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Charged Particle Beams I-1 Charged Particle Beams Stanley Humphries, Jr. Department of Electrical and Computer Engineering University of New Mexico Albuquerque, New Mexico Originally published in1990 by John Wiley and Sons (QC786.H86 1990, ISBN 0-471- 60014-8). Copyright ©2002 by Stanley Humphries, Jr. All rights reserved. Reproduction of translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to Field Precision, Attn: Stanley Humphries, PO Box 13595, Albuquerque, NM 87192. Charged Particle Beams I-2 Preface ________ Charged Particle Beams is the product of a two-term course sequence that I taught on accelerator technology and beam physics at the University of New Mexico and at Los Alamos National Laboratory. The material for the two terms was divided into the dynamics of single charged particles and the description of large groups of particles (the collective behavior of beams). A previous book, Principles of Charged Particle Acceleration (available on the Internet at http://www.fieldp.com/cpa/cpa.html) covered single particle topics such as linear transfer matrices and the operation of accelerators. The new book is an introduction to charged- particle-beam physics. In writing Charged Particle Beams my goal was to create a unified description that would be useful to a broad audience: accelerator designers, accelerator users, industrial engineers, and physics researchers. I organized the material to provide beginning students with the background to understand advanced literature and to use accelerators effectively. This book can serve as an independent reference. Combining Charged Particle Beams with Principles of Charged Particle Acceleration gives a programmed introduction to the field of particle acceleration. I began my research on particle beams with a background in plasma physics. This change in direction involved a difficult process of searching for material, learning from experts, and seeking past insights. Although I found excellent advanced references on specialized areas, no single work covered the topics necessary to understand high-power accelerators and high-brightness beams. The difficulties I faced encouraged me to write Charged Particle Beams. The book describes the basic ideas behind modern beam applications such as stochastic cooling, high-brightness injectors and the free-electron laser. Charged Particle Beams I-3 I was fortunate to have abundant help creating this book. Richard Cooper of Los Alamos National Laboratory applied his proofreading ability to the entire manuscript. In additional to mechanical corrections, his suggestions on technical points and emphasis were invaluable. The creation of this book was supported in part by a sabbatical leave from the Department of Electrical and Computer Engineering at the University of New Mexico. David Woodall. former Chairman of the Department of Chemical and Nuclear Engineering at the University of New Mexico, suggested the idea of the accelerator course sequence. I am grateful for his support during the development of the courses. Several people contributed advice on specific sections of the book. Commentators included Kevin O'Brien of Sandia National Laboratories, John Creedon of Physics International Company, Brendan Godfrey of the Air Force Weapons Laboratory, Edward Lee of Lawrence Berkeley Laboratory, William Herrmannsfeldt of the Stanford Linear Accelerator Center, and Carl Ekdahl of Los Alamos National Laboratory. I would also like to thank A. V. Tollestrup of Fermi National Accelerator Laboratory for permission to paraphrase his article (coauthored by G. Dugan) on Elementary Stochastic Cooling. I want to express appreciation to the students in my beam physics course at the University of New Mexico and at the Los Alamos Graduate Center. Through their contributions, I clarified and expanded the material over several years. Los Alamos National Laboratory supported the courses since their inception. I want to thank Robert Jameson and Alan Wadlinger of the Accelerator Technology Division for their encouragement. The efforts of the Instructional Television Center of UNM made it feasible to present classes at Los Alamos. I have also taught the material in short course format. I am grateful to Thomas Roberts and Stanley Pruett for organizing a course at the Strategic Defense Command. Several accelerator science groups helped in the development of material for the book. I have worked closely with the Heavy Ion Fusion Accelerator Research Group at Lawrence Berkeley Laboratory for several years. I want to thank Henry Rutkowski, Thomas Fessenden, Denis Keefe and Edward Lee for their suggestions on the book and for providing the opportunity to work in the field of accelerator inertial fusion. The long-term support of Charles Roberson of the Office of Naval Research has been critical for accelerator research at the University of New Mexico. The University has also received generous research support from Groups CLS-7 and P-14 of the Los Alamos National Laboratory. I am grateful to Roger Bangerter and the late Kenneth Riepe who initiated the UNM program on vacuum arc plasma sources. I would also like to thank Carl Ekdahl – much of the material in this book evolved from spirited discussions on high-current beam physics. Charged Particle Beams I-4 During the composition of this book, I had the opportunity to participate in several research programs on high-power accelerators. I would like to thank Ralph Genuario and George Fraser of Physics