, d'un guid
banc de mesures, et d'un correcteur de champ, et qu
enables to achieve 1 W peak power at 1,9 mm d'ondes spécial, d'un
13<
fait suite à un accélérateur linéaire d'électrons fonctionnant en régime pulsé
thanks the the bunching of the electrons.
(5o impulsions de fxs/s). Le
des électrons s'étend de i,5 à 3,oMeV
1\1 0 T Z,
THO 1'\,
,\ 1'\ /)
'" HIT E H \' R S T
R.F.
LOAD
DEfLECTED
IRON
PLATE
BEAM
0,5 COUPLER
FIG,
6. Equipment outline for buncher tests.
spectre
i
corresponding to light passing through the two polaroid inches. The filling time is 0.2 microseconds. An input
Motz H.,Thon W. ,Whitehurst R. N. : Experiments on Radiation by Fast
maximum
MeV. polarization. power up to 8 M w is required and was obtained from a
avecwindows
un was 2: 1 in favorà of2,3
perpendicular
Electron Beams , Journ. Appl. Phys. 24, 826--833 (1953)
Subtracting the background makes
the evidence for
Stanford
high power klystron operating at 2856 Me/sec.
L'aimant,
produit
sinusoïdal,
B obtained
960 from
permanent,
un champ
e
gauss,
polarization even
stronger. A quantitative determinaElectron pulses drawn atavec
80 kv are =
a
was not
/= 16tioncm.
Leattempted.
tungsten
filament gun and
injected into the
guide d'ondes, rectangulaire
(dimensions
intérieures
4oaccelerator.
X 25mm)
The gun pulse lasts 1 microsecond and is applied 0.2
microseconds after the klystron pulse.
Tests of this buncher revealed an energy spectrum
A qualitative experiment was also carried out
of
0.2-Mev half-width at 5 Mev. The accelerator
concerning the color distribution of the light. An
interference filter passing a band 100A wide centered collects electrons during the full period of the traveling
on 4400A was used. Theoretically, the color of the light in the accelerator and bunches them to within 30°;
should range from green (5500A) to blue (3400A) in and it may have been better than indicated by the
the energy range from 95 Mev to 120 Mev. The light foregoing numbers. Figure 6 shows a block diagram of
fell on a photomultiplier 1P21, which has a sensitivity the set-up used for testing the buncher. The buncher
curve starting at 3000A, rising sharply to a peak at is followed by a standard (2-ft) accelerator section,
4OOOA, and falling to almost zero at 7500A. We got i.e., by a uniformly disk-loaded section which obtains
maximum transmission at 90-95 Mev andONDULATEUR
almost no power coupled out of the end of the buncher through
transmission at 120 Mev. We consider this as a very a phase shifter which allows variation of the relative
rough indication of agreement with theoretical pre- phases of buncher and standard section ranging over
360°. For energy measurement purposes the beam can
dictions.
be magnetically deflected into a channel leading to a
V. and
MILLIMETER
WAVE GENERATION
Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs
!ERLs),
Hamburg,
Germany,
31
!May
–10monitor.
!June, 2016
It was necessary to insert colliradiation
plan
IIG-inch clearing holes in order to obtain
mators
with
1. The Electron Buncher
good energy resolution.
à
à
• Emission of the radiation spectrum (6 mm)
produced from an undulator installed on a 2.3
MeV accelerator
3. Color
Combes R., Frelot T. , présenté par L. de Broglie, Production d'ondes
millimétriques par un ondulateur magnétique. Comptes-Rendus Hebd.
Scéance Acad. Sci. Paris, 241, 1559 (1955)
M. E. Couprie, CAS School Free
jeudi 2 juin 2016
est étanche et permet le passage du faisceau, compte tenu de la vibration dans
le
vertical(la trajectoire est sensiblement une sinusoïde d'amplitudemm)
Ce guide doit aussi satisfaire certaines conditions relatives l'existence des
Marie-Emmanuelle
COUPRIE
and
Mathieu
VALLEAUvelocity is
2> and the
interval as:
Let’s
consider
theinlongitudinal
velocity
: 1 <
cal,
um
difference
between
average
longitudinal
velocity
electron
longitudinal
relativistic
electron
ofKvenergy
and
velocity
v with respect to R are introduced along the β
s direction.
Its relativ
e s the
=
oordinate
system
given
Fig.A˙1.1
with
1
u
2 Ee
2
β
≈
1
−
−
sin
(k
s)
(55)
�
�
Marie-Emmanuelle
and electrons
Mathieu VALLÉAU
cos
(k→
s)2 = −
B�uon relativistic
βCOUPRIE
β =position
s Bu β4.1
u
c 1−β2
xby
u2γ
s cos (ku s)dt
=
2:Considerations
2π given
−→ s
factor
γ
is
2
→
−
−
p.
z)
the
horizontal
(resp.
vertical)
is
2γ
ver
eo γ 2
s e z = Buz cos(ku s) z
(48)
Buz = Buz cos
2
mcurrent
ent
in the undulator
s introduce
in
the
area
of
the
free
of
an
undulator
creating
a
periodic
permanent
magnetic
˙sm=oλγlaboratory
γ
u
B
β
cos
(k
s)
=
−
B
β
cos
(k
s)dt
β
u
x
u
s
u
u has
One
:
www.lunex5.com
2
2
2
2
mo γ
The
electron
movement
the
KuBcin
Ku c 1L L m
Ku cwith N the number of periods λ . Let’s first consider
oγ
ting
withhas:
the undulator
wavenumber
ku˙given
2by:undulator
1
verage,
one
˙
of
peak
amplitude
,
period
λ
,
length
=
N
λ
(2
− 1)|
=
|
(sin
(2k
s)|
=
(57)
|v− < vs>≈|max
umax
u
u
u
u 2region,
u
so
:
1 component
first order,
cβ=st,| 4γ
so2 uz
βssin
∝ (kγ 2u s)whereas
β
∝
.
In
consequence,
the longitudinal
of theuelectron
u
max
2 γ1
Let’sx4γ
consider
a laboratory
without
current,
with a laboratory
referential (0, x, z, s) with th
4γ
1 2π creating
�
˙
˙
γ
=
the laboratory
free
of
current
an
undulator
a
periodic
permanent
magnetic
2
At
first
order,
s
≈
cβ
t,
so
β
∝
whereas
β
∝
.
In
consequence,
the
longitudinal
component
of
the
electron
=
(49)
k
1
u
s
s
x
2
1 and
<
v >ofvery
movement
of anot
relativistic
electron
ofrelativistic
velocity
vremains
introduced
atE the
origin
of
the
undulator
coordinate
along
2 with
γKu electron
2 the
1 the
γ undulator
λu A
1
−
β
energy
and
velocity
v
respect
to
R
are
introduced
s dir
21 −along
close
to
1.
One
gets
β
≈
1
and
s
≈
ct.
ity
is
practically
modified
by
the
β
2
=
β
s
s
eriod
λ
,
length
L
L
=
N
λ
with
N
the
number
of
periods
λ
.
Let’s
first
consider
<
β
>≈
1
−
−
=
(56)
introduce
in
the
area
of
the
laboratory
free
of
current
an
undulator
creating
a
periodic
permanent
magnetic
K
c
u
u
u
u
u
u
u
s
Marie-Emmanuelle
COUPRIE
and
Mathieu
VALL
ÉAU
β
=
1
−
u2 and β
2
The
undulator
scheme
is
shown
in
Fig.
18.
remains
very
close
to
1.
One
gets
β
≈
1
and
s
≈
ct.
velocity
is
practically
not
modified
by
the
undulator
2
In4γ
thes LUNEX5
case
(in
400the
MeV,
γhelical
= 783),s undulator. The field γcan be created2 by
e maximum coordinate
difference of the
is2γ
c: the
2γ. is
electron
movement
undulator
])
in
the
two
cases
planar
and
s (longitudinal
su∈
[0,
Luvelovity
factor
given
byof
4γ
γ
en,
ofitudinal
peak amplitude
B
,
period
λ
,
length
L
L
=
N
λ
with
N
the
number
of
periods
λ
.
Let’s
first consider
electron
of
velocity
v
introduced
at
the
origin
of
the
undulator
coordinate
along
the
uz
u
u
u
u
u
u
Then,
with
β
the
normalised
velocity
of
the
electron:
= velocity
1.65T
and
period
λu =at1.5cm,
i.e.
= created
2.3,
thisby
difference
is along the
nic
planar
undulator
of peak
uthe
2 field Buof
sovof
:>
ovement
of
a relativistic
electron
v introduced
the origin
ofKand
undulator
coordinate
the
two1cases
and helical
undulator.
The
field
can
be
[0,
Lu ]) inpoles.
nated
Kof
u the2 planar
maximum
difference
between
the
average
longitudinal
velocity
<
the
electron
longitudinal
velocity is
t
is
indeed
very
small.
β
≈
1
−
−
sin
(k
s)
(55)
s
u
1
eB
eB
1
eB
eB
2 Lu ]) in the two
cases
of uthe
and helical
undulator.
The field
canv1beand
created
by
udinal
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u planar
u u 1, then
E
<<
the
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If
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Kuradiation,
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−3
y
:
Synchrotron
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devices
new
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β
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β
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�
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. Numerically,
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.
e, the maximum value of the transverse velocity
γ10β =
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u 2.934
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u
u
ated poles.
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m
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o
o
m
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m
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Synchrotron
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and
Free
Electron
Laser
1
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o
o
mo c
ation, one has:
2
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2
so :
Ku chas : 2
Ku c
Ku c
1
One
:

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2
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|v−
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u of max
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undulator
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the
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Approximation
ultra-relativistic
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2 γ of
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(ku4.2.2
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undulator
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��
4γ
4γ
4γ
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and
the
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If
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<
β
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1
−
−
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(56)
γ
s
�
�
�
2γ
�
eBu
eBu �
eBu γλu
2
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− �
Planar
undulator
case
2
2

2γ
4γ
c
�
�
1
x : horizontal direction ββx eB
0 u s)dt = 
βx �βz
=−
− eBu Kcos(k
s) 2 2
u s)ds = −
u2
λ1u (58)
1eB
1
2c
u mdγE cos(k
u sin(k
v
=
−
β
m
γc
m
γc
2π
2
u
.
comes
:
β
�
β
�
β
�
1
�
�
�β
�
β
�
�
β
�
β
�
1
�
�
o cos(k
o is
o 2 case
by
a: vertical
planar
undulator
Kcreated
sin(k
βdifference
=creating
− by
−of permanent
s)ds
=
−
s)
2of the
x
x
z
. Ininuzthe
LUNEX5
( 400
MeV,
γ β=is
783),
relative
maximum
of
the
velovity
1 longitudinal
Fig.
18 Planar
undulator
scheme,
a periodic
magnetic
field
by2two=
arrays
magnetscos(k
arranged
the
Halbach
2 1
z
direction
=
u s)dt
x
u
u
f
normalized
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γ
given
γ
=
(with
x
z
The
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electrons
given
by
:
2
dv
2
γ
2
γ
2γ
1
−
−
sin
(k
s)
ical
undulator
field
created
by
a
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undulator
4γ
nalthe
average
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< vm
>
electron
longitudinal
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c and
u
undulator
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2 Helical
o2in
configuration
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Vertical field invelocity
green,am
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blue.2γ the
m
m γc 2π
undulator
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by
planar
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o γassociated
o γc K as
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o
d
Let’s
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the
undulator
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u
mass,
e
the
particle
charge
and
c
the
speed
of
=
1.65T
and
period
λ
=
cryogenic
planar
undulator
of
peak
field
B
dτ
u
u
2γvalues of
a planar undulator, creating a field
the vertical
direction
expressed
in(or
the [0,
Lu ]
so along
:
In
the
small
angle
paraxial)
approximation
with
small
age
over
one
undulator
period
One
has
:
−6
consider
first
the
case
of
a
planar
undulator,
creating
a
field
along
the
vertical
direction
expressed
in
the
[0,
L
]
Case
of its
asmall.
planar
of Nparameter
Case
aa1helical
undulator
of�
Nhorizontal
define
associated
consider
aKhelical
creating
magnetic
both
and[0,vertical
offirst
aundulator
dipole,
movement
isdeflection
givenLet’s
etic
field
u periods
u periods
u field inexpressed
2 Lu ]
10
. ItBisdthe
indeed
very
st’s
consider
the
case
of aundulator
planar
undulator,
creating
field along
theofvertical
direction
inMarie-Emmanue
the
u as :a undulator
�
2
E
=
γm
c
24
2
2
2
o
dv


eBu λuThe
total
energy
the
electrons
is−3given
by : n is then given by
βofit=
1−
gle
of
observation
,Numerically,
the
direction
of
observation
al
as:K=u cev
K
K
c is
×B
thevalue
particle
time
τ�
, its
. (57)
gives
2.934
10
.
ansverse,
the
ofcase
the
transverse
velocity
given
by Kγuθ
uc
uK
2maximum
o dτ
d , with
2
Electron
velocity
in the planar
undulator
=
(51)
rval
�
�
�
0
u
γ
= | as:
(2
sin
(k
s)
−
1)|
=
|
(sin
(2k
s)|
=
1
 −→ 2 2
u
u max
� ofmax
�
2
2
2πm
−
−−of−4γ
−
→2dynamics
oλc
4γ 2−→
4γ
position
R(τ)
.the
Infundamental
case
an�uniform
magnetic
θ
�θ
=
1
−
β
Let’s
applyone
equation
the
to the �
case
of
this
planar
undualtor
:


ecapitulation,
has:2π
→
−
→
−
2π
eB
�
x
z
0
with
γ
the
relativistic
factor,
m
the
rest
particle
mass
(m
=
9
10
2
2
u
u

2
→
−
→
−
o
o
(59)
<
β
>
B
=
B
sin(
s)
x
=
B
sin(k
s)
x


γ �. λu �
θ −�<<
��θthe
�
θz velocity
� θz
� 1approximated
�
� θ(48)
ux
ux
uE
u c2
= Buz cos
z−→
B
s)2π
z�→
Buz whose
Ku 11=and
(51)
x→
xcan
→
−puz cos(k
uθ

c of circle,
radius
ρsis given
x
→
−
=
γm
2=
dby
Ku21z→
→
− 1
2
→
−
−
�
o


−
K
c
reduced
be
as
:
If
γ
>>
1,
then

It
is
given
in
practical
units
as
:
=
B
cos
s
z
=
B
cos(k
s)
z
(48)
B
λ
u
Ku →
f =LUNEX5
e(2E(1
++
v x BK)γ )
uz
uz 2πm
uo cγ = energy
−
u
−
→
and
the
kinetic
energy
particle
is
the
sum
of
the
rest
energy
E
case
(
400
MeV,
783),
of the longitudinal velovity
is 4γuz2 . dtIn 1=the
→
−
o
−
u
2π
2
2γ −
sin
(k
s)
so
:
λ
2π
→
sin
(k
s)
u
u
u
=
B
cos
s
cos(k
s)
z
B
z
=
B
→
−z = B cos(ks)uz
→
−z
u
u
γ
→
−
−31 kg
→
−p , being →
−p = γm→
λu γ particle umass (m
=
B
cos
s
(48)
−
with
the=
electron
momentum
c β
. Buz
m
γβ
c
o1.5cm,
with
γ
the
relativistic
factor,
m
the
rest
=
9
10
1.65T
and
period
λ
=
i.e.
of
K
=
2.3,
this
difference
is
peak
field
B
uz
uz
u
o

→
−
1
o
o
u
u
u
K
o

1
mber
k
given
by:


u
−
→
2
u in
In absence
of electric field
and inas
=undulator
(1.1)expression,

Ku =it0becomes:
0.934Bu (Tλ)λ
(52)
24
Marie-Emmanuelle
βmomentum
is
given
practical
units
: the

u (cm)
cos
(kthe
s)kinetic
−
ββenergy
=1(58)
−
hρthe
wavenumber
kusubstituting
given
by:
u
u
β
≈
1
−
=
0
B

.ctory
γ
2
2
eB
us
and
energy Ek as
particle
energy
is
the
sum
of
the
rest
E
2
in the dplanar undulator case
Ku
γ o
2
1
2γ
Ku
2
−3
1
−
−
sin
(k
s)
u velocity
2
Ku
2π the
it2γtransverse
gives
2.934
10 . βx = 0, one can take the integration constant
e of the transverse
velocityentering
is given
bydundulator
With an electron
without
1
2γ 2 2π
γ . Numerically,
1
−
−
=
(49)
k
u of
city inequal
the
vertical
is: zero,
the
movement
takes
place
in the
horizontal
plane
2
with
the
undulator
wavenumber
k1γubegiven
by:
The
total
energy
of
the electrons
given
by the
:(x, s).
=
0.934B
)λ
mitted
radiation
indirection
a cone
solid
angle
2γ 2
2γ(52)
1 isu (cm)
(49)
kK
to zero,
one
gets
u (T
u u=
λ


u
<<
1
and
reduced
velocity
can
be
approximated
as
:
If
γ
>>
1,
then
inutaverage
over
one
undulator
periodleads to :
Ku
λu
γ
ω
with
ω
=
k
c,
a
further
integration
u
u
(ku s)
mation of
the angles from the particle
 frame toElectron velocity in the helical undulator
case
γ sin
Ku
1
own
in
Fig.
18.


Since
the
velocity
in
the
vertical
direction
is
zero,
the
movement
takes place in th
ith
an
electron
entering
the
undulator
without
transverse
velocity
β
=
0,
one
can
take
the
integration
constant
2
(ku s)isinvery
e undulator
schemeradiation
shown
Fig. collimated,
18. 2
x
Ku
→
−
2π
1.2).
Synchrotron
K
γ issin
E
=
γm
c


1
u
o
0
→
−
1
Ku
sin (k
βx =
(53) (ku s) 
cos
−− γleads
γfurther integration
u s)
β
=
(49)
k
β
≈
1

0 ṡ =
zero,
one
gets : the
u
c[1 − 
−
(1
−
cos
(2ω
t))]
With
k
s
=
ω
t
with
ω
=
k
c,
a
to 2: of the undulator,
β
(58)
γ
mtoenergy,
the smaller
collimation
angle.
−
−
−
−
→
Considering
an
electron
arriving
on
axis
without
angle
at
the
one
u

2entrance
u 0
u 
u
u

2
2
−31
8 m/s).
2γ
λ
2
2γ
4γ
u
with
γ
the
relativistic
factor,
m
the
rest
particle
mass
(m
=
9
10
kg),
c
the
speed
of
light
(c=
3
10
(59)
<
β
>
K

o
o
1 theKunumber of photons
The
approach
is to enter
define
the
brilliance
as
2
1 − 2γ12 − 2γu2 sin2 (ku s)
: common
1
−
Considering
the
electron
at
the
origin
position,
one
Kthat
1
2 −
2takes integration con
u
˙
2γ
2γ
and
the
kinetic
energy
E
as
follows
:
particle
energy
is
the
sum
of
the
rest
energy
E
(1
+
)
1
−
g
that
the
electron
enter
at
the
origin
position,
one
takes
integration
constants
equal
to
zero,
and
one
gets
The
total
energy
of
the
electrons
is
given
by
:
With
an
electron
entering
the
undulator
without
transverse
velocity
β
=
0
and
using
β
=
0
one
can
take
the
o
k
z
z
2
The undulator scheme is shown in:ond
Fig. and
18.2γ 2perKuunit
of
phase
space
(or
the
density
distribution
r period
sin (ku s)
βx =
(53)in phase space
integration constant equal to zero, one gets :
→
−
Since the velocity
in the vertical direction is zero,
movement
takes place in the h
γ
− →
d=
β the
− to
2e →



�
E
γm
c
corresponds
to
the
geometrical
optics
frame.
It
enables
describe some
o
Ku c
Ku c
�
β
x
B

=
0
sin
(ω
t)dt
=
cos
(ω
t)
x
=
K
c
K
c
n trajectory
in
the
planar
undulator
case
With
k

s
=
ω
t
with
ω
=
k
c,
a
further
integration
leads
to
:
u
u
u
u
u
u
u
βz =u 0
γ
γωu

dtsin (ωmu(54)
γ −31
x
=
=
−
cosgeneral
(ωut) ex
ot)dt
−−−−→ 


˙
γ
γω
0
propagation
properties
of
the
rays
through
optical
elements.
The
u

ith an electron
entering
the
undulator
without
transverse
velocity
β
=
0
and
using
β
=
0
one
can
take
the
y
=
0
with
γ
the
relativistic
factor,
m
the
rest
particle
mass
(m
=
9
10
kg),
c
the
speed
of
light
(59) z enter
< β >
z c position,
�
 is zero, the
(60)
o
o  one takes
�
�
Considering
that
the
electron
at
the
origin
integration
consta
2
K
K
c
he velocity
in
the
vertical
direction
movement
takes
place
in
the
horizontal
plane
(x,
s).
2
2
2
u
u

K
The
expression
the
longitudinal
electron
velocity
is then
by :of the rest energy
u
K+
Ku is
λu given

(2ω
s =
2π Eyo =
cos
(ω
sin (ω
uzero,
u λu gets
(1
) Kone
1equal
− 12γ212of
and
the
kinetic
energy
E=
follows
:isu t)
particle
energy
the
sum
u t)dt
ation
constant
to
:
c(1
−
−
)t
+
sin
(2ω
t)
=<
v
>
ct
+
sin
t)
k asγω
γ
sin
s
=
B
sin(k
s)
B
u
u
2
of
the
brilliance
B
(or
spectral
brightness
in
a
narrow
bandwidth)
given b
2
2
2
u
u
u
u
: � leads to : 16πγ
16πγ integration
h ku s = ωut with ωu2γ= ku4γ
c, a further
β
λ
x
u

�
2


� �
→
−
→
−
1 Ku


2
Ku λof
2π
u
β
s
=
c(1
−
)t =<
v > ct
one
: mechanics
Using
β
and
B
the
Wigner
distribution
[136,
46]
as
defined
in
quantum
as
1
1
K
z
2 −
2gets
gives,
the1 numerical
LUNEX5,
um amplitude of the transverse motion isβ γ =2π , which
uexample
cos
s a=
B
2 Buof

2 β 2 for


u� cos(ku s)
2γ
4γ
K
c
K
c
1
−
−
=
−
−
sin
(k
s)
λ
K
1
β
=
0
(54)
u
u
s
u
u
dulator
u x z
xsystem
= γ in
sinphase
(ωut)dtspace.
= − γωuThe
cos (ω
β
γ 2twice
γu2t))]
γ 2 aa maximum
µm. In case
the longitudinal direction occurs
at
the
frequency,
with
amplitude
u t)
−
(1
−
cos
(2ω
ṡ = oscillations
c[1 −

