Synchrotron Radiation and Free-Electron Lasers: Principles of Coherent X-Ray Generation

299 Pages·2017·11.479 MB·English

by  Kwang-Je Kim, Zhirong Huang, Ryan Lindberg

SynchrotronRadiationandFree-ElectronLasers
PrinciplesofCoherentX-RayGeneration
Learn about the latest advances in high-brightness X-ray physics and technology with
this authoritative text. Drawing upon the most recent theoretical developments, pre-
eminentleadersinthefieldguideyouthroughthefundamentalprinciplesandtechniques
of high-brightness X-ray generation from both synchrotron and free-electron laser
sources.Awiderangeoftopicsiscovered,includinghigh-brightnesssynchrotronradia-
tionfromundulators,self-amplifiedspontaneousemission,seededhigh-gainamplifiers
with harmonic generation, ultra-short pulses, tapering for higher power, free-electron
laser oscillators, and X-ray oscillator and amplifier configuration. Novel mathematical
approaches and numerous figures accompanied by intuitive explanations enable easy
understanding of key concepts, while practical considerations of performance improv-
ing techniques and discussion of recent experimental results provide the tools and
knowledgeneededtoaddresscurrentresearchproblemsinthefield.
Thisisacomprehensiveresourceforgraduatestudents,researchers,andpractitioners
whodesign,manage,oruseX-rayfacilities.
Kwang-JeKim is a Distinguished Fellow at the Argonne National Laboratory, Illinois,
USA,andaProfessorofPhysicsattheUniversityofChicago.HeisalsoaFellowofthe
AmericanPhysicalSociety.
ZhirongHuangisanAssociateProfessorattheSLACNationalAcceleratorLaboratory
and in the Department of Applied Physics at Stanford University, and a Fellow of the
AmericanPhysicalSociety.
RyanLindbergisaStaffScientistattheArgonneNationalLaboratory,whereheworks
onfree-electronlaserphysics,andonanalyzingandpredictingcollectiveeffectsinlight-
sourcestoragerings.

Synchrotron Radiation and
Free-Electron Lasers
Principles of Coherent X-Ray Generation
KWANG-JE KIM
ArgonneNationalLaboratory,Illinois
ZHIRONG HUANG
SLACNationalAcceleratorLaboratory,California
RYAN LINDBERG
ArgonneNationalLaboratory,Illinois
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DOI:10.1017/9781316677377
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Contents
Preface pageix
ConventionsandNotation xii
1 PreliminaryConcepts 1
1.1 Particle(Electron)Beams 1
1.1.1 ElectronBeamPhaseSpace 2
1.1.2 BeamTransportandLinearOptics 3
1.1.3 BeamEmittanceandEnvelopeFunctions 4
1.1.4 BeamPropertiesunderSimpleTransport 6
1.1.5 ElectronDistributionFunctiononPhaseSpace 9
1.2 RadiationBeams 12
1.2.1 DiffractionofParaxialBeams 13
1.2.2 TheParaxialWaveEquationandEnergyTransport 16
1.2.3 PhaseSpaceMethodsinWaveOptics 18
1.2.4 TransverseCoherence 22
1.2.5 TemporalCoherence 26
1.2.6 BunchingandIntensityEnhancement 29
References 31
2 SynchrotronRadiation 33
2.1 RadiationbyRelativisticElectrons 35
2.2 TheDrivenParaxialWaveEquation 37
2.3 BendingMagnetRadiation 40
2.4 UndulatorRadiation 43
2.4.1 ElectronTrajectoryandaQualitativeDiscussionofUndulator
Radiation 44
2.4.2 ParaxialAnalysisofUndulatorRadiation 48
2.4.3 FrequencyIntegratedPower 52
2.4.4 PolarizationControl 53
2.4.5 Undulator Brightness and the Effects of the Electron Beam
