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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Offers a clear and practical introduction to the essentials of charged particle beam physics, covers the design of accelerator machines and their basic components
A cornerstone of modern accelerator technology, charged particle beam physics encompasses theoretical principles, advanced simulations, and real-world applications. Charged Particle Beam Physics: An Introduction for Physicists and Engineers provides a comprehensive foundation for understanding, modeling, and implementing beam optics components in accelerator systems.
Combining essential concepts with cutting-edge techniques, such as the transfer-matrix method and numerical simulation tools, this detailed yet accessible textbook simplifies the core concepts and principles of the complex field. Reader-friendly chapters systematically address ion sources, beam optics design, advanced diagnostic and vacuum systems, and more. Authors Sarvesh Kumar and Manish K. Kashyap discuss key topics such as electrostatic, magnetostatic, and radiofrequency fields, as well as practical applications in materials science, plasma physics, and radiation biology.
Bridging theoretical knowledge with practical implementation, Charged Particle Beam Physics:
- Provides in-depth coverage of charged particle beam physics, relevant to both single-pass configurations and standard beam transport lines across accelerator systems
- Combines elements of electrodynamics, particle physics, optics, and engineering for a holistic understanding
- Explores state-of-the-art methods such as open-source beam optics codes
- Includes end-of-chapter problems and worked solutions, along with numerical examples using open-source tools such as TRANSPORT and TRACE3d
Charged Particle Beam Physics: An Introduction for Physicists and Engineers is ideal for graduate-level students in physics and engineering courses focused on accelerator physics and beam optics, as well as researchers and professionals working in accelerator design and operation. It serves as both a teaching resource and a reference for practitioners tackling fundamental calculations and developing accelerator components across various disciplines.
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Seitenzahl: 432
Veröffentlichungsjahr: 2025
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Dedication
Foreword
Preface
About the Authors
Acknowledgments
Acronyms
About the Companion Website
Chapter 1: Introduction to Charged Particle Beams
1.1 History of Particle Accelerators and the Chronological Milestones
1.2 Maxwell’s Equations
1.3 Electrostatic Accelerators
1.4 Cyclotrons
1.5 Synchrotrons
1.6 Synchrocyclotron
1.7 Betatron
1.8 Particle Colliders
1.9 FFAG Accelerators
1.10 Wakefield Accelerators
1.11 Radiation Physics
1.12 Beam Conceptual Visualization
1.13 Numerical Problems
Chapter 2: Ion Sources
2.1 ECR Ion Sources
2.2 SNICS Ion Source
2.3 Duoplasmatron
2.4 Electron Beam Ion Source
2.5 Penning Ion Sources
2.6 Laser Ion Sources
2.7 Vacuum Arc Ion Source
2.8 Numerical Problems
Chapter 3: Beam Optics
3.1 Phase Space and Liouville’s Theorem
3.2 Emittance and Acceptance
3.3 Brightness
3.4 Luminosity
3.5 Matrix Formalism
3.6 Equation of Motion in a Co-moving Coordinate System
3.7 Hill’s Equation and Twiss Parameters Formalism
3.8 Horizontal and Vertical Root Mean Square Beam Sizes in Accelerators
3.9 Betatron Phase Advance and Tune
3.10 Chromaticity
3.11 RMS Emittance
3.12 Space Charge Effects on Ion Beam
3.13 Numerical Problems
Chapter 4: Motion in Magnetostatic Devices
4.1 Magnetostatic Devices
4.2 Ampere’s Law for Magnet Design
4.3 Equation of Motion in a Co-moving Coordinate System
4.4 Drift
4.5 Dipole Magnets
4.6 Design of Dipole Magnets
4.7 Quadrupole Magnets
4.8 Beam Rotation Matrix
4.9 Solenoid Magnets
4.10 Sextupole Magnets
4.11 Magnetostatic Steerer/Deflector
4.12 Wien Filter
4.13 Achromatic Magnets
4.14 Septum and Kicker Magnets
4.15 Glaser Lens
4.16 Undulators
4.17 Wigglers
4.18 Numerical Problems
Chapter 5: Electrostatic Devices
5.1 Motion of a Charged Particle in an Electric Field
5.2 Electrostatic Dipole
5.3 Electrostatic Quadrupole
5.4 Electrostatic Thin Lens and Einzel Lens
5.5 Electrostatic Steerer/Deflector
5.6 Electrostatic Accelerating Tube
5.7 Electrostatic Septum
5.8 Numerical Problems
Chapter 6: Radio Frequency Devices
6.1 Longitudinal Beam Dynamics
6.2 Pillbox Cavity
6.3 Traveling Wave Structures
6.4 Standing Wave Structures
6.5 Phase Stability in LINACs
6.6 Radial Impulse and Deflection in an RF Gap
6.7 RF Chopper
6.8 RF Buncher
6.9 RF Acceleration
6.10 Quarter-wave and Half-wave Resonators
6.11 Radio Frequency Quadrupole
6.12 Drift Tube LINACS
6.13 Numerical Problems
Chapter 7: Beam Diagnostics
7.1 Faraday Cups
7.2 Beam Profile Monitor
7.3 Beam Position Monitors
7.4 Beam Current Transformers
7.5 Capacitive Pick-up Probes
7.6 Fast Faraday Cups
7.7 Phase Detector Cavity
7.8 Transverse Beam Emittance by Quadrupole Magnet Scan
7.9 Longitudinal Beam Emittance by Buncher Scan
7.10 Energy Spread Measurements
7.11 Ion Bunch Width Using Detectors
7.12 Numerical Problems
Chapter 8: Vacuum Devices
8.1 Basics of Vacuum Technology
8.2 Vacuum Accessories and Subcomponents
8.3 Vacuum Pumps
8.4 Vacuum Gauges
8.5 Helium Leak Detector: Mathematical Principles
8.6 Numerical Problems
Appendix A: Field-induced Breakdown in Accelerator Technologies
Paschen’s Law for the Breakdown Voltage of Gases
Appendix B: Panofsky–Wenzel Theorem in Accelerator Physics
Appendix C: Child–Langmuir Law and Richardson’s Law
Appendix D: Larmor’s Formula and Its Importance in Accelerator Physics
Appendix E: Stefan–Boltzmann Law and Its Applications in Particle Accelerators
Bibliography
Index
End User License Agreement
List of Illustrations
Chapter 1
Figure 1.1 Velocity behavior of different charged particles as they approach the speed of light.