s
probability
density
of
quantum
Wigner
dis

2
2
0
�
2γ
4γ
K
c
K
c
The
electron
trajectory
is
helical.
There
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in
the
longi
u
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server receivesM.In
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ontinuous
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zontal
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jeudi 2 juin 2016 emission
changing the gap for permanent magnet insertion deI.
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Free
Electron
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rent
for
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time
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s a train of Nu magnetic periods which can be consid1.3
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ssionradiation,
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5
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ogeneous”
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idth
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Synchrotron
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Synchrotron
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5 5
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en different points of the trajectory, leading
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composed
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e so-called ”homogeneous linewidth”
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et 39 pm.mrad
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al peak emission. The ”inhomogeneous”
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cteristics
-observation
angle
= refers to the case of a single electron.
(6)
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rom the electron beam energy spread,
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emitted field interferes between different
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sults from
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Thethe
so-called
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refers
to divergence.
the case of a single electron.
ics of synchrotron radiation
emissioncharacteristics
is then a narrow-band in the frequency domain. In other words, the
ectronThebeam
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
emitted field interferes between different points of the trajectory, leading to sharp
Wiechert
potentials
spectral peak emission. The ”inhomogeneous” broadening of the undulator line rejeudi 2 juin 2016
otron radiation, polarization,
devices
and new
sources
25
I.
The
origins
of
the
Free
Electron
Laser
Synchrotron
radiation,
polarization,
devices
and
new
sources
www.lunex5.com
1.3 The early times of synchrotron radiation
n(s) = Ne S(s)
Synchrotron radiation, polarization, devices
and new sourcesemission
Coherent
n(s) = Ne S(s) (30)
25
Synchrotron radiation, polarization, devices and new sources
n, devices and new sources
E(ω) = Eo (ω)Ne f (ω)
n(s) = Ne S(s)
25
(31)
E(ω) = Eo (ω)Ne f (ω)
(30)
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Ne S(s)
� ∞
� ∞
ωs)
ωs)e f (ω)
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f
(ω)
=
ds
(32)
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n(s) = Ne S(s)
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(31) ds
f (ω) (30)
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−∞
� ∞
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ωs)2 + N ]
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−
1)
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(ω)
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e
e
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2
+
)| hn (0, 0) u |2 c Incoherent(31)
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I
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1)
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o
e
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2
enγ
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case of short electron bunch Gaussian expression order of magni
case of bunched beam Bunched beam
S(s) =
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10 orders of magnitude for λ>>σl
8
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5
for λ=σl
M
∑ S(s − mλr )
m=1
Coherent emission for λ=λr/n with the form factor,
corresponding the bunching efficency (equivalent to the
form factor in Bragg diffraction)
Fig. 17 FEL configurations : a) oscillator case with an optical cavity enabling t
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
Synchrotron radiation and Free Electron Laser
→
− →
−
0
βthe tube), as shown in Fig. 19a. . In the first one, an electric field oscillates on a length ∆ s at a frequency ν
→
−
√
I. The
origins of the Free Electron
Laser
1
ranging between 1 and 10 GHz (i.e. with corresponding wavelengths of 30-3 cm). The electrons, generated
→
−
d velocity
of
the electrons,
with γ =
dγ
eβ .E
2
XX
revoir
equation
XXX
cathode, enter in the first cavity
where
the
dγ
e
β
.
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=
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www.lunex5.com
=
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dt power
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gh
tubeonwhere
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1
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period
electrons, ∆W1 = 0 since
oral
→
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β
01 the electrons have
with γperiod
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√
β
the
velocity
the
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tor for the
generation
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signal
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direct
supplied
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tube.
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XXX
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XXX
phases.
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space
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in of
Fig.
19b),
the
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to accumulate
1−β 2
eeelectron
bunches
passing
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open
cavities
excite
RF
waves
Begining
of
the
twentieth
century
:
rapid
and
spectacular
development
of
electron
beams
inthrough
vacuum
tubes
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∆W1where
dependselectron
on the moment
t whenpassing
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1 is modulated
RF
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It is now
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microwave
ovens.
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isan
a high
power
vacuum
tube
bunches
open
cavities
excite
RF wa
s.
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drift
space
length
adjusted
to
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optimal
electron
bunching.
1
he
frequency
being
determined
by
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geometry
of
the
cavity.
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or
spatial
period
λ
β
.
In
average
over
the
electrons,
∆W
=
0
since
the
electro
at
a
temporal
period
T
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1
2πω
radiodiffusion,
radar
for
iceberg
or military
use
(high
frequency
oscillations
d by Applications
the Russel and: Sigurd
Varian
brothers
[207]
consists
of
twomagnetic
cavities
(metal
boxes
along
oscillations
by detection
interaction
with
the
field, the
frequency
being determined
by needed).
the geometry of the cavity
I.4 :The development of vacuum tubes
crowave signal from the direct current supplied to the tube. Thisdifferent phases. Then, the electrons enter into the drift space (see in Fig. 19b), enabling the electrons to accu
g. 19a. . In the first one, an can
electric
fieldasoscillates
on afor
length
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a frequency
ν=
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drift
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act only
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the
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directelectron
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for microwave ovens.
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klystron
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can not (metal
amplify
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It is now used
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Varian brothers [207] consists device
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boxes
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The
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and Sigurd
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ncavity
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frequency on
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i.e. 30-3 ν = 2
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nding wavelengths
cm).
electrons,
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at
the. In
s→
−30-3
∆
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− ranging between 1 and cm).
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at the cathode,
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the first
the input
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corresponding
wavelengths
cm).cavity
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generated at
ignal is ∆W
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energy
: s.10
. E gain
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1 = Theyβcan
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is applied.
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ion XXX
energy
� ∆s
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dγ
e
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.
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ends on the moment
t when the electron arrives inside the cavity. ∆W is modulated
in time ∆ s
∆W1 = 1 β . E dtαE.β cos ωt.
= E.∆ s. cos ωt
(7
dt
mc
β
0
or spatial period λ β . In average over the electrons, ∆W1 = 0 since
the electrons have
→
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arrivesinto
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inenabling
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hetheelectrons
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19b),The
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rift space (see in Fig. 19b), enabling
the electrons
at a temporal
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= In
2πω or spatial period λ β . In average over the electrons, ∆W1 = 0 since the electrons ha
oscillations
magnetic
field, the
being
dete
ble an optimal electron bunching.
different phases. Then, the electrons
enter intobytheinteraction
drift spacewith
(see the
in Fig.
19b), enabling
thefrequency
electrons to
accumul
act
only
an
oscillator
for
thebunching
generation
of microwave
Fig.
klystron
principle
: a) klystron
b)
electron
by energy modulation
in the klystronsignal
drift space,from
electronsthe
ac
in bunches. The drift space lengthcan
is19adjusted
toasenable
anscheme,
optimal
electron
bunching.
in
bunches,
c)
Phased
electron
in
the
second
klystron
cavity,
electric
field
in
red
Cavity 2the RF signal. It is now used for microwave ovens.
device can not amplify
electrons
haveRussel
the same
with
respect
to the[207] co
The klystron, the
invented
by the
andphase
Sigurd
Varian
brothers
Drift section
electromagnetic
wave
in
cavity,
they arefield
bunched.
theIn tube),
ascavity,
shown
in Fig.
19a.
. Inphase
thethe
first
one,tosince
an
electric
oscillates
the second
the electrons
have
the same
with
respect
the electromagnetic
wave
in the cavit
Second
energy
exchange
:
they have beeninbunched
(see in Fig.
The electrons
second energy
exchange is given by :
stron principle : a) klystron scheme,
b) electron
bunching by
energy modulation
the klystron
drift19c).
space,
accumulate
Then,
the electrons
enter
1
2πω
ranging between 1 and 10 GHz (i.e. with corresponding wavelengths of 3
� l2
c) Phased electron in the second klystron
into thecavity,
drift electric
space),field in redcathode, enter in the first cavity where
→
− →
−input RF signal is applied. They c
the
β . E dt = Ne EL2 cos ωt
∆W2 = ∑
The electrons
electrons 0
� ∆s
accumulate in bunches.
−
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→
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in→
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E the electric
NeLthe
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2 the number
β . E dtαE.β
ωt.field can
= E.∆
1=
the electrons in the second cavity is ruled by ∆W
the electrons
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The drift space length is
region
in
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E
the
electric
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β
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3
6
econd cavity, the electrons have the same phase with respect
to
the
electromagnetic
wave
in
the
cavity,
since
(practically, 10 − 10 ) .
adjusted to enable an
of the electrons in the second cavity is ruled by the
been bunched (see in Fig. 19c).
The
second
energy
exchange
is
given
by
:
The
XXX
revoir
equation XXX
optimal electron
electrons themselves.
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sign
on the moment
t when
the electron
ins
3-106)arrives
bunching.
electric
field of ∆W
� l2
1 depends
.
The
gain
in
electric
field
can
be
very
high
(10
→
− →
−
1
spatial period
λ(1939)
β . In average over the elec
at
a
temporal
period
T
=
β . ER. H.
dtVarian,
=N
∆W2 = ∑
EL
cos
ωt
(71)
S. eF.Varian2 : A high frequency oscillator and amplifier.
Appl. Phys. 10(5), 321--327
2πω J.or
different phases. Then, the electrons enter into the drift space (see in Fig. 19
electrons 0
in bunches. The
space
lengthGermany,
is adjusted
an optimal electron b
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs
!(FELsdrift
and !ERLs),
Hamburg,
31 !May to
–10enable
!June, 2016
e the number of electrons, L2 the interaction region in the second cavity, E the electric field. The phase of
jeudi
2016
klystron
scheme,
b) electron
by energy
the klystron drift
space,
electrons
accumulate
ons
in2 juin
the
second
cavitybunching
is ruled
by themodulation
electronsin themselves.
The
gain
in electric
field can be very high
I. The origins of the Free Electron Laser
www.lunex5.com
I.4 :The development of vacuum tubes
Block diagram of the klystron
High Gain amplifier
Bunching
(velocity modulation)
Coherent interaction
with the EM field
Oscillator
Bunching
(velocity modulation)
- a block for the bunching,
- a block for the phased interaction with the field : a
high intensity electron beam excites the RF wave in
the second cavity.
The klystron can be operated in the oscillator mode
with a feedback loop on the radiation.
Coherent interaction
with the EM field
In a klystron, the cavity and the waveguides should be of the order of the wavelength.
While looking for larger values of the frequency or for short wavelengths, the cavities and
waveguides manufacturing thus limit the operation of the klystron to the microwave region.
=> Another system should be realised for the micrometer and submicrometer spectral ranges.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
I. The origins of the Free Electron Laser
I.4 :The development of vacuum tubes
Example : the accelerator
More generally, an electron bunch can be accelerated or decelerated by an wave which period is longer than the electron
bunch’s one => principle of the linear accelerator
The electrons are produced in an electron gun : a thermo-ionic gun or with a photo-injector where the electrons are
then generated in trains. With the conventional thermo-ionic gun, the electrons travel into the so-called buncher (a subharmonic or harmonic cavity) where the electrons travel on the edge of the RF wave, for acquiring energy spread and
being bunched by the velocity modulation, as in the klystron case.
Then, the electron beam is accelerated by an intense RF wave produced by a klystron and sent in the cavities of the
accelerating sections. The accelerating section can be considered as a series of coupled cavities or as a waveguide where
irises slow down the phase of the RF wave so that it becomes equal to that of the electrons. In the accelerating sections,
the electrons should have the same phase with respect to the RF wave. For being so, they are bunched in small bunches.
For example, for a RF frequency of 1.3GHz, the period is of 0.77 ns, 1 phase corresponds to 2.1ps.
electron gun
sub-harmonic
buncher
accelerating sections
RF wave
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
I. The origins of the Free Electron Laser
I.4 :The development of vacuum tubes
Vacuum tubes such as klystrons and magnetrons and more generally electronics, discovered at the
end of the thirties, knew a wide development during the second world war with applications such
as radiodiffusion, radar detection, where oscillators with high frequencies are needed.
The sources generally use electron beams submitted to electric or magnetic fields, where the
”bunching” is the key concept for the wave amplification.
The use of resonant cavities at the frequency of the emitted wavelength can efficiently insure the
retroaction needed for the production of a coherent wavelength.
=> This field of electronics enables to understand that in setting a loop on a wide band amplifier (in
connecting one part of its output to its entry), on can transform it into a very monochromatic
oscillator.
=> This concept will be used later for the maser and laser inventions.
K. Landecker, Possibility of frequency multiplication and wave amplification by means of some relaticistic effects, Phys. Rev. 36 (6) (1952) 852-855J. Schneider,
Stimulated emission of radiation by relativistic electrons in a magnetic field, Phys. Rev. Lett. 2(12) (1959) 504-505
R. H. Pantell, G. Soncini, H. E. Puthoff, Stimulated Photon-Electron Scattering, IEEE Jounral of Quantum Electronics 4 (11) 906-908 (1968)
R. B. Palmer, Interaction of relativistic particles and Free Electromagnetic waves in the presence of a static helical magnet, J. Appl. Phys. 43(7) (1972)
3014-3023
K.W. Robinson , Nucl. Instr. Meth. A239 (1985)
Csonka (1976)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
Robe r t M. PH I LL I PS
www.lunex5.com
Research and Deve l opment , STAR M i crowave , 546 D i v i s i on St reet , Camp
I. The origins of the Free
Electron Laser
1.5 The ubitron : Undulating
The Beam
h i story of theInteraction
ub i t ron, the or igina l FEL ,
is t raced f rom i ts i
genera t i on in 1964 of mi l l imeter wave power at a level wh i ch rema i ns
1960 : Combining Travelling Wave Tubes and undulators
The Ubitron :
high-power traveling-wave tube which makes use of
the interaction between a magnetically undulated
periodic electron beam and the TE01mode in
unloaded waveguide.
1. Int roduc t i on
The ub i t ron ( ac ronym for undu l a t i ng beam i nteract i on) is an FEL wh i ch was se t t i ng records for r f powe r
R M. Ph i l l i ps / H i s tory of the ub i t ron
genera t i on
3 15 years be fore the t erm " f ree e l ec t ron l aser "
was co i ned . As is so of t en the case , the i nvent i on of the
I NPUT
OUTPUT
W I NDOW
W I NDOW
ub i t ron was acc i dent a l . The year was 1957 and I was
search i ng , at the GE M i c rowave Lab , for an i nt erac t i on
wh i ch wou l d exp l a i n why an X-band per i od i ca l l y
focussed coup l ed cav i ty TWT osc i l l ated when a so l eno i d
I NPUT
OUTPUT
WAVEGU I DE
WAVEGU I DE
focused vers i on d i d no t. The mos t apparent d i f f erence
BEAM
be t ween the t wo was the behav i or of the e l ec t ron beam ;
ELECTRON
GUN
COLLECTOR
one w i gg l ed wh i l e the other s i mp l y sp i ra l ed . Ou t of a
pape r s tudy of ways of coup l i ng an r f wave to an
undu l a t i ng ax i a l l y symme t r i c e l ec t ron beam came the
I NTERACT I ON
45° MATCH I NG
45° MATCH I NG
RAMP
REG I ON
RAMP
i dea of coup l i ng to the TE O, mode by a l l ow i ng the wave
F i g. 3 Schema t i c of f i rst four exper i menta l ub i t rons . These used FEL- l i ke w i gg l ed penc i l beam conf i gurat i on .
to s l ip through the beam such tha t the e l ect r i c f i e ld
The second par t of the ini t i a l i nvest i ga t i on cons i s t ed
be l ow 50 kV was as h i gh as 50% but wou
dropped
i th
l d wreverse
d i rec t i on at the same i nst ant the e l ec t ron
bu
i
l
d
i
ng
an
X-band
to
observe
beam
/
wave
i
ncreas
i
ng
reach
i
ng
a
l
ow
5%
.
The
l
ow
f
tube
vo l tage ,
of
t ransveedl octo i ity
ehav i or . The i nt erac t i on reg i on of thi s and three subsem i ss i on was unexpec t ed bu t was a t t r i but
nade-reversed .
uen t S-band tubes , i l l ust rated schema t i ca l l y i n f i g . 3,
qua t e magne t i c f i e l d amp l i tude and i nsuf f i c i ent
ad j ustcoup
aThe
l ed cav i ty osc i l l at i on turned ou t to be a s lot
had the appearance of the c l ass i ca l FEL. The exper i b i l i ty . Int erac t i on was observed i n the f orm of r f abmode
wh i ch depends , not on the beam w i gg l e , bu t on
ment a l tube p i c tured i n f i g. 4 used a 0 .3 i nch d i ame t er
sorpt i on be l ow synchronous vo l t age and
ga i n , above
R.
M.
Phillips,
The
Ubitron,
a
high-power
traveling-wave
tube
based
on
a
periodic
beam interaction in unloaded waveguide, IRE Transactions
beam w i th a m i croperveance of 0 .7 . I ndox pe rmanen t
synchron i sm . The omega -be t a d i agram der i ved f rom
average
beam d i ame t er . By the t i me thi s was recogn i zed ,
oni sted
Electron
Issue: 4these
), 231
- 241
(1960)
magne t s , ass
by t r i m Devices
coi l s, we re!(Volume:7
used to w i gg l e ,!and
da t a was
a good
ma t ch to the theore t i ca l hyper bo l a for
ocus the R.
beam
i ng perpend
i cu l of
ar to
p l ane of Nuclear
the wavegu i deand
. TheMethods
2 dB max iin
ga i nofwas
Imum
was
fResearch
exp l or i A272
ng my(1988)
new found
M.. Focus
Phillips,
History
thetheubitron,
Instruments
Physics
1-9 fast wave i nterac t i on ,
he w i gg l e occurs automa t i ca l l y as descr i bed i n a pape r
the same for an r f dr i ve of 1 W and 1 kW , i nd i ca t i ng
i neer i ng adventure wh i ch was to l ast for seven
by Stur rock of St anford [1] , the conf i n i ng force be i ng the
tha t the e f fect was mor e than j ust sma l l an
s i gna l eng
.
produc t of w i gg l e ve l oc i ty and ax i a l magne t i c f i e ld .
I present ed these concept s and ini t i a years
l resu l ts, a tspan
the
the f requency range f rom 3 toGE
60 Microwave
GHz andLab
However , i f no ba l anc i ng force
prov i ded
, theSchool
beam Free Electron!Lasers!and!Energy!Recovery!Linacs
17th E l ec t ron Tube Research Con f erence !(FELs
i n Mexand
i co !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
M. were
E. Couprie,
CAS
set
new
wou l d spread un i mpeded i n the p l ane of the w i gg l e .
C i t y i n 1959 [2] . The resu l ts caused qu i t e a st i r amongpowe r genera t i on records wh i ch wou l d s t and
2 ljuin
2016
Th jeudi
i s prob
em was
so l ved by t aper i ng the magne t i c f i e ld
those who apprec i a t ed the i r s i gn i f i cance . One of those
i
t
t
b
m
T
a
p
p
c
t
m
w
p
o
a
compa rab l e i n e f f i c i ency w i th tha t of a s l ow wave
t rave l i ng wave tube , and tha t the r f energy came ul t i www.lunex5.com
ma
t e l y f rom the ax i a l ve l oc i ty , not the much sma l l er
w i gg l e ve l oc i ty . I t is i nterest i ng to not e tha t the resu l ts
p i c tured i n f i g . 2 are qua l i ta t i ve l y s i mi l ar to those
obt a i ned
exper
i ment a l l ytoat the
s i xallowing
LosTE01
A l amos
abou tby
years
Idea
:coupling
mode
ago w i th an FEL.
I. The origins of the Free Electron Laser
1.5 The ubitron : Undulating Beam Interaction
the wave to slip through the beam such that the electric field
would reverse direction at the same instant the electron velocity reversed.
2
R . M Ph i l l i ps / H i story of the ub i t ron
ELECTR IC F IELD FORCE
Y
DECELERATI NG
U a =12
max = 1/2
D -S
Z
avq
ACCELERATI NG
E
(a)
1 .2
PLANAR
s
s
e
1
2
a
+
s
Z =O
- ;r
(b)
s
-
0
r
COAX I AL
N
(C)
()
PHASE POSITION ( Z-T)
S
N
S
C I RCULAR
F i g. 1.Examples
Examp l es of
of beam-guide
beam-gu i de ub
i t ron conf
i gurat i ons wh i which
ch
ubitron
configurations
prov i de 100times
t i mes the
the interact
ion area
of aof
TWT.
provide100
interaction
area
a TWT.
The electron-wave interactionI .exhibits
the same
I NTRODUCT
I ON type of first-order axial beam bunching characteristic of the
conventional slow-wave traveling-wave tube
=> it can be used in extended interaction klystrons and electron accelerators, as well as traveling-wave tubes.
F i g. 2. Ana l og compu t e r ana l ys i s o f ax i a l beam bunch i ng ver i f i ed TWT- l i ke pe r f ormance.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
X-band tube ( rec t angu l ar gu i de and penc i l beam) down
to S-band , whe re co i l s cou l d be used to produce a mor e
f l ex ib l e w i gg l er f i e ld . As was the case w i th the X-band
tube , the b d i mens i on of the gu i de was i ncreased to
www.lunex5.com about 12 t i mes tha t of s t andard wavegu i de in order to
prov i de amp l e room for the penc i l beam to w i gg l e . Th i s
gu i de mod i f i ca t i on , i t wou l d turn out , was respons i b l e
for the poor beam t ransm i ss i on .
The photograph of f ig . 5 is the th i rd of three S-band
tubes wh i ch were f abr i ca t ed and tested . The peak beam
t ransm i ss i on of the f i rst tube was about 60% at vo l t ages
be l ow 50 kV , bu t aga i n dropped w i th i ncreas i ng vo l tage ,
componen t of the acce l era t i ng f i e l d as is passes near
e i ther wa l l , resu l t i ng i n a ne t ax i a l dece l era t i ng force .
The f undamen t a l per i od for thi s per i od i c d i sp l acement
i nt erac t i on is one ha l f tha t of the TE oi per i od i c i nteract ion, so i t occurs at a l ower vo l tage , even though i t is a
h i gher order mode . W i t h the d i scovery of thus compe t i ng fast wave i nteract i on, mode i nter f erence prob l ems
and mode suppress i on t echn i ques were to become a
pr i ma ry concern for the dura t i on of the seven year
ub i t ron deve l opmen t e f for t .
The second S-band tube d i f fered f rom the f i rst on l y
. M. of
Ph i l l i ps / H i story of the ub i t ron
i n the add i t i on of a mode suppressor wh i ch made Ruse
the fact that the TM modes have st rong l ong i tud i na l
cur rent s i n the s i de wa l l s wh i l e the TE oi mode has on l y
t ransverse cur rents . A mode suppressor cons i st i ng of
ver t i ca l s l ots m the wa l l s backed by th i n s l abs of l ossy
ceram i c was added to the next tube . The measured l oss
to the TM , , mode ranged f rom 30 dB near cutof f to 10
dB at the h i ghest t rapped f requency , wh i l e the l oss to
the TE oI mode was l ess than 0 .5 dB at a l l measured
f requenc i es .
The mode suppressor so l ved the prob l em. Beam
t ransm i ss i on was at l east 80% at a l l vo l t ages through
150 kV . The max i mum ne t gam of thi s tube was a
d i sappo i nt i ng 7 dB but the bandw i d t h was an encouragi ng 30%. Us i ng f eedback to obt a i n sa tura t i on , we mea sured a best e f f i c i ency of 10%.
The th i rd tube , tha t shown i n f i g. 5, was mod i f i ed to
obt a i n h i gher ga i n . I t d i f f ered f rom the second i n three
respec ts :
(1) Gun m i croperveance was i ncreased f rom 1 .0 to 1 .45 .
(2) The c i rcu i t l ength was i ncreased by 50% .
(3) Int ent i ona l TEoI mode l oss was i nt roduced to i nsure aga i ns t re f l ec t i on t ype instab i l i t i es . Th i s was
done by ang l i ng the mode suppressor s l ots by 30 °
to the Y ax i s . Inser t i on l oss to the TE oI mode
ranged f rom 19 dB at 2 .55 GHz to 3 dB at 4 GHz.
2 .5
2 .6
2 .7
2
2 9
0
3 .1
3 .2
3 .3
3 .4
3 .5
Beam t ransm i ss i on of at l east 80%.8 was aga i n ob DR3I VE
FREQUENCY (kmc)
t a i ned at a l l vo l t ages. Sma l l s i gna l ga i n at t wo va l ues of
Measured
sma l l i sditgna
l ga i n of the ub i t ron of f ig. 5, at t wo va l ues of beam vo l t age .
beam vo l t age is shown i n fFi igg.. 6.6 . The
3B bandw
h was
about 30% at 125 kV . The peak sma l l s i gna l ga i n ,
I. The origins of the Free Electron Laser
1.5 The ubitron : Undulating Beam Interaction
F i g . 5. Photograph of S-band ub i t ron wh i ch produced 1 .2 MW
of power . Cod cur rents were rheostat cont rol l ed . Ca thode is
h i dden in the oi l t ank .
Experiments : an undulated pencil beam in a rectangular waveguide.
ob t a i ned a t 135 kV , was 13 dB . Max i mum sa tura t i on
powe r was 1 .2 MW and t he ne t e f f i c i ency (a f t er subt rac t i ng dr i ve powe r ) was 10% .
These ear l y resu l ts we r e a l l repor t ed i n a pape r
pub l i shed i n Oc t obe r 1960 [3] . I n tha t paper , I s t a t ed
tha t an e f f i c i ency enhanc i ng t ape red w i gg l e r expe r i men t
was p l anned . The expe r i men t requ i red the w i nd i ng of
spec i a l th i nner co i l s t o a l l ow t he magne t pe r i od to be
dec reased . A t t he t i me of pub l i ca t i on , the expe r i men t
had been comp l e t ed bu t i t was t oo l a te for i nc l us i on i n
the pape r . A 10% t aper i n t he w i gg l er pe r i od i n t he f i na l
1 / 3 of the t ube i nc reased t he max i mum e f f i c i ency f rom
10% to 13% . Th i s i mprovemen t was in pa r t due to the
conserva t i ve me t hod o f compu t i ng e f f i c i ency . Sa tura t i on ga i n as we l l as ou t pu t powe r i ncreased , l eav i ng l ess
dr i ve powe r to be sub t rac t ed f rom the ou t pu t powe r i n
compu t i ng e f f i c i ency .
5
3 .6
3 .7
300 GHz . One o f the 16 GHz t ubes i s shown in the
pho t ogr aph o f f ig . 7 . The r f c i rcu i t cons i s t ed bas i ca l l y o f
a 1 i nch d i ame t e r p i pe made of i ron and coppe r r i ngs ,
w i t h the i ron r i ngs serv i ng as po l e p i eces for rad i a l
A l n i co V pe rmanen t magne t s. These prov i ded bo t h the
undu l a t i on for t he i nt erac t i on and the beam f ocus i ng .
To gua rd aga i ns t mod i ng prob l ems , each o f the spacers ,
wh i ch sepa ra t ed t he s l i ght l y re -ent rant magne t po l e
p i eces , had embedded to t hem t wo l ossy ce ram i c r i ngs .
The mode suppressor produced no measur ab l e l oss to
t he TE ot c i rcu l ar wavegu i de mode bu t prov i ded 10 ' s of
dB o f l oss t o TM modes o f conce rn. The conve rgen t
so l i d beam gun used on th i s t ube was f rom a GE 20
MW S-band k l ys t ron .
Two of these t ubes we r e bu i l t . The f i rst , des i gned for
170 kV opera t i on , prov i ded l ow ga i n and re l a t i ve l y poor
beam t ransm i ss i on due to i nsuf f i c i ent magne t i c f i e l d .
The second t ube was des i gned to ope ra t e nea re r the 250
!ERLs), Hamburg, Germany,
!May
!June,
kV uppe r31l i mi
t o f –10
the modu
l a t2016
or whe r e t he magne t
pe r i od was l onger and the f i e l d h i gher . Beam cur ren t
was approx i ma t e l y 125 A .
unique features :
- very broad interaction bandwidth which results from the absence of a dispersive slow-wave circuit,
- variable interaction phase velocity--hence, variable saturation power level.
Among the physical embodiments of the Ubitron are a number of higher-order mode waveguide and beam configurations.
=>interesting prospect for high-power millimeter wave amplification.
R. M. Phillips,The Ubitron, a high-power traveling-wave tube based on a periodic beam interaction in unloaded waveguide, IRE Transactions
on Electron Devices !(Volume:7 ,! Issue: 4 ), 231 - 241 (1960)
R. M. Phillips, History of the ubitron, Nuclear Instruments and Methods in Physics Research A272 (1988) 1-9
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and
jeudi 2 juin 2016
3. US A i r For ce t akes ove r
www.lunex5.com
I. The origins of the Free Electron Laser
1.6 The maser discovery
Goal : create a «quantum» microwave sources in replacing the amplification by an electron beam by stimulated
emission in molecules.
In order to do a "quantum" microwave oscillator, an excited molecules is introduced in a microwave cavity which is
resonant for the frequency of the molecule transition.
Population inversion:
- Townes, Basov et Prokhorov : spatial separation of excited molecules (SternGerlach type), efficient but not very practical.
Charles
- proper exciting radiation of the atoms and molecules.
Townes
1949 : "optical pumping", with circularly polarised light for selectively filling some
(1905-2015)
Zeeman sub-levels of atoms (Alfred Kastler (1902-1984, Nobel 1966) and Jean
Nobel 1964)
Brossel).
-1951, population inversion by RF radiation enabling to create samples of
temperature", (E. Purcell and R. Pound, working on Nuclear Magnetic
LE"negative
MASER
A AMMONIAC
Resonance)
Nicolay
Gennadiyevi 1954 : first MASER in the micro-waves
LE MASER A AMMONIAC
ch Basov
(NH3 molecule).
(1922-2001)
Nobel 1964
Charles
Townes,
1954
Aleksandr
Mikhailovich
(+Basov,
Prokhorov