International Company, Sidney Putnam of Pulse Sciences Incorporated, Robert Meger of the Naval Research Laboratory, Martin Nahemow of the Westinghouse Research and Development Center, Richard Adler of North Star Research Corporation, Daniel Sloan of CH2M-Hill, Kenneth Moses of Jaycor, and R. Bruce Miller of Titan Technologies. I would like to acknowledge two meetings that I attended during the creation of the book. The first is the NATO Workshop on High Brightness Beams in Pitlochry, Scotland. I express my appreciation to Anthony Hyder for organizing this workshop. I have particularly enjoyed participating in the U.S. Particle Accelerator Schools organized by Melvin Month. Finally, I would to thank John Wiley and Sons Incorporated for graciously reverting the copyright on this book so I could prepare this Internet version. STANLEY HUMPHRIES, JR. Albuquerque, New Mexico November 2002 Charged Particle Beams I-5 Contents ________ 1. Introduction 1 1.1. Charged particle beams 1 1.2. Methods and organization 6 1.3. Single-particle dynamics 9 2. Phase space description of charged particle beams 20 2.1. Particle trajectories in phase space 22 2.2. Distribution functions 28 2.3. Numerical calculation of particle orbits with beam-generated forces 32 2.4. Conservation of phase space volume 36 2.5. Density and average velocity 46 2.6. Maxwell distribution 49 2.7. Collisionless Boltzmann equation 52 2.8. Charge and current density 56 2.9. Computer simulations 60 2.10. Moment equations 65 2.11. Pressure force in collisionless distributions 71 2.12. Relativistic particle distributions 76 Charged Particle Beams I-6 3. Introduction to beam emittance 79 3.1. Laminar and non-laminar beams 80 3.2. Emittance 87 3.3. Measurement of emittance 93 3.4. Coupled beam distributions, longitudinal emittance, normalized emittance, and brightness 101 3.5 Emittance force 107 3.6. Non-laminar beams in drift regions 109 3.7. Non-laminar beams in linear focusing systems 113 3.8. Compression and expansion of non-laminar beams 128 4. Beam emittance - advanced topics 133 4.1. Linear transformations of elliptical distributions 134 4.2. Transport parameters from particle orbit theory 145 4.3. Beam matching 150 4.4. Non-linear focusing systems 157 4.5. Emittance in storage rings 167 4.6. Beam cooling 174 5. Introduction to beam-generated forces 187 5.1. Electric and magnetic fields of beams 188 5.2. One-dimensional Child law for non-relativistic particles 195 5.3. Longitudinal transport limits for a magnetically-confined electron beams 204 5.4. Space-charge expansion of a drifting beam 211 5.5. Transverse forces in relativistic beams 216 Charged Particle Beams I-7 6. Beam-generated forces - advanced topics 224 6.1. Space-charge-limited flow with an initial injection energy 225 6.2. Space-charge-limited flow from a thermionic cathode 227 6.3. Space-charge-limited flow in spherical geometry 232 6.4. Bipolar flow 239 6.5. Space-charge-limited flow of relativistic electrons 242 6.6. One-dimensional self-consistent equilibrium 246 6.7. KV distribution 256 7. Electron and ion guns 262 7.1. Pierce method for gun design 263 7.2. Medium perveance guns 271 7.3. High perveance guns and ray tracing codes 277 7.4. High current electron sources 283 7.5. Extraction of ions at a free plasma boundary 289 7.6. Plasma ion sources 300 7.7. Charged-particle extraction from grid-controlled plasmas 315 7.8. Ion extractors 322 8. High power pulsed electron and ion diodes 328 8.1. Motion of electrons in crossed electric and magnetic fields 329 8.2. Pinched electron beam diodes 337 8.3. Electron diodes with strong applied magnetic fields 346 8.4. Magnetic insulation of high power transmission lines 351 8.5. Plasma erosion 356 8.6. Reflex triode 364 8.7. Low-impedance reflex triode 370 8.8. Magnetically-insulated ion diode 377 Charged Particle Beams I-8 8.9. Ion flow enhancement in magnetically-insulated diodes 388 9. Paraxial beam transport with space-charge 395 9.1. Envelope equation for sheet beams 396 9.2. Paraxial ray equation 400 9.3. Envelope equation in a quadrupole lens array 407 9.4 Limiting current for paraxial beams 412 9.5. Multi-beam ion transport 419 9.6. Longitudinal space-charge limits in RF accelerators and induction linacs 423 10. High current electron beam transport under vacuum 432 10.1. Motion of electrons through a magnetic cusp 433 10.2. Propagation of beams from an immersed cathode 439 10.3. Brillouin equilibrium of a cylindrical electron beam 445 10.4. Interaction of electrons with matter 451 10.5. Foil focusing of relativistic electron beams 457 10.6. Walle-charge and return-current for a beam in a pipe 470 10.7. Drifts of electron beams in a solenoidal field 477 10.8. Guiding electron beams with solenoidal fields 482 10.9. Electron beam transport in magnetic cusps 490 11. Ion beam neutralization 501 11.1. Neutralization by comoving electrons 502 11.2. Transverse neutralization 511 11.3. Current neutralization in vacuum 517 11.4. Focal limits for neutralized ion beams 522 11.5. Acceleration and transport of neutralized ion beams 528 Charged Particle Beams I-9 12. Electron beams in plasmas 535 12.1. Space-charge neutralization in equilibrium plasmas 536 12.2. Oscillations of an un-magnetized plasma 540 12.3. Oscillations of a neutralized electron beam 546 12.4 Injection of a pulsed electron beam into a plasma 552 12.5. Magnetic skin depth 563 12.6. Return current in a resistive plasma 569 12.7. Limiting current for neutralized electron beams 577 12.8. Bennett equilibrium 583 12.9. Propagation in