Figure 1.2 Velocity and magnetic rigidity of different ion beams of mass M (amu) at 500 MeV...
Figure 1.3 Schematic of a Cockcroft–Walton accelerator.
Figure 1.4 Voltage flow in Cockcroft–Walton multiplier circuit.
Figure 1.5 Schematic of a Tandem accelerator.
Figure 1.6 (a) Collection of like charges, which never wants to stay together. (b) Beam ...
Chapter 2
Figure 2.1 Schematic of an ECR ion source.
Figure 2.2 Schematics of MC-SNICS.
Figure 2.3 Schematics of duoplasmatron. EE: extraction electrode; EC: expansion cup; IE: in...
Figure 2.4 Schematics of EBIS. EXT: extraction electrode; ER: electron repeller; EC: electr...
Figure 2.5 Schematics of the Penning ion source, with two cathodes at same potential.
Figure 2.6 Schematics of laser ion source. LEBT: low energy beam transport.
Chapter 3
Figure 3.1 Phase space ellipse in various forms.
Figure 3.2 Mass flux into a given volume.
Figure 3.3 Sinusoidal oscillations of particles and their elliptical phase representations ...
Figure 3.4 (a) Rotated co-moving coordinate system describing the beam motion relative to ...
Figure 3.5 Phase space ellipse characterized by Twiss parameters and emittances.
Figure 3.6 Parallel beam current formed by positively charged particles.
Chapter 4
Figure 4.1 Beam optics of dipole magnet using COSY Infinity. (a) Bending X-plane with rays ...
Figure 4.2 C-type magnet.
Figure 4.3 H-type magnet and window-frame magnet.
Figure 4.4 Poisson simulation [66–68] drawing of the H-type magnet (scales are in mm).
Figure 4.5 Edge focusing and defocusing in dipole magnets.
Figure 4.6 Quadrupole magnet configuration for vertical focusing and horizontal defocusing.
Figure 4.7 Beam optics for a quadrupole triplet magnet using COSY Infinity capable for focu...
Figure 4.8 Longitudinal Field plot for Solenoid magnet as per above equation 4.101.
Figure 4.9 Beam optics for solenoid magnet for 1 MeV proton beam.
Figure 4.10 2D field configuration of solenoid magnet using Poisson/superfish code [67...
Figure 4.11 Longitudinal field mapping of solenoid magnet.
Figure 4.12 Deflection of beam by two steerer magnets and deflection of charged particle by ...
Figure 4.13 Schematics of Wien filter.
Figure 4.14 Beam optics for Wien filter for 1 MeV proton beam with energy spread 1%. It is d...
Figure 4.15 Collective action of kicker and septum over beam, and are deflection ...
Figure 4.16 Axial symmetric Glaser magnet.
Chapter 5
Figure 5.1 Beam optics for a 90° ESD with X profile, Y profile, and resulting transfer matrix ...
Figure 5.2 Focusing and defocusing scheme for a positively charged particle inside electros...
Figure 5.3 Beam optics for a electrostatic quadrupole triplet using COSY Infinity capable f...
Figure 5.4 Schematics of Einzel lens in decelerating accelerating mode.
Figure 5.5 Focusing term in einzel lens versus R.
Figure 5.6 Focal length of einzel lens versus the central voltage for 45 keV ion beam.
Figure 5.7 Two types of einzel configurations.
Figure 5.8 Beam optics using COSY Infinity for two types of einzel configurations as per Fi...
Figure 5.9 Deflection of charged particle in electric field.
Figure 5.10 For calculations of beam focusing by an EAT.
Chapter 6
Figure 6.1 Inherent transverse defocusing effect in RF gap structure [86]/CERN.
Figure 6.2 Voltage across RF gap: B dot for bunching, R dot for acceleration and longitudin...
Figure 6.3 Behavior of T with geometrical parameters and incoming velocity.
Figure 6.4 Arrangement of drift tube inside a LINAC.
Figure 6.5 Radial and longitudinal field plot along the gap.
Figure 6.6 Radial and longitudinal field plot along the gap.
Figure 6.7 Particle riding over RF field.
Figure 6.8 Wideroe structure.
Figure 6.9 Different modes of the cavity.
Chapter 7
Figure 7.1 Beam profiling in transverse directions by wire scanner.
Figure 7.2 Beam pickup signal by pickup electrodes.
Figure 7.3 Schematics of button BPM where A, B, C, and D are pickup electrodes.
Figure 7.4 Beam bunching using a 50 ohm FFC.
Figure 7.5 Schematic of emittance measurements using quadrupole scan method.
Chapter 8
Figure 8.1 Comparison of various vacuum pumps in terms of their approximated capability.
List of Tables
Chapter 1
Table 1.1 Chronological evolution of particle accelerators worldwide.
Table 1.2 Comparison of circular accelerators.
Chapter 2
Table 2.1 Classification of ion sources based on ionization mechanism.
Chapter 4
Table 4.1 Multipoles and their effects on particle motion.
Guide
Cover
Table of Contents
Title Page
Copyright
Dedication
Foreword
Preface
About the Authors
Acknowledgments
Acronyms
About the Companion Website
Begin Reading
Bibliography
Index
End User License Agreement
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Charged Particle Beam Physics
An Introduction for Physicists and Engineers
Sarvesh Kumar
Inter University Accelerator Center, New Delhi, India
Manish K. Kashyap
Jawaharlal Nehru University, New Delhi, India
Authors
Sarvesh Kumar
Inter University Accelerator Center, New Delhi
India
Manish K. Kashyap
Jawaharlal Nehru University, New Delhi
India
Cover Design: Wiley
Cover Image: © TK
All books published by WILEY-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.: applied for
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Bibliographic information published by the Deutsche Nationalbibliothek
The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.
