| | Contents | |
| | | |
| |
| | Preface for 2nd Edition | XIII |
| | Preface for 1st Edition | XVII |
| | Acknowledgments for 2nd Edition | XXI |
| | Acknowledgments for 1st Edition | XXV |
| 1 | Introduction | 1 |
| 1.1 | Exposition | 1 |
| 1.2 | Historical Developments and Applications | 4 |
| 1.3 | Sources of Charged Particles | 7 |
| | References | 14 |
| 2 | Review of Charged Particle Dynamics | 15 |
| 2.1 | The Lorentz Force and the Equation of Motion | 15 |
| 2.2 | The Energy Integral and Some General Formulas | 18 |
| 2.3 | The Lagrangian and Hamiltonian Formalisms | 22 |
| 2.3.1 | Hamilton’s Principle and Lagrange’s Equations | 22 |
| 2.3.2 | Generalized Potential and Lagrangian for Charged Particle Motion in an Electromagnetic Field | 24 |
| 2.3.3 | Hamilton’s Equations of Motion | 26 |
| 2.3.4 | The Hamiltonian for Charged Particles and Some Conservation Theorems | 28 |
| 2.4 | The Euler Trajectory Equations | 33 |
| 2.4.1 | The Principle of Least Action and the Euler Equations | 33 |
| 2.4.2 | Relativistic Euler Equations in Axially Symmetric Fields | 36 |
| 2.5 | Analytic Examples of Charged Particle Motion | 38 |
| 2.5.1 | Planar Diode without Space Charge | 38 |
| 2.5.2 | Planar Diode with Space Charge(Child–Langmuir Law) | 39 |
| 2.5.3 | Charged Particle Motion in a Uniform Magnetic Field | 40 |
| 2.5.4 | Charged Particle Motion in a Radial Electric Field | 41 |
| 2.5.5 | The Harmonic Oscillator | 43 |
| | Reference | 45 |
| | Problems | 45 |
| 3 | Beam Optics and Focusing Systems without Space Charge | 51 |
| 3.1 | Beam Emittance and Brightness | 51 |
| 3.2 | Liouville’s Theorem | 57 |
| 3.3 | The Paraxial Ray Equation for Axially Symmetric Systems | 61 |
| 3.3.1 | Series Representation of Axisymmetric Electric and Magnetic Fields | 61 |
| 3.3.2 | Derivation of the Paraxial Ray Equation | 63 |
| 3.3.3 | General Properties of the Solutions of the Paraxial Ray Equations | 69 |
| 3.4 | Axially Symmetric Fields as Lenses | 72 |
| 3.4.1 | General Parameters and Transfer Matrix of a Lens | 72 |
| 3.4.2 | Image Formation and Magnification | 75 |
| 3.4.3 | Electrostatic Lenses | 78 |
| 3.4.4 | Solenoidal Magnetic Lenses | 88 |
| 3.4.5 | Effects of a Lens on the Trace-Space Ellipse and Beam Envelope | 92 |
| 3.4.6 | Aberrations in Axially Symmetric Lenses | 94 |
| 3.5 | Focusing by Quadrupole Lenses | 98 |
| 3.6 | Constant-Gradient Focusing in Circular Systems | 103 |
| 3.6.1 | Betatron Oscillations | 103 |
| 3.6.2 | The Trace-Space Ellipse and Beam Envelope in a Betatron-Type Field | 107 |
| 3.6.3 | Focusing in Axisymmetric E x B Fields | 111 |
| 3.6.4 | Energy Spread, Momentum Compaction, and Effective Mass | 114 |
| 3.7 | Sector Magnets and Edge Focusing | 119 |
| 3.8 | Periodic Focusing | 122 |
| 3.8.1 | Periodic Focusing with Thin Lenses | 122 |
| 3.8.2 | General Theory of Courant and Snyder | 128 |
| 3.8.3 | The FODO Quadrupole Channel | 135 |
| 3.8.4 | Sector-Focusing Cyclotrons | 137 |
| 3.8.5 | Strong-Focusing Synchrotrons | 143 |
| 3.8.6 | Resonances in Circular Accelerators | 146 |
| 3.9 | Adiabatic Damping of the Betatron Oscillation Amplitudes | 151 |
| | References | 154 |
| | Problems | 154 |
| 4 | Linear Beam Optics with Space Charge | 163 |
| 4.1 | Theoretical Models of Beams with Space Charge | 163 |
| 4.2 | Axisymmetric Beams in Drift Space | 170 |
| 4.2.1 | Laminar Beam with Uniform Density Profile | 170 |
| 4.2.2 | Beam Envelope with Self Fields and Finite Emittance | 180 |
