G8 自由电子激光原理-黄志戎

1、FEL principle 黄志戎 (Zhirong Huang)自由电子激光原理 1D theoryLecture Outline SASE and XFEL FEL R&D3“A solution looking for a problem.Light Bulb vs. Laser A. Schawlow (Nobel prize on laser spectroscopy), Scientific Americans, 1968Radiation emitted from light bulb is chaotic. Pinhole can be used to obtain spati

2、al coherence.Monochromator can be used to obtain temporal coherence.Pinhole and Monochromator can be combined for coherence.Laser light is spatially and temporally coherent.Produced by resonant interaction of a relativistic electron beam with EM radiation in an undulatorFree Electron Laser (FEL)elec

3、tron beamphoton beame- beam dumpundulatorTunable, Powerful, Coherent radiation sourcesJohn MadeyInventor of the FEL (1971) Three FEL modesFEL oscillators(High-average power)Single pass FELs (SASE or seeded)(SR)Bright light sources from relativistic electronsElectrons emit with random phase radiation

4、 intensity N(g is Lorentz factor, N is number of electrons 109) Synchrotron radiationUndulator radiationLinac Coherent Light Source (LCLS) at SLACInjectorExisting 1/3 Linac (1 km)(with modifications)Near Experiment HallFar ExperimentHallUndulator (130 m)X-FEL based on last 1-km of existing 3-km lina

5、cNew e- Transfer Line (340 m)1.5-15 (14-4.3 GeV)X-ray Transport Line (200 m)Proposed by C. Pellegrini in 1992Era of XFEL (2009)XFELs are Extremely Bright and UltrafasttimeXFEL 1012 photonsSynchrotron 106 photons100 fs10 psNote: synchrotron sources are much higher rep. rate than XFELsOrdered Structur

6、esEquilibrium PhenomenaDisordered StructuresNonequilibrium PhenomenaTransient States 19002000futureEra of Crystalline MatterEra of Disordered MatterCoherent X-ray ProbesConventional X-ray ProbesFuture Role of FELs and Advanced SourcesH. Dosch (DESY)Undulator radiationWorks for harmonicslh=l1/hUVSOR,

7、 Okazaki, Japanluforward direction radiation(and harmonics) undulator parameter K = 0.94 BTesla lucmCan energy be exchanged between electrons and co-propagating radiation pulse?l1LCLS undulator K = 3.5, lu = 3 cm, e-beam energy from 3 GeV to 15 GeV to cover 1 = 30 to 1.2 Electron and Photon Interact

8、ion Resonant interaction energy =(-0)/0 phase =(k1+ku)z-1tradiation wavenumberundulator wavenumber Use variablesarrival time at undulator distanceFEL longitudinal dynamics (classical theory) Longitudinal electron motion in combined undulator and radiation fields described by pendulum equations1for p

9、lanar undulator=1 for helical undulatorPendulum EquationLow-gain regime Gain per pass is small, ignore Maxwell equation. Use only particle motion and energy conservation.Radiation gainRadiation lossRadiation frequencyHigh-gain regimeS. Reichelog(radiation power)distanceelectron beamphoton beame- bea

10、m dumpundulator Use slowly varying phase and amplitude approximationBeam cross section area1D Wave Equation Transverse electric field: Transverse currentsaturation efficiency(r 10-3 for short-wavelength FELs)FEL Pierce parameterIA=17 kA is Alfven current Both pendulum equation and wave equation can

11、be scaled by a single scaling parameter peak currentbeta function in und.norm. trans. emittaceHigh-gain solution Illustrate FEL gain by neglecting q dependence of E field (slippage)Power |Exp-im3(2rkuz)|2gain length Cubic equation and solution+-+-+-+-+-+-Slippage leads to coherence length and spiky

12、structureDue to resonant condition, light overtakes e- beam by one radiation wavelength 1 per undulator period (interaction length = undulator length)zSlippage length = 1 N undulator periods: (at 1.5 , LCLS slippage length is: ls 1.5 fs 100-fs pulse length)Each part of optical pulse is amplified by

13、those electrons within a slippage length (an FEL slice)Coherence length is slippage over 2LG (lc ls/10)ML Dz/lc independent radiation sources (modes)N1e-x-raysslippagelengthDz1 mP. Emma10 kW1 MW0.1 GW10 GWFEL startup from e- beam noiseBW = 0.6%BW = 0.15%BW = 0.10%BW = 0.08%spiky temporal structurena

