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| ISBN-13: | 9780486315850 |
|---|---|
| Publisher: | Dover Publications |
| Publication date: | 06/27/2013 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 864 |
| File size: | 63 MB |
| Note: | This product may take a few minutes to download. |
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CHARGED PARTICLE BEAMS
By Stanley Humphries Jr.
Dover Publications, Inc.
Copyright © 2013 Stanley Humphries, Jr.All rights reserved.
ISBN: 978-0-486-31585-0
CHAPTER 1
Introduction
1.1. CHARGED PARTICLE BEAMS
A charged particle beam is a group of particles that have about the same kinetic energy and move in about the same direction. Usually, the kinetic energies are much higher than the thermal energies of particles at ordinary temperatures. The high kinetic energy and good directionality of charged particles in beams make them useful for applications. Although we often associate accelerators with the large machines of high-energy physics, charged particle beams have continually expanding applications in many branches of research and technology. Recent active areas include flat-screen cathode-ray tubes, synchrotron light sources, beam lithography for microcircuits, thin-film technology, production of shortlived medical isotopes, 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 gain a comprehensive understanding of applied electromagnetism and collective physics.
Despite the practical importance and underlying unity of beam physics, the field has not yet achieved a strong identity like plasma physics. Although there are many specialized review papers and texts, few general works cover the full range of beam processes. There are several reasons for fragmentation in the field. Accelerator scientists are largely goal- oriented, concentrating on the theory and technology to solve the problem at hand. Each large accelerator has its own mission and its own group of scientists. Because of the broad range of required beam parameters, different accelerators use a diversity of technologies that often have little in common. Although there are large differences in technology, we shall see that a few basic principles underlie the design of all accelerators and beam transport devices. As the problems of accelerators become more challenging and beam applications become more sophisticated, it is increasingly important for accelerator scientists to share their insights and expertise. In recent years, there have been several efforts to emphasize the unity of the field and to promote communication among researchers. In the United States, examples include the Particle Accelerator Conference with its steadily increasing attendance from all areas of accelerator research, the U.S. Particle Accelerator School and its educational publications, and the recently formed American Physical Society Division of Accelerator Physics.
This book was written to guide students entering accelerator science and to provide researchers with a comprehensive reference. It contains a unified treatment of beam physics at an introductory level. This book and a previous one, Principles of Charged Particle Acceleration, provide a bridge to carry students to advanced work in specialized fields of accelerator science and beam theory. Principles of Charged Particle Acceleration reviews the fundamentals of single-particle dynamics. That book describes how accelerators work, from small low-current devices to the largest machines of high-energy and high-power research. The present book concentrates on problems of beam physics, the acceleration and control of large numbers of charged particles. The range of topics is extensive, with reference material for designers and users of all types of accelerators.
In this section, we begin by reviewing properties of charged particles and particle beams. Section 1.2 discusses some of the problems of collective physics and outlines the organization of the book. Section 1.3 summarizes theoretical results from Principles of Charged Particle Accelerators that will be useful for many of the derivations. The goal of beam theory is to describe how the multitude of particles in a beam interact with one another. For this purpose, we need not consider the internal structure of charged particles. Usually, it is sufficient to represent a particle as a point entity with two properties: charge, q, and rest mass, m0. We assume that the particle characteristics are constant during acceleration and transport. In this book, we will not examine the effects of finite particle dimensions and quantum properties such as spin. Except for specialized applications, these properties have little effect on the formation and acceleration of beams.
Much of the material in this book applies to any charged particle, from the elementary particles of high-energy physics research to hyper-velocity charged clusters. Familiar applications usually involve one of two types of particles: electrons or ions. The electron is an elementary particle with the following characteristics:
qe = -e = - 1.602 × 10-19 C
me = 9.109 × 10-31 kg. (1.1)
We shall apply MKS units exclusively throughout the book with the exception of the electron volt, a useful unit for the energy of individual particles.
Ions are composite particles. An ion is an atom missing one or more electrons or, in the case of negative ions, with an extra electron attached. The following quantities characterize an ion:
A: the atomic mass number, equal to the total number of protons and neutrons in the nucleus.
Z: the atomic number, equal to the number of electrons in the neutral atom.
Z: the charge state of the ion, equal to the number of electrons removed from or added to the atom.
The proton is the simplest ion—it is a hydrogen atom with its single electron removed. The proton is an elementary particle with charge and mass:
qp = + e = + 1.602 × 10-19 C,
mp = 1.673 × 10-27 kg. (1.2)
We denote the charge and mass of other ions as
qi = Z*qp = Z*(1.602 × 10-19) C, (1.3)
mi [congruent to] Amp = A(1.673 × 10-27) kg. (1.4)
The rest energy of a particle equals the rest mass multiplied by the square of the speed of light. The rest energy of an electron is
mec2 = 8.19 × 10-14 J.
