The authors aimed to address a gap by systematically presenting the theory of particle motion in modern accelerators, focusing on new types of cyclic accelerators, especially those using strong focusing. Less emphasis is placed on older accelerators like cyclotrons and betatrons, which are already well-documented in existing literature. This book is targeted at scientists, engineers, students, and graduates in high-energy particle physics and related fields. It also provides basic information on the construction of accelerators to aid in understanding the presented theory.

Translated from the Russian by M. Barbier

You can get the book here and here.

CONTENTS

CHAPTER 1. INTRODUCTION 1
1. Role of accelerators in nuclear and elementary particle physics 1
2. Short review of the development of cyclical accelerators 4
3. A few energy relationships 16
4. Basic concepts in the theory of accelerators 23
4.1. Stability of ideal orbits in accelerators 24
4.2. Influence of an imperfection of the magnetic field on particle motion 31
4.3. The acceleration regimes of the particles 34
4.4. Particle injection into and extraction from accelerators 39

CHAPTER 2. BETATRON OSCILLATIONS OF PARTICLES IN IDEAL
PERIODIC MAGNETIC FIELDS 46
1. Closed orbit and natural system of coordinates 47
2. Equations for small deviations from the closed orbit 52
3. General stability conditions for the solution of differential equations with periodic coefficients 56
4. Betatron oscillations in periodic magnetic systems 64
5. Canonical form of the equation for betatron oscillations 71
6. Adiabatic change of the parameters of betatron oscillations 74
7. Some methods of computing betatron oscillation frequencies 77

CHAPTER 3. BETATRON OSCILLATIONS OF PARTICLES IN NONIDEAL
MAGNETIC FIELDS 86
1. Linear betatron oscillation resonances in non-ideal magnetic systems 86
2. Linear betatron oscillations with perturbations present 93
3. A few questions related to magnetic field correction 109
4. Basic non-linear effects 119
5. General theory of non-linear resonance. One-dimensional oscillations 123
6. Non-linear resonances of two-dimensional oscillations 135
7. Application of the theory of non-linear effects to periodic magnetic systems 138
8. Resonances in a system with slowly varying parameters 142

CHAPTER 4. SYNCHROTRON OSCILLATIONS 147
1. Dependence of orbit parameters on particle energy 147
2. Basic equation of the acceleration regime 154
3. Resonance acceleration regime. Phase equation 156
4. Self-focusing regime and phase oscillations 166
5. Simultaneous consideration of synchrotron and betatron oscillations 177
6. Synchrotron oscillations in the presence of perturbations 180
7. Critical (transition) energy 190
8. The induction regime of acceleration 202

CHAPTER 5. RADIATION EFFECTS IN CYCLIC ELECTRON ACCELERATORS 209
1. Basic properties of the radiation 209
2. Equation of motion of an electron in periodic magnetic fields in the presence of radiation 219
3. Decrements of betatron and synchrotron oscillations 228
4. Methods of damping the oscillations 231
5. Effect of quantum fluctuations on the electron motion in magnetic systems 250

CHAPTER 6. PARTICLE LOSSES CAUSED BY RANDOM PERTURBATIONS
OF THE MOTION 251
1. Basic equations and presentation of the problem 251
2. Particle losses in the absence of damping. Multiple scattering of protons by the residual gas 254
3. The case of strong damping. Loss of particles by quantum fluctuations of radiation 260
4. General remarks on the influence of damping on the losses 266
5. Losses due to single-scattering events 270

CHAPTER 7. PECULIARITIES OF ACCELERATORS OF DIFFERENT
TYPES 275
1. Accelerators of the cyclotron type 275
1.1. The cyclotron 275
1.2. The isochronous cyclotron 283
1.3. The phasotron 289
1.4. An accelerator with variable harmonic number: the microtron 298
2. The synchrophasotron 307
2.1. Strong-focusing synchrophasotrons 308
2.2. The weak-focusing synchrophasotron 321
3. Strong-focusing accelerators with fixed magnetic field (ring-phasotrons) 332
4. Special acceleration modes in systems with magnetic fields constant in time 352
4.1. Multiple acceleration in a fixed field 352
4.2. Storage devices 358
4.3. Stochastic acceleration 361