© 2025 Wiley-VCH GmbH, Boschstraße 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages, text and data mining and training of artificial technologies or similar technologies). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN 9783527414048
ePDF ISBN 9783527832958
ePub ISBN 9783527832972
oBook ISBN 9783527832965
To Our Father Late Shri Mahender Pal
Foreword
There exist in the literature many books and treatises on Charged Particle Beam Physics and, in general, on accelerator physics. So when the first author, Sarvesh, approached me to write the foreword to this book, I was very curious to find out what distinguishes the present one from previous books. After going through the manuscript, I found that almost all aspects of the physics of particle beams have been presented, keeping the beginning student in mind. Beginning with a brief history of the development of accelerators, topics like ion sources and accelerating and beam transport devices, along with their working principles, are described in an easy style with just enough detail for a first introduction to the subject. Numerical problems of practical relevance are included at the end of each chapter, which will aid the learner in understanding the concepts. Another nice feature of the book is the inclusion of diagnostic methods for charged particle beams, vacuum devices, and the measurement of vacuum. References to detailed works on each topic are provided for those interested in pursuing the subjects in detail.
This book provides excellent material for an introductory course in accelerator physics and would also be a handy reference for the relevant concepts for the practitioners.
Amit Roy
Preface
The motivation for writing “Charged Particle Beam Physics: An Introduction for Physicists and Engineers” is to simplify the process of learning accelerator physics. The book directly addresses the fundamental topics required in this field. Although my background is primarily in laboratories utilizing electrostatic and linear accelerators, this book also caters to circular accelerator laboratories, addressing common elements found across various accelerator systems. The beam optics examples provided focus on single-pass configurations and typically deal with standard beam transport lines.
This book represents the culmination of years of extensive research, reflection, and collaboration in accelerator physics. During this time, I had the privilege of visiting Fermilab, USA, and CERN, Geneva, where the insights gained from these experiences, have been invaluable. The process of writing this book has been both challenging and rewarding, prompting me to explore new perspectives and deepen my understanding of the subject.
Charged Particle Beam Physics: An Introduction for Physicists and Engineers is structured into eight chapters, each focusing on a key aspect of accelerator physics. I have incorporated beam optics code simulations to visually illustrate basic concepts in beam optics. Below is a summary of the chapters:
Chapter 1
:
Introduction to different types of accelerators and the historical evolution of accelerator technology.
Chapter 2
:
Basics of particle sources and their working principles.
Chapter 3
:
Fundamentals of beam optics and an introduction to phase space formalism.
Chapter 4
:
Motion of charged particles in various magnetic fields.
Chapter 5
:
Motion of charged particles in various electric fields.
Chapter 6
:
Motion of charged particles in radio frequency fields.
Chapter 7
:
Determining basic beam parameters using standard beam diagnostics utilized worldwide.
Chapter 8
:
Understanding vacuum systems in accelerators, covering vacuum physics, pumps, and gauges.
This book is grounded in my 18 years of experience at the Inter University Accelerator Center, New Delhi, where I have primarily focused on beam optics for designing particle accelerators. I have consistently enjoyed working on hands-on calculations and beam optics simulations using various simulation and tracking codes. Achieving accurate transverse and longitudinal parameter matching for particle beams is a key part of designing effective particle accelerators. It requires careful estimation of beam matching parameters alongside the design parameters of beam optical devices. The conversion of effective beam optics layouts into their physical counterparts must be performed with precision to ensure that the accelerator functions as closely as possible to the ideal model.
The book is written in a broad, accessible format, intended to serve as a primary source and is mainly for undergraduate student to get quick access to the field and also extend the outreach toscientists and engineers worldwide. It is particularly useful for beginners in accelerator physics, providing a clear and concise introduction to key topics. Additionally, it can serve as a practical reference for those involved in designing accelerator components, providing quick insights and essential information before proceeding with computational simulations. The student working at school level in beamline project can quickly get familiar to fundamental concepts in accelerator physics.
Apart from basic physics to undergraduate students, the aim of this book is also to explore the design of accelerator machines and their basic components. The academic community working in accelerator physics often needs to perform fundamental calculations before embarking on detailed simulations, whether for beam optics or the design of beam optical devices. Based on my experience, I have compiled many of the essential elements of accelerator physics into a single resource, allowing students to easily grasp the basic principles. This book serves as both a detailed glossary of accelerator terms and a practical guide for performing the basic calculations associated with most of the accelerator elements.
The content covers electrostatic, magnetostatic, and radiofrequency devices used in accelerator physics, with an emphasis on both transverse and longitudinal beam dynamics. The introductory chapters provide a broad overview of the principles behind various particle accelerators and ion sources. Different types of ion sources are characterized by their beam emittance, current, and profiles, all of which present significant challenges for beam extraction and transport to the target. Accordingly, this book focuses heavily on beam physics, particularly on the optical components that are common across most accelerators.
Beam physics is the core of accelerator physics, involving both theoretical calculations and the practical challenges associated with implementing beam optics designs to transport particles effectively to their intended target. The book covers the design of essential beam optical components – both passive and active. Topics include the design and function of dipole magnets, quadrupole magnets, steerers, scanners, electrostatic dipoles and quadrupoles, sextupoles, radio frequency cavities, bunchers, choppers, electrostatic accelerating tubes, and more.
The transfer matrix approach is used extensively to calculate design parameters for beam optical components, followed by discussions of the hardware design and practical difficulties encountered. To further illustrate the concepts, the open-source beam optics code COSY Infinity is employed to demonstrate first-order beam optics through various optical components. The designs are explained in a general manner so that readers can adapt them to their specific requirements. To access the COSY Infinity code, registration is required on the website of the corresponding research group at the Center for Dynamical Systems, Michigan State University, as detailed below:
https://www.bmtdynamics.org/cosy/register.htm
Registration instructions are available at:
https://www.bmtdynamics.org/cosy/
For any queries related to COSY Infinity, please contact:
I would like to express my sincere gratitude to Dr. Martin Berz and Dr. Kyoko Makino, Department of Physics, Michigan State University, for granting permission to use the COSY Infinity code to generate the beam optics diagrams used throughout this book.