Distribution 56
2.4.6 FromUndulatorRadiationtoFree-ElectronLasers 62
2.5 FutureDirectionsofSynchrotronRadiationSources 64
vi Contents
2.5.1 Multi-Bend Achromat Lattices for Smaller Storage Ring
Emittances 64
2.5.2 EnergyRecoveryLinacs 66
2.5.3 SuperconductingUndulators 67
2.5.4 LaserUndulator 69
References 71
3 BasicFELPhysics 74
3.1 Introduction 74
3.1.1 CoherentRadiationSources 74
3.1.2 WhatIsanFEL? 76
3.2 ElectronEquationsofMotion:ThePendulumEquations 78
3.2.1 DerivationoftheEquations 78
3.2.2 MotioninPhaseSpace 82
3.3 Low-GainRegime 83
3.3.1 DerivationofGain 83
3.3.2 ParticleTrappingandLow-GainSaturation 88
3.4 High-GainRegime 90
3.4.1 MaxwellEquation 91
3.4.2 FELEquationsandEnergyConservation 94
3.4.3 DimensionlessFELScalingParameterρ 95
3.4.4 1DSolutionUsingCollectiveVariables 97
3.4.5 QualitativeDescriptionofSelf-AmplifiedSpontaneousEmission
(SASE) 99
References 102
4 1DFELAnalysis 104
4.1 CoupledMaxwell–KlimontovichEquationsforthe1DFEL 104
4.2 PertubativeSolutionforSmallFELGain 107
4.3 SolutionviaLaplaceTransformationforArbitraryFELGain 110
4.3.1 SpontaneousRadiationandtheLow-GainLimit 112
4.3.2 ExponentialGrowthRegime 113
4.3.3 TemporalFluctuationandCorrelationofSASE 118
4.4 QuasilinearTheoryandSaturation 122
4.5 UndulatorTaperingafterGainSaturation 129
4.6 Superradiance 132
References 136
5 3DFELAnalysis 139
5.1 QualitativeDiscussion 139
5.1.1 DiffractionandGuiding 139
5.1.2 BeamEmittanceandFocusing 142
5.2 ElectronTrajectory 143
5.2.1 NaturalFocusinginanUndulator 144
Contents vii
5.2.2 BetatronMotioninanExternalFocusingLattice 148
5.3 3DEquationsoftheFEL 151
5.3.1 MaxwellEquation 151
5.3.2 3DPendulumEquationsfortheElectronMotion 152
5.3.3 CoupledMaxwell–KlimontovichEquations 154
5.4 SolutionintheLow-GainRegime 156
5.4.1 Low-GainExpressionforNoTransverseFocusing 160
5.5 SolutionintheHigh-GainRegime 162
5.5.1 VanKampen’sNormalModeExpansion 163
5.5.2 DispersionRelationwithFourScaledParameters 167
5.5.3 GainGuidingandTransverseCoherence 168
5.5.4 NumericallySolvingtheDispersionRelation 171
5.5.5 VariationalSolutionandFittingFormulas 176
References 180
6 HarmonicGenerationinHigh-GainFELs 182
6.1 NonlinearHarmonicGeneration 182
6.2 High-GainHarmonicGeneration 186
6.3 Echo-EnabledHarmonicGeneration 189
6.4 RecentDevelopmentsinHarmonicGeneration 194
References 195
7 FELOscillatorsandCoherentHardX-Rays 197
7.1 FELOscillatorPrinciples 197
7.1.1 PowerEvolutionandSaturation 198
7.1.2 QualitativeDescriptionofLongitudinalModeDevelopment 199
7.1.3 LongitudinalSupermodesoftheFELOscillator 200
7.1.4 TransversePhysicsoftheOpticalCavity 203
7.2 X-RayCavityConfigurations 204
7.2.1 Four-Crystal,Wavelength-TunableXFELOCavity 205
7.2.2 DiamondCrystalsforXFELO 208
7.3 XFELOParametersandPerformance 208
7.4 X-RayFrequencyCombsfromaMode-LockedFELOscillator 209
7.5 AHardX-RayMaster–Oscillator–PowerAmplifier(MOPA) 212
References 213
8 PracticalConsiderationsandExperimentalResultsforHigh-GainFELs 215
8.1 UndulatorTolerancesandWakefields 215
8.1.1 UndulatorErrorsandTolerances 216
8.1.2 BeamTrajectoryErrors 217
8.1.3 WakefieldEffects,EnergyLoss,andUndulatorTapering 220
8.2 FELExperimentalResults 223
8.2.1 SASEFELs 224
8.2.2 SeededFEL 230
viii Contents
8.2.3 Short-PulseGeneration 232
