Table Of ContentHands-On Accelerator Physics
®
Using MATLAB
Hands-On Accelerator Physics
®
Using MATLAB
Volker Ziemann
Front cover image reproduced with permission from Marek Jacewicz.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2019 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
Version Date: 20190410
International Standard Book Number-13: 978-1-138-58994-0 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been
made to publish reliable data and information, but the author and publisher cannot assume responsibility for the
validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copy-
right holders of all material reproduced in this publication and apologize to copyright holders if permission to publish
in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know
so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or
utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including pho-
tocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission
from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://
www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA
01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users.
For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been
arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for
identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface xi
Acknowledgments xiii
hapter
C 1(cid:4) Introduction and History 1
hapter
C 2(cid:4) Reference System 13
2.1 THEREFERENCETRAJECTORY 13
2.2 COORDINATETRANSFORMATIONS 16
2.3 PARTICLESANDTHEIRDESCRIPTION 18
2.4 PARTICLEENSEMBLES,BUNCHES 19
hapter
C 3(cid:4) Transverse Beam Optics 27
3.1 MAGNETSANDMATRICES 28
3.1.1 Thin quadrupoles 29
3.1.2 Thick quadrupoles 31
3.1.3 Sector dipole 32
3.1.4 Combined function dipole 34
3.1.5 Rectangular dipole 35
3.1.6 Coordinate rotation 36
3.1.7 Solenoid 37
3.1.8 Non-linear elements 37
3.2 PROPAGATINGPARTICLESANDBEAMS 38
3.3 TWO-DIMENSIONAL 40
3.3.1 Beam optics in MATLAB 40
3.3.2 Poincar`e section and tune 42
3.3.3 FODO cell and beta functions 44
3.3.4 A complementary look at beta functions 47
3.3.5 Beam size and emittance 49
3.4 CHROMATICITYANDDISPERSION 52
3.4.1 Chromaticity 52
3.4.2 Dispersion 54
3.4.3 Emittance generation 58
v
vi (cid:4) Contents
3.4.4 Momentum compaction factor 60
3.5 FOUR-DIMENSIONALANDCOUPLING 60
3.6 MATCHING 65
3.6.1 Matching the phase advance 65
3.6.2 Match beta functions to a waist 66
3.6.3 Point-to-point focusing 68
3.7 BEAM-OPTICALSYSTEMS 70
3.7.1 Telescopes 70
3.7.2 Triplets 71
3.7.3 Doublets 74
3.7.4 Achromats 75
3.7.5 Multi-bend achromats 77
3.7.6 TME cell 78
3.7.7 Dispersion suppressor 79
3.7.8 Interaction region 80
3.7.9 Bunch compressors 81
hapter
C 4(cid:4) Magnets 85
4.1 MAXWELL’SEQUATIONSANDBOUNDARYCONDITIONS 85
4.2 2D-GEOMETRIESANDMULTIPOLES 87
4.3 IRON-DOMINATEDMAGNETS 89
4.3.1 Simple analytical methods 89
4.3.2 Using the MATLAB PDE toolbox 91
4.3.3 Quadrupoles 98
4.3.4 Technological aspects 99
4.4 SUPER-CONDUCTINGMAGNETS 101
4.4.1 Simple analytical methods 102
4.4.2 PDE toolbox 103
4.5 PERMANENTMAGNETS 106
4.5.1 Multipoles 108
4.5.2 Segmented multipoles 110
4.5.3 Undulators and wigglers 112
4.6 MAGNETMEASUREMENTS 114
4.6.1 Hall probe 114
4.6.2 Rotating coil 115
4.6.3 Undulator measurements 116
hapter
C 5(cid:4) Longitudinal Dynamics and Acceleration 119
5.1 PILL-BOXCAVITY 120
5.2 TRANSIT-TIMEFACTOR 124
5.3 PHASESTABILITYANDSYNCHROTRONOSCILLATIONS 124
Contents (cid:4) vii
5.4 LARGE-AMPLITUDEOSCILLATIONS 127
5.5 RFGYMNASTICS 133
5.6 ACCELERATION 134
5.7 ASIMPLEWORKEDEXAMPLE 137
hapter
C 6(cid:4) Radio-Frequency Systems 143
6.1 POWERGENERATIONANDCONTROL 143
6.2 POWERTRANSPORT:WAVEGUIDESANDTRANSMISSIONLINES 145
6.3 COUPLERSANDANTENNAS 153
