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2 A Practical Introduction to Beam Physics and Particle Accelerators

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4 A Practical Introduction to Beam Physics and Particle Accelerators Santiago Bernal Institute for Research in Electronics and Applied Physics, University of Maryland, College Park Morgan & Claypool Publishers

5 Copyright ª 2016 Morgan & Claypool Publishers All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, or as expressly permitted by law or under terms agreed with the appropriate rights organization. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright Clearance Centre and other reproduction rights organisations. Rights & Permissions To obtain permission to re-use copyrighted material from Morgan & Claypool Publishers, please contact info@morganclaypool.com. ISBN ISBN ISBN (ebook) (print) (mobi) DOI / Version: IOP Concise Physics ISSN (online) ISSN (print) A Morgan & Claypool publication as part of IOP Concise Physics Published by Morgan & Claypool Publishers, 40 Oak Drive, San Rafael, CA, 94903, USA IOP Publishing, Temple Circus, Temple Way, Bristol BS1 6HG, UK

6 To the Memory of Martin Reiser ( )

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8 Contents Preface Acknowledgments Author biography ix x xi 1 Rays and matrices Paraxial approximation Thin lens Thick lens 1-4 References Linear magnetic lenses and deflectors Magnetic rigidity, momentum, and cyclotron frequency Solenoid focusing Quadrupole focusing The Kerst Serber equations and weak focusing Dipoles and edge focusing Effective hard-edge model of fringe fields in focusing magnets 2-11 References Periodic lattices and functions Solenoid lattice FODO lattice Lattice and beam functions Uniform-focusing ( smooth ) approximation Linear dispersion Momentum compaction, transition gamma, and chromaticity 3-11 References Emittance and space charge Liouville s theorem and emittance The Kapchinskij Vladimirskij (K V) and thermal distributions The K V envelope equations and space-charge (SC) intensity parameters 4-7 vii

9 A Practical Introduction to Beam Physics and Particle Accelerators 4.4 Incoherent space-charge (SC) betatron tune shift Coherent tune shift and Laslett coefficients 4-14 References Longitudinal beam dynamics and radiation Radio-frequency (RF) linacs Beam bunch stability and RF bucket Synchrotron radiation Insertion devices and free-electron lasers (FELs) Longitudinal beam emittance and space charge 5-11 References Applications and examples Periodic-envelope FODO matching Betatron resonances Examples of linacs Examples of rings 6-10 References 6-17 Appendix Computer resources and their use A-1 viii

10 Preface This book is a brief exposition of the principles of beam physics and particle accelerators with emphasis on numerical examples employing readily available computer tools. The same basic ideas can be found with different styles and emphasis in a number of excellent books on beam and accelerator physics: Bryant-Johnsen, Chao, Davidson-Qin, Edwards-Syphers, Lawson, Lee, Reiser, Rosenzweig, Wangler, Wiedemann, Wille, to name a few, and in countless online documents from accelerator schools (USPAS and CERN). However, we avoid detailed derivations, instead inviting the reader to use general high-end languages such as Mathcad and Matlab, as well as specialized particle accelerator codes (e.g. MAD, WinAgile, Elegant, and others) to explore the principles presented. This approach allows the student to readily identify relevant design parameters and their scaling. In addition, the computer input files can serve as templates that can be easily adapted to other related situations. The examples and computer exercises comprise basic lenses and deflectors, fringe fields, lattice and beam functions, synchrotron radiation, beam envelope matching, betatron resonances, and transverse and longitudinal emittance and space charge. The last chapter presents examples of two major types of particle accelerators: radio frequency linear accelerators (RF linacs) and storage rings. Lastly, the appendix gives the reader a brief description of the computer tools employed and concise instructions for their installation and use in the most popular computer platforms (Windows, Macintosh and Ubuntu Linux). Hyperlinks to websites containing all relevant files are also included. An essential component of the book is its website (actually part of the author s website at the University of Maryland). It contains the files that reproduce results given in the text as well as additional material such as technical notes and movies. We will add new or updated material as it is developed. Although we have chosen Mathcad for most examples, we will add Matlab and Python scripts in the near future. ix

11 Acknowledgments We thank all members of the University of Maryland Electron Ring (UMER) group. The discussions we have had over the years and the study of Professor Martin Reiser s book Theory and Design of Charged-Particle Beams were the inspiration that led to the present book. Special thanks to Max Cornacchia, former visiting scientist at the University of Maryland, for many insightful physics discussions and invaluable help with the Elegant code. We also thank Dr Brian Beaudoin for his hard work and continuous assistance with experiments and for useful hints on longitudinal space charge issues; Dr David Sutter for many insights particularly on experimental and historical aspects of accelerators; Dorothea Brosius for her help in setting up the book s website;drchrisallen(oakridge National Lab) for granting us permission to include his beam envelope code SPOT in our website; Dr Hui Li (Confer Technologies, Inc.) for his Matlab application code Menv, and Dr Valter Kiisk (University of Tartu in Estonia) for his Mathcad program 2D Optical Ray Tracer. We also acknowledge the patience and support from our family and the publishers. Last, but not least, we acknowledge the continuing financial support of the Office of Science, Office of High Energy Physics of the US Department of Energy. Matlab is a registered trademark of MathWorks, Python is a trademark of Python Software Foundation. x

12 Author biography Santiago Bernal Santiago Bernal obtained a BSc in physics from the Universidad Nacional de Colombia in Bogotá, Colombia in 1981, an MSc in physics from Georgia Tech in 1983, and a PhD in physics from the University of Maryland, College Park in He worked for his PhD under the direction of the late Professor Martin Reiser. Before his graduate studies at Maryland, Dr Bernal taught college physics and math in Colombia and Puerto Rico. Dr Bernal joined the UMER group in 2000 as a postdoc, later becoming a research scientist at the Institute for Research in Electronics and Applied Physics (IREAP). He was involved in the design and construction of UMER and has been a leading experimentalist in the project. Dr Bernal helped organize and conduct an experimental course in UMER for the 2008 US Particle Accelerator School. He is the junior coauthor with Charles L Joseph (Rutgers University) of Modern Devices: The Simple Physics of Modern Technology (Wiley, 2016). Chapter 22 of Modern Devices contains a general discussion of a few additional topics on particle accelerators such as cyclotrons, not covered in this book. Besides beam and accelerator physics, Dr Bernal is interested in statistical mechanics and educational aspects of physics. xi