| 4.2.3 | Limitations of the Uniform Beam Model and Limiting Currents | 181 |
| 4.2.4 | Self-Focusing ofa Charge-Neutralized Beam (Bennett Pinch) | 185 |
| 4.3 | Axisymmetric Beams with Applied and Self Fields | 187 |
| 4.3.1 | The Paraxial Ray Equation with Self Fields | 187 |
| 4.3.2 | Beam Transport in a Uniform Focusing Channel | 189 |
| 4.4 | Periodic Focusing of Intense Beams(Smooth-Approximation Theory) | 197 |
| 4.4.1 | Beam Transport in a Periodic Solenoid Channel | 197 |
| 4.4.2 | Beam Transport in a Quadrupole (FODO) Channel | 209 |
| 4.4.3 | Envelope Oscillations and Instabilities of Mismatched Beams | 214 |
| 4.4.4 | Coherent Beam Oscillations due to Injection Errors and Misalignments | 224 |
| 4.5 | Space-Charge Tune Shift and Current Limits in Circular Accelerators | 233 |
| 4.5.1 | Betatron Tune Shift due to Self Fields | 233 |
| 4.5.2 | Current Limits in Weak-and Strong-Focusing Systems | 236 |
| 4.5.3 | Effects of Image Forces on Coherent and Incoherent Betatron Tune | 238 |
| 4.6 | Charge Neutralization Effects | 243 |
| 4.6.1 | Ionization Cross Sections for Electron and Proton Beams in Various Gases | 243 |
| 4.6.2 | Linear Beam Model with Charge Neutralization | 248 |
| 4.6.3 | Gas Focusing in Low-Energy Proton and H- Beams | 250 |
| 4.6.4 | Charge-Neutralization Effects in Intense Relativistic Electron Beams | 254 |
| 4.6.5 | Charge-Neutralization Effects in High-Energy Synchrotrons and Storage Rings | 258 |
| 4.6.6 | Plasma Lenses | 262 |
| | References | 265 |
| | Problems | 266 |
| 5 | Self-Consistent Theory of Beams | 273 |
| 5.1 | Introduction | 273 |
| 5.2 | Laminar Beams in Uniform Magnetic Fields | 275 |
| 5.2.1 | A Cylindrical Beam in an Infinitely Strong Magnetic Field | 275 |
| 5.2.2 | Nonrelativistic Laminar Beam Equilibria | 279 |
| 5.2.3 | Relativistic Laminar Beam Equilibria | 290 |
| 5.2.4 | Paraxial Analysis of Mismatched Laminar Beams in Uniform Magnetic Fields | 297 |
| 5.3 | The Vlasov Model of Beams with Momentum Spread | 300 |
| 5.3.1 | The Vlasov Equation | 300 |
| 5.3.2 | The Kapchinsky–Vladimirsky(K–V) Distribution | 306 |
| 5.3.3 | Stationary Distributions in a Uniform Focusing Channel | 311 |
| 5.3.4 | RMS Emittance and the Concept of Equivalent Beams | 320 |
| 5.4 | The Maxwell–Boltzmann Distribution | 326 |
| 5.4.1 | Coulomb Collisions between Particles and Debye Shielding | 326 |
| 5.4.2 | The Fokker–Planck Equation | 329 |
| 5.4.3 | The Maxwell–Boltzmann Distribution for a Relativistic Beam | 333 |
| 5.4.4 | The Stationary Transverse Distribution in a Uniform or Smooth Focusing Channel | 339 |
| 5.4.5 | Transverse Temperature and Beam-Size Variations in Nonuniform Focusing Channels | 349 |
| 5.4.6 | The Longitudinal Distribution and Beam Cooling due to Acceleration | 352 |
| 5.4.7 | Stationary Line-Charge Density Profiles in Bunched Beams | 359 |
| 5.4.8 | Longitudinal Motion in rf Fields and the Parabolic Bunch Model | 371 |
| 5.4.9 | Longitudinal Beam Dynamics in Circular Machines | 382 |
| 5.4.10 | Effects of Momentum Spread on the Transverse Distribution | 389 |
| 5.4.11 | Coupled Envelope Equations for a Bunched Beam | 399 |
| 5.4.12 | Matching, Focusing, and Imaging | 404 |
| | References | 412 |
| | Problems | 413 |
| 6 | Emittance Growth | 419 |
| 6.1 | Causes of Emittance Change | 419 |
| 6.2 | Free Energy and Emittance Growth in Nonstationary Beams | 422 |
| 6.2.1 | Analytical Theory | 422 |
| 6.2.2 | Comparison of Theory, Simulation, and Experiment | 430 |
| 6.3 | Instabilities | 442 |