14、rrowband-widthAll vertical axes are log scaleDue to noise start-up, SASE is chaotic light with ML coherent modes (i.e., spikes in intensity profile):Longitudinal phase space is ML largerthan Fourier Transform limitSASE energy fluctuation isML is not constant reduced by increased coherence during exp

15、onential growth, and increased with reduced coherence after saturationLCLS near saturation (50 fs): ML 200 W/W 7 %Statistical intensity fluctuation determined by number of longitudinal modes 50 % of X-Ray Pulse Length z = 50 mtemporal spikes appearFEL Bandwidth set by FEL Parameter, r (10-3)LCLS spe

16、ctrumSpectral properties are similar to temporal domain, except that everything is invertedExample, LCLS relative spectral spike width: Dz = 50 fs bunch length: width = 510-6Dz = 5 fs bunch length: width = 510-5Dz = 0.5 fs bunch length: width = 510-4spike width l1/(2Dz)Bandwidth 2SASE 1D Summary Pow

17、er gain length:Exponential growth: P(z) = P0 exp(z/LG)Startup noise power: P0 r 2g mc3/l1 (spontaneous radiation in two gain lengths)Saturation power: Psat r e-beam powerSaturation length: Lsat lu/r 18LGFWHM bandwidth at saturation: 2rCoherence length at saturation: lc l1/(pr)3.5 m1.5 kW20 GW60 m0.1

18、%0.2 fsS. ReicheZ=25 mZ=37.5 mZ=50 mZ=62.5 mZ=75 mZ=87.5 m mSingle mode dominates close to 100% transverse coherenceTransverse coherencePeak Brightness Enhancement From Storage Ring Light Sources To SASE#of photonsx y zB =(i- phase space area)Enhancement Factor# of photonsNlc106 to 107Undulator in S

19、RSASEeeNlcxy(2x) (2yZ compressedB102310331010Nlc: number of electrons within a coherence length lcto 1011SASE FEL Electron Beam RequirementseN 0.5 m at 1 , 15 GeV0.04% at Ipk = 3 kA, K 3, lu 3 cm, 18LG 100 m for eN 1.5 mWe must increase peak current, preserve emittance, and maintain small energy spr

20、ead so that power grows exponentially with undulator distance, z,P(z) = P0 exp(z/LG)FEL power reaches saturation at 18LGSASE performance depends exponentially on e- beam quality ! (challenge)transverse emittance:relative energy spread:FEL gain length: Photocathode rf gunxn 1 m m, Ip 100A Bunch compr

21、essionIp 2-5 kA, Dt 1-100 fs Acceleration320 GeV, l lu/(2g2)adiabatic damping x xn/g l/4p, sg/g r 10-3 Undulator 100-m long, segmented, a few mm toleranceProjects undertaken at US, Germany, Japan, Korea, Swiss, Italyemittancecorrectorrf photocathodegunLinacLinacLinacPulse compressorsSASE UndulatorXF

22、EL accelerator systemLCLS: worlds first hard x-ray FELSASE wavelength range: 30 1.2 Photon energy range: 0.4 - 10 keVPulse length FWHM 5 100 fs (5- 500 fs for SXR only)Pulse energy up to 4 mJ95% accelerator availability1.5 SASE Wavelength range: 3 0.6 Photon energy range: 4 - 20 keVPulse length (10

23、fs FWHM)Pulse energy up to 1 mJSpring-8 SACLA2011More XFELs to comemore to come:PAL-XFEL (2015)SwissFEL (2016)LCLS-II (2020)32European XFEL 2016SRF technology: driver for high-average brightness FELsXFEL cavityLCLS-II Accelerator LayoutNew Superconducting Linac LCLS Undulator HallLCLS-II FAC Review,

24、 July 1-2, 2014 Two sources: high rate SCRF linac and 120 Hz Cu LCLS-I linac North and South undulators can operate simultaneously in any mode1.0 - 25 keV (120 Hz)1.0 - 5 keV (120 kW)0.2-1.3 keV (120 kW)4 GeV SC LinacUndulatorSC Linac (up to 1 MHz)Cu Linac (up to 120Hz)North 0.20 - 1.3 keVSouth1.0 -

