Beam Dynamics in High Energy Particle Accelerators - Wolski, Andrzej (World Scientific Publishing Company, 2014)
11.2.1 Dipole perturbations: closed orbit distortion
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 cavities2 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 Parameters4.3 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 Errors6.5 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