G8-自由电子激光原理_黄志戎

FELprinciple黄志戎(ZhirongHuang)自由电子激光原理1DtheoryLectureOutlineSASEandXFELFELR&D3“Asolutionlookingforaproblem.LightBulbvs.LaserA.Schawlow(Nobelprizeonlaserspectroscopy),ScientificAmericans,1968Radiationemittedfromlightbulbischaotic.Pinholecanbeusedtoobtainspatialcoherence.Monochromatorcanbeusedtoobtaintemporalcoherence.PinholeandMonochromatorcanbecombinedforcoherence.Laserlightisspatiallyandtemporallycoherent.•ProducedbyresonantinteractionofarelativisticelectronbeamwithEMradiationinanundulatorFreeElectronLaser(FEL)electronbeamphotonbeame-beamdumpundulator•Tunable,Powerful,Coherentradiationsources•JohnMadey—InventoroftheFEL(1971)ThreeFELmodesFELoscillators(High-averagepower)SinglepassFELs(SASEorseeded)(SR)BrightlightsourcesfromrelativisticelectronsElectronsemitwithrandomphaseradiationintensityN(gisLorentzfactor,Nisnumberofelectrons~109)SynchrotronradiationUndulatorradiationLinacCoherentLightSource(LCLS)atSLACInjectorExisting1/3Linac(1km)(withmodifications)NearExperimentHallFarExperimentHallUndulator(130m)X-FELbasedonlast1-kmofexisting3-kmlinacNewe-TransferLine(340m)1.5-15Å(14-4.3GeV)X-rayTransportLine(200m)ProposedbyC.Pellegriniin1992EraofXFEL(2009)XFELsareExtremelyBrightandUltrafasttimeXFEL1012photonsSynchrotron106photons100fs10psNote:synchrotronsourcesaremuchhigherrep.ratethanXFELsOrderedStructuresEquilibriumPhenomenaDisorderedStructuresNonequilibriumPhenomenaTransientStates19002000futureEraofCrystallineMatterEraofDisorderedMatterCoherentX-rayProbesConventionalX-rayProbesFutureRoleofFELsandAdvancedSourcesH.Dosch(DESY)UndulatorradiationWorksforharmonicslh=l1/hUVSOR,Okazaki,Japanluforwarddirectionradiation(andharmonics)undulatorparameterK=0.94B[Tesla]lu[cm]Canenergybeexchangedbetweenelectronsandco-propagatingradiationpulse?l1LCLSundulatorK=3.5,lu=3cm,e-beamenergyfrom3GeVto15GeVtocoverl1=30Åto1.2ÅElectronandPhotonInteractionResonantinteractionenergy=(g-g0)/g0phase=(k1+ku)z-1tradiationwavenumberundulatorwavenumberUsevariablesarrivaltimeatundulatordistanceFELlongitudinaldynamics(classicaltheory)Longitudinalelectronmotionincombinedundulatorandradiationfieldsdescribedbypendulumequationsl1forplanarundulator=1forhelicalundulatorPendulumEquationLow-gainregimeGainperpassissmall,ignoreMaxwellequation.Useonlyparticlemotionandenergyconservation.RadiationgainRadiationlossRadiationfrequencyHigh-gainregimeS.Reichelog(radiationpower)distanceelectronbeamphotonbeame-beamdumpundulatorUseslowlyvaryingphaseandamplitudeapproximationBeamcrosssectionarea1DWaveEquationTransverseelectricfield:Transversecurrentsaturationefficiency(r~10-3forshort-wavelengthFELs)FELPierceparameterIA=17kAisAlfvencurrentBothpendulumequationandwaveequationcanbescaledbyasinglescalingparameterpeakcurrentbetafunctioninund.norm.trans.emittaceHigh-gainsolutionIllustrateFELgainbyneglectingdependenceofEfield(slippage)Power~|Exp[-im3(2rkuz)]|2gainlengthCubicequationandsolution+-+-+--+-+-++-SlippageleadstocoherencelengthandspikystructureDuetoresonantcondition,lightovertakese-beambyoneradiationwavelengthl1perundulatorperiod(interactionlength=undulatorlength)zSlippagelength=l1×Nundulatorperiods:(at1.5Å,LCLSslippagelengthis:ls≈1.5fs100-fspulselength)Eachpartofopticalpulseisamplifiedbythoseelectronswithinaslippagelength(anFELslice)Coherencelengthisslippageover~2LG(lc≈ls/10)ML≈Dz/lcindependentradiationsources(modes)Nl1e-x-raysslippagelengthDz~1µmP.Emma~10kW~1MW~0.1GW~10GWFELstartupfrome-beamnoiseBW=0.6%BW=0.15%BW=0.10%BW=0.08%spikytemporalstructurenarrowband-widthAllverticalaxesarelogscaleDuetonoisestart-up,SASEischaoticlightwithMLcoherentmodes(i.e.,spikesinintensityprofile):LongitudinalphasespaceisMLlargerthanFourierTransformlimitSASEenergyfluctuationis…MLisnotconstant–reducedbyincreasedcoherenceduringexponentialgrowth,andincreasedwithreducedcoherenceaftersaturationLCLSnearsaturation(~50fs):ML≈200DW/W≈7%Statisticalintensityfluctuationdeterminedbynumberoflongitudinalmodes←50%ofX-RayPulseLength→z=50mtemporalspikesappearcLlzMD=lengthcoherencelengthbunchLMWW1=DFELBandwidthsetbyFELParameter,r(~10-3)LCLSspectrumSpectralpropertiesaresimilartotemporaldomain,exceptthateverythingisinverted…Example,LCLSrelativespectralspikewidth:Dz=50fsbunchlength:width=5×10-6Dz=5fsbunchlength:width=5×10-5Dz=0.5fsbunchlength:width=5×10-4spikewidth~l1/(2Dz)Bandwidth~2rSASE1DSummaryPowergainlength:Exponentialgrowth:P(z)=P0exp(z/LG)Startupnoisepower:P0≈r2gmc3/l1(spontaneousradiationintwogainlengths)Saturationpower:Psat≈r×e-beampowerSaturationlength:Lsat≈lu/r≈18LGFWHMbandwidthatsaturation:≈2rCoherencelengthatsaturation:lc≈l1/(pr)3.5m1.5kW20GW60m0.1%0.2fsS.ReicheZ=25mZ=37.5mZ=50mZ=62.5mZ=75mZ=87.5mmSinglemodedominatescloseto100%transversecoherenceTransversecoherencePeakBrightnessEnhancementFromStorageRingLightSourcesToSASEEnhancementFactor#ofphotonsNlc~106to107UndulatorinSRSASENeNeNlcΩxΩy(2πx)(2πy)ΩZcompressedDZc=10-310psDZc=10-3100fs210210()212lB102310331010Nlc:numberofelectronswithinacoherencelengthlcto1011SASEFELElectronBeamRequirementsN0.5µmat1Å,15GeV0.04%