References 237
AppendixA Hamilton’sEquationsofMotiononPhaseSpace 240
A.1 FELParticleEquationsfromTransformationTheory 242
A.2 MotionofaTestElectroninaHigh-GainFEL 244
References 245
AppendixB SimulationMethodsforFELs 246
B.1 TheDesignofFELSimulationCodes 247
B.2 ExistingFELCodes 253
References 254
AppendixC QuantumConsiderationsfortheFEL 255
C.1 TheQuantumFormulation 255
C.2 QuantumNoiseintheFELAmplifier 259
C.3 Madey’sTheorem 265
References 267
AppendixD TransverseGradientUndulators 268
D.1 Low-GainAnalysis 271
D.2 High-GainAnalysis 276
References 278
FurtherReading 279
Index 281
Preface
X-raysproducedwhenhighlyrelativisticelectronsareacceleratedalongacurvedtrajec-
tory,generallyreferredtoassynchrotronradiation,haveservedasanimportanttoolfor
studyingthestructureanddynamicsofvariousatomicandmolecularsystems.Thefirst
dedicatedsynchrotronradiationfacilitywasbuiltinthe1970susinganelectronstorage
ring, and since that time the demand for synchrotron radiation has steadily increased
duetoitshighintensity,narrowangularopening,andbroadspectralcoverage.1Overthe
pastfewdecadestheeffectivenessofsynchrotronradiationhasbeenfurtheradvancedby
improvementsinstorageringdesignthatledtoanincreaseintheelectronbeamphase
spacedensity,andbytheuseofmagneticdevicessuchasundulatorsthatdramatically
increase the X-ray brightness over traditional bending magnets. These developments
havewidenedanddeepenedthereachof“photonsciences”aroundtheglobe.
AnotherrevolutionaryadvanceinX-raygenerationwasmadewiththedevelopment
of X-ray free-electron lasers (FELs). The radiation produced in an FEL acts back on
the electron beam in a positive feedback loop, resulting in X-rays with dramatically
improvedintensityandcoherenceoverthoseproducedwithstorage-ringbasedsources.
TheX-rayFELbecamefeasiblethankstoimprovementsinlinearacceleratortechnology
ingeneral,andinparticulartoadvancesintheinjector(electronsource).
High-brightness,high-energyelectronbeamsfromalinearacceleratorcannowdrive
ahigh-gainX-rayFELamplifierinalongundulator.Thegaincanbesohighthattheini-
tially incoherent undulator radiation evolves to an intense, quasi-coherent field known
as self-amplified spontaneous emission (SASE). The SASE pulse can be made ultra-
shortbyusinganultrashortelectronbunch.WithX-rayFELs,experimentaltechniques
developed for traditional synchrotron light sources can be made much more efficient,
andnewareasofmaterial,chemistry,andbiologyresearch,suchasultrafastdynamics,
havebecomeaccessibletostudy.
The advent of X-ray FELs, however, has by no means rendered other synchrotron
radiation sources obsolete. For certain applications, including those that require high
levelsofstabilityorhighlevelsofaverageflux,synchrotronradiationfromstoragerings
can be more attractive than SASE. Future synchrotron radiation facilities can provide
even brighter X-rays than those that are feasible with the current, “third”-generation
1 Thename“synchrotronradiation”cameaboutbecauseitwasfirstobservedinasynchrotronin1947.
However,theoft-usedpracticeofreferringtothestorageringasa“synchrotronsource”shouldbe
avoided,sincethesourceisastorageringinwhichtheelectronbeamisinasteadystate,ratherthana
synchrotroninwhichelectronsgothroughanaccelerationcycle.