(1916-2002)
Prokhorov
:
Nobel 1964
Nobel 1964)
Jet
moléculaire
Focalisation
Inversion de
population
Cavité
micro-onde
Emission
stimulée
Columbia University
Oscillation
! (1954) 282.
J.P. Gordon, H. ->
J. Zeiger
and C.H.auto-entretenue
Townes, Phys. Rev., 95
J. 1954
P. Gordon,
Zeiger and C. H.PTownes,
99GHz
(1955) 1264.
14 J.molécules/sec,
: 10H.
= 10-9Phys.
W, fRev.,
= 24
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
A. Kastler
(1902-1984,
Nobel 1966)
www.lunex5.com
I. The origins of the Free Electron Laser
1.7 The laser discovery
1958 : principle of realisation of the laser by Charles Townes and Arthur
Schawlow (1921-1999, Nobel 1981)
Bell Tel. I.aboratories,
Charles
Townes
(1905-2015
Nobel 1964)
Arthur
Leonard
Schawlow
(1905-1999
Nobel 1981)
«The extension of maser techniques to the infrared and optical
region is considered. It is shown that by using a resonant cavity of
centimeter dimensions, having many resonant modes, maser
oscillation at these wavelengths can be achieved by pumping with
reasonable amounts of incoherent light. For wavelengths much
shorter than those of the ultraviolet region, maser-type
amplification appears to be quite impractical. Although use of a
multimode cavity is suggested, a single mode may be selected by
making only the end walls highly reflecting, and defining a suitably
small angular aperture. Then extremely monochromatic and
coherent light is produced. The design principles are illustrated by
reference to a system using potassium vapor.»
A. L. Schawlow C. H.Townes, Infra-red and optical masers, Phys. Rev. Lett. 1940-1948 (1958)
Patent, Optical Masers and Communication, by Bell Labs.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
mode would
extremely small ( of the order of 1 micrometer) and becomes
λ become
2Lc
lasers).
C.are
Townes
and A.using
Schawlow
not doable at that time. Nowadays, these
cavities
manufactured
nanotech-at Bell Labs, G
n practice, in order to focus the light transversally and to avoid diffraction losses,
www.lunex5.com
Prokhorov
at Lebedev
propose to feedback
nologies (for VCSEL (Vertical Cavity
Surface Emitting
Laser)institute
semi-conductors
of the mirrors should be concave.The light circulating in the optical resonator is
lasers). C. Townes and A. Schawlow(Fabry-Perot
at Bell Labs, G.
Gould at Columbia and A.
a plane wave, and the radius of the light changes along its propagation.
In case of type used in spectroscopy). In a Fabry-P
1.7institute
The propose
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Germany, 31The
!May beam
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I. The origins of the Free Electron Laser
www.lunex5.com
I. The origins of the Free Electron Laser
1.7 The laser discovery
1960 : First Ruby laser (Ion CR3+ in ruby)
Hughes Research Laboratories
T.H. Maiman, Nature, 187 (1960) 493T. Maiman, Stimulated Optical radiation in Ruby, Nature 187, 493-494 (1960).
T. H. Maiman, Hoskins, D’Haenens, Asawa and Evtuhov, Phys. Rev., 123 (1961) 1151.
In 1954, N. Bloembergen, Basov and Prokhorov propose the 3-level MASER concept : with a proper illumination
of a solid such as a Ruby crystal, population inversion takes place.
first working laser by generating pulses of coherent light from a fingertip-sized lump of ruby
illuminated by a flash lamp
Easier to operate than the equivalent gas based maser. It has been used in particular as a very low noise amplifier.
Theodore Harold Maiman
(1927-2007)
!"#$%$&'$(
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
I. The origins of the Free Electron
Laser
editorial
Remembering the laser diode
1.7 The laser discovery
Fifty years ago, researchers at a handful of laboratories around the world were reporting lasing from
the first semiconductor lasers. Our IT infrastructure today relies on their diligence and success.
GENERAL ELECTRIC RESEARCH AND DEVELOPMENT CENTER, COURTESY AIP EMILIO SEGRE VISUAL ARCHIVES
Applied Physics Letters by Marshall Nathan’s
In 2010, the 50th anniversary of
group at IBM’s Watson Research Labs2 and
Ted Maiman’s experimental demonstration
of the first ruby laser quite rightly gave
Ted Quist’s group from the Massachusetts
rise to substantial publicity, including
Institute of Technology Lincoln Labs3.
celebratory events such as the LaserFest series
A flurry of results then followed from
(www.laserfest.org) and much coverage in a
around the world, including the first visible
wide variety of newspapers and magazines.
semiconductor laser by Nick Holonyak’s
74
1964 CHARLES H. TOWNES
However, in many ways it was actually
group at General Electric’s lab in Syracuse
the successful development of the GaAs
(who became famous for inventing the
semiconductor laser diode in 1962 that really
light-emitting diode that same year) as well
ignited the laser revolution. The fabrication
as demonstrations by Cyril Hilsum and
of a semiconductor laser kick-started the
colleagues at the UK’s Services Electronics
important field of optoelectronics and showed
Research Laboratory and a Russian group of
that lasers could, in principle, be fabricated
scientists led by Nikolay Basov.
in a miniature, cost-effective format that
Speaking at the event, Marshall Nathan
showed great promise for mass-production in
says that in early 1962 he was at IBM
a form similar to electronic devices. Shortly
studying the photoluminescence from GaAs
afterwards, the demonstration of electrically
when the department director Rolf Landauer
pumped devices capable of operating at
announced that he wanted IBM to be the
room-temperature with high output powers
first group to make a GaAs laser and threw a
further added to the practicality and appeal of
team of people onto the project. In February,
semiconductor lasers.
Nathan and his co-workers tried using a
FLASH TUBE
In contrast, if lasers had remained limited
flash lamp to pump a sample of GaAs but
to getting their gain from doped glass crystals
were unsuccessful in achieving lasing. Then,
Fig. 3. Schematic diagram of a ruby (optically excited solid-state) laser. When the such
gas as ruby or Ti:sapphire, or gas mixtures
following further research in September
as HeNe
1962, they observed “spectacular line
flash tube is activated, electromagnetic oscillations occur within the ruby rod,such
and
someor CO2, their technological
narrowing”, which suggested that lasing was
impact would have been considerably less
of these light waves are emitted in a beam through one partially reflecting endand
of the
theworld
rod.of photonics would look very
the USA, Yuri Popov from Russia, Maurice
taking place.
Bernard from France, Jim Coleman from the
“We sent the results to Applied Physics
different. Although the use of high-power
USA and Cyril Hilsum, Robin Thompson and Letters, hand-delivered,” said Nathan. “We
lasers for materials processing applications
John Orton from the UK.
then started to get lots of results very quickly,
and welding might still have
Not very long after the ruby laser was developed, Javan, Bennett such
andastocutting
HerThe competition between various
such as continuous-wave lasing at 4.2 K,
come
fruition, many other tasks that we
scientists (such as Gordon Gould,
room-temperature lasing and measurement
take for granted
of today would probably not
riott35 obtained maser oscillations from neon atoms excited by collisions
Charles Townes, Art Schawlow and
of far-field emission patterns,” said Nathan.
have been feasible. Take, for example, optical
Ted Maiman, among others) to achieve the
“The first real semiconductor laser at IBM
storage and communication networks,
the second kind with metastable helium, in accordance with an ideadata
previousfirst experimental demonstration of a laser
was made in October 1962, and we got the
which today represent two of largest and
36
only amarkets for laser technology. in 1960 is well documented (see the excellent patent out in just five days.”
ly put forward by Javan . This system, illustrated in Fig. 4, requires
most important
account in Jeff Hecht’s book “Beam: The
Astonishingly, Nathan says at the time
is unlikely
that fibre-based data networks,
gaseous discharge through a tube containing a mixture of helium ItCDs,
and
neon
Race to Make the Laser”). However, the
that the researchers at IBM didn’t know that
DVDs and BluRay players would have
quest to develop a semiconductor laser two
they had serious competition from General
been seriously
at low pressure, and two reflectors at the ends of the tube. It oscillates
at thepursued or even considered
Electric and were shocked to learn Hall’s APL
practical without the realization of an efficient years later was arguably just as exciting, fastpaced and competitive, with a handful of
paper had been submitted 11 days before
and low-cost laser diode.
research groups all reported working lasers
their own, effectively scooping them. “We had
Given this context, it is pleasing to see
based on GaAs p–n junctions within a short
no idea that General Electric was working on
that the 50th birthday of the laser diode has
1
9
6
4
C
H
A
R
L
E
S
H
.
T
O
W
N
E
S
76
period in the autumn of 1962.
this,” commented Nathan. This story is not
not been overlooked. The Institute of Physics
Ultimately, Robert Hall (pictured) and his only an interesting history lesson, but also a
in the UK organized a two-day celebratory
group at General Electric’s research labs in
valuable reminder of just how exciting and
seminar entitled “50th Anniversary of the
Schenectady is credited as getting there first.
fast-paced research can be.
❒
Laser Diode” at the University of Warwick
Their report of coherent infrared (850 nm)
on 20–21 September 2012, during which
SILVER
RIBBON
emission from
a GaAs laser appeared in
several of the founding fathers of the
References
1. Hall, R N, Fenner, G. E, Kingsley, J. D, Soltys, T. J and Carlson R. O.
the 1 November 1962 issue of Physical
technology reminisced about the early days
Phys. Rev. Lett. 9, 366–369 (1962).
1
Review Letters . This was simultaneously
of its development and the race to make
2. Nathan M,I, Dumke W.P, Burns G, Dill F, H, Jr and Lasher G
the first laser diode. Speakers included
accompanied by reports of lasing from
SILVER-GOLD
Appl. Phys. Lett. 1, 62 (1962).
3. Quist T.M et al Appl. Phys. Lett. 1, 91 (1962).
Marshall Nathan, formerly of IBM
Labs in
GaAs
devices appearing in the journal
EVAPORATED
STRIPE
1966: Mirek Stevenson
and Peter Sorokin at
General Electric
first dye laser
tuneable yellow to red
....
1962 : R. Hall
first semi-conductor
AsGa laser (diode laser)
1960: Ali Javan
first gas laser (He-Ne)
Gaseous discharge
CW source of infra red, 1 mW
p-n junction of the semiconductor gallium arsenide through
which a current is passed can emit near-infrared light from
recombination processes with very high efficiency.
(MICROALLOYED)
NATURE PHOTONICS | VOL 6 | DECEMBER 2012 | www.nature.com/naturephotonics
Fig.4. Schematic
diagram
of a helium-neon
(gas
discharge)
laser. Electrical
excitation
Javan,
Bennett
and Herriott,
Phys.
Rev. Letters,
6 (1961)
106.
can initiate a steady maser oscillation, resulting in an emitted light beam from either end
of the gas discharge, where there are reflecting mirrors.
Fig. 5. Schematic diagram of a gallium arsenide (injection, or semiconductor) laser. A
small
between
the silver
the molybdenum
disc can
produce50
R. J. voltage
Keyes applied
and T.M.
Quist,
Proc.ribbon
IEEEand
(Inst.
Electron. Elec.
Engrs.),
maser oscillations with resulting emission of coherent infrared radiation.
795
1971: Concept of the
Free Electron Laser
1977 : First FEL in the IR
(Stanford, USA)
1983 : First FEL in the
visible (Orsay, France)
(1962) 1822.
Hall, Fenner, Kingsley, Soltys and Carlson, Phys. Rev. Letters, 9 (1962) 366.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
One might consider the population of the virtual level in a Raman maser
(see Fig. 6) to be greater than that of the first excited state, so that there is no
www.lunex5.com
I. The origins of the Free Electron Laser
1.7 The laser discovery
The limitations of the «optical maser»
«As one attempts to extend maser operation towards very short wavelengths,
a number of new aspects and problems arise, which require a quantitative
reorientation of theoretical discussions and considerable modification of the
experimental techniques used.»
...
«These figures show that maser systems can be expected to operate
successfully in the infrared, optical, and perhaps in the ultraviolet regions, but
that, unless some radically new approach is found, they cannot be pushed to
wavelengths much shorter than those in the ultraviolet region.»
A. L. Schawlow and C.Townes, Infra-red and Optical masers», Phys. Rev. 112 1940 (1958)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
e original paper from A. Schawlow and C. Townes �
[207], it was written that :”As one attempts to extend maser
in Table
1, wavelengths,
considering
that 1γof=new aspects
1 − βx2and
− problems
βz2 − βs2arise,
withwhich
the require
deflection
paramen towards
very short
a number
a quantitative
www.lunex5.com
ation
of theoretical discussions and considerable
ofeBthe
experimentaleBtechniques
used. ” and
eBmodification
uz λu
u λu
ux λu
Kuthat
, Kmaser
Ku = 2πm
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= 2πmo c in
, Kthe
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theperhaps
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ux , Ksystems
uz given
uz infrared,
figurester
show
canby
be expected
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and
c ). In
oc
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The
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concept
emergence
:
Motivations
for
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exotic
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K
1
traviolet
regions, the
but that,
unless
radically newu approach
iswith
found,respect
they cannot
be. pushed
to wavelengths
regime,
angle
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the velocity
is
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to
For
K
ux = Kuz = Ku
γ
γ
J. Madey
orterJ. M.
than
those in the ultraviolet region.”
2
K
«Schawlow
and
Townes’
descriptions
of masers
and
lasers
coupled with
π
1
u
J. Madey,
Univ.,
thought
that
”Schawlow
and
Townes
descriptions
of
masers
and
lasers
couandfrom
ϕ =Stanford,
,
one
has
β
=
1
−
−
.
A
second
integration
gives
the
trajectory.
s
2
2
γ2
2γ
new eigenmodes
understanding
theoffered
Gaussian
free space offered
h the new understanding of thethe
Gaussian
of free of
space
a new eigenmodes
approach to highoffrequency
In the
planar case,
the
electrons
execute
smooth
sinusoı̈dal
oscillations
theconstrained
horin that was
not constrained
by the
limits
totothehigh
capabilities
of electron
tubes
[144]
hein
wondered
a established
new
approach
frequency
operation
thatand
was
not
by
plane,
so that
theestablished
radiation
islimits
kept
in the
the
same
cone.
addition,
there zontal
was ”a Free
Electron
Radiation
Mechanism
that
Could
Fulfill
theseemitted
Conditions”
andIn
considered
thethe
the
to
capabilities
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tubes»
t possible
radiation
processes.
He firstthe
examined,
Compton
which direction.
appeared as the
promisbeam
oscillates
at twice
pulsation
in theScattering
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Themost
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didate. Indeed, Stimulated Compton Backscattering has been analysed by Dreicer in the cosmic blackbody
takes place for the wavelengths
for Electron
which nλRadiation
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an integer,
βs these
n = c(1 −Mechanism
- Was there aλnFree
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n. XXXX chercher la REFXXXXX.
theBack
longitudinal
reduced
velocity
the pulse
electrons.
Theoffundamental
resonant
waveConditions?
Compton
Scattering (CBS)
process
between of
a laser
and a bunch
relativistic particles
(electrons,
(1 −theβshead-on
). Using
the expression
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forhigh-energy
n = 1, i.e.
for λcoming
s, etc.)length
leads to the
production of
radiation
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between the photons
1 = λufrom
particles.
In order
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radiation,
itas
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usePromising
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resonant
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harmonics
in the
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Appeared
Most
hich radiation cone is reduced to 1/γ. For relativistic particles (i.e. γ >> 1), he energy of the produced photons
Benefit
given
by : of using relativistic electrons beams:
2
II. The invention of the Free Electron Laser concept
λu
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nλn =2 2 (1 +
)
4γ E2γ
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2
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ECBS
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the energy of the initial photon beam, θ the λ
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nλ
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) radiation could be tuneable.(3)
n easily 2be changed, so the CBS
y. The energy of the relativistic electrons can
2γ
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alysis of the stimulated Compton Backcattering ware carried out [126]. J. M. J. Madey had the idea to make
Needmore
of high
peakbycurrent
= magnetic
> emitted
nomenon
efficient
using
field radiation
of an undulator
He considered
that ”Relativistic
of
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can [123].
be varied
by a modification
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The
wavelength
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s can
also
notbeam
tell the
differencefield
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photons,
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changing
theincident
gap for
permanent
magnet
insertion
periodic transverse magnetic field for the usual counter-propagating real photon beam”[144] . He was aware of
vices
orexperimental
the power[24]
supply
electromagnetic
insertion
devices).
In theThe
time
retical
workcurrent
of Motz, for
where
radiation from bunch
beams has
been observed.
=> [23]
FEL and
concept
J. M. J. Madey,
Nobel Symposium,
June 2015
domain,
the observer
receives a train of Nu magnetic
periods
whichSigtuna,
can Sweden,
be considn be the
one generated
by an undulator.
J. M. J. Madey,Wilson Prize article: From vacuum tubes to lasers
ered
as
quasi-continuous
emission
of
radiation
with
to ST
the
bending
magnet
Can gain be achieved with such a system?
and backrespect
again, Phys. Rev.
Accel.
Beams 17, 074901
(2014)
radiation. The radiation spectrum, square of the Fourier transform of this train, is
E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
he FEL quantumM.approach
jeudi 2 juin 2016
II. The invention of the Free Electron Laser concept
frequencies due to the scattering of an electron beam by
Ation
least
twoin authors
haveionized
considered
in concluding
detail the
the
cores
neutral and
matter
www.lunex5.com
process
of induced gain
bremsstrahlung
at radio
optical
that appreciable
was available
underand
favorable
frequencies
dueThis
to theanalysis
scattering
of an
electron
beam by
conditions.1-3
deals
with
the radiation
JOURNAL OF APPLIED PHYSICS
VOLUME
42,cores
NUMBER
5
the
ion
neutral
and
ionized
matter
concluding
APRIL
1971
emitted
by
a in
relativistic
electron
beam
moving
through
JOURNAL OF APPLIED PHYSICS
VOLUME 42, NUMBER 5
APRIL 1971
that
appreciable
gaindcwas
available
a periodic
transverse
magnetic
field. under
We willfavorable
consider
Stimulated Emission of Bremsstrahlung
in a Periodic
Magnetic
Fieldwith
analysis
the radiation
the
as This
the
scattering
ofdeals
virtual
photons
using the
Stimulated Emission of Bremsstrahlungconditions.1-3
in aprocess
Periodic
Magnetic
Field
emitted
by a relativistic
electrontobeam
through
Weizsacker-Williams
method'
relatemoving
the transition
JOHN M. J. MADEY
JOHN M. J. MADEY
to the
more easily
calculable
rates
arates
periodic
transverse
dc magnetic
field.
Wefor
willCompton
consider
Physics
Department,
Stanford
Stanford,
California
94305
J. M. J. Madey.: Stimulated
emission
of Bremmstrahlung
in aStanford,
periodic
magnetic
field;
J.
Appl.
Phys.,
42,
1906--1913
(1971)
Physics
Department,
Stanford University,
University,
California
94305
Asthe
shall
be seen, finite
gain photons
is available
under
scattering.
the
process as
scattering
of virtual
using
the
(Received
2020February
in final
finalform
form21 21
August
1970)
(Received
February 1970;
1970; in
August
1970)
Stimulated
emission
of Bremmstrahlung
: transition
the appropriate
conditions
from
therelate
far-infrared
through
Weizsacker-Williams
method'
to
the
of laser-type
the
visible
region
raising
the
possibility
rates
toto the
more
easily
rates for
Compton
The Weizsacker-Williams
methodis isused
used to
to calculate
calculate the
gain
due
thethe
induced
emission
ofcalculable
radiation
The Weizsacker-Williams
method
the
gain
due
to
induced
emission
of
radiation
S
TIM
U
L
ATE
D
EM
ISS
ION
0
F
MAG
NET
I
C
B
REM
SST
R
A
H
L
U
N
G
1913
electron
through
periodic
transa single
electromagnetic
mode
paralleltoto the
the motion
motion ofofascattering.
amplifiers
and
oscillators
thesegain
frequencies
with
the
As
shall
bea seen,
finite
is available
under
arelativistic
relativistic
electron
through
a at
periodic
transinto a into
single
electromagnetic
mode
parallel
through
the
visible
region
raising
verse dc magnetic field. Finite gain is available from the far-infrared
further
possibility
of partially
coherent
radiationthrough
sources
is available
from
the the
far-infrared
through
the
visible
region
raising
verse dc
magnetic field.
Finite gain
appropriate
from
far-infrared
at these frequencies
further
the possibility
of continuously
tunable
amplifiers
and oscillators
We have omitted
from this
analysis
the consequences
that conditions
usefulwith
gainthe
would
bethe
available
to beyond
at
these
frequencies
with
the
further
the possibility
of
continuously
tunable
amplifiersinand
oscillators
and
x-ray
to beyond
10 keV.
in the
ultraviolet
of partially
coherent
radiation
the ultraviolet
and
regions
to beyond
10regions
keY.
possibility
of laser-type
the
visible
region
raising
the
possibility
of the absorption
occurring
in thesources
nuclei lying
just
100
A.x-ray
possibility
of
partially
coherent
radiation
sources
in
the
ultraviolet
and
x-ray
regions
to
beyond
10
keY.
numerical
examples
considered.
ON 0 F MAG NET I Several
C B REM
SST
R A
Hthe
Lare
Uabsorbers.
N G
1913effect of this
In geometry,
the devices
suggested
herein with
resemble
the examples
surface
ofare
The
amplifiers
and oscillators
at these
frequencies
the
ACKNOWLEDGMENTS
Several inside
numerical
considered.
5
process is to reduce the reflection coefficient within further
the
by
Motz
in
1950
the undulator
structures
proposed
possibility
of
partially
coherent
radiation
sources
I wish to thank Professor W. M. Fairbank
for his
At leastthat
two
authors
have
considered
thean where
onsequences
useful
gainline
would
beR=
available
beyond
Mossbauer
from
1 to in todetail
for
angle of
6
and
subsequently
developed
by
him
as
sources
to beyond
10 keV.of
in theencouragement
ultraviolet{j=vz/e
ofand
this x-ray
analysisregions
and to acknowledge
my
process
of induced
bremsstrahlung
radio
and
optical
where
At least
two
authors
have
considered
in the
detail
the coefficient
incidence
of 0.47°
while at
leaving
reflection
lying just
100 A.
millimeter
wave
and
infrared
radiation.
However,
withthe
Professor
H. A.
Schwettman
who has
In discussions
geometry,
devices
suggested
herein
resemble
and
due
to thethe
scattering
of an
electron
by this
outside
line essentially
unchanged.
While
would
fect of
this frequencies
process
of induced
bremsstrahlung
at
radio
andbeam
optical
{j=vz/e
ACKNOWLEDGMENTS
had
a
concurrent
and
independent
interest
in
the
'1'=structures
1/ (1substantially
reduce
theelectron
numberconcluding
of reflected
photons,
Motz'
proposal
was{j2)1/2.
entirely
classical
requiring
a5
cores
in neutral
and
ionized
matter
t within
the the ion
by
Motz
in
1950
the
undulator
proposed
and
frequencies
due
to
the
scattering
of
an
beam
by
of a free-electron laser. In this 6application
to the
thank
Professor
W.still
M.appears
Fairbank
for
his enough bunched
estimated
be large
to
an angle of thatI wish
appreciable
gain
was flux
available
under tofavorable
beam
harmonically
related
toasunique
the
magnet
1/recognized
(1{j2)1/2.the
and
subsequently
developed
him
sources
of
the
ion
cores
in
neutral
and
ionized
matter
concluding
In
the
limit
these
fields
approach
inby
detail
those
he
potentially
encouragement
of
analysisdeals
and
to
acknowledge
my the angular partlcularly, '1'=
beThis
of this
experimental
interest
provided
that
n coefficient conditions.1-3
analysis
with
the radiation
not
apply
toin the
process
of
period.
do
of real
photons
moving
associated
withThese
a wave
packet
millimeter
wave
infrared
radiation.
gain
was
available
under
favorable
properties
forrestrictions
the and
construction
of such
a device
of However,
the
discussions
Professor
H. A. beam
Schwettman
who
has
spread
in theelectron
reflected
beam
due to
imperfections
in
the
e this that
would appreciable
emitted
by awith
relativistic
moving
through
In direction
the
limit
these
fields
in detail
those
the
-proposal
z'. Assuming
that
theapproach
matrix element
for
stimulated
emission.
electron
beam
in was
the
superconducting
linear
accelerator
a concurrent
and
independent
in the
conditions.1-3
This
analysis
deals
thewillradiation
mirrors
could
be keptwith
at a interest
minimum.
Motz'
entirely
classical
requiring a
ed photons,
ahad
periodic
transverse
dc
magnetic
field.
We
consider
ofis
real
photons
moving
in this
associated
with
a resemblance
wave
packet
built
at Stanford.
Itchanging
is also
my
pleasure
to
iscloser
a continuous
and
slowly
of the
aNote
free-electron
Inmoving
this application
to
be function
found
between
Added in
Proof.
The
classical
result scattering
for bunched
the Abeing
e enough
to the
emitted
byprocess
a relativistic
electron
beam
through
as
scattering
oflaser.
virtual
photons
using
the
beam
harmonically
related
to
the
magnet
acknowledge
the
contributions
of
R.
H.
Pantell,
the
Assuming
that
the
matrix
element
for
of
thedirection
initial
photon
mass,
in
the
limit
that
the
photon
partlcularly, radiated
he recognized
the potentially
unique
energy
calculated
using
the
synchrotron
radiathe angular
paper and
that
of Pantell,
and the
PuthofF
who
Weizsacker-Williams
method' field.
to relate
the transition
a periodic
transverse dc magnetic
We will
consider
not
apply
of
period.
These
restrictions
do Soncini,
S. isA.
Johnson,
Levinson,
W.
A.
Little,toand
L.process
V.
energy
in the
electron
restM.
frame
is slowly
large
in changing
comparison
properties fortion
the formula
construction
of(38)]
such is
a device
of the
a
continuous
and
function
scattering
[Eq.
also
proportional
to
the
ctions the
in the
rates as
to the scattering
more easilyofcalculable
rates for using
Compton
proposed
the
use University,
of mass
stimulated
Compton
process
virtual photons
the with
Knight
of
Stanford
andexpressions
of A.inverse
Yariv
of the
stimulated
emission.
electronthe
beamsquare
in theofsuperconducting
linear
accelerator
the
photon
mass
excess,
the
zero
the magnetic
field
strength
provided
that
an initial
of
the
photon
mass,
in
the
limit
that
the
photon
be seen, finite
gain is the
available
under
scattering. As shallmethod'
but
werecan
restricted
inbeobtain
gain
tothe
the
infraredthis
by
scattering
California
Institute
of Technology.
Weizsacker-Williams
relate
transition
being built account
at Stanford.
Ittoisof
also
to
is taken
the my
shiftpleasure
in wavelength
of the
(for
Compton
scattering)
be is
used
to
A
closer
resemblance
to
found
between
sult for
the the
energy
in
the
electron
rest
frame
is
large
in
comparison
appropriatethe
conditions
from theoffar-infrared
through
the
low
microwave
photon
densities
obtainable
at
acknowledge
contributions
Pantell,
the
more emitted
easily
calculable
rates
forH.(38)
Compton
radiation.
If WlO
inR.
Eq.
is understood
topaper
be
desired
transition
rates.
otron rates
radia- to
andMarcuse,
that
ofexcess,
Pantell,
Soncini,
and
PuthofF who
the
visible
region
raising
the
possibility
of
laser-type
with
the
photon
mass
the
mass
zero
expressions
'D.
Bell
System
Tech.
J.
41,1557
(1962).
the
frequency
of the
beam
S. A.AsJohnson,
M.
Levinson,
W. backscattered
A.isLittle,
andphotons
L.
V. at a The
virtualD.photon
mass
excess
can be
computed
in
shall
be
seen,
finite
gain
available
under
scattering.
present
as
compared
to stimulated
the
number
of virtual
photons
onal to
the amplifiers
Marcuse,
Bell System
Tech.
J. 42,
415 (963).
proposed
the
use
of
inverse
Compton
and
oscillators
at
these
frequencies
with
the
2
(for
Compton
scattering)
can
be
used
to
obtain
the
'Yomc
in
the
weak
field
limit
and
if
the
actual
energy
of
Knight
of
Stanford
University,
and
of
A.
Yariv
of
the
M.
V.
Fedorov,
Sov.
Phys.
JETP
24,
529
(1967).
the laboratory
frame
since
it is a scalar
invariant:
ded that
the an
appropriate
conditions
from the
far-infrared
through
in atransition
strong
dcrates.
magnetic
orTheory
electric
field.
further
possibility
ofenergy
partially
coherent
radiation
sources
4 W. Heitler,
The Quantum
Radiation
(Clarendon
but
were
restricted
inof gain
to the
infrared by
scattering
beam
is
selected
to
compensate
for
the
wavedesired
California
Institute
of
Technology.
ngth of
the
2
2
2
2
Oxford,
England,
1960),
p.
414.
'
of
laser-type
the visible
raising
the
possibility
and
x-ray
regions
to
beyond
10
keV.
in the region
ultraviolet
e
=
m
c4=ELp
(hw)L
(qh)2e
(2)
.
v
and
length shift due to the magnetic field [Eqs. (43)The
thevirtual
low
microwave
photon
densities
obtainable
at
photon
mass
excess
be computed
in
rstood to be
H. Motz,
J. I.App!.
Phys.
22, 527 can
(1951).
TRANSITION
RATES
amplifiers
and
oscillators
at
these
frequencies
with
the
In
geometry,
the
devices
suggested
herein
resemble
'D.
Marcuse,
Bell
System
Tech.
J.
41,1557
(1962).
(44)], then in the region of validity of Eq. (38)
the
Motz,
J. App!.
Phys.
826
(1953). invariant:
s at a beam
the present
laboratory
frame
since
it 24,
is
a H.
scalar
asH.
compared
to
the
number
of virtual photons
Since
w= 0 in'H.
the
lab
frame:
5
2 D.
Marcuse,
Bell
System
Tech.
J.
42,
415
(963).
R.
Pantell,
G.
Soncini,
and
E. Puthoff, IEEE]. Quanby
Motz
in
1950
the
undulator
structures
proposed
further
possibility
of
partially
coherent
radiation
sources
A
vector
potential
is
given
by
radiated
energy
per
magnet
semi-period
if the actual
M. V. Fedorov, Sov. Phys. JETP 24, 529 6(1967).
tum Electron.
905 (1968). or electric field.
in a strong
dc
magnetic
and
subsequently
developed
byoftohim
as (Clarendon
sources
2=qhe.
e2 iQuantum
i 4,mv
4 W.
Heitler,and
The x-ray
Quantum
Theory
Radiation
beyond
10 keV.
the ultraviolet
e2== (hw)L
m vP.2c4=ELp
(qh)2e 2(Benjamin
(2)
. (3)
8 R.
Feynman,
Electrodynamics
New
2 regions
2 ofq
r the in
waveA(z)
Re[(Bo/q)eiqz]y
Oxford, England,
1960),
p.
414.
' CB)2.
York,1962),p.94.
'
millimeter
wave
and
infrared
radiation.
However,
d
E
('Yo4e
)(X
s. (43) In
and geometry,
the devices
suggested
2
I. frame:
TRANSITION
5 H. Motz, J. App!. dwdfJ
Phys. 22,
527 (1951).herein resemble
Weizsacker-Williams
method
would RATES
then
J. D. Jackson,
Classical
Electrodynamics
(Wiley, be
New York,
c
4mc
Motz'
proposal
was
entirely
classical requiring
a5 The
Since
w
=
0
in
the
lab
Eq. (38)
the
'H.
Motz,
J.
App!.
Phys.
24,
826
(1953).
1962),
p.
481.
in the
frame yields
a magnetic field
by
Motz
in magnet
1950 expected
the undulator
structures
proposed
to!(FELs
belab
applicable
inI. the
limit:
E. Couprie,
CAS School
Free
Electron!Lasers!and!Energy!Recovery!Linacs
and
!ERLs),
Hamburg,
Germany,Dokl.
31 !May
–10Nauk.
!June, SSSR
2016
bunched
beam
harmonically
related
to
the
7 R. H. M.
Pantell,
G.
Soncini,
and H.
E.
Puthoff,
IEEE].
QuanL.
Landau
and
Pomeranchuk,
Akad.
A
vector
potential
given by
This
result
remains
valid
for
arbitrarily
large
magnetic
6
and subsequently
developed
by
him
as
sources
of
e2
tum
Electron.
4,
905
(1968).
92,
535
(1953).
i Vmvi mve2i
i =qhe.
not
to(Benjamin
of
period.
Thesefields.
restrictions
do
B=
xA=
-i) Boeiqz]i.
Evidently
the apply
increase
inthe
theprocess
scattering
hv=an'Yhqe»
qhe,
(4) of (3)
jeudi 2 juin 2016
8 R. P. Feynman,
Quantum
Electrodynamics
New transition
11 For
account
of the=Re[(
experimental
features
this
II.2 The FEL quantum approach
z'.
2
3
5
7
3
9
10
and
where
In the lim
and
associated
the direct
In
the lim
scattering
associated
of the init
the
direct
energy
in
with the p
scattering
(fortheCom
of
ini
desired
tr
energy in
Thethe
virp
with
the
(forlabora
Com
desired tr
The vir
Since
w=
the
labor
The w
We
Since
=
expected
The We
which red
expected
transition
electron
frame red
w
which
E=
field
transition
period Aq
electron
set equal
frame
w
of thisE an
=
field
With
period Aqa
beam
the
set
equal
in this
the ele
of
an
With a
beam the
Since the
in the ele
