Contents -- Preface -- I Electromagnetism and Classical Mechanics -- 1 Electromagnetic Fields in Accelerator Components -- 1.1 Boundary Conditions on Electromagnetic Fields -- 1.1.1 Surface of an infinite permeability material -- 1.1.2 Surface of an ideal conductor -- 1.2 Two-Dimensional Multipole Fields -- 1.2.1 Current distribution for a pure multipole -- 1.2.2 Geometry of iron-dominated multipole magnets -- 1.2.3 Multipole decomposition -- 1.3 Three-Dimensional Fields -- 1.3.1 Cartesian and cylindrical modes -- 1.3.2 Generalised gradients -- 1.4 Fields in Radiofrequency Cavities -- 1.4.1 Rectangular cavities -- 1.4.2 Cylindrical cavities -- 2 Hamiltonian for a Particle in an Accelerator Beam Line -- 2.1 The Hamiltonian for a Straight Beam Line -- 2.2 Dynamical Variables for Beam Dynamics -- 2.3 The Hamiltonian in a Curved Co-ordinate System -- 2.4 Symplectic Transfer Maps and Liouville's Theorem -- II Single-Particle Linear Dynamics -- 3 Linear Transfer Maps for Common Components -- 3.1 Drift Space -- 3.2 Dipole Magnet -- 3.3 Dipole Fringe Fields and Edge Focusing -- 3.4 Quadrupole Magnet -- 3.5 Solenoid -- 3.6 Radiofrequency Cavity -- 3.7 Spin Dynamics -- 4 Linear Optics in Uncoupled Beam Lines -- 4.1 A FODO Lattice -- 4.2 The Courant-Snyder Parameters -- 4.3 Action-Angle Variables -- 4.4 Courant-Snyder Parameters in a FODO Beam Line -- 4.5 Hill's Equation -- 4.6 Courant-Snyder Parameters and Particle Distribution -- 5 Coupled Optics -- 5.1 Transverse-Longitudinal Coupling -- 5.1.1 Dispersion -- 5.1.2 Momentum compaction and phase slip -- 5.1.3 Synchrotron motion -- 5.2 Fully Coupled Motion -- 5.3 Dispersion Revisited -- 5.4 Examples of Coupled Optics -- 5.4.1 Uniform solenoid field -- 5.4.2 Flat-beam electron source -- 6 Linear Imperfections in Storage Rings -- 6.1 The Closed Orbit -- 6.2 Dipole Field Errors.

6.3 Quadrupole Alignment Errors -- 6.4 Focusing Errors -- 6.5 Beam-Based Alignment of Quadrupoles -- 6.6 Coupling Errors -- 7 Effects of Synchrotron Radiation -- 7.1 Classical Radiation: Radiation Damping -- 7.2 Quantum Radiation: Quantum Excitation -- 7.3 Equilibrium Emittance and Lattice Design -- 7.3.1 Natural emittance in a FODO storage ring -- 7.3.2 Double-bend achromat -- 7.3.3 TME lattices and multibend achromats -- 7.4 Computation of Equilibrium Emittances -- 7.5 Synchrotron Radiation and Spin Polarisation -- III Single-Particle Nonlinear Dynamics -- 8 Examples of Nonlinear Effects in Accelerator Beam Lines -- 8.1 Longitudinal Dynamics in a Bunch Compressor -- 8.2 Chromaticity in a Linear FODO Beam Line -- 8.3 Chromaticity in Storage Rings -- 9 Representations of Transfer Maps -- 9.1 Lie Transformations -- 9.2 Power Series Map for a Sextupole -- 9.3 Mixed-Variable Generating Functions -- 10 Symplectic Integrators -- 10.1 Splitting Methods -- 10.2 Explicit Symplectic Integrator for s-dependent Fields -- 10.3 Symplectic Runge-Kutta Integrators -- 11 Methods for Analysis of Single-Particle Dynamics -- 11.1 A Lie Transformation Example: the -I Transformer -- 11.2 Canonical Perturbation Theory -- 11.2.1 Dipole perturbations: closed orbit distortion -- 11.2.2 Quadrupole perturbations: focusing errors -- 11.2.3 Skew quadrupole perturbations: coupling -- 11.2.4 Sextupole perturbations -- 11.3 Resonances and Dynamic Aperture -- 11.4 Normal Form Analysis -- 11.5 A Numerical Method: Frequency Map Analysis -- IV Collective Effects -- 12 Space Charge -- 12.1 The Kapchinsky-Vladimirsky Distribution -- 12.2 The Envelope Equations for the KV Distribution -- 12.3 Elliptically Symmetric Non-KV Distributions -- 12.4 Space-Charge Tune Shifts -- 12.5 Matching a Continuous Beam to a Solenoid Field -- 12.6 Longitudinal Dynamics with Space Charge.

12.7 Beam-Beam Effects -- 13 Scattering Effects -- 13.1 Touschek Effect -- 13.2 Intrabeam Scattering -- 13.2.1 Piwinski formulae -- 13.2.2 Bjorken-Mtingwa formulae -- 13.2.3 High energy approximation -- 14 Wake Fields, Wake Functions and Impedance -- 14.1 Wake Fields in a Resonant Cavity -- 14.2 Resistive-Wall Wake Fields -- 14.3 Wake Functions -- 14.4 Impedance -- 15 Coherent Instabilities -- 15.1 Coupled-Bunch Instabilities -- 15.1.1 Transverse modes -- 15.1.2 Longitudinal modes -- 15.2 Potential-Well Distortion -- 15.3 Coasting Beams: Microwave Instability -- 15.4 Single-Bunch Instabilities -- 15.4.1 Head-tail instability -- 15.4.2 Sacherer's integral equation -- 15.4.3 Discrete modes: Robinson instability -- 15.4.4 Mode coupling -- Bibliography -- Index.