X-Ray Free Electron Lasers

Transcription

1 X-Ray Free Electron Lasers Lecture 5. Self-amplified spontaneous emission. FLASH and the European XFEL in Hamburg Igor Zagorodnov Deutsches Elektronen Synchrotron TU Darmstadt, Fachbereich June 2014

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 2. June 2014 Seite 2

3 Motivation How to obtain a useful external field? SASE Electrons produce spontaneous undulators radiation 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 2. June 2014 Seite 3

4 Motivation Low-energy undulator test line (LEUTL), USA 530 nm PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 4

5 Motivation TESLA Test Facility (TTF), Hamburg PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 5

6 Shot-noise in electron beam Fluctuations of the electron beam current density serve as the input signal in the SAS EFEL P( t ) Laser pulse P( ω) Spectrum ω ~ ρω t[ a. u] ω ω PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 6

7 Shot-noise in electron beam The electron beam current (at the undulator entrance) consists from electrons randomly arriving at time t k N I ( t) = e δ ( t tk ) k= 1 The electron beam averaged over an ensemble of bunches I ( t) enf( t) The electron beam profile function can be, for example, 1 Fg ( t) = e 2πσ T 2 t 2σ 2 T χ 1 F ( t) = ( t) T χ r [0, T ] [0, T ] 1, 0 t T, ( t) = 0, otherwise PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 7

8 Shot-noise in electron beam In frequency domain N N i ω t i ω t i t k k= 1 k= 1 I ( ω) = I ( t) e dω = e e δ ( t t ) dω = e e ω k It follows from central limit theorem that the real and imaginary parts are normally distributed x 2σ p ( x) = e x, x = Re I ( ω), or x = Im I ( ω) 2πσ x The probability density distribution of spectral power x 1 p ( x) = e λ, λ = x, x = I ( ω) λ 2 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 8

9 Shot-noise in electron beam First-order correlation function * 2 N N i ω t i ω ' t I ( ω) I ( ω ') = e e k n = N k= 1n= 1 N i ω ω t iωt iω ' t 2 ( ') 2 = e e + e e e k= 1 k n k k n iωt 1 iωt iωt F( ω) = F( t) e dω = δ ( t t ) k k e dω = e N N k= 1 * 2 2 * I ( ω) I ( ω ') = e NF( ω ω ') + e N ( N 1) F( ω) F ( ω ') PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 9

10 Shot-noise in electron beam First-order correlation function * 2 2 * I ( ω) I ( ω ') = e NF( ω ω ') + e N( N 1) F( ω) F ( ω ') Fg ( ω) 2 2 T ω σ 2 = e F ( ω) = sinc( 0.5ωT ) = * r NF( ω) F ( ω ') << 1, forωσ >> 1 sin 0.5ωT ( ) 0.5ωT ( ) Averaged spectral current density ( white noise ) T * 2 I ( ω) I ( ω ') e NF( ω ω ') I ( ω) 2 2 e N PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 10

11 Current modulation from shot-noise We consider a rectangular averaged current 1 Fr ( t) ( ) T χ I ( t) = enf ( t) χ = [0, T ] t [0, T ] r ( t) 1, 0 t T, = 0, otherwise F r ( ω) = sinc 0.5ωT ( ) I ( ω) = enf ( ω) = ensinc 0.5ωT r ( ) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 11

12 Current modulation from shot-noise Spectral power density of averaged current S( ω) dω = I ( t) dt = I ( ω) dω = T T π = 1 1 T π 0 F r ( ω) T 2 Parseval's theorem dω 2 I ( ω) ( ) 2 S ω = ~ sinc ( 0.5ωT ) 0, for Tω >> 1 πt PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 12

13 Current modulation from shot-noise We are interested in an averaged spectral power density of shot noise, which by analogy can be written as S shot ( ω) I ( ω) 2 2 e N ei = = 0 πt πt π The amplification takes place in bandwidth ω and we can replace the power of the current in this bandwidth by power of the equivalent current with fluctuations at ω at amplitude I 2 rms ɶj ( ω ) = S ( ω ) ω 1 shot 1 I ω S ( ω ) ω I ( ω) e ω rms ( 1 ) shot 1 1,shot = = j0 A 0 b Ab I π 2 2 e N PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 13

