Lecture 5. Self-amplified spontaneous emission. FLASH and the European XFEL in Hamburg
X-Ray Free Electron Lasers
Igor Zagorodnov
Deutsches Elektronen Synchrotron
TU Darmstadt, Fachbereich 1826. June 2017
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 2
Contents
� Motivation
� Shot noise in electron beam
� Current modulation from shot noise
� FEL start up from shot noise
� Statistical properties of SASE radiation
� FEL facilities
� Outlook
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 3
Motivation
Electrons produce spontaneous undulators radiation
How to obtain a useful external field ?
SASE
A. Kondratenko, E. Saldin, Part. Accelerators 10, 207 (1980)
R.Bonifacio et al, Opt. Comm.50, 373 (1984)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 4
MotivationLow -energy undulator test line (LEUTL), USA, 530nmSASE FEL operation in the visible and near-ultraviolet range wasaccomplished in 2001 at the low-energy undulator testline LEUTL at ArgonneNational Laboratory near Chicago, USA
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 5
MotivationTESLA Test Facility (TTF), Hamburg
In 2001 a successful SASE experiment was carried out at DESY in Hamburg at the vacuum-ultraviolet (VUV) wavelength of 109 nm.
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 6
Shot-noise in electron beam
Fluctuations of the electron beam current density serve as the input signal in the SAS EFEL
Laser pulse Spectrum
~ω ρω∆
ω ω∆[ . ]t a u
( )P t ( )P ω
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 7
Shot-noise in electron beam
The electron beam current (at the undulator entrance) consists from electrons randomly arriving at time tk
1
( ) ( )N
kk
I t e t tδ=
= −∑The electron beam averaged over an ensemble of bunches
( ) ( )I t eNF t≡The electron beam profile function can be, for example,
[0, ]1
( ) ( )r TF t tT
χ=2
221( )
2T
t
gT
F t e σ
πσ
−=
[0, ]1, 0 ,
( )0, otherwiseT
t Ttχ
≤ ≤=
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 8
Shot-noise in electron beam
In frequency domain
1 1
( ) ( ) ( ) kN N
i ti t i tk
k k
I I t e d e e t t d e e ωω ωω ω δ ω∞ ∞
= =−∞ −∞
= = − =∑ ∑∫ ∫It follows from central limit theorem that the real and imaginary parts are normally distributed
The probability density distribution of spectral power is an exponential distribution
( )2
221, Re ( ), or Im ( )
2x
x
x
p x e x I x Iσ ω ωπσ
−= = =
( ) 21, , ( )
x
p x e x x Iλ λ ωλ
−= = =
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 9
Shot-noise in electron beamFirst-order correlation function
( )
'* 2
1 1
' '2 2
1
( ) ( ') k n
k k n
N Ni t i t
k n
N Ni t i t i t
k k n
I I e e
e e e e e
ω ω
ω ω ω ω
ω ω −
= =
− −
= ≠
= =
= +
∑∑
∑ ∑
1
1( ) ( ) ( ) k
Ni ti t i t
kk
F F t e d t t e d eN
ωω ωω ω δ ω∞ ∞
=−∞ −∞
= = − =∑∫ ∫
* 2 2 *( ) ( ') ( ') ( 1) ( ) ( ')I I e NF e N N F Fω ω ω ω ω ω= − + −
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 10
Shot-noise in electron beamFirst-order correlation function
* 2 2 *( ) ( ') ( ') ( 1) ( ) ( ')I I e NF e N N F Fω ω ω ω ω ω= − + −2 2
2( )T
gF eω σ
ω−
= ( ) ( )( )
sin 0.5( ) sinc 0.5
0.5rT
F TT
ωω ω
ω= =
* 2( ) ( ') ( ')I I e NFω ω ω ω≈ − 2 2( )I e Nω ≈
*( ) ( ') 1, for 1TNF Fω ω ωσ<< >>
Averaged spectral current density (“white noise”)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 11
Current modulation from shot-noiseWe consider a rectangular averaged current
[0, ]1
( ) ( )r TF t tT
χ= [0, ]1, 0 ,
( )0, otherwiseT
t Ttχ
≤ ≤=
( ) ( )rI t eNF t=
( )( ) sinc 0.5rF Tω ω=
( )( ) ( ) sinc 0.5rI eNF eN Tω ω ω= =
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 12
Current modulation from shot-noise
2 2
0 0 0
2
0
1 1 1( ) ( ) ( )