25、 5.0 keV up to 25 keVhigher peak power pulsesCu Linac Concurrent operation of 1-5 keV and 5-25 keV is not possible4 GeV, 0.3 mA, 1.2 MWSCRF Linac in 1st km of SLAC tunnelExisting LCLSWhat comes next for XFEL R&D?Precise control x-ray properties similar to optical lasers Compact coherent sourcesSASE

26、temporal coherence can be drastically improved by seeding (self or external seeding) or an x-ray oscillatorSASEseededchicane1st undulator2nd undulatorSASE FELgratingSeeded FELgrazing mirrorsslitSelf-Seeding1,2First undulator generates SASEX-ray monochromator filters SASE and generates seedChicane de

27、lays electrons and washes out SASE microbunching Second undulator amplifies seed to saturationLong x-ray path delay (10 ps) requires large chicane that take space and may degrade beam qualityReduce chicane size by using two bunches3 or single-crystal wake monochromator4.1. J. Feldhaus et al., NIMA,

28、1997.2. E. Saldin et al., NIMA, 2001.3. Y. Ding, Z. Huang, R. Ruth, PRSTAB, 2010.4. G. Geloni, G. Kocharyan, E. Saldin, DESY 10-133, 2010.Hard x-ray self-seeding LCLSGeloni, Kocharyan, Saldin (DESY)1 GW25 GWFEL spectrum after diamond crystalPower dist. after diamond crystalMonochromatic seed powerWi

29、de-band power6 mm 20 fs5 MWSelf-seeding of 1-mm e- pulse at 1.5 yields 10-4 BW with low charge mode3710-51551161731HXRSS at LCLS (replacing U16)Bragg diagnostic with cameraChicane magnetDiamond mono chamber38X-raysJ. Amann, P. Emma8.3 keV20 eVSASE spectrum (diamond OUT)Factor of 40-50 BW reductiondi

30、amond INA well seeded pulse (not typical)SASEseededSASESeeded0.45 eV(510-5)insert diamond & turn on chicane0.45 eVchicane OFF chicane ONJ. Amann et al., Nature Photon., 2012 Fourier Transform limit is 5 fs chicanee-Undulator 2-7Undulator 10-18SASE FELgratingSeeded FELM1slitFELX-raysM2M340P. Montanez

31、 et. al.,Soft x-ray self-seeding (0.5 1 keV)4 m41Electron energyFEL PowerElectron energyFEL PowerSeeded bandwidth is a factor of 30 narrower than SASE at photon energy 860 eV (design range 500-1000 eV), with a resolving power of about 5000.10-shot averaged spectral brightness is a factor of 4 higher

32、 than 2.5 mJ SASE.Careful alignments of electron and seed10-shot average spectra comparisonSeeded FWHM bandwidth 0.18 eVSASE scaled to 2.5 mJD. Ratner et. al.,Seeding results (Feb. 17, 2014)Jitter reduced42S. WakatsukiF.-J. Decker, A. Lutman, et al.By adjusting the yaw angle in addition to the usual

33、 pitch angle of the seeding crystal, two-color seeded FEL with two different crystal diffraction planes was demonstrated at the hard x-ray photon energies at LCLS.2-color self-seeding for MAD phasing45 eV separation-Generate two bunches by stacking injector laser-Accelerate off-crest and compress to

34、 get up to 200 fs separation1% energy separation 1 mJ in SASE operation(improvement by 10 with respect to previous schemes)A. Marinelli, et al.SASESASESeeded80 eV apartSeeded2-bunch to provide independent control of time and energy separation to enable MAD and pump/probe experiments432-bunch 2-color

35、 development44C. Behrens, Y. Ding, P. Krejcik et al., Nature Comm., 2014Electron beam is streaked horizontally and viewed on a screen in a vertically resolved energy spectrometer, revealing time-energy phase space after the FEL undulator. The upper right plots show an example of an ultra-short soft x-ray pulse with a measured 2.6-fs pulse duration.Lasing-onLasing-onLasing-offLasing-offReconstructed X-ray profile1keV10keVFemtosecond x-ray diagnostics with XTCAVXTCAV example (150 pC, 10 keV)Taper sectionC. S