14 FEL start up from shot-noise High-gain FEL model with space-charge d n 2 ku n, n 1,2,... N dz ψ = η = dη ek[ JJ ] n iψ == R( Eɶ n ) z n xe 2 e γ r γ r e µ ck[ JJ ] ee ( ψ ) dz m c m c d E ɶ 0 x( z ) = ɶ j z1 dz 4γ r N 2 i m z1 = z0 N ψ m= 1 N jz0 z ( ψ n) = π sgn ψ n ψ m ψ n ψ m Nωε 0 m= 1 ɶj j e E ( ) ( ) ( ) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 14

15 FEL start up from shot-noise Eɶ x Eɶ 2 2 ˆ x E iη ɶ + + ˆ η x ieɶ x = Γ Γ Γ η ˆ η = ρ 3 ɶ j ( ) z x( η, ) = 0 0 j ( η) η = γ j= 1 0 2ω0 E z c e α η γ γ ω ω c 1 Eɶ x(0) α1 α2 α3 c2 = Eɶ x (0) α c 1 α2 α3 3 Eɶ x (0) c Eɶ (0) 1 x 1 c2 = A Eɶ x (0) c 3 Eɶ x (0) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 15

16 FEL start up from shot-noise µ ck[ JJ ] ɶ 0 x (0) = ɶ 0 jz1(0) Ex = 4γ r E ɶ µ ck[ JJ ] (0) ɶj z 1(0) 4γ d ɶj j e 2 k, n 1, 2,... N N 2 i n z1 = z0 N ψ n u n n= 1 dz ψ = η = N N ɶ 2 iψ 2 n iψ j n z = ij z e ψ n = kuij z0 e ηn N n= 1 N n= 1 r ηn(0) η, n = 1, 2,... N ɶj (0) = i2 k ηɶj (0) z1 u z1 ck[ JJ ] Eɶ µ (0) i2 k ɶj (0) 0 x = uη z1 4γ r PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 16

17 FEL start up from shot-noise Start up from current modulation c (0) 1 Eɶ x µ 0cK[ JJ ] c2 = A Eɶ x (0) = A 1 ɶ jz1(0) 4γ r c 3 E (0) i2k x uη ɶ Start up from seed field c1 c 2 c 3 Eɶ x (0) Ein 1 1 = A Eɶ x (0) = A 0 Eɶ (0) 0 x PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 17

18 FEL start up from shot-noise On resonance energy γ γ Eɶ η = r x 0 ieɶ = 0 3 x Γ γ r ɶ z x = Ae α α 3 = iγ 3 E ( i ) α 1 = + 3 Γ 2 ( i ) α 2 α 2 = 3 Γ 2 Imα α 1 Reα Γ α 3 = iγ Eɶ x 3 = j= 1 c e α j j z A * α α α = A = α1 α2 α3 * PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 18

19 FEL start up from shot-noise Start up from seed field Start up from current modulation c1 c 2 c 3 Ein 1 1 Ein = A 0 = * c1 0 α1 1 µ 0cK[ JJ ] 1 µ 0cK[ JJ ] * c2 1 jz1(0) jz1(0) α2 = A ɶ = ɶ 4γ r 3 4γ r c * 3 0 α3 µ ck[ JJ ] ck[ JJ ] e E ɶ µ ω j j γ γ π 0 0 in, shot = z1, shot (0) = rγ rγ I ω 2ρω 1 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 19

20 FEL start up from shot-noise PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 20

21 Statistical properties of SASE radiation Interference Coherence Coherence 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 2. June 2014 Seite 21

22 Statistical properties of SASE radiation Coherence time 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 τ coh 1 1 ~ ~ ω ω ρ PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 22 1

23 Statistical properties of SASE radiation Coherence length Typical length of one spike l coh N = c τ = c l c coh ~ I ce c ρω 1 Number of cooperative electrons Number of spikes (longitudinal modes) P [GW] l coh Laserpuls s[µm] Lb 1 1 M = = : l τ T coh c b PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 23

24 Statistical properties of SASE radiation Spikes in spectrum S( ω ) Spectrum ( ) S ω M = 6 M = 2.6 λ ~ 2ρλ 1 long bunch (~100fs) V. Ayvazyan et al, Eur. Phys.Journ. D 20, 149 (2002) short bunch (~40fs) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 24

25 Statistical properties of SASE radiation Fluctuations of SASE pulse energy PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 25