If the kinetic energy of a particle approaches or exceeds its rest energy, we must use relativistic equations of motion. The MKS energy unit of joules is not convenient for individual charged particles. The standard energy unit in beam physics is the electron volt (eV). One electron volt equals the change in kinetic energy of an electron or proton that crosses a potential difference of 1 V, or
1 eV = 1.6. × 10-19 J. (1.5)
The electron rest energy in electron volts is
mec2 = 5.11 × 105 eV = 0.511 MeV (1.6)
When an electron accelerates through a potential difference of 5.11 x 105 V, the kinetic energy equals the rest energy. Electrons are relativistic when they have kinetic energy above about 100 keV (105eV). The Newtonian equations of motion are approximately correct for electron beams with kinetic energy below this level. The proton rest mass exceeds the electron mass by a factor of 1843—the proton rest energy is correspondingly higher:
mpc2 = 938 MeV (1.7)
Because of the high rest energy, we can use Newtonian dynamics to predict the motion of ions in many applications.
Although single charged particles may be useful for some physics experiments, we need large numbers of energetic particles for most applications. A flux of particles is a beam when the following two conditions hold:
1. The particles travel in almost the same direction.
2. The particles have a small spread in kinetic energy.
A beam is an ordered flow of charged particles. A disordered set of particles, such as a thermal plasma, is not a beam. Figure 1.1 illustrates the difference between a beam and a plasma. The relationship between a charged particle beam and a plasma is analogous to the relationship between a laser and a light bulb. The photons from a laser are directed and monochromatic. The degree of order in a flow of particles is called coherence. A high level of coherence is essential for most applications. For example, the minimum spot size of a scanning electron microscopic depends on the parallelism of the electrons in the beam.
Several quantities are useful to characterize charged particle beams, including (1) type of particle, (2) average kinetic energy, (3) current, (4) power, (5) pulse length, (6) transverse dimension, (7) parallelism, and (8) energy spread. The parameters of charged particle beams for applications extends over a remarkable, range. Table 1.1 gives estimates of high and low values for beam properties. No other field of engineering or applied physics extends over such a broad parameter space.
In conventional accelerators, particle mass spans the range from electrons to the heavy ions used for nuclear physics and accelerator inertial fusion. The mass of a uranium ion is 238 times that of the proton, or 440,000 times the electron mass. The charge state of particles in most accelerators is q = ± e. Heavy-ion accelerators are an exception. In these machines, highly stripped ions (Z* > 50) result when a medium-energy beam passes through a thin foil. The multiply-charged ions then accelerate to high kinetic energy in a linear accelerator.
The kinetic energy of beams for applications spans about 12 orders of magnitude. At the low end, we shall encounter energies less than 1 eV when we study electron emission from a thermionic cathode. The current achievements of high-energy-physics accelerators define the high end of the energy spectrum, about 1 TeV (1012 eV).
The beam current in present devices spans an even broader range, ~ 1015. Ion and electron microprobes have a current of about 1 nA = 10–9 A. Despite the low flux of such beams, we must apply collective beam theory to predict the minimum spot size. At the other extreme, pulsed ion or electron diodes generate beams with current exceeding 1 MA = 106 A.
To characterize beam power, we must distinguish between average power and peak power. Many accelerators have a pulsed duty cycle. The highest peak power, over 1012 W for ~ 50 ns, occurs in experiments on inertial fusion. At the low end, commercial devices such as CRT tubes operate continuously at power levels below 1W. Continuous machines define the upper limit on beam pulse length. At the lower limit, resonant accelerators generate trains of very short pulses. Pulse durations may be less than 100 ps = 10–10 s.
The maximum transverse dimension of charged particle beams is immense if we include astrophysical jets as examples. In conventional applications, industrial sheet beam irradiators create the largest beams, about 2 m in length. Scanning electron microscopes generate small beam spots less than 1 µm in diameter. The parallelism of orbits in beams also has a wide range. Accelerators under development for defense applications have a requirement on angular divergence of about 1 µrad. At the other extreme, intense pinched electron beams may have a divergence angle approaching 1 rad, with a spread in longitudinal kinetic energy comparable to the directed energy.
