Partide Accelerator Physics I

Transcription

1 Partide Accelerator Physics I

2 Springer-Verlag Berlin Heidelberg GmbH Physics and Astronomy ONLINE LIBRARY

3 Helmut Wiedemann Particle Accelerator Physics I Basic Principles and Linear Beam Dynamics Second Edition With 160 Figures ' Springer

4 Professor Dr. Helmut Wiedemann Applied Physics Department and Synchrotron Radiation Laboratory Stanford University, Stanford, CA , USA Cataloging-in-Publication Data applied for Bibliographie information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at < ISSN ISBN ISBN (ebook) DOI / This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1993,1999,2003 Originally published by Springer-Verlag Berlin Heidelberg New York in 2003 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data prepared by the author using a Springer TEX macro package Cover design: design & production GmbH, Heidelberg Printedon acid-free paper 55/3141/XO o

5 To my sons Frank and Martin

6 Preface In this second edition of Partide Accelerator Physics, Vol. 1, is mainly a reprint of the first edition without significant changes in content. The bibliography has been updated to include more recent progress in the field of particle accelerators. With the help of many observant readers a number of misprints and errors could be eliminated. The author would like to express his sincere appreciation to all those who have pointed out such shortcomings and welcomes such information and any other relevant information in the future. The author would also like to express his special thanks to the editor Dr. Helmut Latsch and his staff for editorial as weil as technical advice and support which contributed greatly to the broad acceptance of this text and made a second edition of both volumes necessary. Palo Alto, California November 1998 Helmut Wiedemann VII

7 Preface to the First Edition The purpose of this textbook is to provide a comprehensive introduction into the physics of particle accelerators and particle beam dynamics. Particle accelerators have become important research tools in high energy physics as well as sources of incoherent and coherent radiation from the far infra red to hard x-rays for basic and applied research. During years of teaching accelerator physics it became clear that the single most annoying obstacle to get introduced into the field is the absence of a suitable textbook. lndeed most information about modern accelerator physics is contained in numerous internal notes from scientists working mostly in high energy physics laboratories all over the world. This text intends to provide a broad introduction and reference book into the field of accelerators for graduate students, engineers and scientists summarizing many ideas and findings expressed in such internal notes and elsewhere. In doing so theories are formulated in a general way to become applicable for any kind of charged particles. Writing such a text, however, poses the problern of correct referencing of original ideas. I have tried to find the earliest references among more or less accessible notes and publications and have listed those although the reader may have difficulty to obtain the original paper. In spite of great effort to be historically correct I apologize for possible omissions and misquotes. This situation made it necessary to rederive again some of such ideas rather than quote the results and refer the interested reader to the original publication. I hope this approach will not offend the original researchers, but rather provide a broader distribution of their original ideas, which have become important to the field of accelerator physics. This text is split into two volumes. The first volume is designed tobe self contained and is aimed at newcomers into the field of accelerator physics, but also to those who work in related fields and desire some background on basic principles of accelerator physics. The first volume therefore gives an introductory survey of fundamental principles of particle acceleration followed by the theory of linear beam dynamics in the transverse as well as longitudinal phase space including a detailed discussion of basic magnetic focusing units. Concepts of single and multi particle beam dynamics are introduced. Synchrotron radiation, its properties and effect on beam dynamics and electron beam parameters is described in considerable detail followed IX