As you read through the pages of Charged Particle Beam Physics: An Introduction for Physicists and Engineers, my hope is that you will find the knowledge and insights that will help you to achieve a particular goal or understanding as primary source of information on the exact topic of accelerator physics. This book is meant to be a resource, a guide, and a companion in your journey through world of particle accelerators.
Thank you for taking the time to engage with this work. I am excited to share it with you and look forward to the conversations and ideas that it may inspire. I dedicate this book to the application of particle accelerator technology for the betterment of human life and the peaceful advancement of mankind.
New Delhi, India
August 31, 2024
Sarvesh Kumar
About the Authors
Dr. Sarvesh Kumar was an experimental plasma and accelerator physicist with nearly two decades of experience at the Inter University Accelerator Centre (IUAC), New Delhi. He has participated in significant national and international projects. Notably, he contributed in the design, fabrication, and commissioning of three major accelerator-based facilities: Low Energy Ion Beam Facility (LEIBF), High Current Injector (HCI) for heavy ions and Delhi Light Source (DLS), supported by internationally peer-reviewed and national publications. He had worked with Pelletron accelerators for beam tuning operation. His deep perseverance in developing skills of teaching and education in applied physics led him to author this book, aiming to bridge theory with real-world applications in plasma and accelerator physics. His passion lies in connecting with young graduate/postgraduate students, encouraging out-of-the-box thinking, and guiding them in translating innovative ideas into practical systems. Dr. Kumar had served as a Scientific Associate at CERN, Geneva, designing the RFQ upgrade for LINAC4 accelerator, contributing overall to the Large Hadron Collider project. He combines academic rigor with hands-on innovation in the charged particle, cost-effective accelerators design. He had designed many achromatic bends at IUAC Delhi for heavy ions and electron beams which are now in place and serving the user community of IUAC. His strength lies in designing compact plasma chambers and ion beam systems suitable for university level teaching laboratories. A firm believer in teamwork awakefield acceleration, plasma instabilities, particle accelerator designs, beam optics and beam-plasma interaction.
Prof. Manish K. Kashyap, currently at School of Physical Sciences, Jawaharlal Nehru University (JNU), New Delhi, India, has rich teaching experience of 19 years. He has supervised nine PhD and one post-doctoral students till date, and seven PhD students are still working under his supervision. His areas of interest are Condensed Matter Physics, Plasma Physics, and Accelerator Physics. His work integrates theoretical modeling with experimental perspectives to enhance beam quality and stability in ion accelerators. He has explored novel acceleration mechanisms and diagnostics, advancing both fundamental and applied aspects of beam-plasma systems. He has published 110 research papers in international journals/conference proceedings, earning widespread recognition in the scientific community. His research continues to impact the development of next-generation accelerators and plasma-based technologies in India and abroad. He also works on perovskite solar cells and 2D van der heterostructures.
Acknowledgments
I am grateful to the CERN Accelerator School reports, the resources from the United States Particle Accelerator School, and the various authors of beam dynamics codes, accelerator physics resources worldwide, all of which have made it possible to write this book in a form that is accessible to beginners in accelerator physics, including school and undergraduate students in physics and engineering.
I am deeply thankful to the Director of the Inter University Accelerator Center (IUAC), New Delhi, whose encouragement and unwavering support have been instrumental in bringing this book to fruition. I also wish to express my sincere gratitude to Jawaharlal Nehru University, New Delhi and South Asian University, New Delhi, for providing the research collaboration that made this work possible.
I am especially grateful to our research group working in accelerator and plasma physics: Prof. Jyotsna Sharma (South Asian University, New Delhi), Dr. Ankur Taya (Mukand Lal National College, Yamuna Nagar, Haryana), Dr. Renu Singla (Daulat Ram College, University of Delhi, Delhi), Ms. Niketan Jakhar and Mr. Chandan Thakur (Jawaharlal Nehru University, New Delhi), and Mr. Sandeep Kumar (Indian Institute of Technology, New Delhi) who have provided me an excellent environment to develop this book on accelerator physics.
Lastly, I would like to extend my heartfelt thanks to my colleagues at IUAC, who were my first teachers in accelerator physics. Their guidance and instruction have been a blessing, and without their early teachings, this book would not have been possible.
I am deeply grateful to my family for their unwavering support, giving me the freedom and time to fully dedicate myself to the writing of this book.
Sarvesh Kumar
Acronyms
ACH
Achromat
ASM
Analyzing cum Switching Magnet
AT
Accelerating Tube
BPM
Beam Profile Monitor
DTL
Drift Tube LINAC
ECR
Electron Cyclotron Resonance
EL
Einzel Lens
EQD
Electrostatic Quadrupole Doublet
EQT
Electrostatic Quadrupole Triplet
FFC
Fast Faraday Cup
HCI
High Current Injector
HEBT
High Energy Beam Transport
IH
Inter Digital H type
LEBT
Low Energy Beam Transport
LINAC
Linear Accelerator
MEBT
Medium Energy Beam Transport
MHB
Multi-harmonic Buncher
MQD
Magnetic Quadrupole Doublet
MQT
Magnetic Quadrupole Triplet
RFQ
Radio Frequency Quadrupole
ST
Steerer Magnet
Fundamental constants used in particle accelerators.
