RF Linear Accelerators

465 Pages·2010·3.27 MB·English

ThomasP.Wangler
RFLinearAccelerators
Related Titles
Padamsee,H. Reiser,M.
RFSuperconductivity TheoryandDesignofCharged
ParticleBeams
Science,Technology&Applications
1994
2008
ISBN:978-0-471-30616-0
ISBN:978-3-527-40572-5
Edwards,D.A.,Syphers,M.J.
Brown,I.G.(ed.)
AnIntroductiontothePhysics
ThePhysicsandTechnologyof
ofHighEnergyAccelerators
IonSources
1993
2004
ISBN:978-0-471-55163-8
ISBN:978-3-527-40410-0
Thomas P. Wangler
RF Linear Accelerators
2nd completely revised and enlarged edition
TheAuthor (cid:1) AllbookspublishedbyWiley-VCHarecarefully
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ISBN:978-3-527-40680-7
V
Contents
PrefacetotheSecondEdition XI
PrefacetotheFirstEdition XIII
1 Introduction 1
1.1 LinearAccelerators:HistoricalPerspective 2
1.2 LinacStructures 6
1.3 LinacBeamDynamics 10
1.4 MultiparticleEffects 12
1.5 ApplicationsofModernRFLinacs 13
1.6 Accelerator-Physics
Units,UnitConversions,andPhysicalConstants 15
1.7 UsefulRelativisticMechanicsRelationships 16
1.8 Maxwell’sEquations 17
1.9 ConductingWalls 19
1.10 GroupVelocityandEnergyVelocity 20
1.11 CoaxialResonator 22
1.12 Transverse-MagneticModeofaCircularCylindricalCavity 24
1.13 CylindricalResonatorTransverse-MagneticModes 26
1.14 CylindricalResonatorTransverseElectricModes 27
References 30
2 RFAccelerationinLinacs 32
2.1 ParticleAccelerationinanRFField 32
2.2 EnergyGainonAxisinanRFGap 33
2.3 LongitudinalElectricFieldasaFourierIntegral 36
2.4 Transit-Time-FactorModels 39
2.5 PowerandAccelerationEfficiencyFiguresofMerit 42
2.6 CavityDesignIssues 44
2.7 FrequencyScalingofCavityParameters 46
2.8 LinacEconomics 47
References 52
RFLinearAccelerators.2nd,completelyrevisedandenlargededition.
ThomasP.Wangler
Copyright2008Wiley-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40680-7
VI Contents
3 PeriodicAcceleratingStructures 53
3.1 SynchronousAccelerationandPeriodicStructures 53
3.2 FloquetTheoremandSpaceHarmonics 54
3.3 GeneralDescriptionofPeriodicStructures 57
3.4 EquivalentCircuitModelforPeriodicStructures 59
3.5 PeriodicArrayofLow-PassFilters 61
3.6 PeriodicArrayofElectricallyCoupledCircuits 62
3.7 PeriodicArrayofMagneticallyCoupledCircuits 63
3.8 PeriodicArrayofCavitieswithResonantCouplingElement 64
3.9 MeasurementofDispersionCurvesinPeriodicStructures 65
3.10 Traveling-WaveLinacStructures 68
3.11 AnalysisofthePeriodicIris-LoadedWaveguide 69
3.12 Constant-ImpedanceTraveling-WaveStructure 72
3.13 Constant-GradientStructure 74
3.14 CharacteristicsofNormalModesforParticleAcceleration 76
3.15 Physics
RegimesofTraveling-WaveandStanding-WaveStructures 79
References 81
4 StandardLinacStructures 83
4.1 Independent-CavityLinacs 83
4.2 Widero¨eLinac 87
4.3 H-ModeStructures 89
4.4 AlvarezDrift-TubeLinac 91
4.5 DesignofDrift-TubeLinacs 96
4.6 Coupled-CavityLinacs 98
4.7 ThreeCoupledOscillators 99
4.8 Perturbation
TheoryandEffectsofResonant-FrequencyErrors 101
4.9 EffectsfromOhmicPowerDissipation 103
4.10 GeneralProblemofN+1CoupledOscillators 105
4.11 BiperiodicStructuresforLinacs 108
4.12 DesignofCoupled-CavityLinacs 111
4.13 IntercellCouplingConstant 114
4.14 DecouplingofCavitiesConnectedbyaBeamPipe 116
4.15 ResonantCoupling 117