with E the energy of the initial photon beam, θ the angle between the CBS photons and the electron beam
II. The invention
of the Free Electron Laser concept
trajectory. The energy of the relativistic electrons can easily be changed, so the CBS radiation could be tuneable
ph
www.lunex5.com
First analysis of the stimulated Compton Backcattering ware carried out [126]. J. M. J. Madey had the idea to mak
the phenomenon more efficient by using the magnetic field of an undulator [123]. He considered that ”Relativisti
electrons can also not tell the difference between real and virtual incident photons, permitting the substitution of
strong, periodic transverse magnetic field for the usual counter-propagating real photon beam”[144] . He was aware o
J. M. J. Madey.: Stimulatedtheemission
of Bremmstrahlung
in a periodic
magnetic
field; where
J. Appl. radiation
Phys., 42, from
1906--1913
(1971)has been observed. Th
theoretical
[23] and experimental
[24] work
of Motz,
bunch beams
J. M. J. Madey,
H. A.beSchwettman,
W. M. Fairbank,
IEE Trans. Nucl. Sci. NS-20 (1973) 980
fields can
the one generated
by an undulator.
II.2 The FEL quantum approach
4.4.2
FEL quantum
Virtual photons : associated to
theThe
magnetic
field approach
Weisäcker-Williams approximation:
According to the Weisācher-Williams approximation, the undulator field of period λu can be assumed to be a plana
Undulator : similar to the fieldwave
of a ofplanar
wave of wavelength ; λu
virtual photons. By Lorentz transformation,
the wavelength λ � of planar wave in the moving frame of th
electrons in the undulator, is given by :
Fields in the moving frame of the electrons in the undulator
Undulator wavelength in the electron ‘s frame : λu/Υs = λ’
λ� =
λu
γs
(79
the electrons see the magneticPhoton
field as
a planar wave
emission and absorption are forbidden by conservation of energy and momentum. For free electrons, on
can then consider a two photon process, such as Compton scattering, as shown in Fig. 22. The emission is then again
given
by the Doppler
according
to :
absorption
forbidden
dueeffect,
to the
conservation
Photon emission /
of energy and momentum
=> for free electrons : two photon process: Compton scattering
emission :
Doppler effect λ = λ’ / (1 + βs) Υs= λu/ 2 Υs2 = λu/ 2 Υ2
Stimulated Compton scattering
gain : transition rate(diffusion) - transition rate (absorption)
does not depend on Planck constant.
E. Schrödinger, Annalen der Physik IV, Folge 82, 257 (1927)
P. L. Kapitza, P. A. M.ab Dirac, Proc. Cambridge Phys. Soc. 29, 297 (1933)
H. Dreicer, Phys. Fluids 7 (1964) 735
R. H. Pantell, G. Soncini, H. E. Puthoff, Stimulated Photon-Electron Scattering, IEEE Jounral of Quantum Electronics 4 (11) 906-908 (1968)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
The original calculation, performed in [123], is not reproduced here. One prefers nowadays to use� a classical
approach, which is simpler and which can explain the FEL in the majority of cases.
s
In
the Raman
regime,ofthethe
scattered
wavenumber
k is the
sum / difference o
II. The
invention
Free
Electron
Laser
concept
plasma wavenumber k�p , leading to the Stockes and anti-Stockes lines :
www.lunex5.com
4.4.3
The
FEL
regimes
Synchrotron
andpulsation,
Free Electron
Laser
e in the electron
frame,
with
ω p radiation
the plasma
ωr the
resonant pulsation, and ωs the
Synchrotron
radiationand
andFree
Free
Electron
LaserElectron
II.3 The
nchrotron
radiation
and
Free
LaserFEL regimes
Synchrotron
radiation
Electron
Laser
� is �
�
The FEL can thus be described as a Stimulated Compton Scattering, as shown in Fig. 23. If the electronic density
=
k
±
k
k
The
Raman
FEL
regime
s
i
p
large enough, a plasma wave can develop.
31 31
The
RamanFEL
FELregime
regime Synchrotron radiation and Free Electron Laser
The
Raman
Synchrotron radiation and Free Electron Laser
� is the sum / difference of the incident wavenumbe
In
the
Raman
regime,
the
scattered
wavenumber
k
Raman
regime k� and
�
Compton
regime
s
In the Raman regime,In
theThe
scattered
wavenumber
k
is
the
sum
/
difference
of
the
incident
wavenumber
of the
the
laboratory
frame,
it
comes:
�
s
i k� and
Raman
FEL
regime
�
In the Raman regime,
the
scattered
wavenumber
k
is
the
sum
/
difference
of
the
incident
wavenumber
of the
s to the Stockes and anti-Stockes lines :
i
,
leading
plasma
wavenumber
k
p
, leading
to
the
Stockes
and
anti-Stockes
lines
:
plasma wavenumber
k� �pThe
Raman
FEL
regime
to
the
Stockes
lines :
plasma wavenumber k p , leading
In the Raman regime,and
the anti-Stockes
scattered wavenumber
ks� is�scattered
the sum / wavenumber
difference of the
incident wavenumber k
the
k
s′ is the sum /
� is� the� sum / difference of the incident waven
�anti-Stockes
� the�wavenumber
Inplasma
the Raman
scattered
k
, leading
Stockes
and
linesincident
:s =ω
wavenumber
±
k
ks�� = kto
=
ki ± kofp the
k
s
s
The scattered wavenumber
ks′regime,k�pthe
ω
± ω(83)
difference
wavenumber
i�
p�
s
i
p (83)ki′ and
=
k
±
k
k
�
s
i
p
� wavenumber
to the Stockesofand
anti-Stockes
lines : kp, leading to the
plasma
k p , leading
�the
�:
equals
incident
wavenumber
k
′:
the
plasma
wavenumber
i
avenumber
equals
the
incident
wavenumber
k
In
the klaboratory
frame,
it
comes:
�
�
�
s
i
In the itlaboratory
frame, it comes:
p
=
k
±
k
k
In the laboratory frame,
comes:
s
i
p
Stockes
lines
where the plasma pulsation ω is given
byand
: anti-Stockes
he Raman FEL regime
the Raman regime, the scattered wavenumber k is the sum / difference of the
asma wavenumber k , leading to the Stockes and anti-Stockes lines :
p
ks� = ki� ± k�p
±
ωs = ωi(82)
� ω p ��
In the laboratory frame,ωits comes:
= ωi ± ω p
(84)
ωs = ωi ± ω p
�
� (84)
In the
it comes:
where the plasma pulsation
ω plaboratory
is given by frame,
:
si ± ω p i n ep2
ω
=
ω
J
e
s
where
theω
plasma
pulsation
ω
is
given
by
:
23 Stimulated
Compton
Scattering
scheme
in
the
electron
frame,
with
ω
the
plasma
pulsation,
ω
the
resonant
pulsation, and ω
where theFig.plasma
pulsation
is
given
by
:
e
e
p
r
s the
p
p
�
�
scattered pulsation
ωp �
=
=
2
3
3
� ne eω p is given
�
� Jby
where the plasma pulsation
:
ωs = ωi ± ωε
ee
p o mo γ
ε
m
cγ
o
o
ωp =
(85)
23 =
2
n
e
J
e
3 �
n
e
J
e
e
e
e
e
ε
m
γ
ε
m
cγ
�
o o
o o
ωp =
=is given
(85)
ω
=cγ 3:
=
where the plasma
pulsation
ω
3
2
p
3
3
εo mo γ
εopmoby
Joecγ
e
εothe
mno eγecurrent
εo mdensity
with
n
the
electronic
density
and
J
Je = ne ec .
ω
=
=
with neThe
theCompton
electronic
density
and
J
the
current
density
J
=
n
ec
.
p
e
e
e
e
e
3
3
�
�
FEL regime
εo mo γ
εo mo cγ
done by the
Practically,
one considers
that
the
FEL
is
in
the
plasma
regime
if
the
number
of
plasma
oscillation
with
ne the electronic
density
and
J
the
current
density
J
=
n
ec
.
2
e
e
e
with
ne the
electronic
density
and Jthee that
the
current
density
ne eciplasma
.
nsein
Je eNpp regime
Practically,
one
considers
the
FEL
if the num
e e= the
In the Compton
regime,
the scattered
wavenumber
ks� equals
incident
wavenumber
ki� :isJ
electron
whileone
it travels
intowith
the undulator
is
at
least
one.
ω
=
=
done
by
the
Practically,
considers
that
the
FEL
is
in
the
plasma
regime
if
the
number
of
plasma
oscillation
N
ne the
electronicthat
density
and Jeisthe
current
density
Je =3 nif
. number
pplasma
e ecthe
3p of plasma oscillation N
Practically,
one
considers
the
FEL
in
the
regime
ε
m
γ
ε
m
cγ
Practically,
one
considers
that
the
FEL
is
in
the
plasma
regime
if
the
number
of
plasma
oscillation
o at
o least one.
o
�
� the undulator is
electron
while
itoneistravels
into
electron while it travels
into the
undulator
at least one.
�in the plasma
(82)
kthat
Practically,
considers
regime
if theonumber
of plasma oscillation N p
s = kithe FEL is
while itwhile
travels
into
the
undulator
is
at
least
one.
by the electron
it travels
into
the
undulator
is
at
least
one.
Np doneelectron
p
Nuthe
λu ωundulator
Je e one.
Nu λu into
p andNJu λuthe
electron
it=travels
atcurrent
least
with newhile
theNpelectronic
density Je =�
ne ec .
= e is�
=density
�
3
λ
2πc
2πc
ε
m
cγ
N
λ
ω
N
λ
λ
J
e
N
o oe
u that
u p the FEL
u pu
u u
�if the number of plasma oscilla
Practically,
plasma
regime
= Nu λuis inNthe
Np one
= considers
=
λ
ω
N
λ
ee p
Nu λu
Je e
ucγ
u3λN
pωupλu N
u uλ
u u Nu λJJueeω
N
λ
N
λ
2πc
2πc
ε
m
u
u
u
u
p
o
o
=
N
=
=
electron while it travels into the undulator
atpleast
one. = 2=
p N p = is N
Thus N p > 1 if
=2πc
33 =e
λp λp =
2πc
2πc
εεoom
e
oocγ
2πc
m
cγ
λp
2πc
2πc εo mo c
�
Thus No > 1 if
2
3
3
p
4π εo mo c γ
3 Nu λu
3
N
λ
ω
λ
J
e
N
Thus N pThus
> 1Nifo >if 1 if
(86)
Je <
u
u
p
u
u
e
o
o
o
o
2 λ 2N
2eN
3 3=
=
=
u
4π
ε
3
o mouc γp
Thus No > 1 if Je <
λp
2πc
2πc
ε
m
cγ
o
o
(86)
2 ε2 εm
3cγ3 γ3 3 periodic transverse
4π
m
M.manque
Kroll, P. L. Morton,
M. N.XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Rosenbluth, Stimulated emission from relativistic
through
a
spatially
o
o
AN CLIO
4π
c
eNu2 λu2 electrons passing
o o
J
<
e
<
J
2λ
2
magnetic
field., Phys. Rev
A 17 (1978) 300
e
e
e
e
e
eN
Thus
N
>
1
if
2
2
o
u
u
eNu λu
2
3γ 3
manque AN CLIO XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
4π
m
c
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May
–10 ε
!June,
2016
o o
manque AN CLIO XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
J
<
2
3
3
manque
AN CLIO XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
jeudi4.4.4
2 juin 2016
The FEL classical
approach
4π εo meo c γ
2 2
ks�
=
ki�
k = k ±k
In the laboratory frame, it comes:
ω = ω ±ω
where the plasma pulsation ω is given by :
ω =
�
ne
=
ε m γ
�
Je
ε m cγ
with n the electronic density and J the current density J = n ec .
Practically, one considers that the FEL is in the plasma regime if the number o
I; (Ig
II. The invention of the Free Electron Laser concept
analysis of the small-signal
regime
a free-elecI((s) = 2c
~oh((s) of+((s)l
the
amplification is due to stimulated scattering
www.lunex5.com
and )'o is the classical radius of the electron. The term sin(pL/2)/(pL/2)
appearing in the gain formu
n distribution.
la is a, consequence of the finite length of the cavity. As pointed out by Sukhatme and Wolff, this finit
the momentum
conservation
ness implies
a
field of period
a pure
electromagnetic
field law is relaxed, so that electrons with a momentum with
~, by that
can scatter light from &; to w, Et is therefore natural to consider two cases,
in this approximation
cavity bandwidth
re- Weizsäcker-Williams
of wavelength
:
limits. In the large-cavity
small-cavity
limit, the electron momentum
namely the large-cavity and
Vuat)MF.
MovRλu1Y
PHYSICAL
LETTER
ireplaced by a pure
electromagnetic REVIEW'
field of wavelength
for extreme relativistic =
limit : the static undulator
fieldh7,ofNt
period
broad
the
which
distribution
to
bandwidth,
can
is
compared
cavity
therefore
be
very
approximated
=(1+P)Z,
2~„
~,
by
=
small-cavity limit transverse
to the opposite
corresponds current
case, where the initial electron mome
λi = (1 + 6βfunction.
J
s) λu ≈ 2λThe
u
t
=ch, ((o, =ch, is the frequency of the incident (scattered) field.
hin
tum distribution function and
F(P,(d,
) can be taken as )a () function,
andof phase
approximation, and neglect the depletion of t
ing amplitude Case
erioda pure transverse
(2
F(t.) =I{P.-Po)
sumed to be electromagnetic
very intense.field
or
=>
Usual classical
problem,
to scattering
at a constant
rate inside
thedistribuelectrons
be injected
limit
of a homogeneously
lat
Taking
thethe
broadened
medium.
We shall consider
This corresponds
to of
thiscav
only the
e
We
the
describe
motion
electron
electron motion : collisionless relativistic
complicatedofbythe
the Stanford
relativistic experiment.
nature of
to the condition
ter
since
it
corresponds
case,
adiation
the
collisionless
relativistic
t)
P,
by
f(x,
Boltzmann equation, with P the canonical h'"=n, F(t),
the ),
particles
Maxwell
With
formula,
becomes
the
gain
(29),
anaBoltzma,
nnx equation'
momentum,
the position
equations
the
electron
and
is
the initial electron mom
where
is
density,
F(t),
n,
)
Relevant
radiation
:
off, ~
'
=
n
(sing/)))'+
(sinn/))}'yo'[I
+(Uo/c)'j
(3
sf mh, h;
af o'Uo', der I;correction
«f = af +x]
back
scattered,
with
a
Doppler
shift
h
is
to
d'g
cL
-h;
h,
=0,
+P]'
(3)
'
dt Bt
Bx,
BP&
of
the
wavelength
ewhere vo H~/OPO an
'!
—
=
h")(z,
expl-ia(d(t
c. , n,
)j+c.
z/U.noting
p„f)
reduced
distribution
in
Maxwell
eq. that
that Development
where ofP the
is reduced
the
canonical
momentum,
x
posithe
and
with
and
term
obtain,
Eq.
(18)
distribution
in
perturbations
diaz
n = p. L/2.
is small-signal
»k& for y»=>small
and a: incident
dot expresses
tion, theory
total
derivative with
1, signal gain
and scatteredthe
modes
are kept
Thetime.
the bracket
secondThe
termtotal
inside
is of the orA'"
respect to
number
of electrons
d
n
of
der
New hyp :
fiI
II.3 The FEL classical approach
.
24-
'
——
'„',
—
'
'
N(t)
a.
'
is
- slowly varying amplitude and
phase
(sin))/r)) )(;/2)(L && 1.
= J«3xf«'Pf(x,
- depletion
of the
incident field neglected
N(t)
P, t).
,
(32)
Thenetpoint
η=0 : no
gain g =0 corresponds to the condition for
(4)
rexact
Therefore, except for g = 0, we can neglect this η<0 : v>v
conservation of momentum,
and, at this
in Raman scattering
o, gain, eq. of Stockes line
mag- => electron
The Boltzmann
is coupled via the trans- η>0 : v>vo, absorption, eq. of anti- Stockes line
equation
density fluctuations
(bunching)
responsible
the scattering
verseforcurrent
J~ to the Maxwell
s
+V A —e
the
coefbora-
where A is
equations
We observe that h(') describes the electron density fluctuations
8
A/st
= —poJr, scattering.
The Gain is produced by a bunching of (5)
the electronic density in presence of a field
Introducing h into the Maxwell equation, and integrating
the vector potential, and
small-signal gain n, defined by
F.Jr(x,
A. Hopf,
Scully,P-,
W. H. Louisell, Classical theory of a(6Free Electron Laser, Opt. Comm. 18 (4) (1976) 413-416
ef«'PM.vrO.f(x,
t)P.=Meystre,
F. A. Hopf et al., Classical theory of a free-electron laser, Phys. Rev. Lett 57 (18) 1215-1218 (1976);
t).
the electron charge, and v~ the transHere, M.e E.is
Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
ion
verse component of the electron velocity.
jeudi 2 juin 2016
(bunch
over the len
www.lunex5.com
II. The invention of the Free Electron Laser concept
II.3 The FEL classical approach
Appropriate magnetic field description
Studies on radiation from electrons traveling through a static transverse periodic magnetic field : classical,
semiclassical, and quantum field theories.
Stimulated emission rates and laser evolution equations describing exponential gain and saturation.
One-body classical Lorentz force equation in the presence of periodic magnetic field and a plane
electromagnetic wave.
Phase space paths for electrons are related to those of a simple pendulum and describe laser gain, saturation,
and coherent electron beam modulation.
A single particle classical theory : amplification due to the single electron stimulated Thomson scattering.
necessary tool for the description of the electron dynamics in a storage ring with a free electron laser device.
Saturation : Jacobi elliptical functions
W. B. Colson, Theory of a Free Electron Laser, Phys. Lett. 59A, 187 (1976)
W. B. Colson, One body electron dynamics in a free electron laser, Phys. Lett. 64A (2), 190-192 (1977)
W. H. Louisell, J. F. Lam, D. A. Copeland,W. B. Colson, "Exact" classical electron dynamic approach for a free-electron laser amplifier, Phys. Rev. A 19
(1) (1979) 288-300
W. B. Colson, C. Pellegrini, and A. Renieri, editors for the "Free Electron Laser Handbook", North-Holland Physics, Elsevier Science Publishing Co. Inc.,
The Netherlands (1990).
A. Bambini, A. Renieri ,The free electron laser : A single particle classical model, Lett. Nuovo Cimento 21, 399-404 (1978)
A. Bambini, A. Renieri , S. Stenholm, Classical theory of a free electron laser in a moving frame, Phys. Rev. A 19, 2013-2025 (1979)
gain scheme
electrons
+ Undulator
+ Electromagnetic
wave
Lorentz
equations
electron
bunching
Maxwell
eq.
coherent
emission
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
Marie
The FEL6resonance
Fig. 25 Intensity spectral distribution for different values of N , in red (resp. green), the undulator number of periods
II. The invention of the Free Electron Laser concept
u
multiplied by 5) with respect to the blue case.
In the classical
[124],
let’s consider
plane waveoscillations
traveling in the
sameh
Theapproach
electrons
execute
smooth asinusoidal
in the
radiation,
is
stored
in
an
optical
cavity
(see
Fig.
??a),
ena
electricII.3
field
in
the
trajectory
plane.
This
wave
can
be
the
spontaneous
emission
FEL classical
thatThe
the radiation
is kept inapproach
the same emitted cone. In addition, t
resonator),
an
external
optical
wave
properly
tuned. direction.
optical
wave
on
many
passes.
FEL
oscillators
cover
aMarie-Em
spe
at or
twice
the
pulsation
in
the
longitudinal
The interfere
The
FEL
resonance
6
As shown in Fig. 26, the electron is resonant with the light wave of wavelength
Themirrors
resonance
for
the
wavelengths
when
the
n
In the classical
approach
[124],
let’sλconsider
awhich
plane wave:traveling
in thethe
same direction
as the ele
to
the
VUV,
where
are
available.
After
theoreti
by
λ
,
the
wave
has
travelled
by
λ
+
λ
or
more
generally,
with
n
being
an
integer
u
u
r
The
electrons
execute
smooth
sinusoidal
oscillations
the
hor
Consider a plane wave travelling in the
same
direction
as the
electron,
with
field in
the
trajectory
plane.
electric
field
in the trajectory
plane. This
wave its
canelectric
be the spontaneous
emission
(onein
pass
or stored
The
travel
times
the optical
electrons
resonator),
anby
external
wave properly
tuned.photon writes :
The electron
is resonant
with
the
wave
if :spent
that
theorradiation
isIR
kept
inand
thethe
same
cone. In addition,
ther
concept
in
1971,
the
first
FEL
wasemitted
achieved
in 1977
www.lunex5.com
shown
in Fig.
26, the by
electron
with
lightc(1
wave−
of wavelength
nλthe
βs )t λr if, when the elect
while the electron progresses by λu, theAswave
has
travelled
λu+ isλ,resonant
(λu+ nλ)
n=
to
atλutwice
the
longitudinal
The
interferenc
by
, the wave
has pulsation
travelled by λuin
+ λthe
generally, withdirection.
n being an integer
λu +
nλr .
r or more
λ
+
nλ
λ
u
r
The travel times spent by the electrons and the photon uwrites
=:
(Stanford,
USA)thein
the oscillator
configuration.
ACO
(Or
λu
for
which
:
wavelengths
when
the
λ
n
with n an integer, βs the longitudinal
reduced
velocity of the
v
c
s
λ
λ + nλ
the second
worldwide
FEL
(first
visible
radiation)
in
1983
=
damental
resonant
wavelength
is
obtained
bor
n
=
1,
i.e.
for
λ1 =
v
c
so :
nλprogresses
n = c(1 −byβsλ)t, the wave has travell
Fig. 26 Undulatorsoresonance
condition : when the electron
:
λ
gets the
expression
of the
the
of βand
monic generation
[?]
in the UV
VUV
[?],
followed
byre
s , one
longitudinalUsing
velocity of
the expression
electrons
1λ ( β
) ele
λλ u:11− −
λβu )(1(1+ β−velocity
) βs )(11+
− of
ββsthe
1 s theto
−
β βs λ (1reduced
with n an λ
integer,
longitudinal
uλaccording
and its harmonics,
(
=
λ
=
−
1)
=
)
=
λr [?].
= λiu
= ( First
−β 1) =
)n = β (1(+ β )
n
n
β
β
(1
+
β
)
FEL
(Orsay,
France)
FEL
applications
started
damental resonant
1, +
i.e.βsfor
n βswavelength
n is βobtained
nbor n =
βs (1
) λ1 = λ
s
to + λ /2v
u
s
2
the expression
of
the
reso
Using [?,
the expression
of
βs , one gets
K
λ
UV-FELsLet’s
inconsider
biology
?]
and
surface
science
[?]
in
1993
uβ ≈ 1, the udenominator of the
first
the
case
of
a
planar
undulator.
With
s (1 +
)
and its harmonics,Planar
according nλ
to :n =
2
K
2γ
2 the resonant wa
1
+
in
the
numerator,
2 and built
developing
the expression
of 1 nm
− βs2 =[?].
were then
down
to 190
γ
γ
2
u
u
r
s
u
r
u
s
s
u
s
2
s
s
2
u
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s
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s
s
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) varied by a
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undulator magnetic field (by changing λthe
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)be varied by a mo
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then composed
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(see Fig. ??a),
enabling
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with
the
II.
The
invention
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the
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Electron
Laser
concept
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cillators
cover a spectral range from the THz
The FEL
e. After the theoreticalII.3
prediction
ofclassical
the FEL approach
Energy
exchange
=> bunching
s achieved in 1977
on the
MARK-III
linac => amplification
Light wave-electron
interaction
figuration.
ACO (Orsay,
France) [?] provided
The amplitude of the interaction only depends on the
The FEL oscillator :
e radiation)
in
1983
and
first
FEL
based
harlongitudinal position of the electron in the electron
the historical configuration
UVbunch
[?], followed
by results
λr. on the SuperACO
with the periodicity
optical multi-pass, low gain regime
The electronstarted
tend to bunch
given positions,
pplications
in thealong
infrared
and in the
separated by λr.
e science [?] in 1993.Various FEL oscillators
Bunching (λr separation) takes place by velocity
modulation (electrons set in phase).
→
−→
= E−
v =0
dt for λ= λr, there is no average energy
•
(29)
exchange at first order: half of the electron gain
energy, half of them loose energy
Ku2
2 2
(1 +
+ γ θ )to occur, λ should be slightly (30)
For the interation
2 from λr :
different
one finds that for λ> λr amplification (gain and beam
e ofdeceleration)
mirrors, short wavelength FEL are usu(beam(SASE)
acceleration)
for λ< λr absorption
mplified Spontaneous
Emission
(see
GαLond2/Υ3
Optical feedback
with an optical
cavity
pontaneous
emission
at the
input of the FEL
CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
saturation M.inE. Couprie,
a single
pass after a regime of
jeudi 2 juin 2016
www.lunex5.com
II. The invention of the Free Electron Laser concept
Gain expression
II.3 The FEL classical approach
Gain expression
mall signal gain is given by :
Small signal gain :
�2 ∂
Ku2 Lu 3 �
2πe2
2
)
sinc
G=n
ρ
(
(ξ
)
−
J
(ξ
)
(πNu η)
J
n−1
n+1
e
2
2
2
εo mo c
λu γ
∂γ
e finds
here on
thethemain
ofwave
the isgain.
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sign ofcharacteristics
(λ − λr), the optical
either absorbed to the benefit of a gain of kinetic energy of the
electrons,
or as
is amplified
to the of
detriment
of the
energy ofThe
the electrons.
e gain
varies
the inverse
the cube
ofkinetic
the energy.
higher the energy, the lower the gain. But, ac
onance condition, short wavelength operation requires the use of high electron beam energies. In con
G varies as the inverse of the cube of the energy. The higher the energy, the lower the gain. But, according to the
ame
undulator
length,
gain is operation
smaller requires
at shortthewavelengths
thanbeam
at longer
ones.
resonance
condition,
shortthe
wavelength
use of high electron
energies.
In consequence, for
a same undulator length, the gain is smaller at short wavelengths than at longer ones.
The gain is proportional to the electronic density. The more electrons interact, the larger the gain. For short wavelength
FELs where the gain is naturally small, one should employ beams with high electronic densities.
The gain is proportional to the beam current.
The gain is proportional to the third power of the undulator length, it seems that the longer the undulator, the higher the
gain. As the undulator length, the gain width also decreases by 1/nNu, because of the interference nature of the
interaction. Temporally, the light pulse should remain in the longitudinal bunch distribution, for the interaction to occur.
Similarly, both the optical light and electron bunch should overlap properly all long the undulator propagation.
To account for these effects, letʼs introduce some correction factors in the gain.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
wo 2
wo 2
1
+
(
)
1
+
(
∆
λ
1
perfect
the laser transverse modes and the
2σx
2σz )
ven
by : transverse overlap between
(
)hom = ∆ λ
(164)
1
λn mode
nN
and
σz . Considering a laser of TEM00
of
w
the transverse
u )hom
A first
reduction
factor
can
from a non perfect transverse overlap between
o , occur
( waist
=
(164) the
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Besides,
the
spontaneous
emission broadening
due to
λntheofMadey’s
1 according
u theorem,
transverse
dimensions
thenN
electron
beam
σxterms
and σz(163)
. Considering
a laser of TEM00
s the inhomogeneous broadening
from
different
contributions.
The two
first
are
related to the
�
Ff = � result
II.3
FEL
classical
approach
affect
directly
the
gain.
The
homogeneous
linewidth
given
: are related to the
w
wis
o The
o given
2 factor
2 from
whereas the inhomogeneous
result
different
contributions.
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firstbyterms
filling
by
:
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1
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)
eam emittance.
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2σz
Gain
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terms
electron beam emittance.
1
∆λ
1
2θ 2
�
�
=
(163)
1
∆
λ
γ
• Transverse
filling
factor spontaneous
: Non perfectemission
transverse
overlap due to
ding the
the Madey’s
theorem,
broadening
energy
spread and
emittance
(
)
=
hom
2
2
�
Ff =λn�
wo 2
wo 2
( (TEM00
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(165)
nN
u
the
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transverse
modes
1 + homogeneous
( 2σ
)
1
+
(
)
K
gain. between
The
linewidth
is
given
by
:
w
wo 2 (165)
λn
o 2
( u )div =
2σz
x
1
+
1
+
(
)
1
+
(
2
Ku
2nx and σz.
2σx
2σz )
λ
and the transverse dimensions
of
the
electron
beam
σ
1+ 2
whereas the inhomogeneous broadening
result from different contributions. The two
∆λ
1
2K2 σ 2
2π
∆
λ
electron
beam
emittance.
( : According
)hom Besides,
=due
(164)
• «Inhomogeneous
reduction»
the
the
Madeyʼs
theorem,
spontaneous
emission
broadening
due to energy
spread du
u ∆ λspread
m, spontaneous
emission
broadening
to
energy
and
emittance
according
the
the
Madey’s
theorem,
spontaneous
emission
broadening
2σ
)
=
(166)
(
γ
λ
nN
σ
n
u
and emittance affect directly the gain.
(166)
= homogeneous linewidth is given by :
λ
1 + the
Ku2( gain.
λu2 )σγThe
n
ewidth
is given by :
affect directly
λn The twoγ first terms are related
nhomogeneous
broadening
result from different contributions.
to the γ 2 θ 2
∆
λ
Inhomogeneous
contributions
Homogeneous
linewidth
on
and Free comes
Electron
(
)div =
r contribution
fromLaser
thecomes
electron
beam
energy spread.
mittance.
Another contribution
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electron
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Ku2 1
∆
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λ
•
Electron
energy
spread
•
Electron
beam
emittance
n
∆λ
1
1 +=2
(
)
hom
(
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(164)
2σ
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λ
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2
γ
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2
2
�
�
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θ
γ
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nNu
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λ
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σ
u −1
N
λ
∆ λ (165) 2σγ (167)
(
)div =( λ )σ2 γ = ( γ )σ =
u
u
(167)
Ku =
nF
whereas
the
inhomogeneous
contributions
are
given
by
:
2 λ
2
λn
(
=
)
λ
1
+
K
1
+
σ
γ
n
1 + 2g
u u
are given by :
λ
γ
n
σ
s into anItinhomogeneous
reduction
factor
F
expressed
as
:
l
inh
2θ 2
results into an inhomogeneous
reduction
factor Finh expressed as :
∆
λ
γ
2σ
∆
λ
γ
spread.
)div =
( Another
(166)
)σγ = contribution comes from the electron beam( energy
∆λ
γ 2θ 2
Ku2
λ
λ
γ
∆
λ
∆
λ
∆
λ
2
n
n
2
2
�
�−1
�−1 � ∆ λ 2( � )σ ��(165)
1+ 2
nal(gain)div
can
: � ( ∆ λ )(2λn �)−1
= be expressed
( λn )σas
−1 ( ∆ λ )2 �−1
�
2
div
γ �
)
(
−1
λ
2
2
2
K
n
u 1 + beam energy. spread.
λn σγ
λ+
λnλ σ
∆
2π
K
σ
n div
n
=
1
+
.
1
(168)
butionλcomes
fromF
the
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u
1inh
+
Synchrotron
radiation
Free
Electron
Laser
= 1 + and
.
1
+
.
1
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(168)
∆F
λinh
∆
λ
∆
λ
2
2
2
2
(
)
=
σ
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λ
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λ
∆
λ
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( λn )hom
(
)
(
)
γ
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( λn )hom
( λn )hom
( λnλ)nhom ( 1 )+ K=
λn hom
λn hom
u
u
σ
γ
�
�
2 K2
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2
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λ
γ �
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λ
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K
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L
u
u
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u
3
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expressed
as
: η)
ngitudinal
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bunch
ofan
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the
optical
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should
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main(G
(166)
)longitudinal
inh
l σand
2electron
2 RMS
λ
The
overlap
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the
bunch
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RMS
length
σ
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the
wave
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be be mainσγn=overlap
)
sinc
ρ
F
F
=
(
)
−
J
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)
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J
• Longitudinal
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electron
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l
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n−1
l
u
u
1
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e
g
u
f
inh
n
u
u
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n optical
Fgshort
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e light
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N
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with respect
the respect
electrons,
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for short
electron
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Ku σ distributions,
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c by
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the
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tained.
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o mwave
oshould
(
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an
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u with factor
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newby
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F
�
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g
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:
itAcould
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A
new
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F
λ
1
+
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)
(
g
)
(
(
−1
n
2
2
2
σ
div
γ
λn
λn
λn )σ −
bunch
could escape.
∆
λ distributions,
2π Kuit σ
Fλinh2 = 1 + ∆ λ(167)
. 1 + ∆λ 2
. 1 + ∆λ 2
(
)σ = � 2(The
∆λ 2 �
∆
λ
∆
2
2
It
results
into
an
inhomogeneous
reduction
factor
F
expressed
as : ( )
�
�
�
�
inh )
signal
:
)σ −1
( λn )divgain
( λn expressed
−1
−1 can be
( λas
)
(
λn
1 + K λλn2)σγ small
hom
hom
λ
λn hom
n
n
II. The invention of the Free Electron Laser concept
Finh = 1 + u ∆ λu 2
. 1 + ∆λ 2
2( λn )hom
2 3 2 ( λn )hom
. 1+
(168)
�
�
∆
λ2 2 ∂�
∆ λlength
∆ λopti
2 �−1
2
�
�
�
π
r
λ
N
K
factor Finh expressedoasu: u The
the
electron
bunch
of
RMS
σ
and
the
)
(
)
)
(
(
−1
l
u longitudinal
2
σ
div
�
�
γ
λ
λ
λ
2) F− J=n+11 +
n 2
n
n 2σ
G
=
n
J
sinc
F
F
F
ρ
(ξ
(ξ
)
(πN
η)
n−1
.
1
+
.
1
+
K
2πe
L
gwave
e σinand
f RMS
inh
inhbywave
u mainThe
lightlength
in
advance
Nu λshould
with
respect
and for
3to the
3 tained.
∆λ u
∆electrons,
λ u
∆ λshort
2be
2
2
nal overlap between the electron
bunch of
the
optical
be
u
l
2
2
γ
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γ
(
)
(
)
(
)
)
ρ
F
F
F
G
=
n
(
(ξ
)
−
J
(ξ
)
J
n+1
n−1
e
g
f
inh
hom
hom
λ
λ
λ
n
n
n hom
2
∆λ
∆λ
2
( ∆λλn )2hom
overlap between
2 electrons,
introduced
it respect
could( escape.
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and
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�
�
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εo m
c factor
λdistributions,
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(
−1
u γ as :
σγ
λn div
λn σ −1
introduced
as :The radius
Aectronic
new correction
factor
FgrisCAS
. 1+
.School
1classical
+Free Electron!Lasers!and!Energy!Recovery!Linacs
(168)
M. E. Couprie,
!(FELs
and !ERLs),the
Hamburg,
Germany,bunch
31 !May
–10
!June,
longitudinal
overlap
between
electron
of RMS
σl and the
density,
the
of the
electron.
The
filling
factor
F2016length
represents
theo
2
jeudi 2 juin 2016
hom
∆λ 2 o
( λn )homor
:
f
∆λ 2
( tained.
λn )homThe light wave in in advance by Nu λu with respect to the electrons, and for sh
