The Principles of Circular Accelerators and Storage Rings

384 Pages·2005·8.62 MB·English

by  Philip J. Bryant

This book is a basic introduction to the principles of circular particle accelerators
and storage rings, for scientists, engineers and mathematicians.
Particle accelerators used to be the exclusive province of physicists exploring
the structure of the most fundamental constituents of matter. Nowadays, particle
accelerators have also found uses as tools in many other areas, including materials
science, chemistry, and medical science. Many people from these fields of study,
as well as from particle physics, have learned about accelerators at various courses
organised by CERN, the European Organisation for Nuclear Research, which has
established a reputation as the world's top accelerator facility. Kjell Johnsen and
Phil Bryant, the authors of this book, are distinguished accelerator physicists
who have also run the CERN Accelerator School. The text they present here starts
with a historical introduction to the field and an outline of the basic concepts of
particle accelerators. It goes on to give more details of how the transverse and
longitudinal motions of the particle beams can be analysed, including treatments
of lattice design, compensation schemes, phase focusing, transition crossing, and
other radio frequency effects. Operational and diagnostic techniques and the
optimisation of luminosity are discussed in detail. One chapter is devoted to
synchrotron radiation and the special features of synchrotron light sources.
Although the book emphasises circular machines, much of the treatment applies
equally to linear machines and transfer lines.
The book will be an essential reference for anyone working with particle
accelerators as a designer, operator or user, as well as being a good preparation
for those intending to go to the frontiers of accelerator physics.

The Principles of
Circular Accelerators
and Storage Rings
Philip J. Bryant
CERN, Geneva, Switzerland
Kjell Johnsen
Formerly of CERN, Geneva, Switzerland
CAMBRIDGE
UNIVERSITY PRESS
PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
CAMBRIDGE UNIVERSITY PRESS
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© Cambridge University Press 1993
This book is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 1993
First paperback edition 2005
A catalogue record for this book is available from the British Library
Library of Congress cataloguing in publication data
Bryant, Philip J.
The principles of circular accelerators and storage rings /
Philip J. Bryant, Kjell Johnsen.
p. cm.
ISBN 0 521 35578 8 hardback
1. Particle accelerators. 2. Storage rings. I. Johnsen, Kjell.
II. Title.
QC787.P3B79 1993
539.7'3—dc20 92-17737 C1P
ISBN 0 521 35578 8 hardback
ISBN 0 521619696 paperback
The Principles of
Circular Accelerators and Storage Rings

CONTENTS
Foreword xv
Coordinate system xvii
Symbols xix
Useful constants xxv
1 Introduction 1
1.1 Direct-voltage accelerators 3
1.1.1 Cockcroft-Walton rectifier generator 3
1.1.2 Van de Graaff generator 3
1.1.3 Tandem electrostatic accelerator 4
1.2 Accelerators that use time-varying fields 6
1.2.1 Principle of the Wideroe rf linear accelerator 6
1.2.2 Fixed-frequency cyclotron 7
1.2.3 Synchro-cyclotron or frequency-modulated cyclotron 7
1.2.4 Betatron 9
1.2.5 Synchrotron 10
1.2.6 The linear accelerator revisited 12
1.2.7 Other accelerators 13
1.3 Storage rings 13
1.4 Linear colliders 15
1.5 Concluding remarks 15
2 Basic concepts and constant-gradient focusing 17
2.1 Cyclotron motion 17
2.2 Transverse motion 19
2.2.1 Radial motion 19
2.2.2 Vertical motion 21
2.3 Solutions 21
vn
Contents
2.4 Stability 22
2.5 Acceptance and emittance 23
2.6 Momentum compaction 25
2.7 Historical note 26
3 Alternating-gradient focusing 28
3.1 A segment of a magnet as a focusing element 28
3.1.1 Relation between vertical and horizontal focusing 30
3.1.2 Point lens 32
3.1.3 Doublet 34
3.2 Simple description of an alternating-gradient accelerator 36
3.2.1 Stability criterion 37
3.2.2 'Necktie' stability plot 38
3.3 Edge focusing 40
3.3.1 Hard-edge model 41
3.3.2 Edge focusing in the plane of bending 42
3.3.3 Edge focusing perpendicular to the plane of bending 44
3.3.4 General formulation of edge focusing 46
3.4 Motion with a momentum deviation 46
3.4.1 Equations of motion 47
3.4.2 Local dispersion function 49
3.4.3 Momentum compaction in alternating-gradient lattices 50
3.5 General remarks 52
4 Parameterisation of the transverse motion 53
4.1 Parameterisation 53
4.1.1 Generalised transfer matrix 55
4.1.2 The transfer matrix for a periodic lattice 56
4.2 Invariant of the unperturbed motion 57
4.3 Propagation of the Courant and Snyder parameters 58
4.3.1 3x3 matrix solution 58
4.3.2 2x2 matrix solution 58
4.4 Emittance and acceptance 59
4.5 Distinctions between circular machines and transfer lines 61
4.5.1 Circular machines 61
4.5.2 Transfer lines 63
4.6 Motion with a momentum deviation 63
4.6.1 Principal trajectories 63
4.6.2 Use of principal trajectories to express the dispersion function for a circular
machine 64
4.6.3 Dispersion invariant 66
Vlll
Contents
4.7 A simple approach to lattice design 67
4.7.1 FODO matched cells in arcs and straight sections 68
4.7.2 Dispersion suppressors embedded in a FODO lattice 73
4.7.3 Matching 79
4.7.4 Injection and extraction 87
4.8 General remarks 89
5 Imperfections and resonances 91
5.1 Closed-orbit distortion from dipole kicks 91
5.1.1 Qualitative description of a closed orbit 93
5.1.2 Closed-orbit bumps 95
5.1.3 Harmonic response of the closed orbit 99
5.2 Gradient deviations 100
5.2.1 Stability and tune shifts 100
5.2.2 Betatron amplitude modulation 101
5.3 Weak linear coupling 103
5.3.1 Coupling in uniform skew quadrupole and longitudinal fields: basic
equations 104
5.3.2 Normal modes 109
5.3.3 Observations with coupling 112
5.3.4 Results from a more exact analysis 114
5.3.5 Vertical dispersion and compensation schemes 115
5.4 Non-linear resonances 117
6 Chromaticity 120
6.1 Chromatic effects 120
6.2 Evaluation of the chromaticity 120
6.2.1 Chromaticity and natural chromaticity 120
6.2.2 A more careful evaluation of the chromaticity 123
6.2.3 Higher orders of the chromaticity 124
6.3 Adjusting the chromaticity 124
6.3.1 Compensation of the natural chromaticity of a quadrupole 124
6.3.2 A simple scheme for chromaticity control 125
6.4 The w-vector formulation of chromatic effects 126
6.4.1 Basic theory 126
6.4.2 The w-vector in a FODO lattice 129
6.4.3 Strategy for the chromaticity correction in a collider 129
6.5 Analytic expressions for the chromatic variables 131
6.5.1 Approximate expressions for a and b 131
6.5.2 Exact expressions for a and b 131
6.5.3 Summation over a series of sextupoles 132
ix