Constant
Symbol
Value
Speed of light
2.99792458 × 10
8
m/s
Elementary charge
1.602176634 × 10
−19
C
Mass of electron
9.10938356 × 10
−31
kg
Mass of proton
1.67262192369 × 10
−27
kg
Planck’s constant
6.62607015 × 10
−34
J · s
Reduced Planck’s constant
1.054571817 × 10
−34
J · s
Electric constant (permittivity of free space)
8.854187817 × 10
−12
F/m
Magnetic constant (permeability of free space)
Fine-structure constant
Boltzmann constant
1.380649 × 10
−23
J/K
Avogadro’s number
6.02214076 × 10
23
mol
−1
Rydberg constant
1.0973731568508 × 10
7
m
−1
Fermi coupling constant
1.1663787 × 10
−5
GeV
−2
Gravitational constant
6.67430 × 10
−11
m
3
· kg
−1
· s
−2
Stefan–Boltzmann constant
5.670374419 × 10
−8
W m
−2
· K
−4
About the Companion Website
Charged Particle Beam Physics: An Introduction for Physicists and Engineers
This book is accompanied by a companion site:
https://www.wiley.com/go/Kumar_1e
This website includes:
Answers
Videos
Chapter 1Introduction to Charged Particle Beams
“If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration.”
—Nikola Tesla
In accelerator physics, a particle beam is typically defined as a collection of like-charged particles, all moving with momentum predominantly in one direction compared to the other two transverse directions. This characteristic allows the beam to be transported over long distances using electromagnetic fields and further accelerated to energies reaching several teraelectronvolts (TeV) in modern accelerators. Naturally occurring particle beams exist in space, commonly referred to as cosmic rays or solar particles. A specific example is the stream of charged particles, such as solar wind or proton beams, emitted by the Sun. These particles are captured by Earth’s magnetic field, resulting in collisions with particles in Earth’s upper atmosphere. In the Earth ionosphere, charged particles from the solar wind, guided by Earth’s magnetic field, collide with oxygen and nitrogen atoms in the atmosphere, exciting them and releasing energy as colorful light displays known as the aurora, or Northern Lights.
Curiosity: Have you ever wondered how particle accelerators can speed up tiny particles like protons or electrons to nearly the speed of light? Why do they need a vacuum—can’t particles just move through air like anything else? To push particles forward, accelerators use special devices called RF cavities that work like swings, giving the particle a timed “kick” each cycle. But as particles gain speed, why do we need magnets to bend and focus their paths—why don’t they just go straight? And did you know that your microwave oven uses a tiny kind of particle accelerator called a magnetron? What if, instead of electric fields, we could use sound waves or even gravity to accelerate particles—could that work someday? If batteries produce voltage, why can’t we just use a giant one to reach GeV energy levels? Inside circular accelerators, how do particles manage to stay in sync with the accelerating fields without flying off-track? When too many particles gather close together, do they repel each other and cause the beam to spread out? It’s amazing that the first particle accelerator, built in the 1930s, could fit on a tabletop! And why do fast-moving particles give off brilliant light—called synchrotron radiation—when they are forced to turn? Finally, imagine this: could we one day shrink a whole accelerator down to fit on a tiny microchip? We try to explore some of these curious questions here—but many remain open, inviting you to keep wondering, exploring, and discovering.
The energy (E) of a particle [1] can be related to its temperature using the Boltzmann relation:
and 1 eV corresponds to approximately 11 605 K. This implies that particles accelerated to energies in the kiloelectron volt (keV), megaelectron volt (MeV), and gigaelectronvolt (GeV) range are effectively heated to extremely high temperatures. Understanding particle beam dynamics is crucial in space physics and accelerator sciences.
When ions are generated in a laboratory as a stream of charged particles, they must be accelerated and transported to a target with minimal intensity loss. These ions are used in various fields of science, such as nuclear physics, materials science, and atomic physics. In discussing heavy ions, which are larger than protons, a key difference lies in their approach to the speed of light as they gain energy. The total energy of a charged particle is given by the following equation:
The relativistic energy–momentum relation is:
where is the total energy of the particle, is the relativistic momentum, is the rest mass of the particle, and is the speed of light.
The relativistic momentum is related to the velocity of the particle by:
where (the Lorentz factor) is defined as:
Here . Thus, the total energy of particle is given as follows:
Finally, the kinetic energy is given by:
If we plot the velocity of different charged particles as per Equation 1.6, then the electrons begin to exhibit significant relativistic behavior at energies around 0.511 MeV, which corresponds to their rest mass energy. However, according to special relativity, they can never reach the speed of light, no matter how much energy they gain. Protons become relativistic at much higher energies, near 938 MeV, their rest mass energy. Similarly, heavy ions, they require even higher energies (in the GeV per nucleon range) to exhibit relativistic effects due to their much greater mass. Regardless of particle type, no material particle can attain the speed of light; they can only asymptotically approach it as their energy increases. This is illustrated in Figure 1.1.
Figure 1.1 Velocity behavior of different charged particles as they approach the speed of light.
To maintain particles in a stable orbit as a beam, they must be placed in a constant magnetic field, where they spiral around the magnetic lines of force. This leads to the concept of magnetic rigidity, defined alongside the magnetic force, cyclotron frequency, and gyroradius as follows:
Magnetic force on particle:
Cyclotron frequency of the particle:
Larmor radius (gyroradius) of particle:
Magnetic rigidity:
In terms of practical units:
Here, is the total energy of the particle. Using Equation 1.11, if we plot the magnetic rigidity required to bend different ions with a fixed energy of 500 MeV and a unit charge state, we see that it increases with the mass of the ions. This is shown in Figure 1.2, alongside the corresponding normalized particle velocities. Following conclusions can be drawn:
Maximum magnetic rigidity is calculated for the heaviest mass, highest energy, and unit positive charge state of the beam desired in the accelerator.
Magnetic rigidity increases with mass and energy of charged particles for a given charge state of the beam particles.
Magnetic rigidity is maximum for a unit charge state of an ion beam with target energy.
Magnetic rigidity depends on the mass-to-charge ratio directly, When where is the voltage by which particles are accelerated.
Figure 1.2 Velocity and magnetic rigidity of different ion beams of mass M (amu) at 500 MeV energy.
