Introduction To The Physics Of Particle Accelerators, An (2nd Edition) / Edition 2

by Mario Conte, William W Mackay

Overview

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.

Product Details

ISBN-13:	9789812779618
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	05/05/2008
Edition description:	New Edition
Pages:	392
Product dimensions:	5.90(w) x 8.90(h) x 0.90(d)

Table of Contents

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

Editorial Reviews

A textbook for a one-semester graduate physics course, but also usable for self-study. Provides a concise introduction to the physics of particle accelerators, emphasizing the design of an accelerator for experimental use. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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