m energy loss can occur. The electron energy is decreased due to the kinetic energy loss enabling
∆ γSR
1
can
also be reduced by the accumulated effects of emission
re γo Ku2 ku2 Lu emission along the
= −spontaneous
www.lunex5.com
γo
3
II. The invention of the Free Electron Laser concept
(9
II.3 radius
ThereFEL
e classical−15
=
is 2, 8210 approach
. In the example of LCLS, the tuneable X-ray FE
with re the classical electron
2
4πεo mo c2
∆ γSR
1
2 2
∆ γSR (94)
reλγo K=u k0.15nm,
u Lu
in Stanford, one hasγ:o Ku==−3.5,
L
=
110m,
E
=
14GeV
,
it
comes
u
u
3
γo = 0.17%.
Saturation
In consequence, 2it can happen that the resonance
condition is no more fulfilled. A solution is to adapt the magne
−15 . In the example of LCLS, the tuneable X-ray FEL
l electron
radius
= 4πε embeam
is
2,
8210
field
to thereelectron
energy,
with
the so-called ”tapered undulator” for keeping the resonance condition. One c
2
o oc
• Electron
beam
energy
loss (unsatisfied
resonant
∆ γSR condition)
apply
a
linear
change
of
the
magnetic
field
along
the
longitudinal
coordinate.
Ku = 3.5, λ = 0.15nm, L = 110m, E = 14GeV , it comes
= 0.17%.
u
u
γo
- energy
exchange
can happen that the resonance condition is no more fulfilled. A solution is to adapt the magnetic
- (spontaneous emission)
am energy,
with of
theenergy
so-called
”tapered undulator” for keeping the resonance condition. One can
Increase
spread
of the magnetic field along the longitudinal coordinate.
Besides, the electron bunching and interaction via an energy exchange with the optical wave leads to an increase
the energy spread of the beam, reducing in consequence the gain (intuitively, the gain bandwidth gets larger becau
ead
of the inhomogeneous contribution and the gain distribution flattens).
Increase
of energy
bunching• and
interaction
via anspread
energy exchange with the optical wave leads to an increase of
intuitively,
gain bandwidth
gets
larger because
the inhomogeneous
contribution and the
Slippage
he beam,
reducing inthe
consequence
the gain
(intuitively,
the gainofbandwidth
gets larger because
gain distribution
flattens flattens).
contribution
and
the
gain
distribution
The slippage can stop the interaction : the electrons travel slightly slower than the photons, and one at the exit
the
undulator, the time difference becomes typically Nucλ . For not the radiation to escape from an electron bunch
• Slippage
thatinteraction
the radiation: the
advance
should travel
remainslightly
in the peak
of thethan
distribution
:
duration
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- The slippage
canconsider
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electrons
slower
the photons,
and
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undulator,
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difference
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uλ/c.
the interaction
: theexit
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slightly
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one at theNexit
ofFor not the
σl
Nthe
u λ photons,
<
Nu λ an electron bunch of duration
one
can consider
radiation
to typically
escape from
σl ,an
e difference
becomes
.
For
not
the
radiation
to
escape
electron
bunch ofthat the radiation
c
10from
c
advance
shouldadvance
remain should
in the remain
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:
onsider that
the distribution
peak of the distribution
:
orthe radiation
σl c
σl
Nu λ
Nu <
(9
<
10λ
c
10
which gives 300 periods for 1 nm radiation, 10 fs electron bunch, 300 periods, or for 1 µm, 10 ps electron bunch
Z. Huang, K. J. Kim, Review of the free-electron laser theory, Physical Review Special Topics-Accelerators and Beams, 10(3), 034801.
σl c
10λ
M. E. Couprie, CAS School
–10 !June, 2016
NFree<Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May(95)
u
jeudi 2 juin 2016
www.lunex5.com
III. The first Free Electron Laser experimental results
Gain Measured
The first FEL amplification
in Amplifier
Experiment
Exactly Matches The
24 MeV beam, amplification of a CO2 laser
at 10.6 µm
Amplifier
Experiment
Setup
Undulator period : 3.2 cm, length 5.2 m
single pass gain : 7 %
VOLUME
36, NUMBER 13
PHYSICAL REVIEW LETTERS
29 MwRcH 1976
acceleWinding the Superconducting Helix
tor output with a signal derived from the
rator master oscillator. The local oscillator
phase was set to maximize the signal due to spontaneous radiation by the electron beam. The relative response of the detector to 1300-MHz mod-
ulation was determined by observing the quantum
Quctuations in the radiation from a 600 blackbody.
A 1-m Czerny-Turner
monochromator was used
to analyze the spectral distribution of the spontaneous radiation propagating at angles of up to 1.3
mrad relative to the magnet axis. A heliumcooled germanium bolometer was used with the
monochromator to detect the spontaneous radia-
tion.
Observation
of the spontaneous radiation and the
gain included measurement of (1) the spectral distribution and polarization of the spontaneous radiation, (2) the magnitude of the gain, and (3) the
dependence of the gain on the electron energy, the
polarization of the stimulating radiation fields,
the electron current, the magnetic field, and the
optical power density.
L. Elias et al., ObservationAccording
of the stimulated
of radiationfor
by emisto theory,emission
the wavelengths
relativistic electrons in a spatially
transverse
magnetic
field, Phys.
sion andperiodic
are given
absorption
by
SPON T.
POWER
I
24 MeV
ELECTRON
ENERGY
GAlN
ELECTRON
ENERGY
FIG. 2. (a) The spontaneous power at 10.6 p, m as a
function of the electron energy. (b) The amplitude and
phase of the modulation imposed on the 10.6-pm optical
radiation from the CO& laser. Amplification corresponds to a positive. signal, The instantaneous peak
gain attained a value of 7~/o per pass. The helix field
amplitude was 2.4 kG and the instantaneous peak electron current was 70 mA. The electron energy was
swept through a small range in the vicinity of 24 MeV.
The full width in energy (half-width in wavelength) at
the 1/e points in (a) is 0.4~/0. The power density of the
10.6-pm radiation in (b) was 1.4mlo' W/cm'.
Rev. Lett. 36, 717-720 (1976)
jeudi 2 juin 2016
1/e half-width of the spectrum
is 0.
4%.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany,
31 !May(hv/v)
–10 !June,
2016
The linewidth is close to the theoretical miniwhere r, is the classical electron radius (cm),
mum. No harmonics were observed. The mag-
x = 2πNu (1 − ω/ωr )
III. The first Free Electron Laser experimental results
(157)
he argument which appears in the spontaneous emission expression.
ticewww.lunex5.com
also that :
1 − cos x − 2x sin x
d
x
Fig. 31 Spontaneous
and small signal(158)
free electron laser gain illustrating the Madey ’s theorem : the gain be
= − emission
(sinc )2
3
x
dx
2
Madey’s theorems
the spontaneous emission
2(1 − 1 cos x − 2x sin x)
x
d
= −2 (sinc )2
(159)
3
x
dx
2
an be expressed as the derivative of the undulator spontaneous emission expression as shown in Fig. 31 .
able result which corresponds to the Madey’s theorem [131, 132].
g(x) =
The gain can be expressed as the derivative of the undulator spontaneous emission expression.
It is a remarkable result which corresponds to the Madeyʼs theorem.
The Madey’s theorems are given by :
2αm2o c4 I < ∆ γ 2 >
dΦ
Synchrotron radiation and Free Electron Laser dΩ (θ = 0) =
e2 λ 2 < El2 >
Synchrotron radiation and Free Electron Laser
1 ∂ < ∆ γ2 >
2>
<
1 ∂∆<γ2∆ γ>=
2
∂γ
< ∆ γ2 >=
neous emission and small signal free electron laser gain illustrating the Madey ’s theorem : the gain being the derivative of
s emission
2
∂γ
45
(161)
dΦ
dΦ current,
(θ = spectral
0) the angular
spectral
flux on-axis o
with
α
the
fine
structure
constant,
I
the
beam
flux on-axis
of the undulator
with α the fine structure constant, I the beam current, dΩ (θ = 0) thedΩangular
emission. The first theorem relates the the energy spread < El2 > introduced by the optic
emission.
y’s theorems spontaneous
are spontaneous
given by :
2 > introduced by the optical wave to the spontaneous emission
The first
theorem
relates
the
the
energy
spread
<
E
spontaneous
emission
of
the
undulator.
According
to the second theorem, the second order energy exch
l
2αm c I < ∆ γ >
dΦ
(θ = 0) =
(160)
ofis
theproportional
undulator.
dΩ
e λ <E >
to the derivative of the spontaneous emission of the undulator. Due to the resonance relati
According to the second theorem, the second order energy exchange < ∆ γ2 > is proportional to the derivative of
the
particles’ energy to the emission wavelength, the spectral ”gain” distribution is close to the wavelen
the spontaneous emission of the undulator.
of
thetospontaneous
versus
λ . energy to the emission wavelength, the spectral ”gain”
Due
the resonance emission
relationshipspectrum
linking the
particles’
CONFIRMATION
th Madey
experimentale
distribution
is close to the wavelength
derivative
of the spontaneous emission spectrum versus λ .
2 4
o
2 2
2
2
l
CONFIRMATION th Madey experimentale
Validity : Gain <0.2
J.M.J.Madey,H.A.Schwettman,W.F.Fairbank:,IEEETrans.Nucl.Sci.:20,980–980(1973)
Gain
expression
J.5.3.4
M. J. Gain
Madey:
Relationship
between mean radiated energy, mean squared radiated energy and spontaneous power spectrum in
5.3.4
expression
apower series expansion of the equations of motion in a free-electron laser, Nuovo Cimento 50B, 64 (1979)
The
small
signal
is
given
by :
The
small
signal
gainCAS
isgain
given
by
:
M. E. Couprie,
School
Free
Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
III. The first Free Electron Laser1. experimental results
Our apparatus is shown schematically in Fig.
width observed in the experiment is by no means
A superconducting helix generates a periodic
the limiting linewidth. As established by the ear43-MeV
4
2.
A
field
of
kG.
transverse magnetic
lier experiments, a homogeneously broadened
electron beam from the superconducting acceleragain profile is attainable and the laser linewidth
tor is fired along the axis of the helix. Radiation
can be improved by means of intracavity disperhelix
with
the
the
electron
beam
through
passing
M.
Madey, G.
Ramian, H. A. Schwettman, and sive elements.
Smith The efficiency of the present lasis limited by the fraction of the electrons' enamplified and a pair of mirrors at the ends of
Physics Laboratory, Stanford is
University,
Stanford, California 94305 er
the interaction region provide feedback.
ergy which can be converted to radiation in a sin(Received 17 February
1977)
The characteristics of the oscillator are listed
gle pass through the interaction region. This limin Tables I and II. The wavelength was 3.417 p m
itation would not apply to devices in which the
Fac36
and
the
was
0.
W.
average
output
beam 892
was reaccelerated and recirculated
power
laser oscillator has beenD.operated
above
threshold
at a wavelength
A. G. Deacon
et al,
First Operation
of a' FEL. PRLof38,electron
16, 1977,
toring out the duty cycle of the machine, this
through the interaction region as in an electron
translates to a peak power of the order of V kW.
storage ring, where efficiency above 20% should
With a mirror transmission of 1.5% the intracavbe possible. ' The nanosecond electron bunch
ity power was 500 kW. The total energy collected
experiment in
0.01% of the electron has
on the detector was Our
beamfocused on the in-
www.lunex5.com
eacon, f L. R. Elias,
High Energy
A
free-electron
4 p, m.
'
First Operation of a Free-Electron Laser*
J.
The
first
FEL
in
1977
J.
J.
T. I.
1977 : First Free Electron Laser by J. M. J. Madey in Stanford
the first maser
1954,
ve sought to develop a broadly tunf coherent radiation. Several ingens have been developed, of which the
is the dye laser. Most of these deied upon an atomic or a molecular
, and the wavelength and tuning
refore been limited by the details
electrons. ' '
research
energy.
between radiation and an electron
teraction
beam
THRESHOLD
The laser spectrum is shown in the upper half
in
transverse
periodic spectrum
magnetic field.
a spatially
2 and the spontaneous
in the lowof Fig.
ABOVE
the difference
radiated
er half.
Of
the Note
schemes
whichin the
have
beenpower:
proposed,
this
best
the generation
infrared, the visible,
also
potential for
yielding very high average power. We have pre1
raB
cture.
of a measurement
viously 2 described
C2 the results
4g2
First
demo
:
on
linear
accelerator,
MARK
III, we report
'
hors have realized that the constraints
6 pm.y~c2Inthethis
10.period,
theX,gain
of
Letter
is the at
electron
where
magnet
Stanford,
infra-red
electron
classical
radius, and B
h atomic structure would not apply
energy,
r, theoperation
the
first
of a free-electron
laser oscilthe magnetic field strength. The wavelength varJ.
M.
J.
Madey
3.4l 7p,
ed on stimulated radiation by free
lator.
ies inversely as the square of the electron energy.
Above threshold, the oscillator power increases
suited to
approach
appears the
by a factor of 10' over the spontaneous radiation.
of
radiation
nm the
oscillator linewidth
Thecoherent
(200 6Hz).
was 8 in
The the
electron
experiment was
energy in the and
the
and
ultraviolet,
has chosen to satisfy the wavelength equation'
A.
0.7m p.
INSTRUMENT
Wl DT H
A. q
The experiment
demonstrates the capability of
a free-electron laser to operate at high power at
an
arbitrary wavelength. We note that the lineHELICAL MAGNET
(3.2 cm PERIOD)
43 MeV BUNCHED
TH
TABLE II. Electron beam characteristics.
BEAM
43.5 MeV
RESONATOR
MIRROR
I
1. Schematic
2.7m
Energy (Ref. 8)
Width (full width at half-maximum):
0.05%
~RESONATOR
Average current
MIRROR 130 pA
Peak current (Ref. 7)
2.6 A
Emittance (at 43.5 MeV):
0.06 mm mrad
diagram of the free-electron laser oscillator.
I
3.4lOp
FIG. 2. Emission spectrum of the laser oscillator
above threshold (top) and of the spontaneous radiation
emitted by the electron beam {bottom).
(For more details see Ref. 6.)
893
FEL oscillator at 3.4 µm, 43 MeV, 12.7 m long optical cavity
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
indicates the possibility of laser operation from
er- the infrared to the ultraviolet. The instantaneous
ll- www.lunex5.com
peak current from the superconducting accelerator can be raised to the ampere level by reducing
the duty cycle, and circulating peak currents in
Hope
as- excess of 10 A have beenSaturationobtained in electron
storage rings.
Use of a storage ring would be particularly attractive because the 42rf accelerating field for the
h
ring would have to supply only the energy actually
transformed to radiation in the periodic field. The
III. The first Free Electron Laser experimental results
"
36, NUMBER
in VOLUME
storage
ring13 FELs
PHYSICAL RKVIKW
overall efficiency of such a system thus would not
be limited to the fraction of the electrons' energy
Marie-Emmanuelle COUPRIE and Mathieu VALLÉAU
convertible to radiation in a single pass through
the interaction region. The feasibility of the idea
hinges on the form of the electrons' phase-space
distribution after passage through the periodic
719
field, a subject currently under study.
An electron current of the order of 1 A at 240
L. Elias et al., Observation of the stimulated emission of radiation by relativistic electrons in asufficient
spatially periodic
transverse magnetic field,
for laser
operation at
MeV would be
Phys.
Rev.
Lett.
36,
717-720
(1976)
Fig. 28 Electron bunching due to the electron / optical wave interaction
1000 A for a 1-mm' electron-beam cross section.
• Magnetic elements (dipoles, quadrupoles, sectupoles...)
The measurements indicate that 0. @ of the elec• Emission of synchrotronConsidering
radiationthis
(dipoles,
undulators)
trons'
can be converted to radiation in the
energy
electron bunching will enable to evaluate the
second order
energy exchange.
• Compensation of the energy loss per turn with a radioperiodic field without evidence of saturation; the
frequency cavity
corresponding power output for a ].-A, ].0'-ey
•5.3
Bunching
Gain
electron beam would exceed 10' W.
Weis given
of
acknowledge
gratefully
bending
Let’s consider now the optical wave. The FEL spontaneous emission
by the synchrotron
radiation emittedthe
by contributions
the Nu periods of the undulator. In the historical configuration, the
the oscillator,
the spontaneous
emission ispersonnel
stored in an
magnets
Hansen
and others who
Laboratory
optical
cavity, as shown in Fig. 29. It is the considered optical wave.
synchrotron
have assisted in this effort.
radiation
6e
undulator
source
=
!"
bank,
W
las c
nume
fer
b
4H
~B
J. Qu
V
23S1
N
Repo
8J.
IEEE
~V
S. P
Tech
P
Bev.
i~R
%
*)
() %
&' *-)
$% -+
# +,
(
+
~J.
(197
of 15
ics L
SPEA
*Work supported in part by the U. S. Air Force Office
of Scientific Research.
iJ. M. Madey, Appl. Phys. 42, 1906 (1971).
J.
Th
cess
J.
publi
6*
Fig. 29 Free electron laser oscillator configuration
FEL
Renieri, A. (1979). Storage ring operation of the free-electron laser:The amplifier. Il Nuovo Cimento B Series 11, 53(1), 160-178.
The first
order energy
averageofover
electrons islaser:
zero.the
One
should then
calculate
the second
Dattoli, G., & Renieri,
A. (1980).
Storageexchange
ring operation
the the
free-electron
oscillator.
Il Nuovo
Cimento
B Seriesorder
11, 59
energy exchange < ∆ γ2 > averaged over phases with the bunched electron distribution.
(1), 1-39.
M. E. Couprie, CASThe
School
Free Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
change in electromagnetic power ∆ P is given by :
jeudi 2 juin 2016
Detection of Brillouin Backscattering
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III. The first Free Electron Laser experimental results
After the first FEL ....
Unfortunately, none of the electron-beam sources available at that time had enough electron-beam current and
satisfactory electron-beam quality to make lasing easy. Although gain was measured in several experiments, it
was not until six years later, in 1983, that the second free-electron laser was operated in the optical part of the
spectrum.
The first was at Laboratoire pour l’Utilisation du Rayonnement Electromagnétique (LURE), in Orsay, France,
where the electron beam in the storage ring ACO was used to acheive lasing in the visible.
The second was at Stanford, a team from TRW used the superconducting accelerator previously used by Madey
to acheive laseing in the near infra-red.
The third was Los Alamos, where a newly constructed electron accelerator was used to acheive lasing in the
mid-infrared.
During the same period, development of ubitron-type devices began at several laboratories. Because the
threshold electron-beam current at which space-charge wave can be excited increses as the third power of the
electron energy, these devices were limited to low electron energy (no more than a few MeV), and long
wavelength. Neverthess, Marshall and his co-workers acheived lasing at 400 µm with electron beam having an
energy og 1.2 MeV and a peak current of 25 kA.
sub-mm
collective instabilities involved (space charge waves)
C. Brau, Free Electron Lasers, Advanced in electronics and electron physics, edited by P.W. Hawkes, B. Kazan, supplement 22,
Academic press (1990)
M. Billardon et al., First operation of a storage ring free electron laser» Phys. Rev. Lett. 51, 1652,(1983)
J. A. Edighoffer et al.,Variable-Wiggler Free-Electron-Laser Oscillation, Phys. Rev. Lett 52, 344 (1984)
R.W.Warren et al, First operation of the Los Alamos Free Electron Laser», DOE_Report (1984)
D. B. McDermott et al., High-Power Free-Electron Laser Based on Stimulated Raman Backscattering, Phys. Rev. Lett. 41, 1368
(1978)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
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III. The first Free Electron Laser experimental results
Optical Klystron Experiments
The second Compton FEL : the
first
and
first storage
ringFIELD
FEL
away from
the axis ofvisible
the electron beam
(Fig. 2). The
VERTICAL MAGNETIC
calculated trajectory is shown in Fig. 1 which shows a
209
AAAAAA/1~
Vinokurov et al, Prepint INP,
large wiggle of about 2 mm amplitude for an electron
D.A.G.
Deacon,
Optical klystron experiments for the ACO storage ring FEL, Appl. Phys. B34,
energy
of M.
240Billardon,
MeV andP. Elleaume
a gap of et
33 al,
mm.
1984, 207-219
M. Billardon et al., Phys. Rev. Lett. 51, 1652,(1983)
vvvvvvv lic vvvvvvv '
P. Elleaume, J. Phys. Colloq 44 C1-333 (1983)
Vsible => 100 MeV
2. Spontaneous Emission
HORIZONTAL ELECTRON TRAJECTORY
sotorage ring superior in terms of electronic density, energy spread, emittance => higher optical gain
2.1. General Features of the Fundamental
As was done for the undulator, the electron beam is
initially aligned by optical means into the axis of the
vacuum chamber within + 1 mm [-3].
The spontaneous emission pattern of the optical
klystron
looksisthe
to thetoeye
of an
gain
/pass
lowsame
( 0.1%
10 as%)thatbecause
:Fig. 1. Vertical magnetic field calculated for the Orsay optical
klystron (gap: 33mm) and the corresponding calculated
undulator [7, 6, 3], namely a series of concentric
horizontal
electron trajectory at an energy of 240 MeV
•
Relatively
long
bunch
length
(
several10
ps)
coloured rings with a similar pattern produced by each
harmonic
at progressively
largerisopening
The meters
• Straight
section length
limitedangles.
to a few
big difference appears in the spectrum.
All
storage ring FELs use a modified version of the Undulator
The experimental set up used to measure the
called
“Optical
Klystron”
spontaneous
emission
spectrum has already been
described [6]. It consists of a 1750mm focal length
spherical mirror placed at about 6.5 m from the center
Dispersive
of the optical klystron.
The light Undulator
transmitted by a 75 ~tm Section
pinhole placed at the
Undulator
focal distance from the mirror is sent through a lens
into an M20 uv Jobin Yvon monochromator ( 4 ~
Fig. 2. Dispersive section permanent magnet configuration
resolution with 0.1ram slits). The output of the
optimizing
the low field gain
209
monochromator is then sent into a Hamamatsu R 928
photomultiplier. Fig. 3 shows a spontaneous emission
VERTICAL
MAGNETIC
spectrum
of the fundamental
at an FIELD
energy of 240 MeV
Magnetic
Field
Quality
:
Same
requirement
as other storage ring
for a gap of 34.4 mm at low current in the
ring.
IDs
in terms
of multipole
and shimming G
We have
compared
the envelopecorrection
of the oscillations
with that of the emission spectrum of a perfect
undulator having exactly N sinusoidal periods, the
fields outside these periods being exactly zero. The
I(t)
emission spectrum dI/d2 of such an undulator is:
Undulators for Storage Ring based FEL Oscillator
–
–
Mirror reflectivity degradation observed at 240 MeV
Optical Klystron Experiments
away from the axis of the electron beam (Fig. 2). The
calculated trajectory is shown in Fig. 1 which shows a
large wiggle of about 2 mm amplitude for an electron
energy of 240 MeV and a gap of 33 mm.
2. Spontaneous Emission
2.1. General Features of the Fundamental
–
AAAAAA/1~
vvvvvvv lic vvvvvvv '
V, 5/22 , P. Elleaume,
CAS, Brunnen July 2-9,
2003.
HORIZONTAL
ELECTRON
d~
-
-
TRAJECTORY
(31
As was done for the undulator, the electron beam is
with 6 = n~N (1 - 2a/2),
initially aligned by optical means into the axis of the
where 2R is the resonant wavelength and n is the
vacuum chamber within + 1 mm [-3].
harmonic number. Fitting the envelope to curves given
6oooA
sooo~
The spontaneous emission pattern of the optical
by (3) gives N = 8.1 + 0.1 instead of 7. This discrepancy
Fig. 3. Spontaneous emissionspectrum dI/d2dQ measured for an
Fig.is 1.probably
Vertical magnetic
field
calculatedsection
for thefield
Orsay
optical electron energy of 238 MeV and a magnetic field parameter of
klystron looks the same to the eye as that of an
due to the
dispersive
which
klystron
(gap:
33mm)
andwith
the the
corresponding
calculated
K = 2.09 at low current where the modulation is almost total. The
undulator [7, 6, 3], namely a series of concentric
could be
partly
resonant
other 7 periods.
It is
horizontal
electron
trajectory
at
an
energy
of
240
MeV
current
decay I(t) is superimposed
certainly not due to the fringe field of the half periods
coloured rings with a similar pattern produced by each
which slightly decreases the effective number of
harmonicM.atE.progressively
angles. The
Couprie, CAS larger
School opening
Free Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
periods. The envelope of oscillations also presents a
big difference appears in the spectrum.
long, short wavelength tail with the secondary
Plotting the Nd of each maximum as a function of 1/2,
jeudi 2 juin 2016
The experimental set up used to measure the
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III. The first Free Electron Laser experimental results
he rather general case of a periodic field is considered (period λu x and λu z) and
The second Compton FEL : the first visible and first storage ring FEL
hen analyzed in the case of the planar and elliptical undulator. The general expresion of the resonant wavelength
is given by
:
Spontaneous
Emission
in the visible
ACO
2
2
Kuz
Kux
λu
+
+ γ 2 θx2 + γ 2 θz2 )
λn = 2 (1 +
2γ n
2
2
(30)
eBu xλu
eBu xλu
Ku x =
Ku x =
2πmo c
2πmo c
(31)
COMMENT METTRE DE L’ESPACE ENTRE LES DEUX FORMULES? RAOUTER FORMULE GNRALE K
.1 Angular spectral flux
dφ
→
−
(θ
,
θ
,
ω,
u)
x z
dΩ
he angular spectral flux
at the pulsation ω close the the one of
he undulator harmonics can be expressed for a filament mono-energetic beam in
he direction (θx , θz ) :
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
of the electron beam.
Figure 4 presents two spectra: (a) is recorded
without amplif ication (optical cavity completely
www.lunex5.com
detuned) and (b) is recorded at laser operation
(cavity tuned). For case (b), the laser oscillates
at three wavelengths, with the strongly dominant
one being at A. =6476 A; each wavelength is locatat a maximum
the Lett.
versus
wavelength
gain51,
M. ed
Billardon
et al., Phys.ofRev.
1652,(1983)
ity was obtained between 640 and 655 nm by
changing the magnetic gap [equivalent to a change
of K in Eq. (1)]. The range of tunability is in fact
limited for the moment by the mirror ref lectivity.
A typical 75-&% average output power has been
recorded at 50-mA current of 166-MeV electrons.
This corresponds to a typical 60-mW output peak
III. The first Free Electron Laser experimental results
The second Compton FEL : the first visible and first storage ring FEL
curve. ' Smaller gain/loss ratios would restrict
the number of laser wavelengths to two or one.
Typical laser lines are Gaussian if averaged over
a long time scale of ~ 1 sec, with 2 to 4 A full width
at half maximum. Figure 4 also shows an enlargement of the main laser-line spectrum recorded
charge-coupled-deby using a one-dimensional
closed to
instead of the usual monovice to(CCD) detector threshold
closed
max
Gain/
chromator
exit slit. The aperture time is 3 ms.
loss
Each narrow square peak in this curve is recorded on only one CCD element and corresponds to
a 0.3 A spectral width which is of the same order
as the monochromator resolution. We conclude
that there is a residual inhomogeneous contribution to the laser linewidth probably connected
with the long-time-scale laser-pulse structure
(see Fig. 4). The central wavelength of any line
is always equal to the wavelength of maximum
emission of spontaneous emission with the cavity
completely detuned (no amplification) plus 0.15
'Max
= 600
I
Max
A
[=o4ogA
Max
=23800 =2350
=6476A
=6538A
100
I
6400
0. 15&
6500
l
6600
AA
6700
FIG. 4. Spectra of the cavity output radiation under
two conditions: cuive g, cavity detuned (no amp1ification) and curve b, cavity tuned (laser on).
1654
Transverse profile
Temporal structure
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
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III. The first Free Electron Laser experimental results
The second Compton FEL : the first visible and first storage ring FEL
Second FEL : on storage ring, ACO, Orsay, visible, 1983
M. Billardon et al., Phys. Rev. Lett. 51, 1652,(1983)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
R„~NIf„,
onics. In
e external
where N is the number of periods of the radiator
odulator)
is the spontaneousand I the ring current.
n. www.lunex5.com
This
emission modulation rate, resulting from the inulation in
terference of the two undulators constituting the
s either a
This . interference is
OK, at wavelength
XL /n
eld. Then
driven by the strength of the dispersive section and
harmonic
the energy spread of the electrons and
III. The first
f„ Free Electron Laser experimental results
First coherent harmonic generation results
passing
is
ator)
becomes
of elecmirrors, as
uv light.
existing
avelength
g with a
e,
laser.
multiplicafrom the
rent outy and not
ission by
to the
n fact in
the elecbeen ob-
f„~exp
"n
—242m. (N+ Nd)
sk
y
ACO (Orsay, France), 166 MeV
Nd-Yag at 1.06 µm, 20 Hz, 15 MW, 12 ns
=> CHG at 352 nm
where Nd is the number of wavelength of the yttrium aluminum garnet (YAG) laser passing over an
electron in the dispersive section and characterizes
First undulator
PHYSICAL REVIEW LETTERS
VOLUME 53, NUMBER 25
R3
352 nm
R3 = 3
Drift space
or .
Second undulator
magnetic
dispersive section
L tILL114 I t1
I
. '«sI'-
«'stls'tssu%'Q'F
I
~
emission
I
I t J i t l It
I
I
I
Focused
pulsed laser
'Modulator"
t lk1tll
„[J&.
I;„;;;.
I
t
I
electron
traj
ector y
352 nm
R3 > 100
——
+
—
0.3
"launcher" "Radiator"
FIG. 1. Schematic principle of the experiment (see
text).
B. Girard,Y. Lapierre, J. M. Ortéga, C. Bazin, M. Billardon, P. Elleaume, M.
R Praae res by
e t aan
l /optical
Cohe r en t
70 Y. Petroff, Opitcal frequency multiplication
Bergher, M.Velghe,
The American Physical Society
2405
klystron, Phys. Rev. Lett. 53 (25) 2405-2408 (1984)
4. Exper i ment s
k
0.2
100 ns
ha rmon i c gene ra t i on in t he VUV r ange
Linewidth
FIG. 2. Time
structure sharpening
of the optical klystron emission
Tab
l
e
1
measured on the third harmonic of the fundamental line
at 3550
Thea lpulse
to a passage of the
ExperA.i ment
resulcorresponding
ts on ACO (1987)
—O. i
0)
electron through the OK in coincidence with the laser is
In 1984, we had observed the th i rd ha rmon i c at 3547
shown
a weak i camplification ratio (R3=3); 3(b)
(a) for harmon
Observed
5
ACO (Orsay,
FIG. 3. Amplifica
an ext erna l220
Nd -MeV
YAG lNd-Yag
aser [9] . Aatd i e l ect r i c m i r ror
 of France),
a strong
for Cor
amplification
ratio
100).
3
respond i ng wave l ength(R[Â]
1773 incoherent
1064 emission
separa
t
e
the
ha
rmon
i
c
f
rom
the
f
undamenwas
used
to
1.06 µm (36 MW) /2 = 532 nm, => CHG
Integrated rat io Rnt
350
3-4of 0.2 mrad'
angle
ha
rmon
i
c
s
i
gna
l
was
ana
l
ysed
by
a
norma
l
wave . The
2
2 experiment) a
bars,
monochroma tor bandw i dth [?+]
at 177 andta l106.4
nm
We
value is about 5 to 6 times more.
ous3 emission meas
i nc i dence gra t i ng monochroma t or . In order to ana l yse
monochroma tor angu l ar aper tureexplained
[mrad 2 1 this
1 .4
pulse-to-pulse
fluctuations
effect by considering the
(curve c) the laser
the coherent i ntens i ty in the proper " t i me w i ndow "
of the
6000 Since
100the real spectr
Spectcoherent
ra l rat io emission
R , (X, Sd) when recorded on a fast
l aser Spectral
pu l se , we used a
cor respond
i ngin tothe the
i nc i dent
Coherent Harmonic
Generation
Vacuum
Ultra Violet
less
fluctuations
are/puofl sethe order 1 of
These
scope.
Numbe
r of coherent
photons
.5 X 10 7 10than
5 0. 1 A, the
(166 MeV) was
Range on the Storage
R. Prazeres,
J.M.beam
Ortéga,energy
M. Billardon,
" BoxRing
-Ca rACO,
" averager
. The
to obtain the re
by 07 .07
severalm units
spect raand
l w do
i dthnot[A]appear on Fig. 3 where the
0 .1
C. Bazin, M. Bergher,
H. Fang,
M. Velghe
over
averaged
signal inis angu
too M.E.
l owCouprie,
to ensure
good
stabY.i lPetroff
i ty of , Nuclear
the r i ng, and the
l ar aper
tureabout
[mrad]50 laser pulses. They
02
0 .1
Inst.and Methods in Physics Reasearch A272 (1988), 68-72
electo
time
between
a
the
correspond
jitter
might
l
aser
powe
r
l i fet i me was on l y one hour . The i nc i dent
tron and laser pulses of the order of a few
(PL = 15 MW); th
was 15 MW at 1 . 06 , um . Howeve r , the max i mum i n—102 (PL =100
nanoseconds considering the fact that the laser
t egra t ed rat i o has been measured to be R3 t = 300,
exhibits
2 to
3 !June,
for a
longitudinal
pulse shape
peaks 2016
section). (iii) We
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs and
!ERLs),
Hamburg,
Germany,
31tor
!May
–10
p
l
i
ers
.
The
bo
t
t
om
de
t
ec
(CsTe
ca
thode)
was
devo
cor respond i ng to a spec t ra l rat i o of R 1 (A , 0) = 3000 ,
"radiator"
total duration of 12 nsec. We have also considered
in
thet ed
jeudi 2 juin 2016
the
3rd
harmon
i
c
,
and
the
top
(CuBe
ca
thode)
to
—
for a cur rent to the s torage r i ng of 1 mA . Th i s cor rethe toeffect of the lack of coherence of the laser
10 10 is lost whe
s
)
s
s
I
www.lunex5.com
III. The first Free Electron Laser experimental results
Marie-Emmanuelle COUPRIE and Mathieu VA
Efficiency
simulations of the FEL evolution at saturation, physical
considerations enable
Marie-Emmanuelle COUPRIE and Mathieu VALLÉAU
COUPRIE and Mathieu VALLÉAU
Small signal
gain bandwidth
: 1/2Nu . Using the∆resonance
it comes
ll50signal
gain half