In 1909, Ernest Rutherford bombarded alpha particles onto a thin gold foil. To overcome the Coulomb barrier between the alpha particles and the gold nucleus, high energies were necessary to surmount the Coulomb repulsion. The higher the energy imparted to particles, the shorter their de Broglie wavelength . Just as a living cell is observed under an optical microscope using scattered visible light photons, energetic particles can be used to probe matter, depending on their wavelength. The wavelength of energetic particles determines the size of the object to be resolved, so high-energy particles (with mass , velocity , and energy ) are required to probe deep into atoms and nuclei. The de Broglie wavelength is given by the Planck–Einstein relation, the relationship between energy and momentum:
In terms of practical units:
Here, is the energy of the particle (or photon), is Planck’s constant, is the frequency of the de Broglie wave associated with the particle.
Accelerators have evolved over the last two centuries as a result of applying electricity and magnetism to charged particles, driven by the pioneering work of many great scientists and engineers. Initially motivated by Rutherford’s famous experiment to explore the nucleus, modern particle accelerators are essential tools for probing the structure of atoms, protons, neutrons, and electrons through high-energy collisions that reveal their internal components. They enable the discovery of new particles, such as quarks, leptons, and the Higgs boson, by recreating the extreme conditions necessary for these short-lived particles to manifest. Studying particle interactions at high energies allows scientists to explore the fundamental forces of nature – gravity, electromagnetism, and the strong and weak nuclear forces – and how they behave and unify. Additionally, accelerators like the Large Hadron Collider (LHC) recreate the energy densities present just after the Big Bang, offering insights into the origins of the universe. They also provide a platform to test and confirm theoretical models of quantum mechanics and relativity, including the Standard Model, by observing particle behavior and interactions with exceptional precision.
Thus, the evolution of accelerators has progressed from natural particle accelerators like cosmic rays and radioactive materials to highly engineered devices capable of producing extreme energetic particles. Cosmic rays, consisting of high-energy particles originating from astrophysical events, represent the earliest and most powerful natural accelerators. Similarly, radioactive sources emit high-energy particles during nuclear decay, naturally accelerating alpha, beta, and gamma particles. The first major technological breakthrough in particle acceleration came with the development of the cathode ray tube (CRT), which used high voltage to accelerate electrons and produce visible images, laying the groundwork for more sophisticated human-made accelerators.
In the early twentieth century, the invention of the Van de Graaff accelerator [2] marked a significant advancement in accelerating charged particles like protons and ions using high voltage generated by a moving belt. This innovation paved the way for circular accelerators like the cyclotron, where charged particles like protons and deuterons are accelerated in a magnetic field and gain energy from an alternating electric field. For electrons, which encounter relativistic effects at higher speeds, the betatron was developed, using a time-varying magnetic field to induce electron acceleration in a circular orbit.
As accelerators grew more powerful, the synchrotron was introduced in the mid-twentieth century, where protons, electrons, and ions are accelerated in a circular path with synchronized magnetic and electric fields, achieving energies in the TeV range. Synchrotrons facilitated the discovery of particles like quarks and leptons and contributed significantly to particle physics. Around the same time, the linear accelerator (LINAC) emerged, allowing particles to be accelerated in a straight path using oscillating electric fields. A variant of the Van de Graaff, the Tandem accelerator, was designed to stabilize high-voltage acceleration using a chain of metal pellets to achieve greater reliability and higher energies.
Following these advancements, the microtron was created to reuse circular orbits for electrons, allowing them to gain energy with each pass. In the mid-twentieth century, the fixed-field alternating gradient (FFAG) accelerator was introduced, accelerating particles in a spiral path while maintaining a constant magnetic field. The nonscaling FFAG improved upon this design by allowing more rapid acceleration with variable particle orbits. Meanwhile, the induction LINAC utilized pulsed magnetic fields to accelerate particles like electrons and ions over shorter distances.
In the era of modern high-energy physics, particle colliders like the LHC emerged, accelerating two beams of particles in opposite directions to create collisions at extreme energies, often in the TeV range. Further innovations included the recirculating LINAC, which allowed particles to pass through the same LINAC multiple times to reach higher energies, as well as the energy recovery LINAC, which focuses on energy efficiency by decelerating electron beams and recovering their energy for reuse.
Most recently, breakthroughs in compact acceleration methods have led to the development of laser plasma accelerators, which use high-intensity lasers to generate plasma wakefields, rapidly accelerating particles like electrons to GeV energies. Beam-driven plasma accelerators follow a similar principle, using a high-energy particle beam to generate a plasma wakefield, offering compact and efficient acceleration over shorter distances.
Plasma wakefield accelerators, driven by either high-intensity lasers or particle beams, can achieve acceleration gradients in the order of gigavolts per meter (GV/m), far exceeding the capabilities of traditional accelerators. This allows for compact designs that can potentially reduce the size and cost of future particle accelerators.
1.1 History of Particle Accelerators and the Chronological Milestones
Before going into modern history accelerators, let’s go back to one of the earliest known concepts of the atom in ancient Indian science. Maharishi Kanaad, an ancient Indian sage, was one of the first to propose the idea of atomic theory. He suggested that everything in the universe is made of tiny, indivisible particles called “parmanu,” which are similar to what we now think of as atoms. He believed that these particles combine in various ways to form the objects and substances that we see around us. His ideas are recorded in the Vaisheshika Sutras, an important text in Indian philosophy. This was an early understanding that matter is made of basic building blocks.
Particle accelerators began to develop in the late nineteenth century, following important discoveries like X-rays by Wilhelm Röntgen and beta rays by J. J. Thomson. The discovery of radioactivity motivated scientists to find ways to create and control particles artificially. However, it was Ernest Rutherford’s groundbreaking experiments that gave scientists the roadmap to study the atomic nucleus in more detail. The following is the timeline of key discoveries and advancements that shaped the history of particle accelerator technology and its pioneer discoveries as shown in Table 1.1. A brief history of accelerators and related discoveries is provided in Table 1.1 chronologically.
Table 1.1 Chronological evolution of particle accelerators worldwide.
Year
Developments
1895
Wilhelm Conrad Röntgen discovered X-rays using CRTs, for which he received the first Nobel Prize in Physics in 1901.
