An Introduction To The Physics Of Particle Accelerators

by Conte, Mario; Mackay, William W.

• ISBN13: 9789812779601
• ISBN10: 9812779604
• Edition: 2nd
• Format: Hardcover
• Copyright: 2008-04-28
• Publisher: World Scientific Pub Co Inc

Summary

"This book provides a concise and coherent introduction to the physics of particle accelerators, with attention being paid to the design of an accelerator for use as an experimental tool. In the second edition, new chapters on spin dynamics of polarized beams as well as instrumentation and measurements are included, with a discussion of frequency spectra and Schottky signals. The additional material also covers quadratic Lie groups and integration highlighting new techniques using Cayley transforms, detailed estimation of collider luminosities, and new problems."--BOOK JACKET.

Table of Contents

Preface to the 2nd Edition	p. xiii
Preface to the 1st Edition	p. xiv
Introduction	p. 1
Motivation and overview	p. 1
Direct-voltage accelerators	p. 3
A review of relativistic particle motion	p. 6
Linear accelerators with oscillating electric fields	p. 9
Circular machines	p. 12
Momentum compaction and the synchronous particle	p. 14
Problems	p. 16
Equations of Motion for Weak Focusing	p. 20
Reference system for a circular machine	p. 20
Equations of motion	p. 20
Solutions of the motion equations and transfer matrices	p. 23
Momentum dispersion	p. 27
Weak focusing synchrotron	p. 29
Momentum compaction factor	p. 32
Problems	p. 33
Mechanics of Trajectories	p. 35
Liouville's theorem	p. 35
General transformations	p. 39
Canonical momentum and vector potential	p. 40
Hamiltonian formalism and canonical coordinates	p. 42
Symplectic transformations and matrices	p. 45
The standard canonical coordinates	p. 49
Symplectic generators	p. 52
Symplectic integrators	p. 57
Lie groups and algebras	p. 61
Cayley transforms and symplectification	p. 64
Integration by Cayley transform	p. 67
Runge-Kutta-Munthe-Kas integration	p. 69
Problems	p. 70
Optical Elements with Static Magnetic Fields	p. 76
Transverse fields and multipoles	p. 77
Equipotential surfaces and pole face contours	p. 79
Quadrupole lenses	p. 82
End field effects in a dipole	p. 83
Ideal solenoid with thin fringes	p. 87
Problems	p. 91
Strong Focusing	p. 96
Transfer matrix approach and stability of the linear system	p. 97
Analytical approach	p. 100
Emittances	p. 104
Adiabatic invariants	p. 107
Dispersion	p. 108
Momentum compaction	p. 110
Problems	p. 111
Lattice Exercises	p. 115
The FODO lattice	p. 115
Stability diagrams	p. 116
FODO cell dispersion	p. 117
A few explicit forms of the Twiss matrix	p. 119
Insertions	p. 121
Dispersion suppressors	p. 122
Low beta insertion	p. 125
Coupled motion	p. 127
Finding the eigenvalues of a 4x4 transfer matrix	p. 130
Chromaticity	p. 134
Problems	p. 137
Synchrotron Oscillations	p. 140
Transition energy	p. 140
The phase stability principle	p. 141
Resonant acceleration	p. 142
The phase oscillation equation	p. 144
Large oscillations	p. 146
Hamiltonian formalism	p. 149
Adiabatic invariant	p. 155
Bunch manipulations	p. 156
Problems	p. 161
Synchrotron Radiation	p. 164
Radiated power	p. 164
Radiation damping of energy oscillations	p. 167
Damping of the vertical oscillations	p. 169
Damping of the horizontal oscillations	p. 171
Damping partition numbers	p. 174
Frequency spectrum of the radiation	p. 175
Energy spread and bunch length	p. 178
Transverse excitations	p. 181
Beam lifetime considerations	p. 183
Problems	p. 185
RF Linear Accelerators	p. 188
Maxwell's equations and waves	p. 188
Cylindrical waveguides	p. 191
Electron capture	p. 196
Cylindrical cavities	p. 198
Longitudinal equations of motion in a linac	p. 204
Transverse defocusing	p. 206
Radio frequency quadrupoles	p. 208
Problems	p. 211
Resonances	p. 213
Integer resonances	p. 213
Linear coupling resonances	p. 215
Stability of difference resonance and instability of sum resonance	p. 215
Assessment of resonances	p. 217
Krylov-Bogoliubov method	p. 221
Half-integer resonance	p. 223
The nonlinear third-integer resonance	p. 225
Recapitulation	p. 228
Problems	p. 229
Space-Charge Effects	p. 231
Transverse effects: tune shift	p. 231
Luminosity and collider rings	p. 234
Transverse effects: beam-beam interaction	p. 235
Longitudinal effects	p. 238
How to Baffle Liouville	p. 243
Beam temperatures	p. 243
Electron cooling	p. 246
Stochastic cooling	p. 252
Center of mass of a system of oscillators	p. 256
Noise	p. 258
Mixing	p. 260
Problems	p. 263
Spin Dynamics	p. 265
Introduction	p. 265
Simple nonrelativistic model of a spinning body	p. 265
Magnetic moments of particles in the rest system	p. 268
Basic Thomas precession	p. 271
The Thomas-Frenkel-BMT equation	p. 275
Covariant form of spin precession	p. 279
Relativistic boost of a slowly spinning disk	p. 279
Covariant formulation of the Thomas-Frenkel-BMT equation	p. 282
Review of nonrelativistic quantum mechanics with emphasis on spin	p. 284
Constructing Pauli-like matrices for higher spins	p. 289
Rotation matrices for spinors	p. 295
Spin precession on the closed orbit	p. 297
Spin motion in the standard coordinate system	p. 301
Sector bend magnets	p. 303
Quadrupole magnets	p. 304
Vertical betatron oscillations and intrinsic resonances	p. 305
Froissart-Stora formula for a single resonance	p. 308
Invariant spin field	p. 311
Polarization of electron beams	p. 313
Problems	p. 315
Position Measurements and Spectra	p. 319
Transverse position measurement	p. 319
Coherent and Schottky frequency spectra of beams	p. 323
A single Gaussian bunch	p. 323
Circulating bunches	p. 324
Momentum spread	p. 326
Longitudinal Schottky spectrum of an unbunched beam	p. 327
Synchrotron oscillations of a single particle	p. 328
Transverse Schottky spectrum of an unbunched beam	p. 330
Problems	p. 333
Confusion of Definitions in Other Sources	p. 335
Coordinates	p. 335
Emittance	p. 335
Tunes: Q or v	p. 336
Betatron functions	p. 336
Dispersion function	p. 336
Chromaticity	p. 337
Momentum compaction	p. 337
Multipole numbering	p. 337
Phase slip	p. 337
Longitudinal canonical momentum W	p. 338
Properties of a Generic Optical System	p. 339
Generating Functions	p. 341
Luminosity	p. 344
Basic definition of luminosity	p. 344
Gaussian beam distributions	p. 346
Estimation of luminosities in RHIC	p. 351
Leapfrog Integration of Equations of Motion	p. 356
Some Useful Mathematical Formulae	p. 358
Index	p. 361
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