Short Wavelength SASE FELs: Experiments vs. Theory Jörg Rossbach University of Hamburg & DESY
Contents INPUT (electrons) OUTPUT (photons) Momentum Momentum spread/chirp Slice emittance/ phase space distribution Total charge Long. charge profile Peak current Orbit control FEL machinery Gain length Saturation behaviour Spectrum Harmonics Transverse coherence Pulse length Effective input power Fluctuations Do we understand the machinery? 2
FEL Basics Point-like bunch of electrons radiates coherently P N e! Point means above all: bunch length < radiation 2 Synchrotron radiation of incoherent electron distribution: P N e desired: bunch length < wavelength OR (even better) Density modulation at desired wavelength Potential gain in power: N e ~ 1 6!! Idea: Start with an electron bunch much longer than the desired wavelength and achieve bunching at the optical wavelength automatically Free-Electron Laser (Motz 195, Phillips ~196, Madey 197) 3
Basic theory of FELs Step 1: Energy modulation A: Electron travels on sine-like trajectory v x ( z) c K J cos( 2S Ou z), with undulator parameter: K eo u B 2Sm e c z B: External electromagnetic wave moving parallel to electron beam: Ex ( z, t ) Change of energy dw dz E cos(k L z ZL t ) W in presence of electric field: qe K q && ve sin <, vz JE z with the ponderomotive phase: 4 < ku k L z Z L t M
Basic FEL theory dw dz qek sin z The energy dw is taken from or transferred to the radiation field. For most frequencies, dw/dz oscillates very rapidly. Continuous energy transfer? Yes, if constant. d dz! Resonance condition: u K L 1 2 2 2 2 Same equation as for wavelength of undulator radiation! 5
Step 2: Current modulation dw dz Basic FEL theory Energy modulation by leads to change of Phase : Combined with Step 1: qek sin z yields 2 d 2 dz with d 2 ku dz 2 sin q E res 2 2 2 mc res Kk z u like synchrotron oscillation -- but at spatial period light light 6 current modulation!!
Basic FEL theory Step 3: Radiation Current modulation j Light drives radiation of light: de Light dz const j Light System of Diff. Eqs. defines High Gain FEL: (Kondratenko, Saldin 198) (Bonifacio, Pellegrini 1984) qelight K sin 2 2 mec re s d 2 k dz E u re s Light const j Light Energy modulation Density modulation Radiation 7
Theory: High-gain FEL Most simple case: 3 d E dz 3 i A z 3. Ansatz: i E i E exp( ) i 3 i 3 ; ; 2 2 3 3 1 2 3 1 z : P rad exponential growth: 1 z Pin exp 9 LG L G 3 2 1 IA r u 2 3 4 Î K 1 3 L (current density) G - 1 3 u F E L 4 3 L G 1 1 1 4 2 1. Expect exponential gain with e-folding length L G Major additional assumption: Orbit is perfectly straight 2. Gain should saturate when modulation is complete What do we 8observe?
VISA ATF/BNL 84 nm March 21 LEUTL APS/ANL 385 nm September 2 <E rad > [µj] 1 1 1.1 (a) FLASH DESY 13 nm September 26.1 5 1 15 2 25 3 z [m] 9 For all experiments there exists a reasonable electron beam parameter set such that gain length and saturation level agree with theoretical expectations.
Exponential growth? Reasonable gain length? Achieve full density modulation? But: measurement of relevant beam parameters is not precise enough to just predict gain length with reasonable precision. 1
Bandwidth Gain vs. momentum error =dp/p (momentum spread ) Note: Emittance effect similar normalized gain FEL is a narrow band amplifier Note: Cannot produce few-cycle pulses! 5. FEL 1. FEL FLASH experiment: Bandwidth? 11 12.7 12.9 13.1 13.3 13.5 13.7 Wavelength [nm] (1 Jörg shots) Rossbach, Univ HH
Start-up from noise FEL can also start from initial density modulation given by noise. Equivalent: starting from spontaneous undulator radiation. Self-Amplified Spontaneous Radiation SASE Very robust mode of operation! Theory must model shot noise. Predicts effectiv initial conditions Critical bench mark test for numerical FEL codes, e.g. GENESIS (Reiche) GINGER (Fawley) SIMPLEX (Tanaka) FAST (Yurkov) Equivalent input energy by shot noise:.3 pj 12 numerical simulation