4.16 AcceleratingStructuresforSuperconductingLinacs 121
λ/4SuperconductingStructures 121
λ/2SuperconductingStructures 121
TMSuperconductingStructures 122
RFPropertiesand
ScalingLawsforTMandλ/2SuperconductingStructures 125
Shunt
ImpedanceforTMandλ/2SuperconductingStructures 127
StoredEnergyforTMandλ/2SuperconductingStructures 129
Contents VII
ScalingFormulasforλ/4SuperconductingStructures 131
References 133
5 MicrowaveTopicsforLinacs 135
5.1 ShuntResonantCircuitModel 135
5.2 TheoryofResonantCavities 137
5.3 CouplingtoCavities 138
5.4 EquivalentCircuitforaResonant-CavitySystem 139
5.5 EquivalentCircuitforaCavityCoupledtotwoWaveguides 144
5.6 TransientBehaviorofaResonant-CavitySystem 146
5.7 WaveDescriptionofaWaveguide-to-CavityCoupling 148
5.8 MicrowavePowerSystemsforLinacs 156
5.9 Multipacting 159
5.10 ElectronFieldEmission 162
5.11 RFElectricBreakdown:KilpatrickCriterion 163
5.12 AdiabaticInvariantofanOscillator 164
5.13 SlaterPerturbationTheorem 165
5.14 QuasistaticApproximation 167
5.15 Panofsky–WenzelTheorem 168
References 173
6 LongitudinalParticleDynamics 175
6.1 LongitudinalFocusing 175
6.2 Difference
EquationsofLongitudinalMotionforStanding-WaveLinacs 177
6.3 DifferentialEquationsofLongitudinalMotion 178
6.4 LongitudinalMotionwhenAccelerationRateisSmall 178
6.5 HamiltonianandLiouville’sTheorem 182
6.6 SmallAmplitudeOscillations 186
6.7 AdiabaticPhaseDamping 187
6.8 Longitudinal
DynamicsofIonBeamsinCoupled-CavityLinacs 189
6.9 LongitudinalDynamicsinIndependent-CavityIonLinacs 190
6.10 Longitudinal
DynamicsofLow-EnergyBeamsInjectedintoav=cLinac 192
6.11 RfBunching 194
6.12 LongitudinalBeamDynamicsinH-ModeLinacStructures 196
References 199
7 TransverseParticleDynamics 201
7.1 TransverseRFFocusingandDefocusing 201
7.2 RadialImpulsefromaSynchronousTravelingWave 203
7.3 RadialImpulseneartheAxisinanAcceleratingGap 204
7.4 IncludingElectrostaticFocusingintheGap 207
7.5 CoordinateTransformationthroughanAcceleratingGap 208
VIII Contents
7.6 QuadrupoleFocusinginaLinac 209
7.7 Transfer-MatrixSolutionofHill’sEquation 211
7.8 Phase-AmplitudeFormofSolutiontoHill’sEquation 213
7.9 TransferMatrixthroughOnePeriod 214
7.10 Thin-LensFODOPeriodicLattice 215
7.11 TransverseStabilityPlotinaLinac 217
7.12 EffectsofRandomQuadrupoleMisalignmentErrors 218
7.13 EllipseTransformations 221
7.14 BeamMatching 222
7.15 Current-IndependentBeamMatching 224
7.16 SolenoidFocusing 225
7.17 SmoothApproximationtoLinacPeriodicFocusing 226
7.18 RadialMotionforUnfocusedRelativisticBeams 227
References 230
8 RadiofrequencyQuadrupoleLinac 232
8.1 PrinciplesofOperation 232
8.2 GeneralPotentialFunction 236
8.3 Two-TermPotentialFunctionDescription 238
8.4 ElectricFields 240
8.5 SynchronousAcceleration 241
8.6 LongitudinalDynamics 242
8.7 TransverseDynamics 243
8.8 AdiabaticBunchingintheRFQ 245
8.9 Four-VaneCavity 248
8.10 Lumped-CircuitModelofFour-VaneCavity 249
8.11 Four-VaneCavityEigenmodes 251
8.12 Transmission-LineModelofQuadrupoleSpectrum 254
8.13 Radial-MatchingSection 260
8.14 RFQTransitionCell 265
8.15 BeamEllipsesinanRFQ 271
8.16 TuningfortheDesiredFieldDistributioninanRFQ 273
8.17 Four-RodCavity 274
8.18 FourVanewithWindowsRFQ 276
References 280
9 MultiparticleDynamicswithSpaceCharge 282