26 Statistical properties of SASE radiation Fluctuations of SASE pulse energy (linear regime) M M 1 M u pm ( u) = e Γ( M ) Mu u = U U rad rad Γ = z 1 t ( z) t e dt 0 PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 26

27 Statistical properties of SASE radiation Fluctuations of SASE pulse energy (after saturation, 13 nm, FLASH) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 27

28 Statistical properties of SASE radiation Saturation length (SASE) P ρw b SASE with N c L sat L g = ln N c L electrons on coherence length z g PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 28

29 Statistical properties of SASE radiation Coherence Longitudinal profile with large statical fluctuations radiation electrons Transverse profile is coherent PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 29

30 FEL facilities TESLA Test Facility ( until 2002) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 30

31 FEL facilities TESLA Test Facility ( until 2002) Three undulator modules. Total length 15m PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 31

34 FEL facilities TESLA Test Facility II ( ) From 2003 on, TTF1 was expanded to TTF2, an FEL user facility for the spectral range of soft x-rays, including a new tunnel and a new experimental hall (in the foreground). In April 2006, the facility was renamed FLASH: FEL in Hamburg PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 34

35 FEL facilities FLASH ( from 2006) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 35

38 Phase space linearization rollover compression vs. linearized compression Q=0.5 nc ~ 1.5 ka Q=1 nc ~2.5 ka PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 38

39 Phase space linearization FLASH In accelerator modules the energy of the electrons is increased from 5 MeV (gun) to 1200 MeV (undulator). PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 39

40 Phase space linearization FLASH In compressors the peak current I is increased from A (gun) to 2500 A (undulator). PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 40

41 Phase space linearization FLASH FEL radiation parameters Wavelength Range nm Average Single Pulse Energy µj Pulse Duration (FWHM) Peak Power (from av.) Average Power (5000 pulses/sec) fs 1-3 GW 400 mw Spectral Width (FWHM) % Average Brilliance 10^17-10^21 photons/s/mrad2/mm2/0.1%bw PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 41

42 FEL facilities FLASH 2 ( from 2013) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 42

43 FEL facilities FLASH 2 ( from 2013) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 43

44 FEL facilities FLASH 2 Photon Beam HHG SASE Wavelength range (fundamental) Average single pulse energy Pulse duration (FWHM) Peak power (from av.) Spectral width (FWHM) Peak Brilliance*10-40 nm nm 4-80 nm 1 50 µj µj <15 fs fs 1 5 GW 1 5 GW % % PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 44

45 FEL facilities LCLS E= GeV Intensity distrubution for λ= 0.14 nm radiation power ~ GW pulse length ~30 fs G.Gutt et al, PRL, 108, (2012) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 45

46 FEL facilities LCLS λ=1.4 P. Emma et al, Nature Photon. 4, 641(2010) radiation power ~ GW Pulse length ~30 fs G.Gutt et al, PRL, 108, (2012) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 46

47 FEL facilities European XFEL - kürzeste Wellenlänge - größte Brillanz PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 47

48 FEL facilities European XFEL PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 48

54 FEL facilities European XFEL Parameter Value SASE 1 SASE 2 SASE 3 photon energy [kev] wavelength [nm] peak power [GW] average power [W] photon beam size (FWHM) [µm] photon beam divergence (FWHM) [µrad] bandwidth (FWHM) [%] coherence time [fs] pulse duration (FWHM) [fs] average brillance [x10^25, photons/(s mrad^2 mm^2 0.1% bandwidth)] PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 54

55 FEL facilities Linac Coherent Light Source (LCLS) Spring-8 Angstrom Compact Laser (SACLA) European XFEL Standort USA Japan Deutschland Start der Inbetriebnahme Beschleuniger Technologie Anzahl der Lichtblitze pro Sekunde Minimale Wellenlänge normalleitend normalleitend supraleitend nm 0.1 nm 0.05 nm Länge 1500 m 750 m 3400 m PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 55

56 Outlook Methods for improving of coherence self- seeding Monochromator high harmonics of laser light PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 56

57 Outlook Table-Top-FEL λ=740 nm spontaneous undulator radiation with a laser plasma accelerator H.-P. Schlenvoigt et al, Nature Physics 4, 130 (2008) λ=17 nm M.Fuchs et al, Nature Physics 5, 826(2009) PD Dr. Igor Zagorodnov X-Ray Free Electron Lasers. Lecture 5 2. June 2014 Seite 57