1896
Joseph John Thomson studied the nature of cathode rays, discovering their charge-to-mass ratio and identifying them as electron beams. He was awarded the Nobel Prize in 1906.
1898
Marie Curie discovered groundbreaking work in the study of radioactivity. In 1898, together with her husband Pierre Curie, she discovered two new elements:
polonium
in July and
radium
in December. She also introduced the term “radioactivity” to describe how certain materials give off energy as they break down. Her important discoveries rewarded her two Nobel Prizes: the first in Physics in 1903, shared with Pierre Curie and Henri Becquerel, for their research on radioactivity, and the second in Chemistry in 1911 for discovering radium, polonium, and studying the properties of radium. Marie Curie was the first woman to win a Nobel Prize and is still the only person to have won Nobel Prizes in two different sciences.
1920
John Douglas Cockcroft and Ernest Thomas Sinton Walton conceived the first high-voltage particle accelerator, which used two electrodes inside a vacuum vessel to create a potential drop of around 100 kV.
1923
Rolf Widerøe, a young Norwegian student, first proposed the design of the betatron, incorporating the well-known 2-to-1 rule. Two years later, he refined the design by introducing the condition for radial stability, a crucial factor for successful particle acceleration.
1924
Gustav Ising proposed time-varying fields across drift tubes, introducing the concept of resonant acceleration, which allows for energy levels higher than the system’s maximum voltage.
1928–1932
John Cockcroft and Ernest Walton began designing an 800 kV generator under the guidance of Ernest Rutherford in 1928 at the Cavendish Laboratory in Cambridge. In 1932, they achieved a significant milestone by successfully splitting the lithium atom using high-energy protons accelerated by their Cockcroft–Walton generator. This marked the first artificial nuclear reaction, demonstrating the power of particle accelerators in nuclear physics. Their breakthrough experiment laid the foundation for future accelerator technologies and earned them the Nobel Prize in Physics in 1951 for their pioneering work in atomic transmutation.
1928
Rolf Widerøe demonstrated Ising’s principle with a 1 MHz, 25 kV oscillator to produce 50 keV potassium ions, suggesting the use of RF voltage between consecutive drift tubes. This was successfully tested by D. H. Sloan and E. O. Lawrence in 1931.
1929
Ernest Lawrence was motivated by Rolf Widerøe’s advances in accelerating particles and Gustav Ising’s concept of using electric fields for this purpose. In 1929, Lawrence invented the cyclotron, a device that uses magnetic fields to move particles in a circular path while speeding them up with an electric field.
1930
M. Stanley Livingston, a student of Ernest Lawrence, built and tested the first working cyclotron. This machine accelerated hydrogen ions (protons) to an energy of 80 keV, marking a major step forward in particle accelerator technology.
1930
Robert Van de Graaff developed the Van de Graaff generator, an important type of electrostatic accelerator that allowed for the creation of extremely high voltages. This innovation was a critical step in early particle acceleration, enabling experiments that required high-energy beams.
1932
Lawrence’s cyclotron accelerated protons to 1.25 MeV, successfully achieving atomic splitting shortly after Cockcroft and Walton’s breakthrough. For this pioneering achievement, along with his invention and development of the cyclotron and his contributions to artificial radioactive elements, E. O. Lawrence was awarded the Nobel Prize in Physics in 1939.
1940
Donald W. Kerst revolutionized particle acceleration by redesigning the betatron and constructing the first fully functional machine capable of accelerating electrons to 2.2 MeV.
1944
Vladimir Veksler introduced the principle of phase stability, which made it possible to maintain stable orbits while increasing the energy of particles in synchrotrons. This discovery was vital for the development of modern particle accelerators such as synchrocyclotrons and electron synchrotrons.
1946
Luis W. Alvarez built a 32 MeV proton drift tube LINAC at Berkeley, which operated at 200 MHz, marking an important step in the development of LINACs.
1950
Donald W. Kerst constructed the largest betatron in the world, capable of accelerating electrons to 300 MeV, a record at the time.
1950
Nicholas Christofilos solved the challenge of beam stability in synchrotrons by introducing the concept of strong focusing. This advancement allowed synchrotrons to handle higher energy beams and led to more efficient acceleration in circular accelerators.
1951
J. D. Cockcroft and E. T. S. Walton were awarded the Nobel Prize for their pioneering work on the transmutation of atomic nuclei using artificially accelerated particles.
1951
Edwin M. MacMillan, along with Glenn T. Seaborg, was awarded the Nobel Prize for their research on the chemistry of transuranium elements.
1952
E. Courant, M. Livingston, and H. Snyder at Brookhaven, USA, proposed alternating-gradient (AG) magnetic lattices, consisting of bending magnets with AGs or properly spaced quadrupole magnets with alternating polarities. This innovation solved the weak focusing problem in synchrotrons.
1959
Emilio Segrè and Owen Chamberlain received the Nobel Prize in Physics for their discovery of the antiproton, achieved using a particle accelerator at the Lawrence Berkeley National Laboratory.
1960
Bruno Touschek designed the first practical electron–positron collider, which made it possible to study particle collisions in a controlled environment. His work laid the foundation for later developments in colliders like the large electron–positron collider.
1965
Julian Schwinger, along with Sin-Itiro Tomonaga and Richard P. Feynman, was awarded the Nobel Prize for quantum electrodynamics, which has profound implications for elementary particle physics.
1966
Andrey M. Budker developed the technique of electron cooling, which enhanced beam quality in storage rings and improved the precision of particle accelerator experiments.
1968
Luis W. Alvarez received the Nobel Prize for discovering a large number of resonance states using a hydrogen bubble chamber.
1970
I. M. Kapchinsky and Vladimir Teplyakov introduced the concept of the radio frequency quadrupole in 1970. This innovation improved the acceleration and focusing of low-energy ion beams, leading to more efficient LINACs.
1976
Burton Richter and Samuel Ting were awarded the Nobel Prize in Physics for the independent discovery of the particle, providing evidence for the existence of the charm quark, discovered using high-energy particle accelerators.
