Physics Of Intense Charged Particle Beams In High Energy Accelerators - Ronald C Davidson

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Physics Of Intense Charged Particle Beams In High Energy Accelerators

By: Ronald C Davidson, Qin Hong

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Hardcover | 23 October 2001

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604 Pages

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This is a graduate-level text - complete with 75 assigned problems - which covers a broad range of topics related to the fundamental properties of collective processes and nonlinear dynamics of intense charged particle beams in periodic focusing accelerators and transport systems. The subject matter is treated systematically from first principles, using a unified theoretical approach, and the emphasis is on the development of basic concepts that illustrate the underlying physical processes in circumstances where intense self fields play a major role in determining the evolution of the system. The theoretical analysis includes the full influence of dc space charge and intense self-field effects on detailed equilibrium, stability and transport properties, and is valid over a wide range of system parameters ranging from moderate-intensity, moderate-emittance beams to very-high-intensity, low-emittance beams. The statistical models used to describe the properties of intense charged particle beams are based on the Vlasov-Maxwell equations, the macroscopic fluid-Maxwell equations, or the Klimontovich-Maxwell equations, as appropriate.

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Non-Fiction Science Physics Nuclear Physics Particle & High-Energy Physics Mathematics Applied Mathematics Chaos Theory Booktopia Publisher Services World Scientific Publishing

