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 В 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 of a 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 ............................. 536
7.3.1. Major Milestones before 1993 ................ 536
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
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