Beam Dynamics in High Energy Particle Accelerators (Second Edition)

✍ Scribed by Andrzej Wolski

• Publisher: World Scientific Publishing Company
• Tongue: English
• Leaves: 678
• Edition: 2
• Category: Library

✦ Synopsis

High-energy particle accelerators are as diverse as their uses, which range from scientific research in fields such as high-energy physics, materials science and the life sciences, to applications in industry and medicine. Despite the diversity of accelerators, the particle beams that they are designed to produce behave in ways that share many common features. Beam Dynamics in High Energy Particle Accelerators aims to provide an introduction to phenomena regularly encountered when working with beams in accelerators; from the basic principles of motion of relativistic particles in electromagnetic fields, to instabilities that can affect beam quality in machines operating at high current. This book assumes no prior experience with accelerator physics and develops the subject in a way that provides a solid foundation for more advanced study of specific topics.As well as including numerous revisions and improvements in the text, this second edition features substantial new material, including sections on fringe fields in multipole magnets, Verlet integration for particle tracking, and measurement of beam emittances. References and discussions of current topics have been updated. As with the first edition, the aim is to provide practical and powerful tools and techniques for the study of beam dynamics, while emphasizing the elegance of the subject and helping the reader develop a deep understanding of the relevant physics.

✦ Table of Contents

Contents
Preface to the Second Edition
Preface to the First Edition
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
1.3.3 Analytical expressions for multipole fringe fields
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 eld
5.4.2 Flat-beam electron source
5.4.3 Measurement of normal mode emittances
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
7.4.1 Effects of betatron coupling
7.4.2 Effects of vertical dispersion
7.4.3 Envelope method
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. Particle Tracking by Numerical Integration
10.1 The Störmer–Verlet Method
10.2 Symplectic Integrators
10.2.1 Splitting methods
10.2.2 Explicit symplectic integrator for s-dependent fields
10.2.3 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