Preface	p. VII
Acknowledgments	p. IX
Introduction	p. 1
Exordium	p. 1
Historical Background	p. 3
Characteristic Frequencies	p. 6
Outline of Contents	p. 10
Chapter 1 References	p. 12
Theoretical Models of Intense Nonneutral Particle Beams	p. 23
Introduction	p. 23
Vlasov-Maxwell Description	p. 26
Macroscopic Fluid Description	p. 32
Conservation Relations	p. 36
Discrete Particle Effects	p. 41
Chapter 2 References	p. 46
Particle Orbits in Periodic Focusing Field Configurations	p. 51
Introduction	p. 51
Periodic Focusing Field Configurations	p. 54
Single-Particle Motion	p. 66
Hamilton's Equations of Motion	p. 67
Orbit Equations in the Paraxial Approximation	p. 69
Transverse Orbit Equations for a Continuous Beam	p. 75
Orbit and Envelope Equations for a Continuous Beam	p. 79
Self-Field Potential for a Uniform Density Beam	p. 79
Periodic Focusing Quadrupole Field	p. 82
Periodic Focusing Solenoidal Field	p. 90
Uniform Focusing Field	p. 98
Smooth Focusing Approximation	p. 103
Hamiltonian for Transverse Particle Motion	p. 113
Matrix Transfer Formalism and Phase Advance	p. 116
Orbit and Envelope Equations for a Finite-Length Charge Bunch	p. 128
Chapter 3 References	p. 140
Nonlinear Kinetic Stability Theorem	p. 145
Introduction	p. 145
Nonlinear Vlasov-Maxwell Equations in the Beam Frame	p. 148
Global Nonlinear Conservation Constraints	p. 154
Three-Dimensional Kinetic Stability Theorem	p. 159
State of Minimum Helmholtz Free Energy	p. 166
Chapter 4 References	p. 173
Vlasov-Maxwell Description of Periodically-Focused Intense Beam Equilibria	p. 177
Introduction	p. 177
Theoretical Model	p. 178
Focusing Field Configurations	p. 181
Nonlinear Vlasov Equation and Hamilton's Equations of Motion	p. 184
Conventional Hamiltonian Formulation	p. 185
Alternative Hamiltonian Formulation	p. 189
Intense Beam Equilibria in a Uniform Focusing Field	p. 196
Isotropic Beam Equilibria	p. 198
Anisotropic Beam Equilibria	p. 210
Intense Beam Equilibria in an Alternating-Gradient Quadrupole Field	p. 222
Nonlinear Vlasov-Maxwell Equations	p. 222
Periodically-Focused Beam Equilibria at Low Beam Intensity	p. 224
Periodically-Focused Kapchinskij-Vladimirskij (KV) Intense Beam Equilibrium	p. 234
Intense Beam Equilibria in a Periodic-Focusing Solenoidal Field	p. 242
Nonlinear Vlasov-Maxwell Equations	p. 242
Canonical Transformation to Larmor-Frame Variables	p. 244
Periodically-Focused Intense Beam Equilibria	p. 246
Chapter 5 References	p. 253
Statistically-Averaged Rate Equations	p. 257
Introduction and Theoretical Model	p. 257
Alternating-Gradient Quadrupole Field	p. 259
Periodic Focusing Solenoidal Field	p. 261
Rate Equations for Solenoidal Focusing Field	p. 263
General Rate Equation	p. 264
Conservation of Canonical Angular Momentum	p. 265
Centroid Motion	p. 267
Global Energy Balance	p. 268
Rate Equation for Mean-Square Beam Radius	p. 271
Coupled Rate Equations for RMS Beam Radius and Transverse Emittance	p. 273
Application of Rate Equations for a Solenoidal Focusing Field	p. 276
Rate Equations for Kapchinskij-Vladimirskij Beam Distribution	p. 276
Rate Equations for Beam Distributions with Fixed-Shaped Density Profile	p. 279
Rate Equations for Quadrupole Focusing Field	p. 283
General Rate Equation	p. 284
Rate Equations for Average x- and y- Kinetic Energies	p. 286
Rate Equations for Mean-Square Transverse Beam Dimensions	p. 287
Coupled Rate Equations for Transverse Emittances and RMS Beam Dimensions	p. 287
Rate Equations for Fixed-Shape Density Profile	p. 290
Chapter 6 References	p. 296
Hamiltonian Averaging Techniques Applied to the Nonlinear Vlasov-Maxwell Equations	p. 301
Introduction and Theoretical Model	p. 301
Canonical Transformation to Slow Variables	p. 307
Canonical Transformation	p. 308
Third-Order Transformed Hamiltonian and Coordinate Transformation	p. 319
Nonlinear Vlasov-Maxwell Equations in the Transformed Variables	p. 323
Transformed Vlasov-Maxwell Equations	p. 323
Equilibrium Properties ([partial differential]/[partial differential]s = 0) in the Transformed Variables	p. 325
Density Inversion Theorem	p. 331
Kinetic Stability Theorem	p. 332
Examples of Self-Consistent Beam Equilibria	p. 333
Periodically-Focused Beam Properties in the Laboratory Frame	p. 337
Laboratory-Frame Distribution Function	p. 338
Statistical Averages in the Laboratory Frame	p. 340
Macroscopic Profiles in the Laboratory Frame	p. 343
Range of Validity of Asymptotic Expansion Procedure	p. 346
Conclusions	p. 347
Chapter 7 References	p. 349
Kinetic Stability Properties and Collective Oscillations in Intense Particle Beams	p. 353
Introduction	p. 353
Assumptions and Theoretical Model	p. 355
Linearized Vlasov-Maxwell Equations and the Method of Characteristics	p. 358
Stability Properties for Perturbations About a Kapchinskij-Vladimirskij Beam Equilibrium	p. 365
Eigenvalue Equation for k[subscript z] = 0	p. 365
Stable Surface-Wave Oscillations for [partial differential]/[partial differential]z = 0 and [partial differential]/[partial differential theta] [not equal] 0	p. 371
Stability Properties for Axisymmetric Body-Wave Perturbations with [partial differential]/[partial differential]z = 0 and [partial differential]/[partial differential theta] = 0	p. 376
Nonlinear Perturbative Particle Simulation Method for Describing Collective Processes	p. 383
Stability Properties for Perturbations about a Thermal Equilibrium Beam	p. 389
Validation of Kinetic Stability Theorem	p. 390
Normal-Mode Oscillations Determined from [delta] f Method for [partial differential]/[partial differential theta] = 0 = [partial differential]/[partial differential]z	p. 398
Chapter 8 References	p. 401
Warm-Fluid Stability Properties and Collective Oscillations in Intense Particle Beams	p. 407
Introduction	p. 407
Assumptions and Macroscopic Warm-Fluid Model	p. 409
Macroscopic Equilibrium Properties	p. 414
Equilibrium Force Balance	p. 414
Warm-Fluid Thermal Equilibrium	p. 415
Warm-Fluid Kapchinskij-Vladimirskij (KV) Equilibrium	p. 416
Warm-Fluid Waterbag Equilibrium	p. 418
Cold-Fluid Equilibrium	p. 420
Linearized Fluid-Maxwell Equations	p. 421
Cold-Beam Eigenvalue Equation and Collective Oscillations	p. 423
Warm-Beam Stability Properties for Axisymmetric Flute Perturbations with [partial differential]/[partial differential theta] = 0 = [partial differential]/[partial differential]z	p. 432
Warm-Beam Eigenvalue Equation	p. 432
Stability Properties for Perturbations about a Warm-Beam Kapchinskij-Vladimirskij Equilibrium	p. 435
Stability Properties for Perturbations about the Warm-Beam Waterbag Equilibrium	p. 440
Collective Oscillations and Instability Driven by Pressure Anisotropy	p. 448
Eigenvalue Equation for Perturbations about a Warm-Fluid Waterbag Equilibrium	p. 448
Stability Properties for T[subscript [double vertical line]b] = 0 and [partial differential]/[partial differential theta] = 0	p. 451
Chapter 9 References	p. 460
Special Topics on Intense Beam Propagation	p. 465
Introduction	p. 465
Intense Beam Propagation Through Background Plasma	p. 466
Self-Pinched Beam Propagation--The Bennett Pinch	p. 466
Alfven-Lawson Limiting Current	p. 470
The Plasma Lens Effect	p. 473
Collisionless Damping (Growth) of Collective Excitations	p. 478
The Landau Dielectric Function	p. 479
Kinetic Dispersion Relation for a Multi-component Plasma	p. 485
Landau Damping of Electron Plasma Oscillations	p. 495
Collisionless Damping of Dipole-Mode Sideband Oscillations in Intense Particle Beams	p. 499
Electron-Ion Two-Stream Instability in Intense Particle Beams	p. 503
Kinetic Dispersion Relation	p. 504
Nonlinear [delta] f Simulations of the Electron-Proton Two-Stream Instability	p. 515
Paul Trap Simulator of Intense Beam Propagation	p. 522
Halo Particle Production by Collective Mode Excitations	p. 531
Probing the Beam Microstate	p. 541
The Density Inversion Theorem	p. 542
Collective Excitations	p. 544
Beam Echoes	p. 548
Chapter 10 References	p. 555
Supplementary References	p. 563
Subject Index	p. 577
Table of Contents provided by Syndetics. All Rights Reserved.

Physics Of Intense Charged Particle Beams In High Energy Accelerators

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