lecture 6. new fel schemes and challenges x-ray free electron lasers igor zagorodnov deutsches...
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Lecture 6. New FEL Schemes and Challenges
X-Ray Free Electron Lasers
Igor Zagorodnov
Deutsches Elektronen Synchrotron
TU Darmstadt, Fachbereich 1822. June 2014
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 2
Contents
Motivation Self-seeding scheme Nonlinear harmonic generation High-gain harmonic generation (HGHG) Echo-enabled harmonic generation (EEHG) Harmonic lasing Purified SASE scheme (pSASE) Energy spread cooling scheme Table-top FEL Outlook
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 3
electrons
radiation
Motivation
Longitudinal profile with large statical fluctuations
Transverse profile is coherent
Coherence
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 4
Motivation
Coherence
Cooperation length: lc ~ /4πρ (slippage length within one gain length)
FEL spectrum
c/2πlc
c/lb
FEL power
2πlc
lb
seed
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 5
Self-seeding scheme
J. Feldhaus et al, Opt.Comm. 140, p.341 (1997)
G.Geloni et al, DESY 10-033 (2010)
SASE in the first undulator monochromator filters the
radiation „seeded“ amplification in the
second undulator
Grating monochromator
Gas cell monochromator
SASE
SASE-FEL
electronen
radiation
amplifiermonochromator
0
( )S
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 6
Non-linear harmonic generation
Higher harmonics in undulator (spontaneous radiation)
Spectral density in forward direction.The absolute bandwidth is the same
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 7
Non-linear harmonic generation
0[ ]cos
2
cK JJ EdW e
dt
2
8( ) sin(2 )w
uz uk
z t v t t zz v t
0 cos2
cKEdW e
dt
2 2
0 12 2[ ]
4 2 4 2
K KJJ J J
K K
Higher harmonics in FEL radiation
01
[ ]( )
4xr
cK JJdE z j
dz
0
1( )4xr
cKdE z j
dz
Coupling factor in Lecture 3?
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 8
Non-linear harmonic generationA steady energy transfer?
0
0
( )0
cos( ) cos( )
cos( ) cos( )2
2u z u z
x x u
u u
ik v t ik v ti t ikz t
dW Kev E ec k z E kz t
dt
KEec kz t k z kz t k z
KEec e e e e
0( , ) cos( )xE z t E kz t ( ) cos( )x uK
v z c k z
The electron energy changes as described by the equation
2
8( ) sin(2 )w
uz z uk
z t v t v k t
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 9
Nonlinear harmonic generation
sine ( )iY inn
n
J Y e
2
8w
u
kk
Y 2 z uv k t
2
8sin(2 )( )0
2
wz uku z u z uz
i v k tik v t ik v ti kv tKEdWec e e e e
dt
01( ) ( )
2u zi k k v t in
n nn
KEdWec e J Y J Y e
dt
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 10
Nonlinear harmonic generation
01( ) ( ) cos( )
2 n nn
KEdWec J Y J Y
dt
(2 1)u z u zk k v t n k n k v t t
(2 1) 0u zd
k n k vdt
A steady energy transfer?
1 11
2 1u
z
k
k n
2 1 11
2 1n n
2
8w
u
kk
Y
2
1 21
22u K
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 11
Nonlinear harmonic generation
2 1 1[ ] ( ) ( )n n n n nJJ J Y J Y 2
2(2 1)
4 2n
KY n
K
Effective coupling factors
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 12
Nonlinear harmonic generation
2 1 1[ ] ( ) ( )n n n n nJJ J Y J Y 2
2(2 1)
4 2n
KY n
K
K = 1 K = 3 K = 10
Ratio of power gain length at the n-th harmonic to that at the fundamental:
1( ) 2 3
(1) 2[ ]
[ ]
n
n
L JJ
L n JJ
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 13
Nonlinear harmonic generation
ˆ , 1, 2,...ˆ n nd
n Ndz
Normalized high-gain FEL model
ˆ ˆ( )ˆ
ninx
dE e
dz
11
2ˆ mN
iz
m
j eN
2 2
02
[ ]e rm c
EeK JJ
0
ˆ xx
EE
E
1ˆ ˆ( )
ˆ x zdE z j
dz
z z
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 14
Nonlinear harmonic generation
ˆˆj
jd
dz
(1) (3) 3ˆ ˆ ˆ( )ˆ
n ni inx x
dE e E e
dz
(1)1
ˆ ˆ( )ˆ x zdE z j
dz
2(3) 3
31
ˆ ˆ( )ˆ x z
KdE z j
dz K
11
1
2ˆ
2 2
m
m
Ni
zm
i
j eN
e b
1
2 23 3ˆ(3) (3) (1)3 3
31 1 1
3ˆ ˆ ˆ( ) 3 ( ) ( )2ˆ
i zx x in
d K i KE z i E z E z e
K Kdz
33
1
2ˆ mN
iz
m
j eN
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Nonlinear harmonic generation
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 16
Nonlinear harmonic generation
Near saturation, roughly 1% of the power of fundamental is emitted in the third harmonic
Spectrum has the same width as that of the fundamental
The maximal power is decreasing function of harmonic number
Nonlinear harmonics have larger statistical power fluctuations from shot to shot
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 17
High-gain harmonic generation (HGHG)
energy modulation with frequency ω conversion in density modulations coherent radiation with frequency nω in radiator section
large energy spread
6n
/s
/s /s
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 18
High-gain harmonic generation (HGHG)
in modulator energy changes phase remains approx. the same
0 0sinA
0 0 0 0 0 0( , ) ( ( , )) ( sin )f f f A
0 0 0 0 0( , ) ( )f f
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 19
High-gain harmonic generation (HGHG)
in chicane higher energy particles are bent less than lower energy particles