1977
Rosalyn Yalow was awarded the Nobel Prize in Physiology or Medicine for developing the radioimmunoassay (RIA), a groundbreaking technique for measuring biological substances using radioactive isotopes. While radioisotopes used in RIA can be produced by particle accelerators, the work was primarily linked to medical diagnostics.
1980
Simon van der Meer invented stochastic cooling, a technique used to refine and manipulate particle beams in high-energy accelerators. This breakthrough was key to achieving the precision needed for particle collisions at the European Organization for Nuclear Research (CERN), which led to the discovery of the W and Z bosons.
1984
Carlo Rubbia and Simon Van der Meer were awarded the Nobel Prize for their contributions to the large project that led to the discovery of the W and Z bosons, the carriers of the weak force.
2013
François Englert and Peter Higgs were awarded the Nobel Prize in Physics for the theoretical discovery of the Higgs mechanism, confirmed by the discovery of the Higgs boson at the LHC at CERN.
1.2 Maxwell’s Equations
In accelerator physics, the primary goal is often to solve Maxwell’s equations for specific geometries to understand and optimize the electromagnetic fields in an accelerator components, such as radio frequency (RF) cavities, magnets, and electric components. It helps physicists and engineers to design accelerators with the desired beam dynamics, particle focusing, and energy transfer characteristics.
Consider an electromagnetic field moving through free space, which is an area with no electric charges or currents. The electric field, represented by , and the magnetic field, represented by , change over time and space and affect each other. Maxwell’s equations describe how these fields behave and interact. The symbol stands for charge density, which is the amount of charge in a given space. The term is the current density, indicating the flow of electric charge. Now, here are Maxwell’s equations in both integral and differential forms:
1.2.1 Maxwell’s First Equation: Gauss’s Law for Electricity
This law states that the divergence of the electric field at any point in space is proportional to the local charge density . It describes how electric fields emanate from electric charges. In accelerators, electric fields play a key role in accelerating and focusing on charged particle beams. Longitudinal electric fields provide electrostatic acceleration, while transverse electric fields, particularly in electrostatic quadrupoles, focus the beam. Dipole configurations use electric fields for deflecting or steering particles. Gauss’s law underpins the theoretical framework for understanding how electric fields interact with charges in accelerator environments.
1.2.2 Maxwell’s Second Equation: Gauss’s Law for Magnetism
This law states that the divergence of the magnetic field is zero, implying the absence of magnetic monopoles. Magnetic field lines always form closed loops. In accelerators like cyclotrons, synchrotrons, or betatrons, magnetic fields are essential for bending and focusing on charged particles, following this fundamental property.
1.2.3 Maxwell’s Third Equation: Faraday’s Law of Electromagnetic Induction
Faraday’s law describes how a changing magnetic field induces an electric field. In accelerators like the betatron, this principle is employed to induce electric fields that accelerate particles. A time-varying magnetic field generates a circulating electric field, which accelerates electrons or other particles confined within a circular path. This law is fundamental to devices using electromagnetic induction for acceleration.
1.2.4 Maxwell’s Fourth Equation: Ampère’s Law with Maxwell’s Addition
Ampère’s law, with Maxwell’s correction, incorporates the displacement current alongside the conduction current density . This law describes how electric currents and changing electric fields generate magnetic fields. In accelerator design, this equation is crucial for calculating ampere-turns in dipoles, quadrupoles, sextupoles, and solenoids. It also helps in the design of power supplies for energizing magnets in accelerators.
1.3 Electrostatic Accelerators
As the name suggests, electrostatic accelerators use electric fields to accelerate charged particles. The design of the electric field is crucial, as these accelerators are characterized by a potential gap where a particle experiences a potential difference and accelerates along the direction of the electric field. The voltage can reach very high levels (up to MV) with the use of suitable insulating gases like . Examples of electrostatic accelerators include Cockcroft–Walton accelerators, Van de Graaff accelerators, and tandem accelerators.
When a charge moves through an electric field from one point to another, work is done by the electric field. The work done is given by the change in electric potential energy, which can be expressed as:
where and are the electric potentials at the two points.
If we consider the charge moving from a point of zero potential (grounded) to a point with potential , the work done by the field is:
This work is the energy gained by the charge, so the energy gained by a particle with charge under a voltage is simply given by:
The force (F) on a charge particle in an electric field is given by:
1.3.1 Cockcroft–Walton Accelerator
The Cockcroft–Walton accelerator, first developed in 1932 by John Cockcroft and Ernest Walton [3, 4] played a significant role in nuclear physics. It operates on the principle of cascading voltage multiplication. The system works by charging and discharging capacitors in cascading stages, with the voltage increasing stepwise at each stage. The circuit consists of a series of capacitors and diodes arranged in a specific configuration to create a voltage multiplier. The output voltage increases with the number of stages , the input voltage , and the capacitance of the capacitors, although size and breakdown limits impose certain constraints. In the setup as shown in Figure 1.3, an AC voltage charges the capacitors in parallel so that each stage generates a potential twice the input voltage. The first capacitor charges in an anticlockwise loop, and the second in a clockwise loop, followed by the discharge of the first capacitor. With more stages, the final voltage increases until it reaches the breakdown voltage, as shown in Figure 1.3, where one can stop further cascading.
Figure 1.3 Schematic of a Cockcroft–Walton accelerator.
In a four-stage Cockcroft–Walton voltage multiplier circuit as shown in Figure 1.3, the circuit consists of two columns of capacitors: the oscillating column and the smoothing column. During the first half-cycle of the AC input, the capacitors in the oscillating column (, , , and ) are charged through the odd-numbered diodes (, , , and ). During the next half-cycle, the capacitors in the smoothing column (, , , and ) are charged through the even-numbered diodes (, , , and ). In the steady state, under no-load conditions, each capacitor in the smoothing column is charged to a voltage of , which is twice the peak input voltage.
If the generator supplies any load current , the output voltage will not reach the theoretical value of , as depicted in