1.2. METHODS AND ORGANIZATION
The central issue in beam physics is the solution of collective problems involving large numbers of particles. The orbits of the particles depend on electric and magnetic fields. The fields, in turn, result partly from contributions of the beam particles. Therefore, the field values depend on the positions and velocities of all particles. An exact prediction of beam behavior demands the simultaneous calculation of every particle orbit. The challenge is formidable—a low-current beam may contain more than 1010 particles. Clearly, exact solutions are impossible, even with the most powerful computers.
Collective physics is a science of approximation. Predictions involve insight and experience—to solve problems, we must eliminate unnecessary material but preserve the essential processes. Beam physics can be difficult for beginning students because there are no cut-and-dried methods. Each calculation demands a careful analysis and a reduction with simplifying assumptions. One goal of this book is to give students insights to resolve collective problems. The material of the book was organized with this goal in mind:
1. The order of topics is from the simplest to the most complex. Ideally, the reader should follow the text from the beginning to the end. The early chapters give background material necessary to understand advanced subjects like beam instabilities.
2. In collective problems, the initial analysis and reduction is as important as the correct mathematical solution of the equations. The best mathematical methods are useless if the statement of the problem is not physically correct. Therefore, we shall concentrate on setting up problems, carefully listing all limiting conditions. After defining the governing equations, we shall apply straightforward mathematical methods to find a solution.
3. A frustrating problem in many advanced works on beam physics is that the derivations often have missing steps. These leaps may be obvious to the author but are obscure to nonexperts. To avoid this difficulty, we shall follow all stages of derivations at the expense of some repetition.
This book is an introductory text. It does not address sophisticated methods of mathematical analysis, the history of beam physics, or the vast range of advanced literature. The references in Appendix 1 are a good starting point for further reading on advanced topics.
The material in Chapters 1–6 is the foundation for later chapters. Chapter 2 is a capsule summary of collective physics with an emphasis on charged-particle-beam theory. Collective physics organizes information about the motion of large numbers of particles. Rather than calculate the orbits of individual particles, we try to identify general trends in behavior. The best way to organize information about particles is to plot orbit vectors in phase space. The theorem of conserved particle density in phase space leads to the fundamental equation of collective physics, the Boltzmann equation. From this relationship, we derive moment equations that describe the conservation of particles, momentum, and energy in large groups.
The introductory accelerator theory of Principles of Charged Particle Acceleration concentrates on the orbits of single particles or on laminar beams where all orbits are similar. In Chapter 3, we remove this limitation and study beams where the particles have random spreads in direction and energy. Real beams always have such a diversity of orbits—to design accelerators, we must understand the limitations set by beam imperfections. Chapter 3 defines emittance, a quantity that characterizes the parallelism of beams. The principle of emittance conservation has extensive 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 design of beam-transport systems. Section 4.4 reviews imperfections in charged particle lenses and how they contribute to the growth of beam emittance. The final two sections discuss the importance of beam emittance in storage rings and beam colliders. We shall study methods that circumvent the principle of phase-volume conservation to produce beams with low spreads in direction and energy.
Chapter 5 discusses equilibrium effects of beam-generated electric and magnetic fields. The chapter introduces the idea of self-consistent calculations. In this chapter we follow the motion of beam particles in fields that depend on the instantaneous position of all other particles. The Child derivation is the prototype calculation of a self-consistent beam equilibrium. It leads to the Child limit, a constraint on the current density from a beam extractor. Chapter 6 uses the expressions for the fields generated by equilibrium beams to calculate one-dimensional current flow in several practical cases. The chapter also introduces the KV distribution, a starting point for self-consistent models of two-dimensional equilibria.
Chapters 7 and 8 introduce methods to create beams, while Chapters 9–12 discuss beam transport and acceleration. Chapter 7 deals with electron and ion guns at low to medium current. Sections 7.1–7.3 review design techniques for guns. Section 7.4 discusses electron sources, while Sections 7.5 and 7.6 review ion sources and ion extraction from plasmas. The final two sections describe methods to generate large-area, high-current ion beams.
Chapter 8 is devoted to high-power pulsed electron and ion diodes. These devices use pulsed power technology to generate beams with very high current. Section 8.1 discusses the motion of electrons in crossed electric and magnetic fields—the resulting equations are also useful for conventional devices like the magnetron. The next two sections review the generation of pulsed electron beams. Sections 8.4 and 8.5 discuss two important processes for diode technology, magnetic insulation and plasma erosion. The final four sections cover methods to create pulsed ion beams with current density far beyond the Child limit.
(Continues...)
Excerpted from CHARGED PARTICLE BEAMS by Stanley Humphries Jr.. Copyright © 2013 Stanley Humphries, Jr.. Excerpted by permission of Dover Publications, Inc..
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