8 by a discussion of beam instabilities on an introductory level, beam lifetiroe and basic lattice design concepts. The second voluroe is airoed specifically to those students, engineers and scientists who desire to iroroerse theroselves deeper into the physics of particle accelerators. It introduces the reader to higher order beam dynaroics, Hamiltonian particle dynamics, general perturbation theory, nonlinear bearo optics, chroroatic and georoetric aberrations and resonance theory. The interaction of particle beams with rf fields of the accelerating systero and beam loading effects are described in soroe detail relevant to accelerator physics. Following a detailed derivation of the theory of synchrotron radiation, particle beam phenoroena are discussed while utilizing the Vlasov and Fokker Planck equations leading to the discussion of beam pararoeters and their roanipulation and collective beam instabilities. Finally design concepts and new developroents of particle accelerators as synchrotron radiation sources or research tools in high energy physics are discussed in soroe detail. This text grew out of a nurober of lecture notes for accelerator physics courses at Stanford University, the Synchrotron Radiation Research Labaratory in Taiwan, the University of Sao Paulo in Brazil, the International Center for Theoretical Physics in Trieste and the US Partide Accelerator School as well as froro interaction with students attending those classes and roy own graduate students. During alroost thirty years in this field I had the opportunity to work with nuroerous individuals and accelerators in laboratories around the world. Having learned greatly froro these interactions I like to take this opportunity to thank all those who interacted with roe and have had the patience to explain their ideas, share their results or collaborate with roe. The design and construction of new particle accelerators provides a specifically interesting period to develop and test theoretically new ideas, to work with engineers and designers, to see theoretical concepts becoroe hardware and to participate in the exciteroent of cororoissioning and optiroization. I have had a nurober of opportunities for such participation at the Deutsches Elektronen Synchrotron DESY in Hamburg, Gerroany and at the Stanford University at Stanford, California and am grateful to all colleagues who hosted and collaborated with roe. I wished I could roention thero individually and apologize for not doing so. A special thanks goes to the operators of the electron storage rings SPEAR and PEP at the Stanford Linear Accelerator Center, specifically tot. Taylor, W. Graham, E. Guerra and M. Maddox, for their dedicated and able efforts to provide roe during nuroerous shifts over roany years with a working storagering ready for roachine physics experiroentation. I thank Mrs. Joanne Kwong, who typed the initial draft of this texts and introduced roe into the intricacies of TEX typesetting. The partial support by the Departroent of Energy through the Stanford Synchrotron Radiation Laboratory in preparing this text is gratefully acknowledged. Special thanks X

9 to Dr. C. Maldonado for painstakingly reading the manuscript. Last but not least I would like to thank my family for their patience in dealing with an "ahsent" husband and father. Palo Alto, California April1993 Helmut Wiedemann XI

10 Contents 1. Introduction Short Historical Overview Partide Accelerator Systems Basic Components of Accelerator Facilities Applications of Partide Accelerators Basic Definitions and Formulas Units and Dimensions Basic Relativistic Formalism Partide Collisions at High Energies Basic Principles of Partide-Beam Dynamics Stability of a Chargecl-Partide Beam Problems Linear Accelerators Principles of Linear Accelerators Charged Partides in Electric Fielcis Electrostatic Accelerators lnduction Linear Accelerator Aceeieration by rf Fielcis Basic Principle of Linear Accelerators Waveguides for High Frequency EM Waves Preinjector Beam Preparation Prebuncher Beam Chopper Problems Circular Accelerators Betatron Weak Focusing Adiabatic Damping Aceeieration by rf Fielcis Microtron Cyclotron Synchro Cyclotron Isochron Cyclotron XIII

11 3.5 Synchrotron Storage Ring Summary of Characteristic Parameters Problems Charged Particles in Electromagnetic Fields The Lorentz Force Coordinate System Fundamentals of Charged Partide Beam Optics Partide Beam Guidance Partide Beam Focusing Multipole Field Expansion Laplace Equation Magnetic Field Equations Multipole Fields for Beam Transport Systems Multipole Field Patterns and Pole Profiles Equations of Motion in Charged Partide Beam Dynamics General Solution of the Equations of Motion Linear Unperturbed Equation of Motion Wronskian Perturbation Terms Dispersion Function Building Blocks for Beam Transport Lines General Focusing Properties Chromatic Properties Achromatic Lattices Isochronaus Systems Problems Linear Beam Dynamics Linear Beam Transport Systems Nomendature Matrix Formalism in Linear Beam Dynamics Driftspace Quadrupole Magnet Thin Lens Approximation Quadrupole End Field Effects Quadrupole Design Concepts Focusing in Bending Magnets Sector Magnets Wedge Magnets Reetangular Magnet Partide Beams and Phase Space Beam Emittance Liouville's Theorem XIV