Start-up from noise SASE output will fluctuate from pulse to pulse, -- just as ANY part of spontaneous synchrotron radiation does! Remember: FEL is just an amplifier! single Mode (after monochromator slit) short pulses M=2.6 modes long pulses M=6 modes time time time P(E) P(E) P(E) E/<E> E/<E> E/<E> 13
j Start-up from noise Simple 1D model: Superposition of many wavetrains with random phases A) Short bunch << wavetrain 5 5 yi 1 yi 2 + 5 4 3 2 1 1 2 3 4 5 xi + 5 4 3 2 1 1 2 3 4 5 many = 2 1 yi j 1 2 5 4 3 2 1 1 2 3 4 5 z 2 B) Bunch length >> wavetrain: many Modes 1 M1 E g M (E) de (E) e de (M) xi 5 4 3 2 1 + 1 2 3 4 5 5 4 3 2 + 1 1 2 3 4 5 many = 5 4 3 2 1 1 2 3 4 5 xi Large probability of destructive interference single Mode Extract M from histrogram pulse length P(E)dE exp E de 2 probability 5 1.5.5 1 1.5 2 probability 14 Fluctuation properties? total energy E.175 dgamma ( z 6) 5.4961 5 1 z total energy E 2
Pulse length Time-domain measurement of pulse length: not (yet) available for X-ray (established in the visible, FROG etc.) Alternative: intensity fluctuation translates into spectral fluctuation: Width of frequency spikes ļ length of pulse 15 852 5 1 5 5 4 3 2 1 xi 1 2 3 4 5 T Fourier new_fund_harmonic_w.avi 5 3 2 3 4 2 5 6 3 single pulse Spectra @FLASH: predicted 15 ~25 fs pulse duration @ 32 nm 8 (a) o = simulations 13.5 PAC 27 o ~.4% Ȧ Intensity (arb. units) measured 7 8 i 13.6 13.7 13.8 λ [nm] 13.9 14. 1 fs pulse duration @ 13 nm Jörg Rossbach, Univ HH Pulse length?
Transverse Coherence Emittance of a perfectly coherent ( gaussian ) light beam emittance: Light r FEL theory predicts high transverse coherence of photon beam, if electron beam emittance: electrons 4 Observation of interference pattern at FLASH: double slit intensity modulation FEL simulation Light Light 4-3 -2-1 1 2 1 2 3 4 5 6 7 8 Verified @ 32nm + 13nm 3 4-4 -3-2 -1 1 2 3 4 position / mm 16 9 1 2 4 6 8 1 position / mm coherence Jörg Rossbach,? Univ HH
Higher Harmonics Density modulation becomes anharmonic at high gain: 12 L G / Intensity (arb. units) (b) Intensity (arb. units) (c) current 4.55 4.6 4.65 λ [nm] 3 rd harmonics @ 4.8 nm 2.55 2.6 2.65 2.7 2.75 2.8 2.85 2.9 λ [nm] 5 th harmonics @ 2.75 nm 16 L G 18 L G FLASH typical pulse energies (avg.): Fundamental (13.8 nm): 4 µj 3 rd harmonics (4.6 nm): (.25 ±.1) µj 5 th harmonics (2.75 nm): (1 ± 4) nj new third harmonic 17 Harmonics?
Electron Beam on the fs Scale Most electron beam parameters relevant within slices < coherence length ~1 1 fs relaxes requirements on beam specs complicates measurements and beam dynamics Emittance: Short Pulse length Peak current inside bunch: Energy width: Straight trajectory in undulator s = 1 1 fs Î > 1 ka E /E ~1-3 < 1 m Increasingly difficult for shorter wavelength: longer undulator, smaller emittance, larger peak current E. Prat: THAN 26 18
Beam dynamics simulation tools Flöttmann Dohlus Borland Reiche 19
Longitudinal bunch compression RF gun superconducting TESLA module bunch compressor 127 MeV bunch compressor 38 MeV Laser 4-5 MeV 12/2 MV/m before 1 st BC 1m after 1 st BC 1m after 2 nd BC ~ 2 fs Long initial bunch to reduce space charge on cathode s L = 4.4 ±.1 ps 1 2 3 4 5 Time (ps) Very complicated beam dynamics due to coherent synchrotron radiation Difficult access 2to relevant parameters Ultra-short photon pulses created ~2fs FWHM
Resolving 2 fs with LOLA Three examples for different compressor settings: See talk by M. Röhrs Resolution ~2 fs Time (pixels) 5 fs 5 fs simulation LOLA 21
fs diagnostics with THz radiation Single shot spectrum of coherent infrared radiation exhibits structure in the longitudinal density modulation < 5 m Size of lasing spike Substructure inside spike 22
Do we understand the machinery? INPUT (electrons) OUTPUT (photons) Momentum Momentum spread/chirp Slice emittance/ phase space distribution Total charge Long. charge profile Peak current Orbit control FEL machinery Gain length Saturation behaviour Spectrum Harmonics Transverse coherence Pulse length Effective input power Fluctuations Most probably yes, but we should know more details about the operator (electron beam). 23