1 1( )
T
r
S d I t dt I dT T
F dT
ω ω ω ωπ
ω ωπ
∞ ∞
∞
= = =
=
∫ ∫ ∫
∫
Spectral power density of averaged current
Parseval's theorem
( ) ( ) ( )2
2~ sinc 0.5 0, for 1I
S T TT
ωω ω ω
π= ≈ >>
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 13
Current modulation from shot-noise
( ) ( ) 22
( )shot
IIS
T T
ωωω
π π≡ =
We are interested in an averaged spectral power density of shot noise, which by analogy can be written as
2 2( )I e Nω ≈
( ) 22
0( )shot shot
I e N eIS S
T T
ωω
π π π≡ = = =
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 14
Current modulation from shot-noise
The amplification takes place in bandwidth ∆ω and we can replace the power of the current in this bandwidth by power of the averaged current with fluctuations at amplitude
1,shot 0 0shotav
b b
SI ej j
A A I
ω ωπ
∆ ∆≡ = =ɶ
2
0
( )av shot shotI S d Sω ω ω∞
= ≈ ∆∫
22 2
0 0 0
1 1( ) ( ) ( )
T
avI I t dt I d S dT T
ω ω ω ωπ
∞ ∞= = =∫ ∫ ∫
0shot
eIS
π=
Let us introduce an averaged current
The current density reads
0
0b
IA
j=
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 15
FEL start up from shot-noise
01
[ ]( )
4x zr
cK JJdE z j
dz
µγ
= −ɶ ɶ
2 , 1,2,...n u nd
k n Ndz
ψ η= =
High -gain FEL model with space-charge
2 2 2
( )[ ]( )
2nin z n
xe r r e
d eEeK JJE e
dz m c m c
ψη ψγ γ
== − ℜ −ɶ
( ) ( )( )0
0 1
( ) sgnN
zz n n m n m
m
jE
Nψ π ψ ψ ψ ψ
ωε == − − − −∑
1 01
2m
Ni
z zm
j j eN
ψ−
== ∑ɶ
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 16
FEL start up from shot-noise
23 2
ˆ ˆ2 0x x xx
E E Ei iEη η
′′′ ′′ ′+ + − =
ΓΓ Γ
ɶ ɶ ɶɶ
3( )
1
( , ) ( ) j zx j
j
E z c eα ηη η
==∑ɶ 0 0
0 02
γ γ ω ωηγ ω− −= ≈
1
1 2 3 22 2 2
31 2 3
(0)1 1 1
(0)
(0)
x
x
x
Ec
c E
c E
α α α
α α α
′= ′′
ɶ
ɶ
ɶ
11
2
3
(0)
(0)
(0)
x
x
x
Ec
c E
c E
−
′= ′′
A
ɶ
ɶ
ɶ
ˆηηρ
=
At time t=0
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 17
FEL start up from shot-noise
01
[ ](0) (0)
4x zr
cK JJE j
µγ
′ = −ɶ ɶ 01
[ ](0) (0)
4x zr
cK JJE j
µγ
′′ ′= −ɶ ɶ
1 0 01 1
2 22n n
N Ni i
z z n u z nn n
j ij e k ij eN N
ψ ψψ η− −
= =′ ′= − = −∑ ∑ɶ
1 01
2n
Ni
z zn
j j eN
ψ−
== ∑ɶ 2 , 1,2,...n u n
dk n N
dzψ η= =
1 0 1(0) 2 (0)z u zj i k jη′ = −ɶ ɶ0(0) , 1,2,...n n Nη η≡ =
00 1
[ ](0) 2 (0)
4x u zr
cK JJE i k j
µηγ
′′ =ɶ ɶ
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 18
FEL start up from shot-noise
11 1 0
2 1
03
(0) 0[ ]
(0) 1 (0)4
2(0)
x
x zr
ux
EccK JJ
c E j
i kc E
µγ
η
− −
′= = −
′′
A A
ɶ
ɶ ɶ
ɶ
11 1
2
3
(0)
(0) 0
0(0)
x in
x
x
E Ec
c E
c E
− −
′= = ′′
A A
ɶ
ɶ
ɶ
Start up from current modulation at t=0
Start up from seed field at t=0
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 19
FEL start up from shot-noise
On resonance energy
0r
r
γ γηγ−= ≡ 3
0xx
EiE
′′′− =
Γ
ɶɶ
zxE Aeα=ɶ 3 3iα = Γ
( )1 3 2iα = + Γ
Γ
Imα
Reα
( )2 3 2iα = − Γ3 iα = − Γ
1α2α
3
1
j zx j
j
E c eα
==∑ɶ
*
11 2 32 2 2
1 2 3
1 1 11 1
3 3α α α
α α α
−
= =
*A A
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 20
FEL start up from shot-noise
*11
1 *0 02 1 1 2
*3 3
0[ ] [ ]1
1 (0) (0)4 3 4
0z z
r r
ccK JJ cK JJ
c j j
c
αµ µ α
γ γα
−
= − = −
A ɶ ɶ
11
2
3
1
0 13
0 1
inin
EcE
c
c
− = =
A
Start up from current modulation
Start up from seed field
0 0, 1, 0 0
[ ] [ ](0)
4 4in shot z shotr r
cK JJ cK JJ eE j j
I
µ µ ωγ γ π
∆= =Γ Γ
ɶ
12ω ρω∆ ≈
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 21
FEL start up from shot-noise
zΓ
b
P
Wρ
SASE vs. seeded FEL
SASE
seeded
beam energybW − gain parameterΓ −
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 22
Statistical properties of SASE radiationInterference
CoherenceCoherence is a property of waves that enables interference.
