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

Theory and Design of Charged Particle Beams......Page 5
Contents......Page 9
Preface for 2(nd) Edition......Page 15
Preface for 1(st) Edition......Page 19
Acknowledgments for 2(nd) Edition......Page 23
Acknowledgments for 1(st) Edition......Page 27
1.1 Exposition......Page 31
1.2 Historical Developments and Applications......Page 34
1.3 Sources of Charged Particles......Page 37
References......Page 44
2.1 The Lorentz Force and the Equation of Motion......Page 45
2.2 The Energy Integral and Some General Formulas......Page 48
2.3.1 Hamilton’s Principle and Lagrange’s Equations......Page 52
2.3.2 Generalized Potential and Lagrangian for Charged Particle Motion in an Electromagnetic Field......Page 54
2.3.3 Hamilton’s Equations of Motion......Page 56
2.3.4 The Hamiltonian for Charged Particles and Some Conservation Theorems......Page 58
2.4.1 The Principle of Least Action and the Euler Equations......Page 63
2.4.2 Relativistic Euler Equations in Axially Symmetric Fields......Page 66
2.5.1 Planar Diode without Space Charge......Page 68
2.5.2 Planar Diode with Space Charge (Child–Langmuir Law)......Page 69
2.5.3 Charged Particle Motion in a Uniform Magnetic Field......Page 70
2.5.4 Charged Particle Motion in a Radial Electric Field......Page 71
2.5.5 The Harmonic Oscillator......Page 73
Problems......Page 75
3.1 Beam Emittance and Brightness......Page 81
3.2 Liouville’s Theorem......Page 87
3.3.1 Series Representation of Axisymmetric Electric and Magnetic Fields......Page 91
3.3.2 Derivation of the Paraxial Ray Equation......Page 93
3.3.3 General Properties of the Solutions of the Paraxial Ray Equations......Page 99
3.4.1 General Parameters and Transfer Matrix of a Lens......Page 102
3.4.2 Image Formation and Magnification......Page 105
3.4.3 Electrostatic Lenses......Page 108
3.4.4 Solenoidal Magnetic Lenses......Page 118
3.4.5 Effects of a Lens on the Trace-Space Ellipse and Beam Envelope......Page 122
3.4.6 Aberrations in Axially Symmetric Lenses......Page 124
3.5 Focusing by Quadrupole Lenses......Page 128
3.6.1 Betatron Oscillations......Page 133
3.6.2 The Trace-Space Ellipse and Beam Envelope in a Betatron-Type Field......Page 137
3.6.3 Focusing in Axisymmetric E × B Fields......Page 141
3.6.4 Energy Spread, Momentum Compaction, and Effective Mass......Page 144
3.7 Sector Magnets and Edge Focusing......Page 149
3.8.1 Periodic Focusing with Thin Lenses......Page 152
3.8.2 General Theory of Courant and Snyder......Page 158
3.8.3 The FODO Quadrupole Channel......Page 165
3.8.4 Sector-Focusing Cyclotrons......Page 167
3.8.5 Strong-Focusing Synchrotrons......Page 173
3.8.6 Resonances in Circular Accelerators......Page 176
3.9 Adiabatic Damping of the Betatron Oscillation Amplitudes......Page 181
Problems......Page 184
4.1 Theoretical Models of Beams with Space Charge......Page 193
4.2.1 Laminar Beam with Uniform Density Profile......Page 200
4.2.2 Beam Envelope with Self Fields and Finite Emittance......Page 210
4.2.3 Limitations of the Uniform Beam Model and Limiting Currents......Page 211
4.2.4 Self-Focusing of a Charge-Neutralized Beam (Bennett Pinch)......Page 215
4.3.1 The Paraxial Ray Equation with Self Fields......Page 217
4.3.2 Beam Transport in a Uniform Focusing Channel......Page 219
4.4.1 Beam Transport in a Periodic Solenoid Channel......Page 227
4.4.2 Beam Transport in a Quadrupole (FODO) Channel......Page 239
4.4.3 Envelope Oscillations and Instabilities of Mismatched Beams......Page 244
4.4.4 Coherent Beam Oscillations due to Injection Errors and Misalignments......Page 254
4.5.1 Betatron Tune Shift due to Self Fields......Page 263
4.5.2 Current Limits in Weak- and Strong-Focusing Systems......Page 266
4.5.3 Effects of Image Forces on Coherent and Incoherent Betatron Tune......Page 268
4.6.1 Ionization Cross Sections for Electron and Proton Beams in Various Gases......Page 273
4.6.2 Linear Beam Model with Charge Neutralization......Page 278
4.6.3 Gas Focusing in Low-Energy Proton and H(–) Beams......Page 280
4.6.4 Charge-Neutralization Effects in Intense Relativistic Electron Beams......Page 284
4.6.5 Charge-Neutralization Effects in High-Energy Synchrotrons and Storage Rings......Page 288
4.6.6 Plasma Lenses......Page 292
References......Page 295
Problems......Page 296
5.1 Introduction......Page 303
5.2.1 A Cylindrical Beam in an Infinitely Strong Magnetic Field......Page 305
5.2.2 Nonrelativistic Laminar Beam Equilibria......Page 309