width is of
γ
1 ∆ condition,
λ
1Marie-Emmanuelle
50
=
=Marie-Emmanuelle COUPRIE and Mathieu VALLÉAU
2 λ
4Nu
∆γ
1 ∆λ
1γ
1 ∆λ
1
=
= ∆γ
(181)
Resonance condition =>
(181)
γ
λ ∆4N
γ u 1=∆ λ
1=
1
of
its
kinetic
ener
n the electron travels on half
the2 width
of=γ the2gain
curve,
it
can
deliver
up
to
λ
4N
=
(181)
u
4N
u
γ it 2canλ deliver
4Nuup to 1 of its kinetic energy, the
ectron
travels: on half the width of the gain curve,
y r comes
4Nu deliver up to 1 of its kinetic energy, the
When
the
electron
travels
on
half
the
width
of
the
gain
curve,
it
can
diation
andtheFree
Electron
Laser
3
mes
:When
electron
travels
on half the width of the gain curve, it can deliver up to 4N1 u of4Nitsu kinetic energy, the
efficiency r comes :
efficiency r comes :
1
1
r =at
mple of the CLIO infra-red free
with 48 undulat
(182)
r = electron laser
1 Lab. Chimie Physique (Orsay)
1
4Nu
(182)
r = 4Nu
(182)
r
=
fficiency is of the order of 0.5 %.
4Nu 4Nu
1
m
efficiency
is
found
in
considering
the
total
width
of
the
gain
curve,
which
would
lead
to
r
=
. It would lead
2Nwhich
maximum
efficiency
is
found
in
considering
the
total
width
of
the
gain
curve,
to r =
u
1 r = 1 provides
can
be
overcome
in
using
tapered
undulator,
as
already
introduced.
The
tapered
undulator
The
maximum
efficiency
is
found
in
considering
the
total
width
of
the
gain
curve,
which
would
lead
to
.
It
The
maximum
efficiency
is
found
in
considering
the
total
width
of
the
gain
curve,
which
would
lead
to
r
=
.
It
2N
realistic because energy spread effect can limit the process.
u
2Nu
er
less
realistic
because
energy
spread
effect
can
limit
the
process.
isofhowever
however
less
realistic
because
energy
spread
effect
limit
the
process.
less
realistic
energy
spread
effect
can
limit
the
butprocess.
just
changing
the angle
of the array on which a
netic
field
along
thebecause
longitudinal
direction
Bcan
z (s)
leis
the
CLIO
infra-red
free
electron
laser
at Lab.
Chimie
Physique
(Orsay)
with 48 undulator
periods,
In the
the
example
of
theCLIO
CLIO
free
electron
at at
Lab.
Chimie
Physique
(Orsay)
with
48 undulator
In
example
the
infra-red
electron
laserlaser
at Lab.
Chimie
Physique
(Orsay)
with
undulator
periods,
example
of
CLIO
infra-red
free
electron
laser
Lab.
Chimie
Physique
with
48periods,
undulator p
of
the
order
of the
0.5of%.
ndulator
magnets.
There
isinfra-red
alsofree
the
possibility
to
vary
the
period,
but
it is48(Orsay)
slight
less
convenient.
the
efficiency
theorder
order
0.5
the
efficiency
isis
ofof
the
ofof
0.5A.
%.%.
N.
50 periods, r =The
0.1 %tapered undulator provides a
n
be
overcome
in
using
tapered
undulator,
as
already
introduced.
ency
is
of
the
order
of
0.5
%.
anceThe
condition
becomes
: inusing
limit
overcome
in
tapered
undulator,
as already
introduced.
The
tapered
undulator
provides
a
The
limitcan
canbe
be
overcomedirection
using
tapered
undulator,
as already
introduced.
The
tapered
undulator
provides
a
ic
field
along
the
longitudinal
B
(s)
but
just
changing
the
angle
of
the
array
on
which
are
z
imit
canmagnetic
be overcome
inthethe
using
tapered
undulator,
as
already
introduced.
tapered
undulator
pro
varying
field
along
longitudinal
direction
Bz (s)
but
just
changing
the
angle
of the The
array
on
which
are
varying
magnetic
field
along
longitudinal
direction
B
(s)
but
just
changing
the
angle
of
the
array
on
which
are
z
�
�
ulator magnets. There is also the possibility to vary the period,
but it is slight
less convenient.
�
�
2
located
the
magnets.
is also
possibility
to vary
theubut
period,
butchanging
it but
is slight
less
magnetic
field
along
the There
longitudinal
direction
Bztoz(s)λ
(s)
theconvenient.
angle
of the array on wh
λthe
1 eB
(s)
located
theundulator
undulator
There
is also
possibility
vary
the just
period,
it is slight
less
convenient.
u the
ce
condition
becomes
: magnets.
λ
=
1
+
(14
The
resonance
condition
becomes
:
The
resonance
condition
becomes
:
2
2
he undulator magnets. There�is also
the possibility
toovary
the period, but it is slight less convenient.
2γ
2
c
� 2πm
s
�
�
� u (s)
1 eBλz (s)λ
λu :
� 1 �2eB�(s)λ (s) �2 � � �
esonance condition
becomes
z eBlaser.
u(s)λ
uparameter
2 Generators of Coherent Radiation,
(183)1, 89--112(183)
1 M.
+ Nλ:Variable
λP.=
1
λ
(s)
Kroll, N. M., Morton,
L., Rosenbluth,
free-electron
In Free-Electron
(1980)
z
u
u
2
2
1
+
=
maintain the resonance. 2γ
Efficiency
1-2
%
XXXXXX
was
reported
[134]
2 λ of
2πm
c
o
2
2
(183)
1
+
=
s
2γs 2γ 2 �2 22πm2πm
oc
2
�
c
o
s
�
�2
jouter
ref,
Los
Alamos,
tapered
und,
aintain
the
resonance.
Efficiency
of
1-2
%
XXXXXX
was
reported
[130]
1
λ
eB
(s)λ
(s)
Storage
Ring
based
FEL
:
z
u
u
enables to maintain the resonance. Efficiency of 1-2 % XXXXXX was reported [130]
enables
to maintain
the resonance.
Efficiency
1-2
% XXXXXX was reported [130]
1+
2λ = P of
uter
ref,
Los Alamos,
und,
2 α IE42
2
Renieri
limit ref,
: tapered
<P>
χ (∆σtapered
agramme
LEL
XXXXRajouter
Losα
Alamos,
γ/γ) Pund,
sync 2γ
, sync
2πm
c
o
XXXXRajouter
Los Alamos, tapered und,s
amme
LELdiagrammeref,
schma
LEL
EL
sur
anneau
de stockage
Renieri, A. (1979). Storage ring operation of the free-electron laser:The amplifier. Il Nuovo Cimento B Series 11, 53(1), 160-178.
schma
diagramme
LEL
sur
anneau
de
stockaga
Cas
du
LEL
sur
anneau
de&stockaga
es to maintain theDattoli,
resonance.
1-2of %
XXXXXX
was reported
G.,
Renieri, A. Efficiency
(1980). Storage ring of
operation
the free-electron
laser: the oscillator.
Il Nuovo Cimento[130]
B Series 11, 59(1), 1-39.
Cas du LEL sur anneau de stockaga
E. Couprie,
CAS School Free
Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
XRajouter ref,M.Los
Alamos,
tapered
und,
jeudi 2 juin 2016
conducting accel. erator is ssteered down the axis
of the tapered wiggler. The eel.ectron beam c aracteristics are s bown
own in Table I. The cavity
www.lunex5.com
tween the sides of each wigg er
' '
magnnets is increased the fie
gap between the m
'
'
axis falls, creating a m ag netic field taper.
t
of the electrons from
e
a taper~ thee deviations
III. The first Free Electron Laser experimental
results
e
-ll.
:-:".
-'.
, "-b. .".-'-.
' con- tron thi th.
t
r fo,
ac
is
on
based on the Ha
Hal. bach design,
Th ewiiggler
t'
SlS lllg of a pair of linear arrays
ra s oof SmCO, perSICAL
NUMBER
VOLUME
manent52,magne
t s. 5 The arrays arepHy
t AL
in
constant
—
el. en th (X = 3 .6 cm ) but can be made to var
vary
Th
th
i
o
path leng
decelerate through the wigg er,
REVIEW
ecf r equency LETTERS
need not change.
e. This al. l,ows gotheJANe vAR»&84
'
'
trons t o s t ay in resonance with the op tical ie l.d
PNEUMATIC
ADJUSTABLE
tthe full l.eng th of the wiggl. er. An advantage
- 1/ 4X
ENTRANCE/EXIT ASSEMBLY -1
CAVITY MIRROR
ACTUATED
control 1ing th e spacing between
the magnet p anes.
SCREEN
er is that the configuration and
/
g&,
The wiggler consis
h conamoun t of t ap er may be adjusted for study.
en
f
OPTICAL
DIAGNOSTICS
!
i uration used
taining f ifteen periods. The conf igur
lerI one
incorporate in o
t ns
large5 smal, l-signal
gain comp REVIEW LETTERS
PHYSICAL
p
NUMBER
VOLUME 52,
The Stanford experiment in the taper configuration
I
1984
JANLJARY
ELECTRON
SPECTROMETER
TV MONITOR
SUPE RCONDUCT ING
ACCELERATOR
)0
i e BEAM
sections
ler
s
give arge
characFEL oscillator
AM
TABLE
ENTRANCE CONSTANT
E
ELECTRO
SECTION II. Tapered-wiggler
CONSTANT
EXIT
TAPERASLE
W GGL E R
90K IN 6teristics.
TAPER
TAPER
SECTIONS
WIGGLER
MAGNETIC
At IhFTig h er optical
klystron.
Var jouss dijag nostics
g ain as in an optical.
6-1/2X
6-1/2X f u I. in the operation
15K
320.04 cm
15K are help
' 34cm
53
34
cm
53.
58.
59
cm
28 58 cm
28.
58
cm
fields the prebunc cher
c er prrrovides momentum m oduinser
of th' FEL. A total of fourteen
(a)
'
cm
542
t'
g'
erd p
rescent screens,s nine inside the wiggler,
ag
66lation
MeV of the el.ectron beam;
'd'
NUMBER 2.9
3.6
cm
period,
Halbach
type,
VOLUME
52, Power'
4Wb
elecsion section (b y p rovi ing a momentum-dependen
m
nt
iinformation
on 5the kG
f theREVIEW
oruntapered
positio PHYSICAL
MWb
2
1.
Peak
power
1268 cm
at op tical. waveo
a set of horizontatal
tron beam. For eac h scrreen
path eng )
460 MWb
Peak cavity
power
FEL
oscillator
TABLE
Tapered-wiggler
II.
" characthe alignlengths at the entrance o
p
ll
GW/cms for
Peak cavity intensity
teristics.
the tapered
Wavelength
1.57 pm
d t a FIG.
ment of
m
the
ing within
t xc ofedthe multicomponent
1. Schema
i electron
ler FEL esystem.
wigg
h'ich defines the4 psc
section and, therefore, higher extraction e
beam ewlength
ls. Focus
ocus
laserMicropuls
optical axis.
I
DR
rou p s.. '
gro
eral.
An op t'ica l. kl. ystron variant of a
stant wiggl. er oscillated a
TABLE
I. Characteristics of the su p erconducting ac7
4
Macropulse length
Repetition rate
5 ms
10 Hz
ciency.
~
Power'
Bandwidth
LASING SPECTRUM
LETTERS
I
I
I
I
)0
(a)
JANLJAR
LASING SPECTR
1.3% FWHM
1.3% 4Wb
power
2-0.1.2 MWb
constant
d th e 0.
of the main wigEfficiency,
When Peak
wiggler
magnets
untapere,
MWb
460
Peak1%cavity
taper power ce a maximum
1.1%
field of 2. 9 kG
produ
gl. er sections
celerator in the experiment.
2 $ GW/cm "
Peak Oio(Sic
1.ll
cavity
taperintensity
2P
these sec ions
e front an d re ar1.of
on axis.
i . 1.
Wavelength
57 pm
pp
were
measured
over
These
quantities
averaging
Micropuls e length
Emittance
0.15~from
mm mrade 'at 66 MeV)
1.
t by h h 4 tpsc l th
A 66-MeV
electron beam
shots.
many
Macropulse
length
spreaderator is s
Energy accel.
0.03$()
tween the sides of each wigg 5erms
steered
down the axis 1% taper.
conducting
rate
CONSTANT
' ' 10 Hz
PREBUNCHERRepetition
TAPERED
DISPERSION
Bunch length
4.3 ps
SECTION
MAGNETS
Inferred
under
the
the optical
assumption
pulse
the~ magn
m thatSECTION
nets
is
increased
the fie on
between
arThe
el.
ectron
beam
of the tapered
e
c
wiggler.
gap
Bandwidth
1.
3%
Current
0.5-2.5 A
' shape.
'
measured electron pulse2-0.
shape is the same as the
constant
axis
Efficiency,
0. field wiggler
creating
t
taper.
are s bown
ag netic
acteristicsEnergy
own in Table66I.MeV
The cavity
t swiggler
elemen
of a
themmulticomponent
2.falls,
Key deceleration.
BasedFIG.
on electron
taper
1.
1%
1%
of the electrons from
e
e
a taper~ thee deviations
system.
I
1.3% FWHM
4%%u()
SPONTANEOUS SPECTRUM
I,
-'. -ll.:-:"."-b. .".-'-.
4%%u()
1.2 $
2P taper
1.4
1.5
1.7
,
is controlled by four sets of quadrupole coils exth.measured
Th
tron
r byalignment
were
ac design, conTh ewiiggler is based on the Hal.
Ha bach
path leng
averagingth over i t o
teriorThese
to
thequantities
mirror
Cavity
wiggler.
FIG. 3. {a) Lasing spectrum and (4) spontaneous outshots.
decelerate
use of the the
reflection
accomplished
s oof SmCO, per- wasmany
SlSt'lllg of a pair of linear arrays
ra
wigg of the
by through
the outcoupler.
of the FEL
as measuredof through
put
To compensate for the average energy loss of the electrons
totaper.
the optical.
wave,
the
magnetic
field is made
aecfunction
the wiggler
1%
insertionbeam
onto
one
of
three
HeNe
alignment
al.
l,
f
need
not
This
ows
the
change.
e
time-averaged
peak lasing power is 95 kW while
manent magne t
The arrays are constant t in
equency
that the optical pulseThe
Inferred
under the assumption
'
'
al.
and
position,el.compensating
for
average
changes
in
the
electron
energy,
y,
so
that
X,
in
the
resonant
condition
remains
constant.
The0.95 mW.
the
of
the
as
ayertures
cavity
peaking
Q
spontaneous
power is only
peak ie
= 3 6 cm ) but can be made to vary
in measured
resonance
the shape.
tical
l.d
o bysline
t
with pulse
opthe
en th (X —
var seen
is the tsame
as the
electron
ay
shapetrons
laser
(514 nm) of antoargon
by the green
reduction of the magnetic field decreases the path length traveled
by
the=l.eng
el.ectrons
compensate
for their slowing down. This
electron
deceleration.
Based on
o
the
full
th
f
the
t
wiggl.
99.
at the third harmonic An advantage
(mirror ref lectivity
tapering
allows
to remain
resonance
they
traverse
the wiggler, even
significant
amounts
of their
energy.where N is
of the
fundamental).
control
1ing electrons
th e spacing
between inthe
one expects
magnet as
an efficiency
of 1/(2N),
that lose
and
er as
is they
the configuration
p anes.
1.4
1.5
1.7
the effective en
characteristics
ofer
the
oscillator
are listed
number of wiggler periods (131
exsets
of quadrupole
coils
is controlled
The wiggler consis
h con- The
byf tfour
be adjusted
amoun t o
for
study.
may
ap
J. A. Edighoffer et al.,Variable-Wiggler Free-Electron-Laser
Phys.
Rev.
Lett
344
57
Table II.
The wiggler.
was
and
the (1984)
wavelength
1.mirror
periods with the dispersion section turned off)
p, m52,
toOscillation,
the
alignment
Cavity
uration used in terior
taining f ifteen periods. The conf iigur
in
o
lerFIG.
one
incorporate
spectrum and
spontaneous
3.to{a)
macrothe
linac
average
output
during
0.Lasing
38% efficiency.
power
This (4)comuse
of
the reflection of thewhich amounts
was accomplished bysmal,
the outcouple
put of the FEL
l-signal
large tayer. With
gaincycle
comp pares favorably
p
was t4 Wnswith
the duty
yulse
with as
the measured
measured through
efficiency
of
insertiononto
one
of three
HeNe alignment beam
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs
and
!ERLs),
Hamburg,
Germany,
31
!May
–10
!June,
2016
The
time-averaged
is
lasing
power
peak
0.4/o. Benson etal. demonstrated about 0.2% 95 kW w
of the machine factored out this translates to a
al. ayertures and by peaking the Q of the cavity as
the peak spontaneous power is only 0.95 mW.
efficiency
with a 160-period wiggler.
peak power of 1.2 MW. With a mirror transmisFor the
jeudi 2 juin 2016
i ler sections give arge s
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The SSG was rout i ne l y measured at the beg i nn i ng of t he enhancemen t f or th i s w i gg l e r.
Opt i ca l output powe r was not the on l y parameet er
-beam
a f f ec t ed by the no i se in the e l ec t ron beam . Spec t raEne
l rgy each l as i ng exper i ment by
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21 MeV
12
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1 . 5-5a nC
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3 . 2 . Compa r i son w i t h ca l cu l a t i ons
The qua l i ta t i ve f ea tures of the spect ra , that is, waveEm
9145-2HS) . The SSG depended
s tad
rong l y on the peak
- i t t ance
3 rr mm mr
y l sew i det hl ecpt rron
cur rent r, . and
necav
t =10
vail tues
rang irng
15 ttoi ma
60%
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ebunche
The
yps powe
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pu lhse
i ghes t e f f i c i enc i es ob t a i ned f rom each w i gg l e r
cons
t
ant
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rom
macropu
l
se
macropu
l
se
,
but
the
deta
i
l
s
were
recorded
for
respec
t
i
ve
peak
cur
rents
f
rom
30
to
m
to
Charac t er i s t i cs o f t he w i gg l ers and sys t em pa r ame t e rs used
w i d t hs o f 10 ps . The ex t r ac t i on e f f i c i enc i es comb
r epriesen
na t iton we r e compa r ed w i t h co r r espond i ng ca l cuFWHM 50
unnorma
l i zed
var
. Alamos
In
spec
ral epresent
i nexperiment
sect
.4, we
l ec°)rt edwas
A The
cur rent requ i red to reach the l as i ng thresho l d
Los
oscillator
wave. 5l eng
t h se
t ape
t he expe
r ii ed
men
t s . the
The
w i tgg
r w i t h ed
12%
ave r ages t aken ove r a numbe r o f mac ropu l sesl a tand
re
i ons amade
us i ng t he e - beam code PARMELA t o
was 5 A. A s l ight l y h i gher va l ue of 7 A was necessary to
i st ii ous
c examp
arget s.numbe
of l mea
The rw i gg
e r w-i t h
used mcharacter
our prev
amp l lies
f i erf rom
expear i lmen
=
20%
be
l
ow
t
he
h
i
ghes
t
s
i
ng
l
e
pu
l
se
ex
t
r
ac
t
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on
ob
mode
l
t
he
acce
l e r a t or and beam l i ne and t o gene r a t e an
produce s i gn i f i cant output powe r measurab l e w i th our
surement
for r disi scuss
i onon oft he the
i ri gnquadl ii scussed
tat i ve , i not
n re f .
30% wave
l eng t hs t ape
based
des
irques
se
rpyroe
ved . lene
The
t taec. ftor
or . tFhe
gg
i s spa
t he e l ec tl ron
-beam
When
bo
t h w ti echn
i near
ec t rgy
r i cdade[7]
i g. 30%
8 shows
anl eexamp
l e rofse .
deta i l ed, features , Some proper t i es of the opt i ca l beam
[4] .
t
he
i
r
ag
r
eemen
t
was
w
i
t
h
i
n
abou
t
tAhe
l rl ,o fi a tl he
sysstar
t ems
same gene
r aal- t r end w i t h
exponent
r i se,
t i ngshow
f rom t he
i ncoherent
spont
were qu i t e i nsens i t i ve to the no i se . Spa t i a l beam qua lwe
i t yr e usedthet oge
15% .
neous
i on . Th
osc i12%
l l ogram
is l ac
was a pr i me examp l12%
e , show i ng no ev
i dence of dePre
t er- i ora30%
cav em
i t yi sspowe
r . i sThe
w i gg
e rtua
, lwl iy t ah measure
and w i t hou t pr e t i on f rom no i se , w i gg l e r
of
the
SSG
of
the
pu
l
se
energy
,
ra
ther
than
w i gg l e r
bunche r
bunche r , shows sa t ur a t i on . Th i s maypower
be , caused t by ' 2`o VJ I GGLER
- -because
l i mi t ed bandw i d t h of the de t ec t i on sys2 . 5 . Pr ebunche
r tofh the
0
g
row
m
t
he
e
-beam
'
s
em
i
t
t
ance
when
t
he
m
i
c
ropu
l
se
30
'
,
V
,
'
I
GGLER
.
66
W i gg l e 4.2
r
73 ( i n i t i a l )
273
3
Fas t in i t i a l t rans2i ent
t em ( - I GHz ) re l at i ve to the - 30-ps opt i ca l pu l ses .
of e l ec t ron ene rgy
chanumer
rge iapp
3 nC . t empora
The cur
ves i n f i g . 1 a r e zi n- i 2 " - PREBUNCHER - Wave l eng t h ( cm)
2 44 ( f i na l )
210
3 . 66
F rom
ca l roaches
anarl ystios of
l tprof
The use
o f a p r ebunche
i mpthe
rove ex t r ac
i on i leef -of the
4
O
30 ° - PREBUNCHER 0 196
B W i gg l e rA( i nsecond
i t i a l ) (T)
. 29 e l ec t ron
t endedl se ,to wei lde
l ust erm
t ra tienedt r that
ends and
do no t purlepr
prob l 029
em present ed by0 the
beam
se esen t any
f i c i enc i es cur
a t rent
h i ghpu
op t i ca l powe
r was desc r ithe
bedSSG
i n r eatf . the
[4] .
300
.0 l er Tapeoccur
r (X)red at the star12
. 0 of osc i l l at i on
peakt heor
t up
. When the0acce
shouyl .d be 10% grea t er than measured because the
The p r ebunche r i s a shor t (2 . 5 pe r i od) w i gg l e r p l aced i n
pa
rabo
l
i
c
powe
r
ga i n depends
Fo rm oaftor
t ape
r
=
l
i
near
on thedoes
was turned on at the beg i nn i ng of each macropu l se ,
i ns tno
ant aneous
l ue
of s the
exh
i b va
i t pass
any
i gn o f sa t ur a f ron t o f t he p The
r i ma r30%
y w iw
ggi gg
l e r.l e rAs
t he etl ec
t rons
U
.
i ts e l ect r i c f i e ld i ncreased i n a rough l y exponent i a l
m i cropu
l
se
cur
rent
A
l
so
,
the
measured
va
l
ues
shou
l
d
be
. 4 zGW and
t
i
on
up
t
o
a
cav
i
t
y
powe
r
o
f
app
rox
i
ma
t
e
l
y
8
t
hrough
t
he
pr
ebunche
r
,
t
he
i
r
ve
l
oc
i
t
y
i
s
modu
l
a
t
ed
so
Op t i ca l
i ncreased by an add i t i ona l 20% to accoun t for the w_ 3 ,
f ash i on . Once the f i e ld was w i th i n a f ew percent of i ts
e f f ri esonan
c i enc i es
i nc r eased
may be
capab
l e o f st i lal round
h i ghe rt he
t . The U
Las i ng wave l eng t h
10 . 88 - 11 . 4 l m
as t o p roduce
bunch
i ng
knowna non
l i near
i ty acoft i on
the photode t ec tor . By app l i ca- I l
f ina l va l ue and st i l l i ncreas i ng , three th i ngs happened :
a l lrows
a t t a, i nmen t o f h i ghe r
gg l e r a rre cor
ec t l yt he
spaced
coppe r
n w i t h r tand
he pwr iebunche
pa r t i c l e . I f t ga
he ibunche
Cav i (1)
t y the cur rent through the undu
l a tor i ncreased form
w
l i ght i sbeam
an i ncur
t egra
l t and e f f i c i enRay l ezero
i gh dtoi s ti ts
ance
0 . 52 M
i t y t he
powe
r st rons
f or and
t he same
r en
s l i ppage be tcav
ween
e l ec
f i na l va l ue , (2) the
max i mum of the SSG
z' t
ween pr e Ou t pu
t coup
ng response to the energy
0 . 5% change , sh i f ted f rom
numbe r o f wave
t hs itni mes
t he hdri ghe
i f t space
c i es l eng
1 . 5-2
r . Th i be
s tenhancemen
t i s 0expec t ed
func
t i on ,l im
2e l ec
t rons
/ pass to i ts f ina l 3va- 3l ue. 5%
r andf rom
w i gg tl heor
e r . The
Cav i tl onger
y r i ngdown
wave l engths
, and (3) becausebunche
of
y f orbunched
bo t h w i gg
l e rs
, buatr et hei n-r e i s no U
t enough
Q
concen
tr ic
l e r a t t he op tw ii mum
f or tcap
ur e
nomsochronous
60° bends , the m i cropu l se sepj ec t ed i n t o t da
he twai ggf or
Nea rthe
gg l e phase
r w i t hou
p rt ebunche
r t o ve r i f y
t he 30%
ara t i on i nterva l measured at the undu l a tor sh i f ted f rom
and dece l e r a t i on , p roduc i ng an i mp r ovemen t i n ga i n
x
w
t he enhancemen t f or th i s w i gg l e r.
e -beama s i gn i f i cant l y shor t t i me to i ts norma l 46 ns. A l l three
and e f f i c i ency o f t he l ase r by a l mos t a f ac t or o f 2.
Ene rgy
of these processes occur red w21i thMeV
i n the f i rst 10 I ts of
cha rgewe observed rap 1i d. 5-5
nC of the opt i ca l
M i c ropu
l sewhen
3 . 2 . Compa r i son w i t h ca l cu l a t i ons
l as i ng
growth
Em i t st iance
3 rr mm
mr adgrowth and
gna l . Norma l l y , al l three t ended
to reduce
3. Expe r i men t a l r esu l t s
=10
cont
thatpswas not cons i st ent
Pu l sew
i drt ihbut ed to a measured SSG
The h i ghes t e f f i c i enc i es ob t a i ned f rom each w i gg l e r
w i th the measured sa tura t ed powe r or ext rac t i on ef r e opcompa
r ed rw i t h co r r espond i ng ca l cut i onvewe
3 .1 . Ex t r ac t i comb
on e f fi ina
c i ency
rsus
t i ca l powe
°) FWHM
unnorma
i zed
f i c i ency
and , ladd
i t i ona l l y , var i ed er rat i ca l l y f rom day to
l a t i ons made us i ng t he e - beam code PARMELA t o
day re f l ect i ng m i nor changes i n the t i me dependence of
e f - t o gene r a t e an
F i g . 1 shows
va lacce
ues lob
nedand
f or beam
ex t r ac
i on and
CAV I TY POWER ( GW )
mode tlhet he
e rtaatior
l itne
the acce l ara tor f i e ld .
III. The first Free Electron Laser experimental results
The Los Alamos experiment
i c i enc i es ve r sus es t i ma t ed i n t r acav i t y powe r whe r e bo t h
t he e l ec t ron -beam ene rgy [7] . When bo t h t echn ifques
t ape rt ed w i gg l e rs a r e ope r a t ed w i t h and w i t hou t t he
Opt i ca
l resu
we r e 5.
used
t oge
t he rl ts
, t he i r ag r eemen t was w i t h i n abou
Fig 1
40 % gain
15% .
Ex t rac t i on e f f i c i enc i es versus cav i t y powe r for severa l
w i gg l e r -prebunche r comb i na t i ons .
A d i scuss i on of the opt i ca l resu l ts is d i v i ded i nto
F i g. 8, Exponent i a l r ise of the l as ing mi cropu l se energy f rom
seven top i cs tha t i nc l ude the fo l l ow i ng :
t ss' 2`o
VJ
GGLERto saturat
- at the star t of the
spont
emi
en I route
R.r W.,h Newnam,
B. E.,Winston, J. G., Stein,W. E.,Young, L. M.,aneous
& Brau,
C. iA.on(1983).
Results- of-ionthe
Los Alamos free-electron laser experiment. Quantum Electronics, IEEE
2 . 5 . PrWarren,
-ebunche
The growt
of opt i ca l powe r w i th t i me f rom spont a0
30 ' , V l, se.
' I GGLER
e l ec t ron-beam macropu
A net sma l l -s igna l energy ga in of
Journal
19(3),
neousof,em
i ss i on391-401.
to sa tura t i on , i nc l ud i ng measure 34% per cav izty round
t r ip is represented
. -The cor respond i ng
i 2 " - PREBUNCHER
B. E.
W.
Sheffield,
Goldstein,
Brau:powe
Ther Los
Alamos
free electron-laser
oscillator: Optical performance, Nuclear Instruments and Methods in
men
t so fofaoptp irR.
ca
l gaWarren,
i n , r t oR. L.
The
useNewnam,
ebunche
i mp
rove exJ. tC.
r ac
t i on e f - C. A.gross
ga
i
n
is
52%.
4
O
30 ° - PREBUNCHER -
A: Accelerators,
f i c i encPhysics
i es a t Research
h i gh op t iSection
ca l powe
r was desc rSpectrometers,
i bed i n r e f . [4]Detectors
.
and Associated Equipment 237 (1), 187--198 (1985)
The p r ebunche r i s aM.
shor
t (2 . 5 peCAS
r i od)
w i gg Free
l e r pElectron!Lasers!and!Energy!Recovery!Linacs
l aced i n
E. Couprie,
School
f ron t
of
t he p r i ma r y w i gg l e r.
jeudi 2 juin 2016
As
t he e l ec t rons pass
U
z
!(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
www.lunex5.com
III. The first Free Electron Laser experimental results
Accelerators for FELs
Storage ring
RF linac
ACO,VEPP 3, Super-ACO, DUKE, NIJI IV, UNSOR, DELTA, ELETTRA...
Electrostatic accelerator
Induction linac
Stanford, Los Alamos, Boing / Spectra Techno...
Santa-Barbara, 6 GeV, 2 A
120-800 µm
L. Elias et al.,The UCSB electrostatic accelerator free
electron laser: First operation, Nuclear Instruments and
Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment,
Volume 237, Issues 1–2, 15 June 1985, Pages 203-206
ETA, Lawrence Livermore
Nat. Lab.
3.5 MeV, 9 mm, 40 %
efficiency
operated as amplifier
T. J. Orzechowski et al. Phys. Rev. Lett. 54, 889 (1985)
T. J. Orzechowski et al. Phys. Rev. Lett. 57, 2172 (1986)
Microtron
ERL
M.Tigner Nuovo Cimento 1965
ENEA Frascati
2.3 MeV, 2-3.5 mm
Ciocci, F., Doria, A., Gallerano, G. P., Giabbai, I.,
Kimmitt, M. F., Messina, G., ... & Walsh, J. E.
(1991). Observation of coherent millimeter and
submillimeter emission from a microtron-driven
Cherenkov free-electron laser. Physical review
letters, 66(6), 699.
Jefferson Lab.
2.3 MeV, 2-3.5 mm
S. Benson et al., NIM A (1999)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
III. The first Free Electron Laser experimental results
FEL oscillator properties
Temporal properties
Gain reduction (u. a.)
Transverse modes
Desalignement (u. a.)
M. E. Couprie et al., NIMA
304 (1991) 47-52
VEPP3 (Russia)
λ/∆λ = 10-5
Optical cavities for storage ring FELs in the UV, M.E.
Couprie, D. Garzella, M. Billardon, 1995, Nucl. Inst.
Meth. A 358, 382-386 (1995)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
e!ects due to the nanosecond and sub-nanosecond
timescale dynamics of the process have been obTABLE II. Fluorescence measurements of NADH performed with the super-ACO FEL.
www.lunex5.com
served by scanning the FEL-to-SR delay with an
! , ns
c
! , ns
! , ns
¯! , ns
Temperature
c
optical delay line on
the FEL
path.
Photochemistry
and beam
Photobiology,
2005, 81 717
#0.01
#0.02
c
#0.2
#0.01
(°C)
#1%
#1%
,
3216
Rev. Sci. Instrum., Vol. 74, No. 7, July 2003
Edwards et al.
10
61%
0.30
38%
0.70
1%
1.7
0.47
1.30
Fig. 2 shows the SPV intensity #uctuations as
20
68%
0.28
32%
0.62
%0.1%
1.8
0.39
1.20
a function of the delay between the two pulses for
40
78%
0.24
22%
0.55
%0.01%
2.1
0.31
1.24
0.8
three di!erent surface qualities of cleaved
Arrhenius fits for different fluorescence decays.
Human
surgery 0.6
Photon
echo
Si(1 1 1)2!1. The long-time behavior is due to the
!
!
¯!
E
1.4#0.3 kcal/mole
1.5#0.1 kcal/mole
2.6#0.3 kcal/mole
steady-state regime of photocarrier relaxation as
4#3$10 s
0.4
2#1$10 s
2#1$10 s
A
observed in the bulk. In contrast, the strongly oscilThermodynamical parameter K!c /c !exp("%G/RT) with others techniques. Edwards, G. S., Austin, R. H.,
Edwards,
G.
S.,
Allen,
S. J.,
0.2
lating
transient regime, observed during the "rst
Carroll,
F. mole#
E., Copeland, M.
"kcal/mole# R. F., Nemanich,
Technique
%H "kcal/mole#
%S "cal/K
G Haglund,
Fluorescence
"5.0#0.2
"18.5#0.7M. E., Gabella, 0
&0.1#0.4
is attributed to the ! (bonding)
L., Couprie,
R. J., Redlich, B.,half-nanosecond,
Simon, J. D.,
NMR
("5.6#0.2)
("17.5#1)
("0.8#0.2) (&0.4#0.1)
-10 0 10
20 30
40(2005).
50 60!H70(anti-bonding) electronic surface states [11].
W. E., ... & Joos, K. M.
& Yang,
W. C.
and
Time (ps) of One
(2003). Free-electron-laserApplications
Free‐ can then understand the very di!erent behavsample,
on
an
X
–
Y
–
Z
manipulator.
The
pump
beam
can
the emissions process, which is related to rotational BrownFigure
10.
Vibrational
photon
echo
decay
data
taken
W(CO)6 in 2based biophysical and
Electron Lasersior
in ofthe
observed
on a surface showing many defects
MTHF
at
16
K.
The
inset
is
a
semilogarithmic
plot
showing
the
data decay
ian motion of the
moleculesbiophysical
in solution.instrumentation
The decay of anisotbe moved instrumentation.
and focused
precisely in the region
where the
FEL-based
3233 then
biomedical
exponentially. Reprinted with
pemission from
reference
28.
Biological
and
Material
ropy of a chromophore rigidly attached to a sphere can be
probe beam intersects the sample. This region where the two known to accelerate the electronic relaxation (curve
scientific
FIG.Review
8. Positionof
of the
patient prior to incision. The arrow shows
location of Photochemistry
Sciences.
described by r(t)!r 0 exp("t/!) where r 0 is the static anisot- thephoton
beams‘‘T’’"
intersect
isdata
optimized
with the signal
obtained
tumor
!circled
based
on
from
the
neuronavigational
system.
FIG. 7. Preoperative MRI scan !axial T1 weighting with gadolinium conMetal carbonyl solutes and
in glassy
and liquidcsolvents
in
the "gure). These results, as well as recent data
instruments,
74(7),
photobiology,
81(4),
ropy
related
to
the
angles
between
the
moments
associated
to
by
a
charge
coupled
device
"CCD#
camera
in
steady-state
trast". The arrow points to the tumor and its compression of the right temVibrational
photon was
echo,performed
pump-probe at
anda transient-grating experiabsorption
3207-3245.
operation.
The time-resolved
experiment
711-735.
poral lobe. and to emission and ! is the relaxation coefficient,
on other silicon interfaces [16], are very
temple to expose the skull ments
over the
tumor, rather
than the mode ofobtained
of kHz,
the asymmetric
CO-stretch
tungsten hexacarwhich is inversely proportional to the rotational diffusion typically
lower repetition
rate,
i.e.,
83.2
than
the
normal
one
large skin flap one bony1
uses just
to ensure
that the
tumor
(w[co]6)
in various
solvents
have provided
a foundation for for the understanding of surface recomimportant
coefficient
a sphere. The measurements of fluorescence is"8.32
MHz#
using a Pockel’s
A. Humanof
neurosurgery
within
the exposed
area.understanding
A 5cell.
cm bone
flap
was
raised,
the dynamics of molecular vibrations in condensedanisotropy decay lead to very fast depolarization of the nico- exposing
Acridine
from Prolabo,
used
without
further
purification,
bination
phenomena and their role in the dynamics
the underlying
dura,
which
linesThe
the
inside
of
the
matter
systems.
seminal
experiment
investigated
the asymThe
first
patient
had
a
suspected
meningioma
of
at
least
tinamide ring, independent of the rest of the NADH mol- skull.
was studied.
Absorption
spectra
were
recorded
using
a
Cary
-5 0
5
10 15 20 25 2
The tumor, attached tometric
the CO-stretch
deep, or brain
of the
mode side,
of W(CO)6
in 2-methyltetrahydrofuran (23 cm We
in size,
in hydrodynamic
Fig. 7, and wasvolume
neurologically
of
photon-induced
electron/hole
pairs.
ecule.
find asanshown
average
of 1000 dura,
210 was
"Varian
Inc.#
spectrophotometer.
Typically,
a
0.1
cm
or
a
MTHF)
(28). The
FELneuronavigawas tuned to 5.10 pm and the micropulse
Time (ps)
easily located using
the wand
of the
3234
III. The first Free Electron Laser experimental results
Edwards et al.
Rev. Sci. Instrum., Vol. 74, No. 7, July 2003
1
1
2
2
3
2
3
User applications started
1
a
2
10
2
"1
10
"1
11
"1
1
0 °C
3
stableÅprior
the procedure.
patient
was operated
by
fortoNADH,
which The
would
correspond
to a on
sphere
#100
an experienced
neurosurgical
in Vanderbilt’s
Keck
with
radius of 6.2
Å. This isteam
in good
agreement
withFEL
the
Center. While this was the first human operation
in this fa3
volume of a folded configuration (836 Å ) given by a van
cility utilizing the Mark-III FEL, the facility had been perder Waals model. The spatial conformations deduced are
forming both conventional laser and nonlaser human surgery
shown in Fig. 38 in folded and open conformations. These
!primarily orthopedic procedures" on a daily basis for several
results are in agreement with those obtained from previous
months prior to this operation. There are extraordinary needs
nuclear
magnetic resonance "NMR# studies of aqueous
for a 81neurosurgical operation of this complexity. It became
NAD.
clear early on in the design of these operating rooms that
was
2.7around
psconcentration
at athe
repetition
rate of 1 kHz. Because the
1 cmsystem.
quartz A
optical
used.
Itscut
final
tional
1 cm cell
cuff was
ofduration
dura
was
borderwas
Figure 11. Beating evident in photon echo decays and fits for the
of
vibrations
to
the
heat
bath,
i.e. mechanical degrees of
coupling
First
use
of
the
UV
Super-ACO
Free
asymmetric CO-stretching mode for W(CO)6 in DBP as a function of
$
M
and
1.6
mM,
giving
an
absorbance
of
about
0.5
116
of the tumor and then folded back to expose the tumor. The at
freedom
external
to
the
molecule,
is
substantially
weaker
than
that
temperature.
Reprinted with permission from reference 37.
Electron
Laser
: fluorescence
350 nm and
absorbance
about
1 at 363
nm,any
respectively,
surrounding
normal
brain of
was
protected
from
possible in
of electronic states, the dephasing times are relatively long for the
decays
rotational
dynamics
of
the 0.1
cm
path
of amoistened
quartz
cuvette.
stray
laserand
energy
by
cottonoids
!Fig. 9".
vibrational photon echo, and there are little or no solvation
The beats are interpreted as multilevel coherence of the anharmonic
surgically
exposed,
1500 macropulses
ofpulses are appropriate for this
The absolute
intensity
of
a differential
transient
absorptheOnce
NADH
coenzyme
, M.dynamics.
E.about
Consequently,
picosecond
oscillator. Figure 11 exhibits beats in the photon-echo decay curve,
m radiation
32 mJ/macropulse
were
deliv6.45
tion#spectrum
%A(&,t)
isinvestigation.
directly
proportional
to the
popuThe temperature
was
varied from 300 to 16 K, taking
Couprie,
P.Tauc,
F.averaging
Merola,
A.