| 6.3.1 | Transverse Beam Modes and Instabilities in Periodic Focusing Channels | 442 |
| 6.3.2 | Longitudinal Space-Charge Waves and Resistive-Wall Instability | 448 |
| 6.3.3 | Longitudinal Instability in Circular Machines and Landau Damping | 463 |
| 6.4 | Collisions | 472 |
| 6.4.1 | The Boersch Effect | 472 |
| 6.4.2 | Intrabeam Scattering in Circular Machines | 476 |
| 6.4.3 | Multiple Scattering in a Background Gas | 483 |
| 6.5 | Beam Cooling Methods in Storage Rings | 486 |
| 6.5.1 | The Need for Emittance Reduction | 486 |
| 6.5.2 | Electron Cooling | 487 |
| 6.5.3 | Stochastic Cooling | 489 |
| 6.5.4 | Radiation Cooling | 491 |
| 6.6 | Concluding Remarks | 497 |
| | References | 501 |
| | Problems | 504 |
| 7 | Beam Physics Research from 1993 to 2007 | 507 |
| 7.1 | Introduction | 507 |
| 7.2 | Longitudinal Beam Physics Research | 507 |
| 7.2.1 | Studies in the Long Periodic Solenoid Channel | 507 |
| 7.2.2 | Resistive-Wall Instability Studies in a Long Solenoid Experiment | 508 |
| 7.2.3 | Studies of Energy Spread due to Coulomb Collisions | 510 |
| 7.3 | Transverse Beam Physics | 516 |
| 7.3.1 | Major Milestones before 1993 | 516 |
| 7.3.2 | Overview of Milestones Since 1993 | 518 |
| 7.3.2.1 | Definitions | 518 |
| 7.3.2.2 | The Parameter Range and Characterization of Charged Particle Beams | 520 |
| 7.3.3 | Theoretical Research on Beam Mismatch and Halo Formation | 522 |
| 7.3.4 | Resonances and Instabilities | 526 |
| 7.3.5 | Equipartitioning and Stability of Anisotropic Beams | 528 |
| 7.3.6 | Related Experiments (with contributions by Santiago Bernal and Rami Kishek) | 535 |
| 7.3.6.1 | The Bernal Experiments | 535 |
| 7.3.6.2 | The Los Alamos Low-Energy Demonstration Accelerator (LEDA) | 537 |
| 7.3.6.3 | The Paul Trap Simulator Experiment (PTSX) at the Princeton Plasma Physics Laboratory | 540 |
| 7.4 | The University of Maryland Electron Ring | 544 |
| 7.4.1 | History and Developments of the Ring Concept | 544 |
| 7.4.2 | Scaling Laws for Charged Particle Beams (with contributions by Santiago Bernal) | 548 |
| 7.4.3 | Construction and Initial Operation of UMER | 553 |
| 7.4.4 | Other Ring Experiments and Theory | 562 |
| 7.4.4.1 | The LLNL Heavy Ion Recirculator | 562 |
| 7.4.4.2 | The Small Isochronous Ring(SIR) Project at Michigan State University(MSU) | 564 |
| 7.4.4.3 | The Proton Storage Rings (PSR) of the Institute for Nuclear Physics(INP) at Novosibirsk | 565 |
| 7.4.4.4 | The Intersecting Storage Rings (ISR) at CERN | 571 |
| 7.5 | Issues Related to Electron Photoinjectors | 577 |
| 7.5.1 | The Problem | 577 |
| 7.5.2 | Background | 578 |
| 7.5.3 | Space-Charge Limited Current and Instabilities in Photoinjectors | 579 |
| 7.5.4 | UMER and Related Experiments on Longitudinal Perturbations | 581 |
| 7.6 | Concluding Remarks | 583 |
| | References | 586 |
| | Problems | 594 |
| | Appendix 1. Example of a Pierce-Type Electron Gun with Shielded Cathode | 599 |
| | References | 601 |
| | Appendix 2. Example of a Magnetron Injection Gun | 603 |
| | References | 605 |
| | Appendix 3. Four-Vectors and Covariant Lorentz Transformations | 607 |
| | References | 617 |
| | Appendix 4. Equipartitioning in High-Current rf Linacs | 611 |
| | References | 625 |
| | Appendix 5. Radial Defocusing and Emittance Growth in High-Gradient rf Structures (Example: The rf Photocathode Electron Gun) | 619 |
| | References | 625 |
| | List of Frequently Used Symbols | 627 |
| | Bibliography (Selected List of Books) | 635 |
| | Index | 639 |