12 5.4.3 Transformation in Phase Space Measurement of the Beam Emittance Betatron Functions Beam Envelope Beam Dynamics in Terms of Betatron Functions Beam Dynamics in Normalized Coordinates Dispersive Systems Analytical Solution (3 x 3)-Transformation Matrices Linear Achromat Spectrometer Path Length and Moment um Campaction Problems Periodic Focusing Systems FODO Lattice Scaling of FODO Parameters Betatron Motion in Periodic Structures Stability Criterion General FODO Lattice Beam Dynamics in Periodic Closed Lattices Hill's Equation Periodic Betatron Functions Periodic Dispersion Function Scaling of the Dispersion in a FODO Lattice General Solution for the Periodic Dispersion Periodic Lattices in Circular Accelerators Synchrotron Lattice Phase Space Matehing Dispersion Matehing Magnet Free Insertions Low Beta Insertions Example of a Colliding Beam Storage Ring Problems Perturbations in Beam Dynamics Magnet Alignment Errors Dipole Field Perturbations Existence of Equilibrium Orbits Closed Orbit Distortion Closed Orbit Correction Quadrupole Field Perturbations Betatron Tune Shift Resonances and Stop Band Width Perturbation of Betatron Functions XV

13 7.4 Resonance Theory Resonance Conditions Coupling Resonances Resonance Diagram Chromatic Effects in a Circular Accelerator Chromaticity Chromaticity Correction Problems Charged Partide Aceeieration Longitudinal Partide Motion Longitudinal Phase Space Dynamics Equation of Motion in Phase Space Phase Stability Aceeieration of Charged Particles Longitudinal Phase Space Parameters Separatrix Parameters Momentum Acceptance Bunch Length Longitudinal Beam Emittance Phase Space Matehing.... Problems XVI Synchrotron Radiation Physics of Synchrotron Radiation Coulomb Regime Radiation Regime Spatial Distribution of Synchrotron Radiation Radiation Power Synchrotron Radiation Spectrum Photon Beam Divergence Coherent Radiation Temporal Coherent Synchrotron Radiation Spatially Coherent Synchrotron Radiation Spectral Brightness Matehing Insertion Devices Bending Magnet Radiation Wave Length Shifter Wiggler Magnet Radiation Undulator Radiation Back Scattered Photons Radiation Intensity.... Problems

14 10. Partide Beam Parameters Definition of Beam Parameters Beam Energy Time Structure Beam Current Beam Dimensions Damping Robinson Criterion Partide Distribution in Phase Space Equilibrium Phase Space Transverse Beam Parameters Variation of the Equilibrium Beam Emittance Beam Emittance and Wiggler Magnets Damping Wigglers Variation of the Damping Distribution Damping Partition and rf Frequency Robinson Wiggler Damping Partition and Synchrotron Oscillation Can We Eliminate the Beam Energy Spread? Problems Beam Life Time Beam Lifetime and Vacuum Elastic Scattering lnelastic Scattering Ultra High Vacuum System Thermal Gas Desorption Synchrotron Radiation Induced Desorption Problems Collective Phenomena Linear Space-Charge Effects Self Field for Partide Beams Forces from Space-Charge Fields Beam-Beam Effect Wake Fields Parasitic Mode Losses and lmpedances Beam Instabilities Problems Beam Emittance and Lattice Design Equilibrium Beam Emittance in Storage Rings Beam Emittance in Periodic Lattices The Double Bend Achromat Lattice (DBA) The Tripie Bend Achromat Lattice (TBA) 410 XVII