energy of particles remains approx. the same
0 1 56k R
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 20
High-gain harmonic generation (HGHG)
0 1 56 0 0
0 0 1 56 0
sin0 0 0 0
0 1 56 0 0 0
( , )
( )
( ) ( )
ih ihh
ih k R A
ih im ihk Rm
m
b e d d e f
d d e f
d e e J hk R A d e f
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 21
High-gain harmonic generation (HGHG)
1 56 01 56 0 0 0( ) ( )ihk Rh hb J hk R A d f
2022
0 0( ) ~f e
21 561
21 56( )hk R
h hb J hk R A e
1 56 1.2hk R A h 561
1.2R
k A
2
0.72(1.2 )
h
Ah hb J h e
h A
h
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 22
High-gain harmonic generation (HGHG)
L.H.Yu et al, PRL 91, 074801 (2003)
HGHG was demonstrated at the third harmonic of 800 nm
temporally coherent radiation
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Echo-enabled harmonic generation
G. Stupakov, PRL 102, 074801 (2009)
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 24
Echo-enabled harmonic generation
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 25
Echo-enabled harmonic generation
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 26
Echo-enabled harmonic generation
For HGHG
210.721 30.7 hA
hb eh
For EEHG
11 3h
F Ab
h
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 27
Echo-enabled harmonic generation
the first laser produces energy modulation the first chicane is strong, rotates phase space the second laser produces again energy modulation The second chicane converts the energy modulation in
density modulation
G. Stupakov, PRL 102, 074801 (2009)
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 28
Echo-enabled harmonic generation
D.Xiang et al, PRL 108, 024802 (2012)
experiment for EEHGonly the second laser ON
both lasers ON
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 29
Harmonic lasing
non-linear harmonicgeneration
harmoniclasing
ˆˆj
jd
dz
( )ˆ ˆˆ
nh hinx
h
dE e
dz
2( )
1
ˆ ˆ( )ˆ
h hx zh
KdE z j
dz K
ˆˆj
jd
dz
( )ˆ ˆˆ
nh hinx
dE e
dz
2( )
1
ˆ ˆ( )ˆ
h hx zh
KdE z j
dz K
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 30
Harmonic lasing
retuned to fundamental
harmonic only
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 31
Harmonic lasing
retuned to fundamental
harmonic only
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 32
Harmonic lasing
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 33
Purified SASE scheme
U1 U2 U3 … … U7 U8 U9 U10 U11 U12 U13 … U18
K = 2, λ1 =0.6 nm
6 GeV K=6.3,λ1 =4.2 nm
λ1 =0.6 nm
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 34
Purified SASE scheme
U1 U2 U3 … … U7 U8 U9 U10 U11 U12 U13 … U18
K = 2, λ1 =0.6 nm
6 GeV K=6.3,λ1 =4.2 nm
λ1 =0.6 nm
At the exit of U10
At the exit of U11
At the exit of U9
2πlc≈1 fs
At the exit of U12
2πlc≈ 4~ 5 fs
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 35
Energy spread cooling schemeH.Deng , arXiv:1305.7041 (2013)
16x R
0( ) (1 )K x K x
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 36
Energy spread cooling scheme1
2 200 12 2
u K
2
21
22u K
22 00 16
0
20
0 16 020
1
12 2
2
ur
K R
KR
K
21
2 2u
rK
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 37
Energy spread cooling scheme
20
0 16 0202
rK
RK
Two electrons through modulator
0 0 0 0, ,
0 0, ,
2 ud
kdz
0
4 4 ru uN N
0 0 0 0 0sinA A
0 2A
2
0 016 20 0 0
21 1
2
uN A KR
K
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 38
Energy spread cooling scheme
20 0
16 200 0
21 1
2
uN A KR
K
-1m
16 mR
30b
H.Deng , arXiv:1305.7041 (2013)
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 39
Energy spread cooling scheme
H.Deng , arXiv:1305.7041 (2013)
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 40
Energy spread cooling scheme
1D simulations 3D simulations
H.Deng , arXiv:1305.7041 (2013)
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 41
Table-top FEL
External injection
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Table-top FEL
“Bubble” regime
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Table-top FEL
M.Fuchs et al, Nature Physics 5, 826(2009)
H.-P. Schlenvoigt et al, Nature Physics 4, 130 (2008)
λ=740 nm
λ=17 nmspontaneous undulator radiation with laser-plasma accelerator
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 44
Table-top FEL
M.Fuchs et al, Nature Physics 5, 826(2009) no FEL radiation so far
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 45
European XFEL
3rd SR generation
2nd SR generation
1st SRs
Outlook
Growth of brillance of X-ray and growth of computer power
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 46
Outlook
Saturation?Wavelength of radiation
λ= 0.25 AMaRIE (Los Alamos)concept
Q. R. Marksteiner, FEL 2011, TUPA28, 2011
λ=0.5 A
PD Dr. Igor Zagorodnov| X-Ray Free Electron Lasers. Lecture 6 | 22. June 2014 | Seite 47
Outlook
shorter wave length
shorter radiation pulses
higher brilliance
longitudinal coherence
compact facilities
„Meine Vision für DESY ist dass wir die deutsche Nobelpreisschmiede werden.“
Professor Helmut Dosch (Film „Licht der Zukunft“)