low-density plasmas and weakly-ionized gases 587 13. Transverse instabilities 592 13.1. Instabilities of space-charge-dominated beams in periodic focusing systems 594 13.2. Betatron waves on a filamentary beam 610 13.3. Frictional forces and phase mixing 615 13.4. Transverse resonant modes 622 13.5. Beam breakup instability 631 13.6. Transverse resistive wall instability 640 13.7. Hose instability of an electron beam in an ion channel 645 13.8. Resistive hose instability 655 13.9. Filamentation instability of neutralized electron beams 664 14. Longitudinal instabilities 674 14.1. Two-stream instability 675 14.2. Beam-generated axial electric fields 687 14.3. Negative mass instability 697 14.4. Longitudinal resistive wall instability 704 Charged Particle Beams I-10 15. Generation of radiation with electron beams 720 15.1. Inverse diode 722 15.2. Driving resonant cavities with electron beams 736 15.3. Longitudinal beam bunching 749 15.4. Klystron 762 15.5. Traveling wave tube 772 15.6. Magnetron 781 15.7. Mechanism of the free-electron laser 796 15.8. Phase dynamics in the free-electron laser 803 Bibliography Index [...]... begin the study of beam transport This chapter discusses the effect of space-charge and emittance on beams in conventional accelerators The beams in these devices are paraxial - particle orbits make small angles with respect to the axis Sections 9.1 through 9.3 7 Introduction Charged Particle Beams derive envelope equations for beams in several focusing systems These equations, based on transverse force... decelerates particles in the phase range 0 > N > -B We can define conditions where a particle stays at a constant phase A particle with this property is a synchronous particle - its phase is the synchronous phase, Ns Figure 1.2 shows that the synchronous particle experiences a constant axial electric field, Ezs = Eo sinNs Limiting attention to non-relativistic ions, the synchronous particle velocity changes... radiation processing of food, and free-electron lasers The importance of accelerators for applications in research and industry sometimes overshadows beam physics as an intellectual discipline in its own right The theory of charged particle beams is much more than a tool to design machines - it is one of the richest and most active areas of classical physics In our study of charged particle beams, we shall... traveling wave can also decelerate particles - this is the basis for many microwave devices and the free-electron laser The conditions for synchronized deceleration are cosNs > 0 and sinNs < 0, or: (1.78) 20 Phase space description of charged- particle beams Charged Particle Beams 2 Phase-space description of charged particle beams This chapter introduces theoretical tools for application... Representation of particle motions in phase-space (a) Laminar phase-space trajectories of particle orbit vectors with no collisions (b) Effect of a collision on the phase-space position of a particle orbit vector 23 Phase space description of charged- particle beams Charged Particle Beams (2.1) (2.2) Equations (2.1) and (2.2) represent a parabola in phase space Fig 2.3a illustrates some orbits of protons in an... widely separated in velocity space after one particle suffers a collision Figure 2.2b shows phase-space trajectories in the presence of collisions The trajectories are no longer laminar In most charged- particle- beam accelerators and transport systems, the effect of collisions is small Changes in phase trajectories from collisions usually take place slowly compared with the motion of particles under... in the rest of the book We shall review methods to predict the average behavior of large numbers of particles The emphasis is ]on beams, where the particles have high kinetic energy, have good directionality, and may be relativistic Section 2.1 discusses the representation of particle orbits in phase-space For non-relativistic particles, phase-space is a six-dimensional space with axes in space (x,... electrons to ion beams Section 11.4 reviews focal limits on neutralized ion beams, while Section 11.5 describes methods to control and to accelerate high-flux ion beams Chapter 12 discusses the propagation of electron beams through plasmas We shall review the properties of plasmas that affect their response to all types of pulsed beams Sections 12.1 and 12.2 introduce two basic plasma quantities, the... applications to accelerators and beam optics systems Chapter 4 discusses consequences of beam emittance in low current beams with small space-charge forces The first three sections define the transport parameters of a beam and review transport theory This theory is useful for the the design of beam transport systems Section 4.4 reviews imperfections in charged particle lenses and how they contribute to the growth... motions of the beam Sections 13.2 through 13.4 review background material Section 13.2 classifies transverse beam oscillations in focusing systems Section 13.3 summarizes the effects of wall resistance and a spread of particle momentum on coherent oscillations Section 13.4 reviews the theory of 8 Introduction Charged Particle Beams transverse resonant modes in accelerator cavities These modes can effectively . material. Section 13.2 classifies transverse beam oscillations in focusing systems. Section 13.3 summarizes the effects of wall resistance and a spread of particle. low-density plasmas and weakly-ionized gases 587 13. Transverse instabilities 592 13.1. Instabilities of space-charge-dominated beams in periodic focusing