15 The Triplet Achromat Lattice (TAL) The FODO Lattice Optimum Emittance for Colliding Beam Storage Rings. 416 Problems Appendices A. Suggested Reading 419 B. Bibliography 424 References 427 Author Index 437 Subject Index 441 XVIII

16 Particle Accelerator Physics II

17 Springer-Verlag Berlin Heidelberg GmbH Physics and Astronomy ONLINE LIBRARY

18 Helmut Wiedemann Particle Accelerator Physics II Nonlinear and Higher-Order Beam Dynamics Second Edition With u8 Figures i Springer

19 Professor Dr. Helmut Wiedemann Applied Physics Department and Synchrotron Radiation Laboratory Stanford University, Stanford, CA , USA Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at < ISSN ISBN ISBN (ebook) DOI / This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1993,1999,2003 Originally published by Springer-Verlag Berlin Heidelberg New York in 2003 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data prepared by the author using a Springer TE,X macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper 55/3141/XO a

20 Preface This second edition of "Particle Accelerator Physics II" does not contain major changes in content. Primarily, errors have been eliminated as far as they have been detected. Progress made in the field of accelerator design since the publication of the first edition made it necessary to udate the bibliography. The author appreciates the many suggestions made by observant readers to reduce errors and misprints. Paolo Alto, October 1998 Helmut Wiedemann

21 Preface to the First Edition This text is a continuation of the first volume of "Particle Accelerator Physics I" on "Basic Principles and Linear Beam Dynamics". While the first volume was written as an introductory overview into beam dynamics, it does not include more detailed discussions of nonlinear and higher-order beam dynamics or the full theory of synchrotron radiation from relativistic electron beams. Both issues are, however, of fundamental importance for the design of modern particle accelerators. In this volume, beam dynamics is formulated within the realm of Hamiltonian dynamics, leading to the description of multiparticle beam dynamics with the Vlasov equation and including statistical processes with the Fokker Planck equation. Higher-order perturbations and aberrations are discussed in detail, including Hamiltonian resonance theory and higher-order beam dynamics. The discussion of linear beam dynamics in Vol. I is completed here with the derivation of the general equation of motion, including kinematic terms and coupled motion. To build on the theory of longitudinal motion in Vol. I, the interaction of a particle beam with the rf system, including beam loading, higher-order phase focusing, and the combination of acceleration and transverse focusing, is discussed. The emission of synchrotron radiation greatly affects the beam quality of electron or positron beams and we therefore derive the detailed theory of synchrotron radiation, including spatial and spectral distribution as well as properties of polarization. The results of this derivation are then applied to insertion devices such as undulator and wiggler magnets. Beam stability in linear and circular accelerators is compromized by the interaction of the electrical charge in the beam with its environment, leading to instabilities. Theoretical models of such instabilities are discussed and scaling laws for the onset and rise time of instabilities are derived. Although this text builds upon Vol. I, it relates to it only as a reference for basic issues of accelerator physics, which could be obtained as well elsewhere. This volume is aimed specifically at those stud~nts, engineers, and scientists who desire to aqcuire a deeper knowledge of particle beam dynamics in accelerators. To facilitate the use of this text as a reference, many of the more important results are emphazised by a frame for quick detection. Consistent with Vol. I we use the cgs system of units. However, for the convenience of the reader used to the system of international units, conversion factors have been added whenever such conversion is necessary,

22 VIII Preface to the First Edition e.g. whenever electrical or magnetic units are used. These conversion factors are enclosed in square brackets like [v' 471" and should be ignored by those who use formulas in the cgs system. The conversion factors are easy to identify since they include only the constants c, 71", 100,/. 0 and should therefore not be mixed up with other factors in square brackets. For the convenience of the reader, the sources of these conversion factors are compiled in the Appendix together with other useful tools. I would like to thank Joanne Kwong, who typed the initial draft of this text and introduced me to the intricacies of 'lex typesetting, and to my students who guided me through numerous inquisitive questions. Partial support by the Division of Basic Energy Sciences in the Department of Energy through the Stanford Synchrotron Radiation Laboratory in preparing this text is gratefully acknowledged. Special thanks to Dr. C. Maldonado for painstakingly reading the manuscript and to the editorial staff of Springer Verlag for support during the preparation of this text. Palo Alto, California March 1994 Helmut Wiedemann