Temporal coherence is the measure of correlation between the wave and itself delayed. it characterizes how well a wave can interfere with itself at a different time. The delay over which the phase or amplitude wanders by a significant amount is defined as the coherence time
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 23
Statistical properties of SASE radiation
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 24
Statistical properties of SASE radiationCoherence time
1
1 1~ ~cohτ
ω ω ρ∆
The time-averaged intensity (blue) detected at the output of an interferometer plotted as a function of delay. The interference envelope gives the degree of coherence
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 25
Statistical properties of SASE radiation
c cohI
N lce
=
Typical length of one spike
cohl
b b
coh c
L TM
l τ= =
Coherence length
1~coh c
cl cτ
ρω=
Number of cooperative electrons
[µm]s
Laserpuls[GW]P
Number of spikes (longitudinal modes)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 26
6M = 2.6M =
Statistical properties of SASE radiation
1~ 2λ ρλ∆Spikes in spectrum
V. Ayvazyan et al, Eur. Phys.Journ. D 20, 149 (2002)
Spectrum
long bunch (~100fs) short bunch (~40fs)
( )S ω ( )S ω
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 27
Statistical properties of SASE radiationFluctuations of SASE pulse energy
radiation energyradU Pdt= −∫rad
rad
Uu
U= 1u = ( )22 u uσ = − 2M σ −=
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 28
Statistical properties of SASE radiationFluctuations of SASE pulse energy (linear regime)
1
( )( )
M MMu
MM u
p u eM
−−=
Γrad
rad
Uu
U= 1
0
( ) z tz t e dt∞
− −Γ = ∫Gamma distribution, M – number of modes
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 29
Statistical properties of SASE radiationFluctuations of SASE pulse energy (after saturation, 13 nm, FLASH)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 30
0 10 20 30 400
0.5
1
1.5
2
Statistical properties of SASE radiation
b
P
Wρ
g
z
L
3 3 lnsatc
g
LN
L= +
SASE with
cN
electrons on coherence length
Saturation length (SASE)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 31
electrons
radiation
Statistical properties of SASE radiation
Longitudinal profile with large statical fluctuations
Transverse profile is coherent
Coherence
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FEL facilitiesTESLA Test Facility ( until 2002)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 33
FEL facilitiesTESLA Test Facility ( until 2002)
Three undulator modules. Total length 15m
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FEL facilitiesTESLA Test Facility ( until 2002)
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FEL facilitiesTESLA Test Facility ( until 2002)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 36
FEL facilitiesTESLA Test Facility II ( 2002-2006)
From 2003 on, TTF1 was expandedto TTF2, an FEL user facility for thespectral range of soft x-rays, includinga new tunnel and a new experimentalhall (in the foreground). In April 2006,the facility was renamed FLASH: FELin Hamburg
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 37
FEL facilitiesFLASH ( from 2006)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 38
FEL facilitiesFLASH ( from 2005)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 39
FEL facilitiesFLASH ( from 2005)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 40
Phase space linearizationrollover compression vs. linearized compression
~ 1.5 kA
~2.5 kAQ=1 nC
Q=0.5 nC
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 41
Phase space linearization
In accelerator modules the energy of the electrons is increased from 5 MeV (gun) to 1200 MeV (undulator).