which are accounted for by a three-level model with a modulation
ered
through
an
articulated
arm
toM.the
outer
surface
ofthat
the theliquid and then to a glass.
the
sample
from
a liquid
to a supercooled
lation
of theD.
molecule
in
an
excited
state.
Assuming
Delboulbé,
Garzella,
T. Hara,
frequency of 2.3 ps and a vibrational anharmonic splitting of
Photon
echoes
observed
from
16 to 140 K, where T, is 90 K,
tumor.
armonly
terminates
awere
hand
piece,
where
pumpThe
beam
via65(5)
theintransition
S 0 →S
1 , the
Billardon
,articulated
Rev.interacts
of Scient.
Inst.,
14.7 ? 0.3 cm-'.
and
the
photon-echo
decay
curve
at
16abK is shown in Fig. 10. The
a saturation
calcium fluoride
lens
with
a
focal
length
of
12.5
cm
fo!1/
'
(&)
where
'
(&)
is
the
fluence
is
F
Vibrational spectral diffusion has been investigated with pumpS
(0
a0
great care was required to minimize the likelihood of forgetMay 1994,
1485-1495
constant
for
decay
is# m.
15 ps,
A2 )theathomogeneous dephasing
cused
the cross
FEL section
beam to
atime
spot
sizestate
of the
310!20
probe and transient-grating techniques using 1.3 ps pulses from the
sorption
of
the
ground
"in
units
of
cm
ting
a
seemingly
insignificant
device,
medicine,
supply,
or
is 60
and the
the homogeneous
linewidth is 5.2 GHz, which
B. Transient absorption experiments
helium–neon
beam
wastime
used
to ps
guide
excision.
By
Surface
States
and Space
FEL and 10 ps pulses from an optical parametric amplifier (38). An
wavelength pilot
&. The
pulse
fluence
the
pump
be of
part. Thus a track record was established of successful, roushould
beofcompared
withshould
the inhomogeneous
linewidth of 540
practicing
one
final
time
with
some
sterile
paper
on
a
side
ensemble of solute molecules will sample all possible solvent
39 shows
transient
absorption
experimental
Charge
Layer
Dynamics
on Si
the same order as the saturation
fluence
in order
to excite
a to the homogeneous
tineFigure
cases using
these the
operating
rooms
prior to the
first FEL
GHz.
The
pure
dephasing
time
contribution
environments and thus a distribution of transition energies on some
table, the surgeon was able linewidth,
to then position
hand
piece of conformational fluctuasetup
ofpower
theElectron
influence
aThe
measure
case. employed at Super-ACO. Control of the spatial overlap
large fraction of the molecules.
on the
(111)2x1
:FEL
athe
Free
timescale.
Consequently, the homogeneous line spectrally diffuses
with the visible pilot beam tions
to keep
thevibrational
focus on the tumor
on the
level
spacing, is 1.6 GHz.
between
pulses
critical.toToa holding
monitor area
this,from
we mounted
The the
patient
wasisbrought
the main a
sample is limited to a maximum
of 100 mW,energy
which
correLaser-Synchrotron
radiation
throughout
the full inhomogeneous line on a timescale that is long
controlling FEL-beamSubsequent
delivery measurements
with a foot-pedal10 investigated W(CO)6 in 2-methylquartz
lens,where
whichanesthesiologists
was used to focusprepared
the pump
ontofor
the surface,
hospital,
thebeam
patient
photons/
sponds to energy of 12 nJ per
pulse
"i.e.,
2$10
with
respect
to the homogeneous dephasing time. Measurements of
study
, M.from
Marsi,
M.
E.expoCouprie,
actuated beam block. In the pentane
first
operation,
total
FEL
(2-MP)
room
temperature
to 10 K (36). The FEL was
general anesthesia. The patient was prepped and brought into
transient spectral hole demonstrate spectral diffusion and
pulse#. The pump beam istuned
focused
onto about
theand
sample
to within
to 5.04
thes,pulse
sure administered in multiple
passes
tookpm,
50
ablatL. Nahon,
D.
Garzella,
A. duration was -1.5 ps. These aorientational
one of the two operating rooms fitted for use of the FEL.
motion of the asymmetric CO-stretching mode for
$
m,
leading
to
the
possibility
of
fluence
a
diameter
of
)20
results
suggest
that
the asymmetric
CO-stretch
mode can be
ing approximately a cubic centimeter
‘‘divot’’
from
the
outer
Delboulbé,
T.
Hara,
R.
Bakker,
G.
W(CO)6
in
2-MP. Intriguingly, the lifetime increases with
Once
under
anesthesia,
the
patient
was
positioned
in
a
supine
approximately
equal The
to theremainder
saturationoffluence.
In the
simplest
. 37. Single photon counting data obtained with the Super-ACO SRsurface
inhomogeneously
broadened
in
liquid solutions and that inof the tumor.
the
tumor
was
retemperature.
Indlekofer,
M.
Billardon,
A.
Talebposition
with
a
shoulder
roll
under
her
right
shoulder,
thus
broadening
occurs at toroom temperature. The
L: !A" Total fluorescence decay F(t) of NADH at pH 8, 10 °C, $ exc 350sected
situation,
the !Fig.
pump/probe
signal observed
is proportional
en bloc
10". homogeneous
allowing
to be easilyinstrumental
positioned function
nearly horizontally
1.6
ps,
the
homogeneous
linewidth was
apparent
decay
time
was
Ibrahimi,
,
Appl.
Phys.
Lett.
$ em
460 nm,her
andhead
corresponding
g(t); !B" residu- theOnce
population
thattheistumor
not inwas
thedivided
groundand
state.
Thus,
if
the
removed,
a portion
of 70(7)
Native and mutant myogiobins
!Fig. 8".
49 (1997)
GHz and
the
inhomogeneous
linewidth
was
-300
GHz. The
obtained
from maximum entropy method analysis of the decay in !A"; ground state is the only absorbing
895-897
state,
then
thefor
pump/probe
the tumor that did not include
the
defect
was
sent
neuroroom temperature observation of the photon echo is attributable to
Investigation of the dynamics of the CO-stretching mode in
A standard
neurosurgical
autocorrelation
of the
residuals. approach was used in the right
A is a linewidth
conobservable is given by S(t)!A
* P ex(t)
+ where
the relatively
sharp
homogeneous
of asymmetric COmyoglobin
provided
insight 2016
into protein dynamics (39).
temporal area, guided by a Pickar®
neuronavigational
sysM. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs
31 has
!May
–10 !June,
stant determined by experimental
parameters
such
as theand
la- !ERLs), Hamburg, Germany,
2-MP.
stretch
mode
for
W(CO)6
in
O2
in muscle tissue. CO or O2
Myoglobin
stores
and
transports
tem which utilized a computer topography !CT" scan that
ser
intensity
and
the
probability
that
the
system
is
found
in
Infrared
photon-echo
beats
have
been
observed
with
-700
fs
binds
to
the
iron
atom
located
in
a
symmetric
protoheme,
i.e. for
Fig. 2. SPV intensity as a function of the
FEL/SR
delay
2 contrast
juin 2016
showed
obtained
the dayneither
prior to the
procedure.
This in
%. jeudi
The
oxided
form
(NAD")
absorbs
nor emits
www.lunex5.com
III. The first Free Electron Laser experimental results
Wavelength limits of oscillator configuration
• Storage rings
VEPP3 (Russia)
Super-ACO (France)
NIJI-IV (Japan)
UVSOR (Japan)
Duke (USA)
ELETTRA (Italy)
- limited straight section length
- planar undulator : mirror
degradation due to harmonic content
• Linacs
Stanford
Los Alamos
FELI (Japan)
.....
• ERLs :
Jefferson Lab
JAERI
Novosibirk
Limits in mirror performances
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
IV. The high gain Free Electron Laser
www.lunex5.com
High gain studies
Strong signal case : Case of «long» undulator, «high» current : The change of electric field in one pass can not be neglected
treatment with a set of generalised Bloch equations
F. A. Hopf, P. Meystre, M. O. Scully,W. H. Louisell, Strong-signal theory of a Free Electron laser, Phys. Rev. Lett 17 (30) (1976) 1342-1345
Hamiltonian despcription
G. Dattoli, A. Marino, A. Renieri, F. Romanelli, Progress in the Hamiltonian Pictoure of the Free-Electron l Laser, IEEE journal of Quantum Electronics QE17 (8) 1371-1387 (1981)
N. M. Kroll, P. L. Morton, M. N. Rosenbluth, in Free Electron generators of coherent radiation, edited by S. F. Jacobs et al. Physics of Quantum Electronics 7 (Addison_Wesley), 147 (1980)
A. Gover, P. Srangle, IEEE J. Quantum Electron. 17, 1196 (1981)
Collective instability
the electron communicate with each other through the radiation and the space charge field.
=> electron «self bunching» on the scale of the radiation wavelength periods.
The electrons have nearly the same phase and emit collectively coherent synchrotron radiation.
Exponential growth of the radiation. Ex of cooperative effect in radiation-matter interaction
R. Bonifacio et al., Cooperative and chaotic transition of a free electron laser Hamiltonian model, Optics Communications 40(3), 1(1982),
219-223
R. Bonifacio, Pellegrini C. and L.M. Narucci, Collective instabilities and high-gain regime in a free electron laser, Opt. Comm. 50, 376 (1984)
Sprangle, P.,Tang, C. M., & Roberson, C.W. (1985). Collective effects in the free electron laser. Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 239(1), 1-18.
Bonifacio, R., Casagrande, F., Cerchioni, G., de Salvo Souza, L., Pierini, P., & Piovella, N. (1990). Physics of the high-gain FEL and
superradiance. La Rivista del Nuovo Cimento (1978-1999), 13(9), 1-69.
Start-up from spontaneous emission
First considered by Saldin and Kondratenko in order to amplify the emission in the high gain regime until saturation.
Considered cases : infra-red FEL @ 10 MeV, shorter wavelengths (20 GeV, 0.25 keV).
A.M. Kondratenko et al, Sou Phys. Dokl. 24 (12), 1979, 989
Kondratenko A.M., Saldin E.L.: Generation ofCoherent Radiation by a Relativistic Electron Beam in a Undulator. Part. Accelerators 10, 207–216 (1986)
Y.S. Derbenev, A.M. Kondratenko, E.L. Saldin: On the possibility of using a free electron laser for polarisation control in a storage ring, Nucl. Instr. Meth. A
193, 415–421 (1982)
K. J. Kim et al, PRL57, 1986, 1871
C. Pelligrini et al, NIMA475, 2001, 1
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
IV. The high gain Free Electron Laser
Self Amplified Spontaneous Emission (SASE)
High density electron beam and long undulator :
• a strong bunching takes place (space charge)
• the change in electric field can no more be neglected
=>
- coupled pendulum equation, describing the phase space evolution
of the particules under the combined undulator magnetic field and
electric field of the optical wave
- evolution of the optical field
- evolution of the bunching coupled to the longitudinal sapce charge
forces
=> evaluation of the electronic density and current
evaluation of the light wave evolution
Undulator Magnetic field
B
electron
equations of
motion
J
Maxwell wave
equation for the
radiation field
Er
Collective instability
the electron communicate with each other through the radiation and the space charge field
The FEL parameter defines the growth rate, measured in undulator periods
Review papers : Z. Huang, K. J. Kim, Review of the free-electron laser theory, Physical Review Special Topics-Accelerators and Beams, 10(3), 034801.
Pellegrini, C., A. Marinelli, and S. Reiche. "The physics of x-ray free-electron lasers." Reviews of Modern Physics 88.1 (2016): 015006.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
IV. The high gain Free Electron Laser
www.lunex5.com
Evolution of the light wave in the High gain regime
SASE : Self Amplified Spontaneous Emission
start-up from spontaneous emission noise
exponential growth due to a collective instability (self-organisation of
the electrons from a ramdon initial state)
At saturation, the amplification process is replaced by a cyclic energy
exchange between the electrons and the radiated field.
Light
Start-up
4
1) energy modulation
Exponential
gain regime
2) density modulation
3) Coherent emission
Energy
1
2
eEnergy
3
Saturation
Optical guiding
• gain guiding (quadratic gain medium, Kogelnick 1965)
• refractive index
=> undulator longer than a few Rayleigh lengths is possible
Phase
Scharlemann, E.T., A.M. Sessler and J.S.Wurtele, 1985, Physical Review Letters 54, 1925.
Scharlemann, E.T., Sessler, A. M., & Wurtele, J. S. (1985). Optical guiding in a free electron laser. Nuclear Instruments and Methods in Physics Research Section A:
Accelerators, Spectrometers, Detectors and Associated Equipment, 239(1), 29-35.
Z. Huang, K. J. Kim, A Review of X-ray Free-Electron Laser theory, Phys. Rev. Spe.Topics AB, 10, 034801 (2007)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
IV. The high gain Free Electron Laser
www.lunex5.com
Evolution of the light wave in the High gain regime
SASE : Self Amplified Spontaneous Emission
start-up from spontaneous emission noise
exponential growth due to a collective instability (self-organisation of
the electrons from a ramdon initial state)
At saturation, the amplification process is replaced by a cyclic energy
exchange between the electrons and the radiated field.
Light
Start-up
4
1) energy modulation
Exponential
gain regime
2) density modulation
3) Coherent emission
Energy
1
2
eEnergy
3
Saturation
Optical guiding
• gain guiding (quadratic gain medium, Kogelnick 1965)
• refractive index
=> undulator longer than a few Rayleigh lengths is possible
Phase
Phase
Scharlemann, E.T., A.M. Sessler and J.S.Wurtele, 1985, Physical Review Letters 54, 1925.
Scharlemann, E.T., Sessler, A. M., & Wurtele, J. S. (1985). Optical guiding in a free electron laser. Nuclear Instruments and Methods in Physics Research Section A:
Accelerators, Spectrometers, Detectors and Associated Equipment, 239(1), 29-35.
Z. Huang, K. J. Kim, A Review of X-ray Free-Electron Laser theory, Phys. Rev. Spe.Topics AB, 10, 034801 (2007)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
FELs as part of the Star Wars program, and promised a much higher electron
IV.
The
high
gain
Free
Electron
Laser
beam
brightness.
Robert
Palmer
and
I,
at
the
Center
for
Accelerator Physics at
www.lunex5.com
Brookhaven National Laboratory, decided in 1986-87 to develop this new
Limits
in storage rings and electron gun development
technology for application in laser acceleration and FELs. An S-band version of
the Los Alamos gun, optimized for high peak power and small emittance, was
Limits in storage ring
designed at Brookhaven.
J. B. Murphy and C. Pellegrini, J. Opt. Soc. Am. B, 2 (1985)
Batchelor, K., H. Kirk, K. McDonald, J. Sheehan
Developments of photo-injectors
and M. Woodle. 1988. Development of a High
Fraser, J.S. and R.L. Sheffield. 1987. High- brightness injectors for RF-driven freeBrightness
Electron
Gun 1489-1496.
for the Accelerator Test
electron lasers.
IEEE J. Quantum
Electron. QE-23:
Batchelor, K.,Facility
H. Kirk, K. McDonald,
J. Sheehan and
M.Woodle.Laboratory.
1988. Development
at Brookhaven
National
Proc.
of a High Brightness Electron Gun for the Accelerator Test Facility at Brookhaven
of the Proc.
1988
European
Particle
Accelerator
Conf.,
National Laboratory.
of the
1988 European
Particle Accelerator
Conf., Rome,
pp. 54–958.Rome, pp. 54–958.
with a linac and a photoinjector it is possible to reach the nm region at a beam energy of 1.5 GeV, with about 6 mJ/pulse starting
from noise
in an 11
m long
Later
work
onundulator
photo-injector development was done at UCLA and a program was started
later at
SLACNuclear
by Herman
Winick,
andA272,
continued
with a BNL-SLAC-UCLA collaboration.
C. Pellegrini
Instruments
and Methods
364-367 (1988).
Sigtuna, June 14-18, 2015
C. Pellegrini
10 fs-10 ps,
εα1/E
10-30ps, εαE2
25
Energy spread : 0.01 %
Repetition rate : depending on the linac (room
temperature or superconducting)
Energy spread : 0.1 %
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
IV. The high gain Free Electron Laser
www.lunex5.com
Historical observations of SASE
SASE at saturation mm waves (80’s: LLNL, MIT)
T. Orzechowski et al. Phys. Rev. Lett 54, 889 (1985)
SASE at start-up µm (CLIO, L. A., Stanf.)
Prazeres, R., Ortega, J. M., Glotin, F., Jaroszynski, D. A., & Marcouillé, O. (1997). Observation of
self-amplified spontaneous emission in the mid-infrared in a free-electron laser. Physical
review letters, 78(11), 2124
Saturation at 100 nm (TESLA-TTF, 2001)
Ayvazyan,Valeri, et al. "A new powerful source for coherent VUV radiation:
Demonstration of exponential growth and saturation at the TTF free-electron
laser." The European Physical Journal D-Atomic, Molecular, Optical and
Plasma Physics 20.1 (2002): 149-156.
Bunching (CESTA, 8mm)
SASE operation of the VUV FEL at 30 nm
(DESY, 2005), 4 nm (2007)
Gardelle, J., Lefevre,T., Marchese, G., Rullier, J. L., & Donohue, J.T. (1997). High-power
operation and strong bunching at 3 GHz produced by a 35-GHz free-electron-laser
amplifier. Physical review letters, 79(20), 3905.
Ackermann,W. A., Asova, G., Ayvazyan,V., Azima, A., Baboi, N., Bähr, J., ... &
Brinkmann, R. (2007). Operation of a free-electron laser from the extreme
ultraviolet to the water window. Nature photonics, 1(6), 336-342.
5 orders of magnitude of amplification (IR, UCLA/Los
A.) and Saturation at 12 µm (UCLA/L. Alamos, 1998)
SCSS Test Acceletator at 60-40 nm
M. J. Hogan et al., Phys. Rev. Lett. 80, 289 (1998)
M. J. Hogan et al., Phys. Rev. Lett. 81, 4867 (1998)
Saturation at 530 nm, 385 nm (LEULT, 2000)
Milton, S.V., Gluskin, E., Biedron, S. G., Dejus, R. J., Den Hartog, P. K., Galayda, J. N., ... &
Sereno, N. S. (2000). Observation of self-amplified spontaneous emission and exponential
growth at 530 nm. Physical review letters, 85(5), 988.
S.V. Milton et al, Exponential gain and saturation of a Self-Amplified Spontaneous Emission
Free- Electron Laser, www.sciencexpress.org / 17 May 2001 / Page 1/ 10.1126/science.
1059955
Saturation at 800 nm (UCLA, 2001)
Shintake,T.,Tanaka, H., Hara,T.,Tanaka,T.,Togawa, K.,Yabashi, M., ... & Goto,
S. (2008). A compact free-electron laser for generating coherent radiation in
the extreme ultraviolet region. Nature Photonics, 2(9), 555-559.
SASE operation of the LCLS at 0.15 nm
Emma, P., Akre, R., Arthur, J., Bionta, R., Bostedt, C., Bozek, J., ... & Ding,Y.
(2010). First lasing and operation of an ångstrom-wavelength free-electron
laser. nature photonics, 4(9), 641-647.
SASE operation at SACLA at 0.08 nm
Ishikawa,T., Aoyagi, H., Asaka,T., Asano,Y., Azumi, N., Bizen,T., ... & Goto, S.
(2012). A compact X-ray free-electron laser emitting in the sub-angstrom
region. Nature Photonics, 6(8), 540-544.
Tremaine, A.,Wang, X. J., Babzien, M., Ben-Zvi, I., Cornacchia, M., Nuhn, H. D., ... &
Rosenzweig, J. (2002). Experimental characterization of nonlinear harmonic radiation from a
visible self-amplified spontaneous emission free-electron laser at saturation. Physical review
letters, 88(20), 204801.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
the
theinput
inputofofthe
theFEL
FELamplifier
amplifierisisamplified,
amplified,typically
typicallyup
uptotosaturation
saturationininaasingle
singlepass
passafter
afteraaregime
regimeofofexponential
exponential
wth.
growth.
growth.
IV. The high gain Free Electron Laser
www.lunex5.com
SASE : Conditions for amplification
3.4
Conditions
amplification
Conditions
forfor
amplification
3.4
Conditions
for
amplification
Conditions for amplification
discuss
now
the
for
SASE
amplification.
Let’s
discuss
now
theconditions
conditions
for
SASE
amplification.
sLet’s
discuss
now
the
conditions
for
SASE
amplification.
•
The
electron
beam
should
be
rather
"cold",
its
energyspread
spreadshould
should be
be smaller
smaller than
the
bandwidth,
i. e.i. e.
The
electron
beam
should
be
rather
"cold",
its
energy
than
the
bandwidth,
The electron
beam
should
rather
"cold",itsitsenergy
energyspread
spread should
should be
bandwidth,
i. e.i. e.
The electron
beam
should
be be
rather
"cold",
besmaller
smallerthan
thanthethe
bandwidth,
σγ
σσγ γ <<ρρFEL
FEL
γγ < ρFEL
γ
(172)
(172)
εεn n λλ
<<
γ
λ
εnγ 4π
4π
(173)
(173)
(172)
There
should bebeaaproper
matching
(size,
divergence)
between
the
beam
and the
There
propertransverse
transversematching
matching
(size,
divergence)
between
theelectron
electron
beam
thephoton
photon
• Thereshould
should be a proper
transverse
(size,
divergence)
between
the electron
beam and
the and
photon
beam
There
should
beundulator
a properprogression
transversefor
matching
(size,
divergence)
between
the
beamshould
and the
photon
beam
along
insuring
aaproper
interaction.
ItItthat
means
the
be
beam
along
the
undulator
progression
for
insuring
proper
interaction.
means
thatelectron
theemittance
emittance
should
not
be
along
thethe
undulator
progression
for insuring
a proper
interaction.
It means
thethat
emittance
should not
be toonot
large
mtoo
along
the
undulator
progression
forundulators,
insuring
aintermediate
proper
interaction.
It
means
that
the segments.
emittance
should
large
atatshort
For
long
between
undulator
segments.
at
short
wavelength.
For
long
undulators,
intermediate
focusing
isfocusing
then put is
between
undulator
It writes
: not be
too
large
shortwavelength.
wavelength.
For
long
undulators,
intermediate
focusing
isthen
thenput
put
between
undulator
segments.
ItItwrites
: : wavelength. For long undulators, intermediate focusing is then put between undulator segments.
large
at short
writes
rites :
<
(173)
ItItonly
γ
4πbecause
onlybecame
becamepossible
possibletotoreach
reachFEL
FELatatshort
shortwavelenght
wavelenght
becauseofofthe
theprogresses
progresseson
onelectron
electronguns.
guns.
The
radiation
diffraction
be
than
the
FEL
i.e.
length
should
be
It only
became
possible tolosses
reach should
FEL
at short
wavelength
ofgain,
the progresses
on electron
guns.
The
radiation
diffraction
losses
should
besmaller
smaller
thanbecause
thebecause
FEL
gain,
i.e.the
theRayleigh
Rayleigh
should
belarger
larger
t only
became
possible
to reach
FEL
at short
wavelenght
of the
progresses
onlength
electron
guns.
than
thanthe
thegain
gainlength.
length.
The radiation
diffraction
losses
smallerthan
than
the Rayleigh
length
should
• The radiation
diffraction
lossesshould
should be
be smaller
thethe
FELFEL
gain, gain,
i.e. thei.e.
Rayleigh
length should
be larger
thanbe
thelarger
gain length.
n the gain
length.
(174)
Zr > Lgo
Zr > Lgo
Corrections
Correctionsterms
terms(from
(fromthe
the3D
3Dtheory)
theory)can
canbe
beintroduced
introduced
XXXREF
REFM.
M.XieXXXX
XieXXXX
Zr > LgoXXX
Corrections terms (from the 3D theory) canCorrections
be introduced
XXX REF M. XieXXXX
terms
M. Xie Nucl. Inst. Meth. A 445, 59 (200)
M. Xie, Porceedings PAC 1995, 183
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
(174)
(174)
IV. The high gain
Free Electron
Laser
1 Seeding
FELS with HHG
www.lunex5.com
13
while an FEL amplifier has a relative
amplification
bandwidth of the order
SASE
properties
and coherence:
only the noise
infrom
the noise,
FEL bunching
amplification
spectral
f ∼ Limited
2ρf el [31]
temporal
start-up
on different
trainsrange
of the bunch
will be
amplified.
We need
to calculate
the fluctuations in a frequency
=> “spikes”
in spectral
andthen
temporal
distribution
: slippage
over one
gain length
the portion
of beam
that we have to consider for the
angeCooperation
∆ω ∼ 2ωρflength
el and
Nberhas
of spikes
= bunch
lengthof/ cooperative
length length, lc ∼ λ/4πρf el . The
verage,
to be of
the order
the cooperation
umber of electrons in a cooperation length is
Spikes : separated
nec
by one
cooperative
length
We
may
therefore
spectral
width
:ρ
.12, 1.14 and 1.15
Statistics :
Gamma
distribution
= Ipeak lc /e0 c = Ipeak λ/ (4πe0 cρf el )
(1.15)
estimate the shot noise intensity combining equations
Isn ∼ 18e−
√
2
ρ
f el
3
ω
γm0 c2 ∼ 3 ωρ2f el γm0 c2
Σb
(1.16)
• jitterfunction
from
This
is proportional to the square of the ρf el parameter, grows
pulse to
nearly
with the frequency and with the electron beam energy. Assuming
pulse
ypical values for the main parameters (ρf el ∼ 10−3 , λu = 3 cm and K = 2)
we have plotted in Fig. 1.5 the power corresponding to the intensity 1.16 over
transverse
mode area equivalent to the electron beam transverse size.
Handling :
single spike
taper
seeding and self seeding
S. Reiche et al., NIMA 593 (2008) 45-48
L. Giannessi et al., Phys. Rev. Lett. 106, 144801 (2011)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
IV. The high gain Free Electron Laser
www.lunex5.com
SASE properties
FLASH
SCSS Test Accelerator : 60-40 nm
M. Kuhlmann et al, FEL06
P. Mercère et al, , Optics Letters, 28 (17), 1534-1536 (2003)
A. Singer et al. PRL 101, 254801 (2008)
Single-shot wavefront analysis of SASE harmonics in different FEL regimes, R. Bachelard, P.
Mercere, M. Idir, M. E. Couprie, M. Labat, O. Chubar, G. Lambert, P. Zeitoun, H. Kimura, H. Ohashi,
A. Higashiya, M.Yabashi, N. Nagasono,T. Hara,T. Ishikawa, accpeted in Phys. Rev. Lett. 2011
Wavefront quality : ability to properly focus
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
IV. The high gain Free Electron Laser
SASE Versus seeding and echo
SASE (Self Amplified Spontaneous Emission) : no laser - electron interaction
• short wavelength operation (1 Å)
• good transverse coherence => low
emittance required=> gun, energy
• spike
• single spike (low charge, chrip/taper),
self-seeding
S. Reiche et al., NIMA 593 (2008) 45-48
R. Bonifacio et al, Opt. Comm. 50, 1984, 376, K. J. Kim et al, PRL57, 1986,
1871, C. Pelligrini et al, NIMA475, 2001, 1, A.M. Kondratenko et al, Sou
L. Giannessi et al., Phys. Rev. Lett. 106, 144801 (2011)
Phys. Dokl. 24 (12), 1979, 989
Seeding : one laser-electron interaction
• temporal coherence given by the external seed laser
• improved stability (intensity, spectral fluctuations and
jitter) => pump-probe experiments
• quicker saturation => cost and size reduction L. H.Yu et al, Science 289, 2000, 932
• good transverse coherence
L. H.Yu et al, PRL912003, 074801
• Seed : laser and HHG ( 60 nm)
T. Saftan APAC 2004, Gyeongu
Echo : Echo Enable Harmonic Generation : two laser - electron interactions
1
"echo
=
1 1
+ !
"1 "2
G. Stupakov., PRL 102, 074801 (2009)
high order harmonics
reached in a compact
manner
Zhao et al., Proceed FEL conf, Mamö (2010)
D. Xiang et al., PRL 105, 114801 (2010)
! !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs
jeudi 2 juin 2016
IV. The high gain Free Electron Laser
www.lunex5.com
X-ray FELs
FLASH.
FLASH2 Operation
Started
2 mJ, 1.4 Å
LCLS
Free-Electron Laser
in Hamburg
SACLA
1.5 Å saturation at 65 m (of 112 m)
now 6 mJ, 96.7 % availability
> Official permission for FLASH2 beam operation
February-7, 2014
Electron beam on 4FL2EXTR
March-4, 2014
> Electron beam operation started in March 2014
ƒ first electron beam in extraction March-4, 2014
ƒ first beam to dump May-23, 2014
Electron beam on 3FL2DUMP
May-23, 2014
ƒ only few days available for FLASH2 beam operation
before simultaneous operation established
> Simultaneous operation of FLASH1 (SASE) and
FLASH2 (electron beam) starting end of May 2014
!"#$%&'()*(+*,-./0*1'&2*/2($&*/./34,3-*
ƒ FLASH2 runsFLASH
now in parallel to FLASH1 whenever possible,
5%6'%&'()*789:#:*
mainly
during
FLASH1
photon user <1A9$BC38D$
experiments
=>$<989:1-4$
J/191-$
6..'7'389:-;$<93,.9,3'4$
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ĺWLPHDYDLODEOHIRUFRPPLVVLRQLQJLQFUHDVHGVLJQLILFDQWO\
LGM$ K:8;-149:.4$
Photon beam on FL2_CE_YAG
August-20, 2014
!"#$%&'
ƒ dedicated FLASH2 beam time reserved as well
=>$@,-$
?84'34$
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#$&'($ "#)$&'($
"*#)$&'($ 2014
> First
lasing:5#)$&'($
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!"#$%$
FERMI
Katja Honkavaara | FEL Conference 2014 | August-27, 2014
!"
to come : E XFEL, PAL FEL, Swiss FEL ....
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
IV. The high gain Free Electron Laser
www.lunex5.com
LETTER
Applications of FELs in the X-ray domain
RESEARCH LETTER
Jet (10 m/s)
Towards imaging of living cells
using the program RADDOSE14) and a peak power density in excess of
1016 W cm22 at 70-fs duration. In contrast, the typical tolerable dose in
conventional X-ray experiments is only about 30 MGy (ref. 1). A single
LCLS X-ray pulse destroys any solid material placed in this focus, but
the stream replenishes the vaporized sample before the next pulse.
The front detector module, located close to the interaction region,
recorded high-angle diffraction to a resolution of 8.5 Å, whereas the
rear module intersected diffraction at resolutions in the range of 4,000
to 100 Å. We observed diffraction from crystals smaller than ten unit
200 μm
cells on a side, as determined by examining the data recorded on the
Rear pnCCD
es
rear pnCCDs (Fig. 2). A crystal with a side length of N unit cells gives
(z = 564 mm)
rise to diffraction features that are finer by a factor of 1/N than the
Front pnCCD
Interaction
Bragg spacing (that is, with N 2 2 fringes between neighbouring Bragg
(z = 68 mm)
point
peaks), providing a simple way to determine the projected size of the
nanocrystal. Images of crystal shapes obtained using an iterative phase
second nanocrystallography. Nanocrystals flow in their
retrieval method15,16 are shown in Fig. 2. The 3D Fourier transform of
21
a gas-focused, 4-mm-diameter jet at a velocity of 10 m s
the
crystal shape is repeated on every reciprocal lattice point. However,
Liquid
the pulsed X-ray FEL beam
that isjet
focused on the jet. Inset,
the diffraction condition for lattice points is usually not exactly satisfied,
anning electron micrograph of the nozzle, flowing jet and
so each recorded Bragg spot represents a particular ‘slice’
of the Ewald
wo pairs of high-frame-rate pnCCD detectors12 record lowpnCCD
s FEL repetition sphere through the shape transform, giving aRear
sethe
variety of Bragg spot
lat
ffraction from single X-ray FEL pulses,
u
p
(z
=
564
mm)
y
-raorientations
stals arrive at random times
in the beam, and profiles in a pattern; these are apparent in Fig. 2. The sum of counts
Xand
S
L
LC
hitting one is proportional
to the crystal concentration.
in each Bragg spot underestimates the underlying structure factor
square modulus,
representing
Front
pnCCD a partial reflection.
Interaction
Figure
3a
shows
of the X-ray pulses was 1.8 keV (6.9-Å wavelength), with
(z = 68strong
mm) single-crystal diffraction to the highest
point
photons per pulse at the sample and pulse durations of angles of the front detector. The nanocrystal shape transform is also
s (ref. 13). An X-ray fluence of 900 J cm22 was achieved apparent in many patterns at the high angles detected by the front
FEL beam to a full-width at half-maximum of 7 mm, detector, giving significant measured intensities between Bragg peaks
Figure
nanocrystallography.
Nanocrystals
flow
in their
as is noticeable in Supplementary
Fig. 3a. These
mid-Bragg
intensities
o a sample dose
of up to1
700| Femtosecond
MGy per pulse (calculated
21
using the program RADDOSE14) and a peak power density in excess of
Mimivirus
(Acanthamoeba
polyphaga) : le plus
1016 W cm22 at 70-fs duration. In contrast,
the typical tolerable
dose in
conventional X-ray experiments
only about 30 MGy
(ref. connu
1). A single
RESEARCH isLETTER
virus
(diamètre de 0.75 µm)
LCLS X-ray pulse destroys any solid material placed in this focus, but
the stream replenishes the vaporized sample
before the next pulse.
a
b
The front detector module, located close to the interaction
region,
Diffraction pattern
recorded high-angle diffraction to a resolution of 8.5 Å, whereas the
rear module intersected diffraction at resolutions in the range of 4,000
to 100 Å. We observed diffraction from crystals smaller than ten unit
cells on a side, as determined by examining the data recorded on the
rear pnCCDs (Fig. 2). A crystal with a side length of N unit cells gives
rise to diffraction features that are finer cby a factor of 1/N than the
Bragg spacing (that is, with N 2 2 fringes between neighbouring Bragg
peaks), providing a simple way to determine the projected size of the
nm
nanocrystal. Images of crystal shapes obtained200
using
an iterative
LETTERphase
RESEARCH
Membran protein photosystem 1
15,16
Diffraction
pattern
d
retrieval method
are shown in Fig. 2. The 3D Fourier transform of e
buffer solution in a gas-focused, 4-mm-diameter jet at a velocity of 10 m s
Micrographie
the crystal shape is repeated on every reciprocal lattice
point.
However,électronique
1
perpendicular
to
the
pulsed
X-ray
FEL
beam
that
is
focused
on
the
jet.
Inset,
Upper font detector
a
a
b
b for lattice points is usually not exactly satisfied,
¯the
21 11
0
diffraction
condition
0 1¯ 1
¯ ¯2
15 20
environmental scanning
electron
micrograph
of
the
nozzle,
flowing
jet
and
¯0
22 6
¯ 4¯
14 24
002
so each recorded
Bragg spot represents a particular ‘slice’ of the Ewald
focusing gas30. Two pairs of high-frame-rate pnCCD detectors12 record low¯
13
12
0
19 2 0
and high-angle diffraction from single X-ray FEL pulses, at the FEL repetition sphere through the shape transform, giving a variety of Bragg spot
¯ 2̄
16
¯ and
12 1
1
profiles
in a 7pattern;
these are apparent in Fig. 2. The sum of counts
rate of 30 Hz. Crystals arrive at random times and orientations in the beam,
¯0
79
11 0 1
¯ 2̄
4 14
¯ 0 Bragg
57
the probability of hitting one is proportional to the crystal concentration.
in
each
spot
underestimates
the underlying structure factor
¯ 0 921 811
19 10
3 5¯ 0
square modulus, representing a partial reflection.
1,000 nm
010
Lower font detector
¯ 2¯ 6¯
Figure 3a shows
strong single-crystal diffraction to the highest
14
photon energy c*of the X-ray pulses was 1.8 keV (6.9-Å wavelength), with
¯ 17 4̄
13
¯ 21 4¯
10
020
1¯4 9 4̄
of the front detector. The nanocrystal shape
transform is also
per pulse at the sample and pulse durations
of 14¯angles
more than 1012 photons
14 4̄
010
010
22
715 nm
620
nm
the front
10, 70, and 200b*fs (ref. 13). An X-ray fluence of 900 J cm was achieved apparent19¯in