6.4 POWERTOTHEBEAM:RESONATORSANDCAVITIES 156
6.4.1 Losses and quality factor Q of a pill-box cavity 156
0
6.4.2 General cavity geometry with the PDE toolbox 159
6.4.3 Disk-loaded waveguides 160
6.5 TECHNOLOGICALASPECTS 163
6.5.1 Normal-conducting 163
6.5.2 Super-conducting 164
6.6 INTERACTIONWITHTHEBEAM 165
6.6.1 Beam loading 165
6.6.2 Steady-state operation 166
6.6.3 Pulsed operation and transient beam loading 167
6.6.4 Low-level RF system 170
hapter
C 7(cid:4) Instrumentation and Diagnostics 173
7.1 ZEROTHMOMENT:CURRENT 173
7.2 FIRSTMOMENT:BEAMPOSITIONANDARRIVALTIME 175
7.3 SECONDMOMENT:BEAMSIZE 180
7.4 EMITTANCEANDBETAFUNCTIONS 183
7.5 SPECIALTYDIAGNOSTICS 185
7.5.1 Turn-by-turn position monitor data analysis 186
7.5.2 Beam-beam diagnostics 188
7.5.3 Schottky diagnostics 189
hapter
C 8(cid:4) Imperfections and Their Correction 193
8.1 SOURCESOFIMPERFECTIONS 194
8.1.1 Misalignment and feed down 194
8.1.2 Tilted components 196
8.1.3 Rolled elements and solenoids 197
8.1.4 Chromatic effects 197
8.1.5 Consequences 197
8.2 IMPERFECTIONSINBEAMLINES 198
8.2.1 Dipole kicks and orbit errors 198
viii (cid:4) Contents
8.2.2 Quadrupolar errors and beam size 198
8.2.3 Skew-quadrupolar perturbations 200
8.2.4 Filamentation 201
8.3 IMPERFECTIONSINARING 203
8.3.1 Misalignment and dipole kicks 203
8.3.2 Gradient imperfections 204
8.3.3 Skew-gradient imperfections 205
8.4 CORRECTIONINBEAMLINES 207
8.4.1 Trajectory knobs and bumps 208
8.4.2 Orbit correction 209
8.4.3 Beta matching 212
8.4.4 Dispersion and chromaticity 213
8.5 CORRECTIONINRINGS 213
8.5.1 Orbit correction 214
8.5.2 Dispersion-free steering 215
8.5.3 Tune correction 215
8.5.4 Chromaticity correction 216
8.5.5 Coupling correction 217
8.5.6 Orbit response-matrix based methods 217
8.5.7 Feedback systems 218
hapter
C 9(cid:4) Targets and Luminosity 221
9.1 EVENTRATEANDLUMINOSITY 221
9.2 ENERGYLOSSANDSTRAGGLING 222
9.3 TRANSVERSE SCATTERING, EMITTANCE GROWTH, AND LIFE-
TIME 226
9.4 COLLIDINGBEAMS 228
9.5 BEAM-BEAMLUMINOSITY 229
9.6 INCOHERENTBEAM-BEAMTUNESHIFT 233
9.7 COHERENTBEAM-BEAMINTERACTIONS 235
9.8 LINEARCOLLIDERS 237
hapter
C 10(cid:4) Synchrotron Radiation and Free-Electron Lasers 241
10.1 EFFECTONTHEBEAM 242
10.1.1 Longitudinally 242
10.1.2 Vertically 244
10.1.3 Horizontally 244
10.1.4 Quantum lifetime 246
10.2 CHARACTERISTICSOFTHEEMITTEDRADIATION 247
10.2.1 Dipole magnets 248
10.2.2 Undulators and wigglers 249
Contents (cid:4) ix
10.3 SMALL-GAINFREE-ELECTRONLASER 251
10.3.1 Amplifier and oscillator 251
10.4 SELF-AMPLIFIEDSPONTANEOUSEMISSION 254
10.5 ACCELERATORCHALLENGES 257
hapter
C 11(cid:4) Non-linear Dynamics 259
11.1 AONE-DIMENSIONALTOYMODEL 259
11.2 TRACKINGANDDYNAMICAPERTURE 261
11.3 HAMILTONIANSANDLIE-MAPS 263
11.3.1 Moving Hamiltonians 265
11.3.2 Concatenating Hamiltonians 267
11.4 IMPLEMENTATIONINMATLAB 267
11.5 TWO-DIMENSIONALMODEL 271
11.6 KNOBSANDRESONANCE-DRIVINGTERMS 272
11.7 NON-RESONANTNORMALFORMS 275
hapter
C 12(cid:4) Collective Effects 279
12.1 SPACECHARGE 279
12.2 INTRABEAMSCATTERINGANDTOUSCHEK-EFFECT 282
12.3 WAKEFIELDS,IMPEDANCES,ANDLOSSFACTORS 283
12.4 COASTING-BEAMINSTABILITY 286
12.5 SINGLE-BUNCHINSTABILITIES 288
12.6 MULTI-BUNCHINSTABILITIES 291
hapter
C 13(cid:4) Accelerator Subsystems 295
13.1 CONTROLSYSTEM 295
13.1.1 Sensors, actuators, and interfaces 295
13.1.2 System architecture 296
13.1.3 Timing system 297
13.1.4 An example: EPICS 297
13.2 PARTICLESOURCES 299
13.2.1 Electrons 299
13.2.2 Protons and other ions 301
13.2.3 Highly charged ions 302
13.2.4 Negatively charged ions 302
13.2.5 Radio-frequency quadrupole 303
13.3 INJECTIONANDEXTRACTION 304
13.4 BEAMCOOLING 306
13.5 VACUUM 307
13.5.1 Vacuum basics 307
13.5.2 Pumps and gauges 308