FLASH
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 42
Phase space linearization
In compressors the peak current I is increased from 1.5-50 A (gun) to 2500 A (undulator).
FLASH
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 43
Phase space linearization
FLASH
FEL radiation parameters
Wavelength Range 4.1 - 45 nm
Average Single Pulse Energy 10 - 400 µJ
Pulse Duration (FWHM) 50 - 200 fs
Peak Power (from av.) 1 - 3 GW
Average Power (5000 pulses/sec) 400 mW
Spectral Width (FWHM) 0.7 - 2 %
Average Brilliance10^17 - 10^21 photons/s/mrad2/mm2/0.1%bw
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 44
FEL facilitiesFLASH 2 ( from 2013)
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FEL facilitiesFLASH 2 ( from 2013)
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 46
FEL facilitiesFLASH 2
Photon Beam HHG SASE
Wavelength range(fundamental)
10 - 40 nm 4 - 80 nm
Average singlepulse energy
1 – 50 µJ 1 – 500 µJ
Pulse duration(FWHM)
<15 fs 10 – 200 fs
Peak power (fromav.)
1 – 5 GW 1 – 5 GW
Spectral width(FWHM)
0.1 – 1 % 0.5 – 1.5 %
Peak Brilliance*10 - 40 nm
1028 - 10311028 - 1031
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 47
FEL facilities
Intensity distrubution
for λ= 0.14 nm
radiation power ~ GW G.Gutt et al, PRL, 108, 024801 (2012)
E= 3.5-14 GeV
pulse length ~30 fs
LCLS
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 48
FEL facilitiesLCLS
P. Emma et al, Nature Photon. 4, 641(2010)
radiation power ~ GW
Pulse length ~30 fs
G.Gutt et al, PRL, 108, 024801 (2012)
λ=1.4 �
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FEL facilitiesEuropean XFEL
- kürzeste Wellenlänge
- größte Brillanz
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FEL facilitiesEuropean XFEL
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FEL facilitiesEuropean XFEL
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 52
FEL facilitiesEuropean XFEL
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 53
FEL facilitiesEuropean XFEL
Parameter Value
SASE 1 SASE 2 SASE 3
photon energy [keV] 12.4 - 4.0 12.4 - 3.1 3.1 - 0.2
wavelength [nm] 0.1 - 0.31 0.1 - 0.4 0.4 - 6.4
peak power [GW] 24 22 100 - 135
average power [W] 72 66 300 - 800
photon beam size (FWHM) [µm] 110 110 65 - 95
photon beam divergence (FWHM) [µrad] 0.8 0.8 3 - 27
bandwidth (FWHM) [%] 0.09 0.08 0.28 - 0.73
coherence time [fs] 0.3 0.3 0.3 - 1.9
pulse duration (FWHM) [fs] 100 100 100
average brillance [x10^25, photons/(s mrad^2 mm^2 0.1% bandwidth)]
1.6 1.6 0.52 - 0.03
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 54
Linac Coherent Light Source(LCLS)
Spring-8 Angstrom Compact Laser (SACLA)
European XFEL
Standort USA Japan Deutschland
Start der Inbetriebnahme
2009 2011 2017
Beschleuniger –Technologie
normalleitend normalleitend supraleitend
Anzahl der Lichtblitze pro Sekunde
120 60 27 000
Minimale Wellenlänge
0.15 nm 0.1 nm 0.05 nm
Länge 1500 m 750 m 3400 m
FEL facilities
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 55
Outlook
� self-“seeding“
� high harmonics of laser light
Methods for improving of coherence
Monochromator
PD Dr. Igor Zagorodnov | X-Ray Free Electron Lasers. Lecture 5 | 26. June 2017 | Seite 56
Outlook“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 a laser plasma accelerator