23 Contents 1. Hamiltonian Formulation of Beam Dynamics Hamiltonian Formalism Lagrange Equations Hamiltonian Equations Canonical Transformations Action-Angle Variables Hamiltonian Resonance Theory Nonlinear Hamiltonian Resonant Terms Resonance Patterns and Stop-Band Width Third-Order Resonance Hamiltonian and Coupling Linearly Coupled Motion Higher-Order Coupling Resonances Multiple Resonances Symplectic Transformation Problems General Electromagnetic Fields General Transverse Magnetic-Field Expansion Third-Order Differential Equation of Motion Periodic Wiggler Magnets Wiggler Field Configuration Focusing in a Wiggler Magnet Hard-Edge Model of Wiggler Magnets Superconducting Magnet Problems Dynamics of Coupled Motion Conjugate Trajectories Particle Motion in a Solenoidal Field Transverse Coupled Oscillations Equations of Motion in Coupling Systems Coupled Beam Dynamics in Skew Quadrupoles Equations of Motion in a Solenoid Magnet Transformation Matrix for a Solenoid Magnet... 83

24 X Contents Betatron Functions for Coupled Motion Problems Higher-Order Perturbations Kinematic Perturbation Terms Control of the Central Beam Path Dipole Field Errors and Dispersion Function Dispersion Function in Higher Order Chromaticity in Higher Approximation Nonlinear Chromaticity Perturbation Methods in Beam Dynamics Periodic Distribution of Statistical Perturbations Statistical Methods to Evaluate Perturbations Problems Hamiltonian Nonlinear Beam Dynamics Higher-Order Beam Dynamics Multipole Errors Nonlinear Matrix Formalism Aberrations Geometric Aberrations Filamentation of Phase Space Chromatic Aberrations Particle Tracking Hamiltonian Perturbation Theory Tune Shift in Higher Order Problems Charged Particle Acceleration Accelerating Fields in Resonant rf Cavities Wave Equation Waveguide Modes rf Cavities Cavity Losses and Shunt Impedance Determination of rf Parameters Beam-Cavity Interaction Coupling Between rf Field and Particles Beam Loading and rf System Higher-Order Mode Losses in an rf Cavity Beam Loading in Circular Accelerators Higher-Order Phase Focusing Path Length in Higher Order Higher-Order Phase Space Motion Stability Criteria FODO Lattice and Acceleration

25 Contents XI Transverse Beam Dynamics and Acceleration Adiabatic Damping Problems Synchrotron Radiation Theory of Synchrotron Radiation Radiation Field Synchrotron Radiation Power and Energy Loss Spatial Distribution of Synchrotron Radiation Synchrotron Radiation Spectrum Radiation Field in the Frequency Domain Spectral Distribution in Space and Polarization Angle-Integrated Spectrum Problems Hamiltonian Many-Particle Systems The Vlasov Equation Betatron Oscillations and Perturbations Damping Damping of Oscillations in Electron Accelerators Damping of Synchrotron Oscillations Damping of Vertical Betatron Oscillations Robinson's Damping Criterion Damping of Horizontal Betatron Oscillations The Fokker-Planck Equation Stationary Solution of the Fokker-Planck Equation Particle Distribution Within a Finite Aperture Particle Distribution in the Absence of Damping. 301 Problems Particle Beam Parameters Particle Distribution in Phase Space Diffusion Coefficient and Synchrotron Radiation Quantum Excitation of Beam Emittance Horizontal Equilibrium Beam Emittance Vertical Equilibrium Beam Emittance Equilibrium Energy Spread and Bunch Length Phase-Space Manipulation Exchange of Transverse Phase-Space Parameters Exchange of Longitudinal Phase-Space Parameters Polarization of Particle Beam Problems Collective Phenomena 10.1 Statistical Effects