5.2.3 Relativistic Laminar Beam Equilibria......Page 320
5.2.4 Paraxial Analysis of Mismatched Laminar Beams in Uniform Magnetic Fields......Page 327
5.3.1 The Vlasov Equation......Page 330
5.3.2 The Kapchinsky–Vladimirsky (K–V) Distribution......Page 336
5.3.3 Stationary Distributions in a Uniform Focusing Channel......Page 341
5.3.4 RMS Emittance and the Concept of Equivalent Beams......Page 350
5.4.1 Coulomb Collisions between Particles and Debye Shielding......Page 356
5.4.2 The Fokker–Planck Equation......Page 359
5.4.3 The Maxwell–Boltzmann Distribution for a Relativistic Beam......Page 363
5.4.4 The Stationary Transverse Distribution in a Uniform or Smooth Focusing Channel......Page 369
5.4.5 Transverse Temperature and Beam-Size Variations in Nonuniform Focusing Channels......Page 379
5.4.6 The Longitudinal Distribution and Beam Cooling due to Acceleration......Page 382
5.4.7 Stationary Line-Charge Density Profiles in Bunched Beams......Page 389
5.4.8 Longitudinal Motion in rf Fields and the Parabolic Bunch Model......Page 401
5.4.9 Longitudinal Beam Dynamics in Circular Machines......Page 412
5.4.10 Effects of Momentum Spread on the Transverse Distribution......Page 419
5.4.11 Coupled Envelope Equations for a Bunched Beam......Page 429
5.4.12 Matching, Focusing, and Imaging......Page 434
References......Page 442
Problems......Page 443
6.1 Causes of Emittance Change......Page 449
6.2.1 Analytical Theory......Page 452
6.2.2 Comparison of Theory, Simulation, and Experiment......Page 460
6.3.1 Transverse Beam Modes and Instabilities in Periodic Focusing Channels......Page 472
6.3.2 Longitudinal Space-Charge Waves and Resistive-Wall Instability......Page 478
6.3.3 Longitudinal Instability in Circular Machines and Landau Damping......Page 493
6.4.1 The Boersch Effect......Page 502
6.4.2 Intrabeam Scattering in Circular Machines......Page 506
6.4.3 Multiple Scattering in a Background Gas......Page 513
6.5.1 The Need for Emittance Reduction......Page 516
6.5.2 Electron Cooling......Page 517
6.5.3 Stochastic Cooling......Page 519
6.5.4 Radiation Cooling......Page 521
6.6 Concluding Remarks......Page 527
References......Page 531
Problems......Page 534
7.2.1 Studies in the Long Periodic Solenoid Channel......Page 537
7.2.2 Resistive-Wall Instability Studies in a Long Solenoid Experiment......Page 538
7.2.3 Studies of Energy Spread due to Coulomb Collisions......Page 540
7.3.1 Major Milestones before 1993......Page 546
7.3.2.1 Definitions......Page 548
7.3.2.2 The Parameter Range and Characterization of Charged Particle Beams......Page 550
7.3.3 Theoretical Research on Beam Mismatch and Halo Formation......Page 552
7.3.4 Resonances and Instabilities......Page 556
7.3.5 Equipartitioning and Stability of Anisotropic Beams......Page 558
7.3.6.1 The Bernal Experiments......Page 565
7.3.6.2 The Los Alamos Low-Energy Demonstration Accelerator (LEDA)......Page 567
7.3.6.3 The Paul Trap Simulator Experiment (PTSX) at the Princeton Plasma Physics Laboratory......Page 570
7.4.1 History and Developments of the Ring Concept......Page 574
7.4.2 Scaling Laws for Charged Particle Beams (with contributions by Santiago Bernal)......Page 578
7.4.3 Construction and Initial Operation of UMER......Page 583
7.4.4.1 The LLNL Heavy Ion Recirculator......Page 592
7.4.4.2 The Small Isochronous Ring (SIR) Project at Michigan State University (MSU)......Page 594
7.4.4.3 The Proton Storage Rings (PSR) of the Institute for Nuclear Physics (INP) at Novosibirsk......Page 595
7.4.4.4 The Intersecting Storage Rings (ISR) at CERN......Page 601
7.5.1 The Problem......Page 607
7.5.2 Background......Page 608
7.5.3 Space-Charge Limited Current and Instabilities in Photoinjectors......Page 609
7.5.4 UMER and Related Experiments on Longitudinal Perturbations......Page 611
7.6 Concluding Remarks......Page 613
References......Page 616
Problems......Page 624
Appendix 1. Example of a Pierce-Type Electron Gun with Shielded Cathode......Page 629
Appendix 2. Example of a Magnetron Injection Gun......Page 633
Appendix 3. Four-Vectors and Covariant Lorentz Transformations......Page 637
Appendix 4. Equipartitioning in High-Current rf Linacs......Page 641
Appendix 5. Radial Defocusing and Emittance Growth in High-Gradient rf Structures (Example: The rf Photocathode Electron Gun)......Page 649
List of Frequently Used Symbols......Page 657
Bibliography (Selected List of Books)......Page 665
Index......Page 669