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Cyclotron illustration Principles of Charged Particle Acceleration

Stanley Humphries
Professor Emeritus
University of New Mexico

Scout Report for Science and Engineering

Welcome to the Principles of Charged Particle Acceleration site. The text was originally published by John Wiley and Sons (ISBN 0-471-87878-2, QC787.P3H86) in 1986. A low-cost printed edition is currently available from Dover Press.

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Table of contents

1. Introduction

2. Particle Dynamics
2.1. Charged Particle Properties
2.2. Newton's Laws of Motion
2.3. Kinetic Energy
2.4. Galilean Transformations
2.5. Postulates of Relativity
2.6. Time Dilation
2.7. Lorentz Contraction
2.8. Lorentz Transformations
2.9. Relativistic Formulas
2.10. Non-relativistic Approximation for Transverse Motion
3. Electric and Magnetic Forces
3.1. Forces between Charges and Currents
3.2. The Field Description and the Lorentz Force
3.3. The Maxwell Equations
3.4. Electrostatic and Vector Potentials
3.5. Inductive Voltage and Displacement Current
3.6. Relativistic Particle Motion in Cylindrical Coordinates
3.7. Motion of Charged Particles in a Uniform Magnetic Field
4. Steady-State Electric and Magnetic Fields
4.1. Static Field Equations with No Sources
4.2. Numerical Solutions to the Laplace Equation
4.3. Analog Met hods to Solve the Laplace Equation
4.4. Electrostatic Quadrupole Field
4.5. Static Electric Fields with Space Charge
4.6. Magnetic Fields in Simple Geometries
4.7. Magnetic Potentials
5. Modification of Electric and Magnetic Fields by Materials
5.1. Dielectrics
5.2. Boundary Conditions at Dielectric Surfaces
5.3. Ferromagnetic Materials
5.4. Static Hysteresis Curve for Ferromagnetic Materials
5.5. Magnetic Poles
5.6. Energy Density of Electric and Magnetic Fields
5.7. Magnetic Circuits
5.8. Permanent Magnet Circuits
6. Electric and Magnetic Field Lenses
6.1. Transverse Beam Control
6.2. Paraxial Approximation for Electric and Magnetic Fields
6.3. Focusing Properties of Linear Fields
6.4. Lens Properties
6.5. Electrostatic Aperture Lens
6.6. Electrostatic Immersion Lens
6.7. Solenoidal Magnetic Lens
6.8. Magnetic Sector Lens
6.9. Edge Focusing
6.10. Magnetic Quadrupole Lens
7. Calculation of Particle Orbits in Focusing Fields
7.1. Transverse Orbits in a Continuous Linear Focusing Force
7.2. Acceptance and P of a Focusing Channel
7.3. Betatron Oscillations
7.4. Azimuthal Motion of Particles in Cylindrical Beams
7.5. The Paraxial Ray Equation
7.6. Numerical Solutions of Particle Orbits
8. Transfer Matrices and Periodic Focusing Systems
8.1. Transfer Matrix of the Quadrupole Lens
8.2. Transfer Matrices for Common Optical Elements
8.3. Combining Optical Elements
8.4. Quadrupole Doublet and Triplet Lenses
8.5. Focusing in a Thin-Lens Array
8.6. Raising a Matrix to a Power
8.7. Quadrupole Focusing Channels
9. Electrostatic Accelerators and Pulsed High Voltage
9.1. Resistors, Capacitors, and Inductors
9.2. High-Voltage Supplies
9.3. Insulation
9.4. Van de Graaff Accelerator
9.5. Vacuum Breakdown
9.6. LRC Circuits
9.7. Impulse Generators
9.8. Transmission Line Equations in the Time Domain
9.9. Transmission Lines as Pulsed Power Modulators
9.10. Series Transmission Line Circuits
9.11. Pulse-Forming Networks
9.12. Pulsed Power Compression
9.13. Pulsed Power Switching by Saturable Core Inductors
9.14. Diagnostics for Pulsed Voltages and Current
10. Linear Induction Accelerators
10.1. Simple Induction Cavity
10.2. Time-Dependent Response of Ferromagnetic Materials
10.3. Voltage Multiplication Geometries
10.4. Core Saturation and Flux Forcing
10.5. Core Reset and Compensation Circuits
10.6. Induction Cavity Design: Field Stress and Average Gradient
10.7. Coreless Induction Accelerators
11. Betatrons
11.1. Principles of the Betatron
11.2. Equilibrium of the Main Betatron Orbit
11.3. Motion of the Instantaneous Circle
11.4. Reversible Compression of Transverse Particle Orbits
11.5. Betatron Oscillations
11.6. Electron Injection and Extraction
11.7. Betatron Magnets and Acceleration Cycles
12. Resonant Cavities and Waveguides
12.1. Complex Exponential Notation and Impedance
12.2. Lumped Circuit Element Analogy for a Resonant Cavity
12.3. Resonant Modes of a Cylindrical Cavity
12.4. Properties of the Cylindrical Resonant Cavity
12.5. Power Exchange with Resonant Cavities
12.6. Transmission Lines in the Frequency Domain
12.7. Transmission Line Treatment of the Resonant Cavity
12.8. Waveguides
12.9. Slow-Wave Structures
12.10. Dispersion Relationship for the Iris-Loaded Waveguide
13. Phase Dynamics
13.1. Synchronous Particles and Phase Stability
13.2. The Phase Equations
13.3. Approximate Solution to the Phase Equations
13.4. Compression of Phase Oscillations
13.5. Longitudinal Dynamics of Ions in a Linear Induction Accelerator
13.6. Phase Dynamics of Relativistic Particles
14. Radio-Frequency Linear Accelerators
14.1. Electron Linear Accelerators
14.2. Linear Ion Accelerator Configurations
14.3. Coupled Cavity Linear Accelerators
14.4. Transit-Time Factor, Gap Coefficient and Radial Defocusing
14.5. Vacuum Breakdown in rf Accelerators
14.6. Radio-Frequency Quadrupole
14.7. Racetrack Microtron
15. Cyclotrons and Synchrotrons
15.1. Principles of the Uniform-Field Cyclotron
15.2. Longitudinal Dynamics of the Uniform-Field Cyclotron
15.3. Focusing by Azimuthally Varying Fields (AVF)
15.4. The Synchrocyclotron and the AVF Cyclotron
15.5. Principles of the Synchrotron
15.6. Longitudinal Dynamics of Synchrotrons
15.7. Strong Focusing