26 XII Contents Schottky Noise Stochastic Cooling Touschek Effect Intra-Beam Scattering Collective Self Fields Transverse Self Fields... '.' Fields from Image Charges Space-Charge Effects Longitudinal Space-Charge Field Beam-Current Spectrum Wake Fields and Impedance Definitions of Wake Field and Impedance Impedances in an Accelerator Environment Coasting-Beam Instabilities Negative-Mass Instability Dispersion Relation Landau Damping Transverse Coasting-Beam Instability Longitudinal Single-Bunch Effects Potential-Well Distortion Transverse Single-Bunch Instabilities Beam Break-Up in Linear Accelerators Fast Head-Tail Effect Head-Tail Instability Multi-Bunch Instabilities Problems Insertion Device Radiation Particle Dynamics in an Undulator Undulator Radiation Undulator Radiation Distribution Elliptical Polarization Problems Appendix References Suggested Reading Author Index Subject Index

27 Contents to Volume I 1. Introduction 1.1 Short Historical Overview 1.2 Particle Accelerator Systems Basic COJllPonents of Accelerator Facilities Applications of Particle Accelerators 1.3 Basic Definitions and Formulas Units and Dimensions Basic Relativistic Formalism Particle Collisions at High Energies 1.4 Basic Principles of Particle-Beam Dynamics Stability of a Charged-Particle Beam Problems 2. Linear Accelerators 2.1 Principles of Linear Accelerators Charged Particles in Electric Electrostatic Accelerators Induction Linear Accelerator 2.2 Acceleration by rf Fields Basic Principle of Linear Accelerators Waveguides for High Frequency EM Waves 2.3 Preinjector Beam Preparation Prebuncher Beam Chopper Problems 3. Circular Accelerators 3.1 Betatron 3.2 Weak Focusing 3.3 Adiabatic Damping 3.4 Acceleration by rf Fields Microtron Cyclotron Synchro Cyclotron Isochron Cyclotron

28 XIV Contents to Volume I 3.5 Synchrotron Storage Ring 3.6 Summary of Characteristic Parameters Problems 4. Charged Particles in Electromagnetic Fields 4.1 The Lorentz Force 4.2 Coordinate System 4.3 Fundamentals of Charged Particle Beam Optics Particle Beam Guidance Particle Beam Focusing 4.4 Multipole Field Expansion Laplace Equation Magnetic Field Equations 4.5 Multipole Fields for Beam Transport Systems 4.6 Multipole Field Patterns and Pole Profiles 4.7 Equations of Motion in Charged Particle Beam Dynamics 4.8 General Solution of the Equations of Motion Linear Unperturbed Equation of Motion Wronskian Perturbation Terms Dispersion Function 4.9 Building Blocks for Beam Transport Lines General Focusing Properties Chromatic Properties Achromatic Lattices Isochronous Systems Problems 5. Linear Beam Dynamics 5.1 Linear Beam Transport Systems Nomenclature 5.2 Matrix Formalism in Linear Beam Dynamics Driftspace Quadrupole Magnet Thin Lens Approximation Quadrupole End Field Effects Quadrupole Design Concepts 5.3 Focusing in Bending Magnets Sector Magnets Wedge Magnets Rectangular Magnet 5.4 Particle Beams and Phase Space Beam Emittance Liouville's Theorem

