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Electron storage rings play a crucial role in many areas of modern scientific research. In light sources, they provide intense beams of x-rays that can be used to understand the structure and behaviour of materials at the atomic scale, with applications to medicine, the life sciences, condensed matter physics, engineering, and technology. In particle colliders, electron storage rings allow experiments that probe the laws of nature at the most fundamental level. Understanding and controlling the behaviour of the beams of particles in storage rings is essential for the design, construction, and operation of light sources and colliders aimed at reaching increasingly demanding performance specifications. Introduction to Beam Dynamics in High-Energy Electron Storage Rings describes the physics of particle behaviour in these machines. Starting with an outline of the history, uses, and structure of electron storage rings, the book develops the foundations of beam dynamics, covering particle motion in the components used to guide and focus the beams, the effects of synchrotron radiation, and the impact of interactions between the particles in the beams. The aim is to emphasise the physics behind key phenomena, keeping mathematical derivations to a minimum: numerous references are provided for those interested in learning more. The text includes discussion of issues relevant to machine design and operation, and concludes with a brief discussion of some more advanced topics, relevant in some special situations, and a glimpse of current research aiming to develop the “ultimate” storage rings.
1 Introduction 1.1 A brief history of electron storage rings and their uses 1.2 General features and subsystems 1.2.1 Magnets 1.2.2 Radiofrequency cavities 1.2.3 Feedback systems 1.2.4 Vacuum systems 1.2.5 Diagnostics 1.2.6 Control systems 1.2.7 Injection systems 1.2.8 Personnel protection 1.3 Some examples of electron storage rings Bibliography
2 Linear Optics 2.1 Co-ordinate system and transfer matrices 2.1.1 Drift spaces 2.1.2 Dipole magnets 2.1.3 Quadrupole magnets 2.1.4 Radiofrequency cavities 2.1.5 Transfer matrices in three degrees of freedom 2.1.6 Fringe fields and edge focusing in dipole magnets 2.2 Betatron oscillations 2.2.1 Hill’s equation and the Courant–Snyder parameters 2.2.2 The matched distribution in a periodic lattice 2.2.3 Betatron phase advance and the betatron tunes 2.2.4 Action–angle variables 2.3 Emittance 2.4 The closed orbit 2.5 Dispersion 2.6 Coupling 2.7 Momentum compaction factor 2.8 Synchrotron oscillations and phase stability Bibliography
3 Synchrotron Radiation 3.1 Features of synchrotron radiation 3.1.1 Radiation power spectrum 3.1.2 Brightness 3.1.3 Opening angle of the radiation beam 3.1.4 Polarisation 3.2 Radiation damping and quantum excitation 3.2.1 Damping of synchrotron oscillations 3.2.2 Damping of betatron oscillations 3.2.3 Quantum excitation 3.3 Natural emittance and lattice design 3.3.1 FODO lattice 3.3.2 Double-bend achromats 3.3.3 Theoretical minimum emittance lattice and multi-bend achromats Bibliography
4 Nonlinear Dynamics 4.1 Chromaticity 4.1.1 Natural chromaticity in a storage ring 4.1.2 Correction of chromaticity using sextupole magnets 4.1.3 Coupling and nonlinear effects from sextupole magnets 4.2 Resonances 4.3 Dynamic aperture 4.4 Energy acceptance Bibliography
5 Collective Effects 5.1 Touschek scattering and space charge 5.2 Ion trapping 5.3 Wake fields, wake functions and impedances 5.4 Potential-well distortion 5.5 Microwave instability 5.5.1 Microwave instability in a “cold” beam 5.5.2 Energy spread and beam stability: Landau damping 5.6 Coupled-bunch instabilities Bibliography
6 Further Topics 6.1 Advanced tools for beam dynamics 6.2 Some other phenomena 6.2.1 Spin dynamics 6.2.2 Beam-beam effects 6.2.3 Electron-cloud effects 6.3 The future: “ultimate” storage rings, and beyond Bibliography 1 Introduction 1.1 A brief history of electron storage rings and their uses 1.2 General features and subsystems 1.2.1 Magnets 1.2.2 Radiofrequency cavities 1.2.3 Feedback systems 1.2.4 Vacuum systems 1.2.5 Diagnostics 1.2.6 Control systems 1.2.7 Injection systems 1.2.8 Personnel protection 1.3 Some examples of electron storage rings Bibliography
2 Linear Optics 2.1 Co-ordinate system and transfer matrices 2.1.1 Drift spaces 2.1.2 Dipole magnets 2.1.3 Quadrupole magnets 2.1.4 Radiofrequency cavities 2.1.5 Transfer matrices in three degrees of freedom 2.1.6 Fringe fields and edge focusing in dipole magnets 2.2 Betatron oscillations 2.2.1 Hill’s equation and the Courant–Snyder parameters 2.2.2 The matched distribution in a periodic lattice 2.2.3 Betatron phase advance and the betatron tunes 2.2.4 Action–angle variables 2.3 Emittance 2.4 The closed orbit 2.5 Dispersion 2.6 Coupling 2.7 Momentum compaction factor 2.8 Synchrotron oscillations and phase stability Bibliography
3 Synchrotron Radiation 3.1 Features of synchrotron radiation 3.1.1 Radiation power spectrum 3.1.2 Brightness 3.1.3 Opening angle of the radiation beam 3.1.4 Polarisation 3.2 Radiation damping and quantum excitation 3.2.1 Damping of synchrotron oscillations 3.2.2 Damping of betatron oscillations 3.2.3 Quantum excitation 3.3 Natural emittance and lattice design 3.3.1 FODO lattice 3.3.2 Double-bend achromats 3.3.3 Theoretical minimum emittance lattice and multi-bend achromats Bibliography
4 Nonlinear Dynamics 4.1 Chromaticity 4.1.1 Natural chromaticity in a storage ring 4.1.2 Correction of chromaticity using sextupole magnets 4.1.3 Coupling and nonlinear effects from sextupole magnets 4.2 Resonances 4.3 Dynamic aperture 4.4 Energy acceptance Bibliography
5 Collective Effects 5.1 Touschek scattering and space charge 5.2 Ion trapping 5.3 Wake fields, wake functions and impedances 5.4 Potential-well distortion 5.5 Microwave instability 5.5.1 Microwave instability in a “cold” beam 5.5.2 Energy spread and beam stability: Landau damping 5.6 Coupled-bunch instabilities Bibliography
6 Further Topics 6.1 Advanced tools for beam dynamics 6.2 Some other phenomena 6.2.1 Spin dynamics 6.2.2 Beam-beam effects 6.2.3 Electron-cloud effects 6.3 The future: “ultimate” storage rings, and beyond Bibliography