9.1 BeamQuality,PhaseSpace,andEmittance 283
9.2 RMSEmittance 285
9.3 TransverseandLongitudinalEmittance 287
9.4 EmittanceConventions 288
9.5 Space-ChargeDynamics 289
9.6 PracticalMethodsforNumericalSpace-ChargeCalculations 292
9.7 RMSEnvelopeEquationwithSpaceCharge 296
9.8 ContinuousEllipticalBeams 297
Contents IX
9.9 Three-DimensionalEllipsoidalBunchedBeams 299
9.10 BeamDynamicsIncludingLinearSpace-ChargeField 300
9.11 Beam-CurrentLimitsfromSpaceCharge 302
9.12 OverviewofEmittanceGrowthfromSpaceCharge 303
9.13 EmittanceGrowthforrmsMatchedBeams 306
9.14 ModelofSpace-Charge-InducedEmittanceGrowthinaLinac 314
9.15 EmittanceGrowthforrmsMismatchedBeams 316
9.16 Space-ChargeInstabilities
inRFLinacsfromPeriodicFocusing:StructureResonances 318
9.17 Longitudinal-TransverseCoupling
andSpace-ChargeInstabilitiesforAnisotropicLinacBeams 319
9.18 BeamLossandBeamHalo 325
9.19 LosAlamosBeamHaloExperiment 329
9.20 ScalingofEmittanceGrowthandHalo 331
9.21 Longitudinal
BeamDynamicsConstraintontheAcceleratingGradient 332
References 338
10 BeamLoading 341
10.1 FundamentalBeam-LoadingTheorem 342
10.2 TheSingle-BunchLossParameter 344
10.3 EnergyLosstoHigher-OrderCavityModes 344
10.4 BeamLoadingintheAcceleratingMode 345
10.5 EquationsDescribingaBeam-LoadedCavity 347
GeneralResults 348
OptimumDetuning 350
ExtremeBeam-LoadedLimit 351
NumericalExampleofaBeam-LoadedCavity 351
ExampleofaHeavilyBeam-LoadedSuperconductingCavity
withBunchesInjectedontheCrestoftheAcceleratingWave 352
10.6 Generator
PowerwhentheBeamCurrentisLessthanDesignValue 352
10.7 TransientTurn-OnofaBeam-LoadedCavity 354
References 360
11 Wakefields 361
11.1 ImageForceforLineChargeinRoundPipe 362
11.2 Fieldsfrom
aRelativisticPointChargeandIntroductiontoWakefields 364
11.3 WakePotentialfromaRelativisticPointCharge 367
11.4 WakePotentialsinCylindricallySymmetricStructures 368
11.5 ScalingofWakePotentialswithFrequency 370
11.6 BunchWakePotentialsforanArbitraryChargeDistribution 371
11.7 LossParametersforaParticularChargeDistribution 376
11.8 BunchLossParametersforaGaussianDistribution 377
11.9 Beam-CouplingImpedance 378
X Contents
11.10 Longitudinal-andTransverse-ImpedanceDefinitions 380
11.11 ImpedanceandWakePotentialforaSingleCavityMode 381
11.12 Short-RangeWakefields-ParasiticLosses 383
11.13 Short-RangeWakefields:EnergySpread 383
11.14 Short-Range
Wakefields:CompensationofLongitudinalWakeEffect 384
11.15 Short-RangeWakefields:Single-BunchBeamBreakup 384
11.16 Short-RangeWakefields:BNSDampingofBeamBreakup 386
11.17 Long-RangeWakefieldsandMultibunchBeamBreakup 389
11.18 MultipassBBUinRecirculatingElectronLinacs 397
References 402
12 SpecialStructuresandTechniques 405
12.1 Alternating-PhaseFocusing 405
12.2 AcceleratingStructuresUsingElectricFocusing 406
12.3 Coupled-CavityDrift-TubeLinac 410
12.4 BeamFunneling 411
12.5 RFPulseCompression 413
12.6 SuperconductingRFLinacs 414
BriefHistory 415
Introduction
tothePhysicsandTechnologyofRFSuperconductivity 416
12.7 ExamplesofOperatingSuperconductingLinacs 419
Atlas 419
CEBAF 419
SpallationNeutronSource 421
12.8 FutureSuperconductingLinacFacilities 423
InternationalLinearCollider 423
Next-GenerationRareIsotopeFacility 426
Free-ElectronLasers 427
References 430
Index 433