29 Contents to Volume I XV Transformation in Phase Space Measurement of the Beam Emittance 5.5 Betatron Functions Beam Envelope Beam Dynamics in Terms of Betatron Functions Beam Dynamics in Normalized Coordinates 5.6 Dispersive Systems Analytical Solution (3 x 3)-Transformation Matrices Linear Achromat Spectrometer 5.7 Path Length and Momentum Compaction Problems 6. Periodic Focusing Systems 6.1 FODO Lattice Scaling of FODO Parameters 6.2 Betatron Motion in Periodic Structures Stability Criterion General FODO Lattice 6.3 Beam Dynamics in Periodic Closed Lattices Hill's Equation Periodic Betatron Functions 6.4 Periodic Dispersion Function Scaling of the Dispersion in a FODO Lattice General Solution for the Periodic Dispersion 6.5 Periodic Lattices in Circular Accelerators Synchrotron Lattice Phase Space Matching Dispersion Matching Magnet Free Insertions Low Beta Insertions Example of a Colliding Beam Storage Ring Problems 1. Perturbations in Beam Dynamics 7.1 Magnet Alignment Errors 7.2 Dipole Field Perturbations Existence of Equilibrium Orbits Closed Orbit Distortion Closed Orbit Correction 7.3 Quadrupole Field Perturbations Betatron Tune Shift Resonances and Stop Band Width Perturbation of Betatron Functions

30 XVI Contents to Volume I 7.4 Resonance Theory Resonance Conditions Coupling Resonances Resonance Diagram 7.5 Chromatic Effects in a Circular Accelerator Chromaticity Chromaticity Correction Problems 8. Charged Particle Acceleration 8.1 Longitudinal Particle Motion Longitudinal Phase Space Dynamics Equation of Motion in Phase Space Phase Stability Acceleration of Charged Particles 8.2 Longitudinal Phase Space Parameters Separatrix Parameters Momentum Acceptance Bunch Length Longitudinal Beam Emittance Phase Space Matching Problems 9. Synchrotron Radiation 9.1 Physics of Synchrotron Radiation Coulomb Regime Radiation Regime Spatial Distribution of Synchrotron Radiation Radiation Power Synchrotron Radiation Spectrum Photon Beam Divergence 9.2 Coherent Radiation Temporal Coherent Synchrotron Radiation Spatially Coherent Synchrotron Radiation Spectral Brightness Matching 9.3 Insertion Devices Bending Magnet Radiation Wave Length Shifter Wiggler Magnet Radiation Undulator Radiation 9.4 Back Scattered Photons Radiation Intensity Problems

31 Contents to Volume I XVII 10. Particle Beam Parameters 10.1 Definition of Beam Parameters Beam Energy Time Structure Beam Current Beam Dimensions 10.2 Damping Robinson Criterion 10.3 Particle Distribution in Phase Space Equilibrium Phase Space Transverse Beam Parameters 10.4 Variation of the Equilibrium Beam Emittance Beam Emittance and Wiggler Magnets Damping Wigglers 10.5 Variation of the Damping Distribution Damping Partition and rf Frequency Robinson Wiggler Damping Partition and Synchrotron Oscillation Can We Eliminate the Beam Energy Spread? Problems 11. Beam LiCe Time 11.1 Beam Lifetime and Vacuum Elastic Scattering Inelastic Scattering 11.2 Ultra High Vacuum System Thermal Gas Desorption Synchrotron Radiation Induced Desorption Problems 12. Collective Phenomena 12.1 Linear Space-Charge Effects Self Field for Particle Beams Forces from Space-Charge Fields 12.2 Beam-Beam Effect 12.3 Wake Fields Parasitic Mode Losses and Impedances 12.4 Beam Instabilities Problems 13. Beam Emittance and Lattice Design 13.1 Equilibrium Beam Emittance in Storage Rings 13.2 Beam Emittance in Periodic Lattices The Double Bend Achromat Lattice (DBA) The Triple Bend Achromat Lattice (TBA)

32 XVIII Contents to Volume I The Triplet Achromat Lattice (TAL) The FODO Lattice 13.3 Optimum Emittance for Colliding Beam Storage rungs Problems Bibliography References Author Index Subject Index