9 7¯ many patterns at the high angles detected by Reconstruction
f Unconstrained
Sphere
Icosahedron g Unconstrained
Sphere
Icosahedron
¯
20
14
7̄
by focusing the FEL beam to a full-width at half-maximum of 7 mm, detector, giving significant measured intensities between Bragg peaks
¯
¯
19 19 7
¯ 26 7¯
15
c corresponding to a sample dose
d
in¯ Supplementary 100
Fig. 3a. These mid-Bragg intensities
of up to 700 MGy per pulse (calculated
¯ 22 7¯ as is noticeable
18
2¯3 9 10
gros
1
0
1
0
1
0
c
a
100
b
0 1¯ 1
1¯ 1 0
20 Å
d
h 1.0
i 1.0
0.8
M.0.8M. Seibert
Single
particles
and
PRTF = 0.5 intercepted
PRTF = 0.1
PRTF = 0.5et al.,PRTF
= 0.1 mimivirus
0.6
0.6
imaged with an X-ray laser,0.4Nature, 470, 2011, 78
0.4
PRTF = 0.5
PRTF
002
a*
0.2
32 nm
0.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
b*
160 nm
290 nm
0
200 nm
PRTF = 0. 1
PRTF
010
Resolution shell (nm–1)
Figure 2 | Single-shot diffraction patterns on single virus particles give
0.2
32
nm
32 nm
0.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Resolution shell (nm–1)
modes19 and two averaged images after fitting unconstrained low-res
corresponding high-angle
pattern.
In c we count
seven fringesand
in the
b*
Figure
3 | Diffraction
intensities
electron
density of photosystem
I. 73patterns, displayed on the linear colour scale shown on the right. c, d, Region of
H. Chapman et al., Femtosecond
X-ray
protein
nanocrystallography,
Nature,
470, 2011,
interpretable results. a, b, Experimentally recorded far-field diffraction
modes to a spherical or an icosahedral profile, respectively. The orien
direction, corresponding
to nine unitpattern
cells,
or 250
nm. Insets,
images
a, Diffraction
recorded
onreal-space
the front
pnCCDs with a single 70-fs pulse the
2mF 2 DF electron density map at 1.0s (purple mesh), calculated from
ent crystal diffraction. Low-angle diffraction patterns
ear pnCCDs, revealing coherent diffraction from the structure
m I nanocrystals, shown using a logarithmic, false-colour
indices of the peaks in a were identified from the
c
patternso(inand
false-colour
representation)
from individual
virus particles
the icosahedron2016
was determined from the diffraction data. The resul
of the nanocrystal,
by
phase retrieval
(using the Shrinkwrap
M. E. Couprie,
CAS determined
School
Free
Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs
!ERLs),
Hamburg,
Germany,
31
!Mayofat–10
70-fs
data
(c)
and from
conventional
synchrotron
data
truncated
a small!June,
background
subtraction
and correction of saturated pixels. Some peaks are the
circled
coherent Bragg
shape transform.
algorithm ) of theafter
captured in two different
orientations.
c, Transmission
electron
micrograph
differences between the spherical and icosahedral fits. h, i, The
jeudi 2 juin 2016
VOL 470 | 3 FEB RUARY 2011
15
labelled with their Miller indices.
0 1 0 The resolution in the lower detector corner is
8.5 Å. b, Precession-style pattern of the [001] zone for photosystem I, obtained
7
resolution
of 8.5
Å and collected
at a temperature
of 100 Kappearance
(d) (Methods).
The
.
an unstained
Mimivirus
particle, showing
pseudo-icosahedral
reconstructions
where the unconstrained low-resolution modes were
refined
model is depicted
in yellow.
d, e, Autocorrelation
functions
for a (d) and b (e). The shape and size of each an icosahedron. All reconstructions gave similar resolutions. We cha
Conclusion and prospects
www.lunex5.com
Conclusion
2011
2008
2009
EUV SASE FEL
2001
2002
VUV SASE FEL
VUV FEL oscillator
Seeded high Gain SASE FEL Visible SASE FEL 2000
1990
1983
Second FEL oscillator (visible)
Free Electron Laser amplification 1976
First Free Electron Laser oscillator (infra-red) 1977
1980
1971
Free Electron Laser concept
First laser (Ruby)
Ubitron
1970
1958
1960
Undulator concept
Laser invention
1946
1947
1951
1953
1954
1955
Undulator radiation observation
Maser
Undulator radiation observation
HHG seeded FEL
First X-ray FEL
2010
FERMI Seeded FEL user facility
Second X-ray FEL
X-ray FEL oriented History
Energy loss
Lab observation of synchrotron radiation
1950
1939
Varian brothers : klystron 1940
1930
1920
Einstein, black body radiation
1917
Historical survey of FELs :
- exchange of ideas and concepts in various domains : creativity !
- attempting to show how the new ideas arise
- subjective (apologize for cherished non cited papers...)
C. Pellegrini,The history of X-ray free-electron lasers, Eur. Phys. J. H, 37(5), 659-708. DOI: 10.1140/epjh/e2012-20064-5
Maturity of X-FEL => X-ray FEL applications for new investigation of matter are blooming up
Bostedt, C., Boutet, S., Fritz, D. M., Huang, Z., Lee, H. J., Lemke, H.T., ... & Williams, G. J. (2016). Linac Coherent Light Source:The first
five years. Reviews of Modern Physics, 88(1), 015007.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
Conclusion and prospects
www.lunex5.com
Approach diffraction and Fourier limits in a wide spectral range, with
flexibility for users
high
High rep. rate :
stability
higher
photon
energies
single spike,
modified
SASE, XFELO
FEL property
manipulations
seeding, echo,
up frequency
conversion
Compact accelerator :
Laser wakefield
acceleration, dielectric
acceleration,
inverse FEL
Short FEL
interaction
superconducting
linacs, rings
as pulses / high
energy
resolution
(BW : 10-6)
multiple users
Combinaison with
lasers and THz (e.g.
pump-probe...)
Compact undulator
Make «more compact» FELs
Physics and applications of High Brightness Beams : towards a fifth generation light source, Puerto-Rico, March 25-28, 2013
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
Poincare! sections are illustrated in Fig. 6b, for
which the number of intercepts n of the attractor
with the plane of the Poincare! section is a
signature of the ‘‘nT’’ regime, and where a folded
shape which does not fill the whole space
corresponds to the chaos. From the observation
of the attractors, the origin of the irregular
patterns of the FEL can be attributed to the
deterministic chaos rather than to noise.
The evolution of the system when a given
control parameter is varied can be followed by
the observation of the bifurcation diagram, in
which the intensity sampled at a definite time of
Conclusion
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Various regimes and studies
• MOPA
• Chaos and control
• Regerative FEL
• Vortives
Fig. 7. Bifurcation diagrams (a) for a change of f between 200
and 400 Hz, a ¼ 14:3 Hz and (b) for a change of a between 0
and 60 Hz, f=600 Hz.
the modulation period is plotted versus the control
parameter. As the stroboscopy is synchronized
with the modulation, a nT regime delivers a nvalued output and random answers reflect the
statistics of the chaos. Fig. 7 illustrates a 1T–2T
bifurcation for a change of the frequency of the
modulation in (a), and a 1T, 2T, chaos, 2T, 3T
sequence for a modification of the amplitude of
modulation. Bifurcation diagrams are powerful
tools for the observation of the transitions between
the different regimes.
• Mode locking
• Q-switching
• Super-radiance
5. Conclusion
• CPA
• limit cycles
• 2 color operation....
Fig. 6. (a) IðtÞcosð2pft), IðtÞsinð2pft), Iðt þ tÞ attractors reconstructed from intensity evolution of Fig. 3. 2T regime for
a ¼ 12 Hz, chaos for a ¼ 20 Hz, 3T regime for a=46 Hz. (b)
Corresponding Poincar!e sections.
M. Billardon, PRL 65 (6) , 713 (1990)
M. E. Couprie, NIM A 507 (2003) 1-7
Clear bifurcation and chaos sequences have
been observed in the response of the FEL to a
detuning modulation. In a further work, the
sequences (period doubling, inverse cascade, logistic map, etc.) corresponding to various parameters
set-ups should be studied, for the determination of
the basins of attraction. Clear analysis of the data
E. Hemsing et al. , Nature Physics 9, 549–553 (2013)
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
Question for the end
Is FEL a real laser?
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
Question for the end
www.lunex5.com
Is FEL a real laser?
Quantum description ?
yes
very heavy....
needed for some particular effects
(electromgantic undulator...)
no
Macroscopical quantum system?
Light Amplification by Stimulated Emission ?
theoretically : yes if stimulated
diffusion considered as stimulated
emission
experimentally : light amplifier (with
optical resonator, SASE...)
Spatial and longitudinal coherence properties
yes
M. Orzag, R. Ramirez, Quantum features of a fre electron laser, J. Opt. Soc. Am. B , 3 (6) , 895-900 (1986)
C. B. Schroeder, C. Pelligrini, P. Chen, Quantum effects in high gain FELs, Phys. Rev. E (64), 056502
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
Books....
Laser Handbook,
Volume 6: Free
Electron Lasers
by W.B. Colson, A.
Renieri, Claudio
Pellegrini Noth
Holland
Free-Electron Lasers in the
Ultraviolet and X-Ray Regime
Physical Principles, Experimental
Results,Technical Realization
Authors: Schmüser, P., Dohlus, M.,
Rossbach, J., Behrens, C.
The Physics of Free
Electron Lasers
Authors: Saldin,
Evgeny,
Schneidmiller, E.V.,
Yurkov, M.V.
Introduction to the
physics of Free
electron laser and
comparison with
conventional laser
sources, G. Dattoli
et al., ENEA, RT /
2009 / 44/FIM
Lectures on the
Free Electron Laser
Theory and Related
Topics, G. Dattoli, A.
Renieri, A.Torre,
World Scientific, 1
janv. 1993 - 637
pages
Principles of FreeElectron Lasers
!H. P. Freund
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
Books....
Elleaume P., Onuki
H. : Undulators,
wigglers and their
applications.Taylor
and Francis, London
(2003)
Synchrotron Radiation, Polarisation, Devices and
New Sources, M. E. Couprie, M.Valléau, in
“Magnetism and Synchrotron Radiation:Towards
the Fourth Generation Light Sources”, Proceedings
of the 6th International School “Synchrotron
Radiation and Magnetism”, Mittelwihr (France),
2012, edited by E. Beaurepaire, H. Bulou, L. Joly, F.
Scheurer Springer Proceedings in Physics Volume
151, 2013, pp 51-94
S. Krinsky, M.L. Perlman and R.E.
Watson Characteristics of
Synchrotron Radiation and Its
Sources "Handbook on Synchrotron
Radiation",Vol 1 ... A. Hofmann, Proc.
of CERN-Accelerator School (CAS) on
Synchrotron Radiation and free
Electron Lasers, 90-03, 115 (1990).
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
worldwide16–21. This mode of operation allows successfully tested in user experiments at Linac Coherent Light
1.4
he dynamics of ultra-fast processes triggered by a Source (LCLS) in a wide variety of fields.
1.2
-ray pump, with a time resolution on the order of
1.0
www.lunex5.com
onds.
For example, in the field of time-resolved
0.8
pectroscopy, two colour pulses allow the selective Results
olecular and atomic processes, such as chemical Twin-bunch experiment at hard X-rays. The twin-bunch
0.6
and rearrangement. High-intensity two-colour method is schematically illustrated in Fig. 1. The electrons are
0.4
w the study of warm dense matter with time- generated by a photocathode illuminated by a train of two laser
0.2
pump/X-ray probe experiments22,23 as well as the pulses (generated with a pulse stacker, see the Methods section)
0.0
vestigation of X-ray-induced Coulomb explosion with a variable delay on the order of a few picoseconds,
10
11
12
13
rs and
nanocrystals
at the Instr.
femtosecond
scale.A407,
generating
two separate
electron
are
R.Prazeres
et al. Nuclear
and Methods,
464 (1998),
R.Prazeres,
et al.,bunches.
Eur. Phys.The
J. D3,two
87 bunches
(1998)
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7369
A
Photon energy (keV)
field of coherent X-ray imaging, there is a accelerated up to 15 GeV in the LCLS linear accelerator and
rest in extending multiple wavelength anomalous compressed from a peak current of 20 A to roughly 4 kA by
a
c
Phase-space
Phase-space at undulator exit (lasing on)
bat undulator exit (lasing off)
D) imaging24 to fourth-generation light sources means of two magnetic chicanes. As a result of the bunch com13.5
13.5
5
E
=
5800
MeV
and
E
=
1.5
keV
b
!
tosecond crystallography .
25
2.15
pression, the final arrival time difference of the electron bunches
HEAD
HEAD
TAIL
an intense electron bunch travels in a magnetic is on the order of a few tens of femtoseconds. As the acceleration/
TAIL
13.4
13.4 2.1
rating a high-power X-ray pulse (ranging form a compression system generates a time–energy correlation in the
20
Magnetic (between nd
ral tens1stof
GW) with
narrow bandwidth
2 electron
undulatorbeam,
sectionthe two bunches also have different energies at the
2.05
undulator
section
Chicane
13.3
13.3
and duration between a few femtoseconds and a end ofK2the accelerator. Finally, the two compressed bunches are
–40
–20
0
20
40
–40
–20
0
20
40
Time15
(fs)
Time (fs)
mtoseconds1. K1
The central wavelength lr is given sent into the undulator where they emit two X-ray pulses of
2.0
ee-formula25
Controlled
b
d
different energies. Although we will present experimental data at
Current distribution at undulator exit
X-ray temporal profile
8
Delay
2
100
a photon energy x-ray
of 8.3 keV, the scheme described can work at any
10
1 þ K2 x-ray
6
nd Color
the available LCLS range (nominally from 300
lr ¼ lw
ð1Þ photon energy 2in
st;
2.05
2g2 1 Color
50
4
to 10 keV).
2
5
2.1
The recently developed X-band transverse deflector13 provides
undulator period, g is the beam’s Lorentz factor
0
0
ed
amplitude of the magnetic field. At X-ray an effective diagnostic tool for this two-bunch technique.
+ variants
–40
–20
0
20
40
–20
0
20
40
K2 = 2.15 –40
Time (fs)
Time (fs)
ethods developed so far rely on generating two Figures 2a and 2c show the measured longitudinal phase-space
0
by- using
twoslotted
distinct emittance
values of Kspoiler
with a quasi
of to
the control
two bunches
for2 the
double
enabling
the at the end of the undulator beamlineFigure
| Time-resolved measurements. (a) Measured9.5
longitudinal phase-space
of the 10.5
two unspoiled electron
the end of th
10.0
11.0 bunches at11.5
16,20,21. Although this approach
(theaFEL
process being suppressed). (b) Associated current profile of the two bunches. (c) Measured longitudinal phase-space of the tw
electron
beam
unspoiled
beam
(that
is,
suppressing
the
lasing
process
with
large
Photon energy (keV)
delay (fresh bunch)
A. A. Lutman et al.,, PRL 110,after134801
(2013)
lasing. (d) Temporal
profile of the two X-ray pulses reconstructed from the two phase-space measurements. The error bars are der
beam
control of the time and energy separation, the transverse perturbation in the electron orbit) and for the
averaging
of 100 unspoiled
phase-space measurements, as discussed in ref. 13. The horizontal axis represents the arrival time with respe
Marinelli
Phys.
Rev.for
Lett.
111,
134801
spectra of the two-colour XFEL. (a) Spectrum
after slightly
the lasingdetuned
process. TheA.
peak
currentetis al.,
roughly
5 kA
a total
h -pulses
is lower
the(phase
saturation
level because
observer
(the beam head is on the left).
T.Figure
Hara2 |etMeasured
al., Nature
Communications, 4, 2919, 2013
iSASE
with than
delay
shifter),
undulators
measured by scanning a monochromator with K1 ¼ 1.7 and K2 ¼ 2.15.
(2013)separation of 70 MeV. Figure 2d
on bunch is used for lasing twice, yielding a total charge of 150 pC, with an energy
(b) Consecutive single-shot spectra measured by an in-line spectrometer.
to act 5asand
phase
(K1), power.
U2 (K2),shows
U1(K1),
U2(K2)profile of the X-ray pulses reconstructed from
the temporal
between
15% shifters.
of the full U1
saturation
Intensity (a.u.)
IV. The high gain Free Electron Laser
Two-color operation (SASE)
First two color operation at CLIO on a FEL oscillator
Power (GW)
I (kA)
pulse stacking
Undulator
Chicane 2
Linac
Chicane 1
SASE
ARTICLE
–5
0
The line at 11.4 keV is emittedb from
the first undulator section and the
6
Average
number of undulators is reduced5 from eight to seven atSingle
around
Shot 13 min on
the ordinate. K2 is varied stepwisely from 2.15 to 2.0 in the lower part and
4
from 2.0 to 2.15 in the upper part of the figure. The accelerator was
3
operated at 10 Hz and the sampling
frequency of the in-line spectrometer
2
was 1 Hz.
Intensity (arb.units)
Laser
∆ Eelectron (MeV)
a
LCLS with twin bunch
ID 01– 08
Time (min)
ID 02– 08
Energy (GeV)
Energy (GeV)
Delay by chicane and different K
5
1
0
NATURE COMMUNICATIONS | DOI: 10.1038/
0
20
40
60
–60 –40 –20
Intensity (arb. units)
∆ Eelectron (MeV)
Energy
Energy
60 electron
20 40 the
0
second colour increases. In the TCDP operation,
∆ Ephoton (eV)
∆ Ephoton (eV)
beam energy spread resulting
a
b 15 from the first-colour lasing affects
22
Average
–3
the
gain
of
the
second
colour
Figure 3 | Spectral measurements: SASE. (a) Spectral intensity as a function of beam .energy and photon energy
in the SASE regime. (b
Single shot
and single-shot spectrum for a–2
fixed beam energy
(the
data
are
binned
over
electron
beam
energy
fluctuations).
This relation is more clearly shown in Figure 3, in which the
Beam Direction
10
–1
shot-to-shot intensity correlation
between the first and second
~5 ps
Spectral
properties.
the double-colour
the longitudinal phase-space
measurement
(see
the
Methods
0
colour
pulses
is
plotted.
K
and
K
were
setToatillustrate
2.14 (9.75
keV) and
Self-seeded
1
~50 fs
X-rays,2Fig. 3 shows X-ray spectra taken under th
section and ref. 13). The two bunches emit two X-ray pulses the
1.95pulse
(11and
keV),
and
energies
estimated
from
the i
Time
5
conditions
as Fig. were
2. Figure
3a shows the
spectral
with a peak power of 76 GW1for the head
62 GW
for the
the pulse
integrated
spectral
area
measured
by
the
in-line
spectrometer
function
of
electron-beam
energy
and
photon
ener
tail,
and
a
full-width
at
half-maximum
(FWHM)
pulse
duration
of
2
A. Marinelli et al., High-intenisty double-pulse X-ray
are
binned in beam
energythe
using
a single-shot
me
approximately 8 and 10 fs, 3respectively.
Thea two
pulses arefitnot
Photon Energy
using
Gaussian
(see
methods).
To
vary
electron
beam
Time
free-electron laser, Nature Comm. 6:6369
(2015)
Fourier transform limited as the FEL process is initiated by noise in the0average electron energy in order to deconvolve
energy
generated
by the
the 60
number of
–60 –40
–20 0spread
20 40
60
–60 first-colour
–40 –20
0 lasing,
20
40
the electron
operation commonly referred shot-to-shot energy fluctuations. The peak-to-p
tic representation of the experiment. Illustration not to scale. From right to left: a laser pulse train generates two electron bunches
at a distribution, a mode of the
∆ Ephoton (eV)28 of the first section was
(eV)
∆ Ephoton
undulators
changed
between
eight
aro
to as self-amplified spontaneous emission or SASE . The fine separation of the two colours is 90 eV centred
right inset shows the measured longitudinal phase-space at the photo-injector exit). The two bunches are accelerated in the
LCLS
The
photon
energy
of
the
two
pulses
is
correlated
spiky
temporal
structure
of
the
two
SASE
pulses
is
not
resolved
by
(ID01-08)
and
four
(ID05-08)
by
opening
the
undulator
gaps.
Figure 4 | Spectral measurements: self-seeding. (a) Spectral intensity as a function of beam energy and photon energy in the self-seede
energy
and
the
colour
separation
is independentino
this
diagnostic,
which atspectrum
this energy
time
resolution
of 4 are
fs binned
sed by means of two magnetic chicanes (the left inset shows the measured phase-space at the end of the beam line). Finally,
(b)
Average
and single-shot
for When
ahas
fixeda beam
(the undulators
data
over
electron
beam energy
fluctuations).
allenergy
eight
were
closed
(brown
diamonds
beam 2016
energy variations (note that this implies that
root
mean
squareHamburg,
(RMS). For Germany,
this data set,31
the !May
pulse energy
M.
E.
Couprie,
CAS
School
Free
Electron!Lasers!and!Energy!Recovery!Linacs
!(FELs
and
!ERLs),
–10
!June,
re sent to an undulator for the emission of two X-ray FEL pulses. The two X-ray pulses have a tunable energy difference in averaged
the range
Fig.a 3),
the first-colour
was
to saturation.
Underarethis
tions of
theclose
energies
of the two bunches
cor
over 100 shots is 1.207 mJ with
shot-to-shot
fluctuation lasing
ndjeudi
a variable
time
delay
of
tens
of
fs.
condition,
the
pulse
energy
of
the
first
colour
(9.75
keV)
was
bandwidth
of
the
two
pulses
differs
slightly.
This
level
of
12%.
These
data
illustrate
the
main
advantage
of
this
two2 juin 2016
–60 –40 –20
colour scheme, which ais that of generating peak power levels and b different features in the longitudinal phase-space
www.lunex5.com
electron-beam duration and by the possibility of generating
long-enough (chirped) seed pulses characterized by
significant local power at their tails.
In the following, we concentrate on the analysis of the
so-called low-gain regime. In this low-gain regime, the
relative FEL gain bandwidth B (approximately equal to
the relative maximum spectral separation) is proportional
IV. The high gain Free Electron Laser
Two-color operation (seeded)
Pulse splitting
P H Y S+I Cchirp
A L R E@
V I FERMI
EW LETTERS
801 (2013)
week ending
8 FEBRUARY 2013
AR
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3476
FIG. 3. Projected spectral and temporal FEL intensities for
sing
focu
different seed powers. Left panel:K–Bexperimental
spectral splitting,
matic layout of a seeded single-pass FEL
s
optic
measured at FERMI@Elettra
[7]; central and right panels:
ration scheme).
ne
Onli eter
simulated spectral
and temporal splitting (using the code
trom
spec
r
ulato
PERSEO
). The ∆tset of parameters, valid both for the experiment
Und plifier
m
a
L
e propose overcomes all the issues related to
FIG. 2.G. De
Seed-electron
interaction
and
resulting
FEL (temporal FEand for the simulation, is the following: normalized energy
Ninno
et
al.
PRL,
110,
064801
(2013)
mentioned schemes.
10FE3L, energy spread ð#$ Þ ¼ 2:544 & 10#1 , peak
and spectral) outputs for different seed configurations: no chirp ð$0 Þ ¼ 2:544 &
Twin es
uls
Ls can rely on different configurations
and moderate seed intensity (left panel), no chirp and high current ðIpeak Þ ¼p 200 A, bunch duration ¼ 1 ps (rms); modulaCCD
work, we focus on the so-called harmonic
seed intensity (central panel), chirped seed with high intensity tor period ¼ 0:1 m, modulator
length ðLu Þ ¼ 3 m, modulator
detector
Twin seed
eme, in which a relativistic electron beam
(right panel). The meaning of the symbols is explained in ∆tthe laser
parameter
ðKÞ ¼ 5:7144, radiator period ð&w Þ ¼ 55 & 10#3 m,
pulses
ΘPump periods ðN Þ ¼ 264, central modulator wavetext.
number of radiator
rough the static and periodic magnetic field
u
ΘProbe
length ð’ 2%c=!0 Þ ¼ 261 nm, central radiator wavelength
an undulator
modulator)
interacts
M. Labat et(called
al. Phys.aRev.
Lett. 103 (2009)
264801
ð&rad Þ ¼ 32:6 nm, harmonic number ðnÞ ¼ 8; seed-laser power
ar externally injected optical pulse (seed)
Gaussian seed will have, at the radiator entrance, a bunch∆t
ðP0 Þ ¼ 50–500
MW, strength of the dispersive
section ðR56 Þ ¼
Ti dispersive
ngth !0 ; see Fig. 1. The interaction modu37.2 37.3 37.4 37.5
ing larger than optimum (overbunching). Because of the 20 'm,1 µmlasergratingspot size in the 37.1
modulator
! (nm) ð#r Þ ’ 300 'm,
tron-beam
energy.
Energy modulation
Two
delayed
pulsesis @ large
FERMI
andenergy
SPARC
laser-induced
spread, the FEL emission from ð!R ; !I Þ3 ¼ ð5 & 10#5 fs#2 ; 3:2 & 10#5 fs#2 Þ.
nto spatial bunching, when the electron
! (nm)
37.0
this part of the bunch will be significantly attenuated. The
37.1
tes through a magnetic chicane (dispersive
larger the seed peak intensity, the larger the overbunched
37.2
E. Allaria ethas
al.,aNature
Com.
(2013).
bunching (as the energy modulation)
064
37.3
zone
will3476
be. The
beam portions having optimum bunching
ual to the seed wavelength.
However,
it Phys.
also Rev.(seeded
37.4
A. Petralia
et al.,
Lett. 115,
(2015)
by 014801
the lateral
parts of the Gaussian seed) will be
37.5
ficant components at the harmonics of the
located both at the right and at the left of that zone. As a
37.6
!0 (where !0 ¼ 2"c=!0 , c being the speed
consequence, in these conditions the FEL pulse will be
–500
0
500
1,000 1,500 2,000 2,500
an integer number). Finally, the bunched
Delay
(fs)
characterized, in the time domain, by two lateral peaks
m is injected into a long undulator chain
1 | Generation andintense
characterization
[(see Fig. 2(b)] or, if the seed Figure
is sufficiently
to of the twin-seeded FEL pulses and experimental set-up. (a) Energetically distinct two ultraviole
pulses
with
an
adjustable
delay
interact
with a single electron bunch. Inside the FEL amplifier, the two seeded regions emit XUV radiation. The
ator), where it emits coherently at one of
suppress the emission from the
central
part,of generated
by two
and temporal
separation
twin FEL pulses are determined by the parameters of the seed laser pulses and the spectral purity, pulse
onics. In the radiator, M.
theE. electromagnetic
and the
widthsseed
of!(FELs
the pulses
is monitored
by an ‘online’ spectrometer.
(b) Typical
of the 2016
twin-FEL pulses. (c) Sequence of FEL spectra
Couprie, CAS School Free
Electron!Lasers!and!Energy!Recovery!Linacs
!ERLs), to
Hamburg,
Germany, 31
!Mayspectrum
–10 !June,
separated
subpulses [8]. Because
is and
assumed
during
a
temporal
scan
of
the
seed
laser
pulse
pair
with
respect
to
the
electron
bunch.
The
zero
time is defined as the instant when the first
rated from bunched electrons is amplified,
be monochromatic, the two subpulses
have the same
jeudi 2 juin 2016
interacts with the electron bunch. Increasing the arrival time delay of the laser pulses with respect to the electron bunch, the emission of th
www.lunex5.com
FEL configurations
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
Low gain regime of Free Electron Lasers
First FELs : Linac based detuning curve
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
www.lunex5.com
Low gain regime of Free Electron Lasers
First FELs : storage ring based FEL, detuning curve
Billardon, M., Garzella, D., & Couprie, M. E. (1992). Saturation mechanism for a storage-ring free-electron laser. Physical review letters, 69(16), 2368.
M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
jeudi 2 juin 2016
4.4.5Synchrotron
Limits of
the classical approach : quantum effects
radiation and Free Electron Laser
35
Even
though
first
FEL
theory
approached
quantum
mechanics,
subsequent
classical
theory
approach
Even
though
the the
first
FEL
theory
has has
beenbeen
withwith
quantum
mechanics,
subsequent
classical
theory
approach
4.4.5
Limits
of
the
classical
approach
: approached
quantum
effects
www.lunex5.com
be applied
majority
of the
experimental
set-ups.
consider
quantum
effects
can influence
the FEL
cancan
be applied
for for
the the
majority
of the
experimental
set-ups.
Let’sLet’s
consider
howhow
quantum
effects
can influence
the FEL
process.
Even though the first FEL theory has been approached with quantum mechanics, subsequent classical theory approach
process.
Limits of the classical approach : quantum effects
can be applied for the majority of the experimental set-ups. Let’s consider how quantum effects can influence the FEL
process.
Quantum
recoil
Quantum
recoil
Quantum recoil
When
a electron
emits
a photon
h̄ω
its energy
is reduced
by such
an amount
toquantum
the quantum
recoil.
the energy
When
a electron
emits
a photon
h̄ω ph
, its
is reduced
by such
an amount
due due
to the
recoil.
If theIfenergy
ph ,energy
Quantum
recoil
change
to�the
recoil
of the
order
or larger
the FEL
bandwidth
i.e. given
by spontaneous
the spontaneous
emission
change
duedue
to�the
recoil
is ofisthe
order
or larger
thanthan
the FEL
gaingain
bandwidth
i.e. given
by the
emission
When a electron
emits a photon h̄ω ph , its energy is reduced by such an amount due to the quantum recoil. If the energy
∆ ω ∆ ω ≈ ∆ ω( ∆2ω )2 +
∆ ω( ∆2ω )2 , then the quantum recoil may significantly affect the FEL gain. Consider a typical
width
width
≈
(
)
+
(
)inh
, inh
then
may
significantly
affect
thebyFEL
gain. Consider
a typical
change
due
to
the
recoil
is of
orderthe
or quantum
larger thanrecoil
the FEL
gain
bandwidth i.e.
given
the spontaneous
emission
h
ω
ω
ω the
ω
ω h
ω
�
h̄ω
∆ω
∆ ω−32 −3 ∆ ω 2
ph
−6 , the
ph h̄ωConsider
−610
width
≈
(
)
+
(
)
,
then
the
quantum
recoil
may
significantly
affect
the
FEL
gain.
a typical
bandwidth
of
10
,
for
a
short
wavelength
FEL,
the
fraction
of
the
energy
change
is
more
than
gaingain
bandwidth
of
10
,
for
a
short
wavelength
FEL,
the
fraction
of
the
energy
change
is
more
than
10
,
the
ω
ω h
ω inh
E
E
h̄ω
ph
−3
−6 and high
quantum
electron
recoil
is then
negligible.
It FEL,
can
start
toofplay
a role
with
energy
electron
beams
and high
quantum
electron
recoil
is, then
It can
thenthen
start
to play
atherole
withchange
low low
energy
electron
beams
gain bandwidth
of 10
for
a negligible.
short
wavelength
the
fraction
energy
E is more than 10 , the
energy
emitted
photons
in the
X-ray
in using
an optical
undulator
(created
byoptical
an optical
energy
emitted
photons
(foris(for
example
in the
X-ray
range),
as inaasusing
an optical
undulator
(created
by an
quantum
electron
recoil
thenexample
negligible.
It can
thenrange),
startsuch
to such
play
role
with
low
energy
electron
beams
and
high
wave).
wave).
energy emitted photons (for example in the X-ray range), such as in using an optical undulator (created by an optical
wave).
Quantum
diffusion
Quantum
diffusion
Quantum diffusion
The
emission
of spontaneous
emission
radiation,
if not
affecting
the electron
energy
a significant
amount,
The
emission
ofdiffusion
spontaneous
emission
radiation,
if not
affecting
the electron
energy
by aby
significant
amount,
intro-introQuantum
Theanemission
of spontaneous
emission
radiation,
not affecting
the
electron
energy
aemission
significant
amount,
introduces
an
energy
as described
above.
Inifif addition,
thethe
discrete
nature
ofbyby
photon
emission
(over
a wide
duces
lass
as
described
justjust
above.
In addition,
the discrete
nature
of photon
(over
aintroduces
wide
energy
Theenergy
emission
oflass
spontaneous
emission
radiation,
not affecting
electron
energy
a significant
amount,
anenergy
duces an energy
lass asthe
described
just above.
In addition,
the isdiscrete
nature
of photon
emission
(over in
a wide
energyring. The
spectrum)
increases
uncorrelated
energy
spread.
similar
to the
quantum
excitation
a storage
spectrum)
increases
the uncorrelated
spread.
Itemission
isItsimilar
toa the
quantum
excitation
in a storage
ring. The
energy
loss.
In addition,
the
discreteenergy
nature
of
photon
(over
wide
energy
spectrum)
increases
the
uncorrelated
spectrum) increases the uncorrelated energy spread. It is similar to the quantum excitation in a storage ring. The
energy
spread.
Itenergy
is energy
similar
to
the
diffusion
of the
spread
is given
by :[?] : in a storage ring.
diffusion
raterate
of the
spread
isquantum
given
byexcitation
[?]
diffusion rate of the energy spread is given by [?] :
2 >2 7 7
<
(∆
γ)
dd<<d(∆
γ)
>
234 K
3 2 k3 F(K )
(∆ γ) >2 = −=7−r λ re λCompton
4γo4 K
2 uγ
k
e
Compton
o
u uu) u ) u
u F(K
=
−
r
λ
γ
K
k
F(K
e
Compton
o
u
u
ds
15
ds
15
ds
15
(96) (96) (96)
−13 the Compton wavelength. In the LCLS
11 1
−13
−13
)==1.2K
1.2K
+ 1+1.33K
and
λ
=
h̄/m
c
≈
3.86
10
and
λ
=
h̄/m
c
≈
3.86
10
the
Compton
wavelength.
InLCLS
the LCLS
withwith
F(KF(K
o
Compton
and
λ
=
h̄/m
c
≈
3.86
10
the
Compton
wavelength.
In the
with
F(K
2
u) =
u+
o
Compton
2
uu) 1.2K
u u+
o
Compton
1+1.33K
u +0.40K
1+1.33K
u +0.40K
u u2 u
u +0.40K
case,
quantum
diffusion
process
increases
the
uncorrelated
energy
spread
in 110
the
110
m
long
undulator
to more
case,
the the
quantum
diffusion
process
increases
the
energy
spread
m long
undulator
to more
than than
case,
the
quantum
diffusion
process
increases
the uncorrelated
uncorrelated
energy
spread
inin
thethe
110
m long
undulator
to more
than
LCLS case,
quantum
diffusion
process
theDespite
uncorrelated
energy
spread
in is
the
longtoo
undulator
to
than
−4
−4the
assuming
anthe
initial
energy
spread
equal
to zero.
in asuch
a the
case,
the
effect
ismtoo
not
themore
quantum
10
assuming
initial
energy
spread
equal
toincreases
Despite
ininsuch
effect
not
too
large,
thelarge,
quantum
10In
assuming
an an
initial
energy
spread
equal
to
zero.
Despite
such
acase,
case,
the
effect
is110
not
large,
the quantum
1 1011−4
1 1084 assuming an initial energy spread equal to zero. Despite in such a case, the effect is not too large, the quantum diffusion
diffusion
process
isis
likely
impose
limits
in achievable
achievable
wavelength
forparameters.
given
beam
parameters
[?].[?]. [?].
diffusion
process
to
impose
limits
in
achievable
wavelength
for given
beam
parameters
diffusion
process
is likely
totoimpose
in
wavelength
given
beam
parameters
process
is likely
to likely
impose
limits
inlimits
achievable
wavelength
for
given
beamfor
faut
avoir
laladiscussion
surles
lesvaleurs
valeurs
de la
ladedispersion
dispersion
en
dede
l’mittance.....XXXXXXXXXXXXXXXXXX
IlIl faut
avoir
fait
discussion
sur
les
valeurs
la dispersion
en nergie,
de l’mittance.....XXXXXXXXXXXXXXXXX
Il faut
avoir
faitfait
la discussion
sur
de
ennergie,
nergie,
l’mittance.....XXXXXXXXXXXXXXXXXX
Dattoli M. E. Couprie, CAS School Free Electron!Lasers!and!Energy!Recovery!Linacs !(FELs and !ERLs), Hamburg, Germany, 31 !May –10 !June, 2016
cfcfDattoli
cf Dattoli
jeudi 2 juin 2016