Theory and Design of Charged Particle Beams, Second Edition (Wiley Series in Beam Physics and Accelerator Technology)

677 Pages·2008·4.23 MB·English

by  Martin Reiser

MartinReiser
TheoryandDesignof
ChargedParticleBeams
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Martin Reiser
Theory and Design of
Charged Particle Beams
With Contributions by Patrick O’Shea,
Santiago Bernal, and Rami Kishek
Second,UpdatedandExpandedEdition
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carefullyproduced.Nevertheless,authors,
Prof.Dr.MartinReiser
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TothememoryofIlyaM.Kapchinsky(1919–1993),
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andJohnLawson(1923–2008)

VII
Contents
Prefacefor2ndEdition XIII
Prefacefor1stEdition XVII
Acknowledgmentsfor2ndEdition XXI
Acknowledgmentsfor1stEdition XXV
1 Introduction 1
1.1 Exposition 1
1.2 HistoricalDevelopmentsandApplications 4
1.3 SourcesofChargedParticles 7
References 14
2 ReviewofChargedParticleDynamics 15
2.1 TheLorentzForceandtheEquationofMotion 15
2.2 TheEnergyIntegralandSomeGeneralFormulas 18
2.3 TheLagrangianandHamiltonianFormalisms 22
2.3.1 Hamilton’sPrincipleandLagrange’sEquations 22
2.3.2 GeneralizedPotentialandLagrangianforChargedParticleMotion
inanElectromagneticField 24
2.3.3 Hamilton’sEquationsofMotion 26
2.3.4 TheHamiltonianforChargedParticlesandSomeConservation
Theorems 28
2.4 TheEulerTrajectoryEquations 33
2.4.1 ThePrincipleofLeastActionandtheEulerEquations 33
2.4.2 RelativisticEulerEquationsinAxiallySymmetricFields 36
2.5 AnalyticExamplesofChargedParticleMotion 38
2.5.1 PlanarDiodewithoutSpaceCharge 38
2.5.2 PlanarDiodewithSpaceCharge(Child–LangmuirLaw) 39
2.5.3 ChargedParticleMotioninaUniformMagneticField 40
2.5.4 ChargedParticleMotioninaRadialElectricField 41
VIII Contents
2.5.5 TheHarmonicOscillator 43
Reference 45
Problems 45
3 BeamOpticsandFocusingSystemswithoutSpaceCharge 51
3.1 BeamEmittanceandBrightness 51
3.2 Liouville’sTheorem 57
3.3 TheParaxialRayEquationforAxiallySymmetricSystems 61
3.3.1 SeriesRepresentationofAxisymmetricElectricandMagnetic
Fields 61
3.3.2 DerivationoftheParaxialRayEquation 63
3.3.3 GeneralPropertiesoftheSolutionsoftheParaxialRay
Equations 69
3.4 AxiallySymmetricFieldsasLenses 72
3.4.1 GeneralParametersandTransferMatrixofaLens 72
3.4.2 ImageFormationandMagnification 75
3.4.3 ElectrostaticLenses 78
3.4.4 SolenoidalMagneticLenses 88
3.4.5 EffectsofaLensontheTrace-SpaceEllipseandBeamEnvelope 92
3.4.6 AberrationsinAxiallySymmetricLenses 94
3.5 FocusingbyQuadrupoleLenses 98
3.6 Constant-GradientFocusinginCircularSystems 103
3.6.1 BetatronOscillations 103
3.6.2 TheTrace-SpaceEllipseandBeamEnvelopeinaBetatron-Type
Field 107
3.6.3 FocusinginAxisymmetricE×BFields 111
3.6.4 EnergySpread,MomentumCompaction,andEffectiveMass 114
3.7 SectorMagnetsandEdgeFocusing 119
3.8 PeriodicFocusing 122
3.8.1 PeriodicFocusingwithThinLenses 122
3.8.2 GeneralTheoryofCourantandSnyder 128
3.8.3 TheFODOQuadrupoleChannel 135
3.8.4 Sector-FocusingCyclotrons 137
3.8.5 Strong-FocusingSynchrotrons 143
3.8.6 ResonancesinCircularAccelerators 146
3.9 AdiabaticDampingoftheBetatronOscillationAmplitudes 151
References 154
Problems 154
4 LinearBeamOpticswithSpaceCharge 163
4.1 TheoreticalModelsofBeamswithSpaceCharge 163
4.2 AxisymmetricBeamsinDriftSpace 170
4.2.1 LaminarBeamwithUniformDensityProfile 170