RF Linear Accelerators

Borne out of twentieth-century science and technology, the field of RF (radio frequency) linear accelerators has made significant contributions to basic research, energy, medicine, and national defense. As we advance into the twenty-first century, the linac field has been undergoing rapid development as the demand for its many applications, emphasizing high-energy, high-intensity, and high-brightness output beams, continues to grow. RF Linear Accelerators is a textbook that is based on a US Particle Accelerator School graduate-level course that fills the need for a single introductory source on linear accelerators. The text provides the scientific principles and up-to-date technological aspects for both electron and ion linacs. This second edition has been completely revised and expanded to include examples of modern RF linacs, special linacs and special techniques as well as superconducting linacs. In addition, problem sets at the end of each chapter supplement the material covered. The book serves as a must-have reference for professionals interested in beam physics and accelerator technology.

Table of Contents:
Preface to the Second Edition xi Preface to the First Edition xiii 1 Introduction 1 1.1 Linear Accelerators: Historical Perspective 2 1.2 Linac Structures 6 1.3 Linac Beam Dynamics 10 1.4 Multiparticle Effects 12 1.5 Applications of Modern RF Linacs 13 1.6 Accelerator-Physics Units, Unit Conversions, and Physical Constants 15 1.7 Useful Relativistic Mechanics Relationships 16 1.8 Maxwell’s Equations 17 1.9 Conducting Walls 19 1.10 Group Velocity and Energy Velocity 20 1.11 Coaxial Resonator 22 1.12 Transverse-Magnetic Mode of a Circular Cylindrical Cavity 24 1.13 Cylindrical Resonator Transverse-Magnetic Modes 26 1.14 Cylindrical Resonator Transverse Electric Modes 27 References 30 2 RF Acceleration in Linacs 32 2.1 Particle Acceleration in an RF Field 32 2.2 Energy Gain on Axis in an RF Gap 33 2.3 Longitudinal Electric Field as a Fourier Integral 36 2.4 Transit-Time-Factor Models 39 2.5 Power and Acceleration Efficiency Figures of Merit 42 2.6 Cavity Design Issues 44 2.7 Frequency Scaling of Cavity Parameters 46 2.8 Linac Economics 47 References 52 3 Periodic Accelerating Structures 53 3.1 Synchronous Acceleration and Periodic Structures 53 3.2 Floquet Theorem and Space Harmonics 54 3.3 General Description of Periodic Structures 57 3.4 Equivalent Circuit Model for Periodic Structures 59 3.5 Periodic Array of Low-Pass Filters 61 3.6 Periodic Array of Electrically Coupled Circuits 62 3.7 Periodic Array of Magnetically Coupled Circuits 63 3.8 Periodic Array of Cavities with Resonant Coupling Element 64 3.9 Measurement of Dispersion Curves in Periodic Structures 65 3.10 Traveling-Wave Linac Structures 68 3.11 Analysis of the Periodic Iris-Loaded Waveguide 69 3.12 Constant-Impedance Traveling-Wave Structure 72 3.13 Constant-Gradient Structure 74 3.14 Characteristics of Normal Modes for Particle Acceleration 76 3.15 Physics Regimes of Traveling-Wave and Standing-Wave Structures 79 References 81 4 Standard Linac Structures 83 4.1 Independent-Cavity Linacs 83 4.2 Wideröe Linac 87 4.3 H-Mode Structures 89 4.4 Alvarez Drift-Tube Linac 91 4.5 Design of Drift-Tube Linacs 96 4.6 Coupled-Cavity Linacs 98 4.7 Three Coupled Oscillators 99 4.8 Perturbation Theory and Effects of Resonant-Frequency Errors 101 4.9 Effects from Ohmic Power Dissipation 103 4.10 General Problem of N + 1 Coupled Oscillators 105 4.11 Biperiodic Structures for Linacs 108 4.12 Design of Coupled-Cavity Linacs 111 4.13 Intercell Coupling Constant 114 4.14 Decoupling of Cavities Connected by a Beam Pipe 116 4.15 Resonant Coupling 117 4.16 Accelerating Structures for Superconducting Linacs 121 λ/4 Superconducting Structures 121 λ/2 Superconducting Structures 121 TM Superconducting Structures 122 RF Properties and Scaling Laws for TM and λ/2 Superconducting Structures 125 Shunt Impedance for TM and λ/2 Superconducting Structures 127 Stored Energy for TM and λ/2 Superconducting Structures 129 Scaling Formulas for λ/4 Superconducting Structures 131 References 133 5 Microwave Topics for Linacs 135 5.1 Shunt Resonant Circuit Model 135 5.2 Theory of Resonant Cavities 137 5.3 Coupling to Cavities 138 5.4 Equivalent Circuit for a Resonant-Cavity System 139 5.5 Equivalent Circuit for a Cavity Coupled to two Waveguides 144 5.6 Transient Behavior of a Resonant-Cavity System 146 5.7 Wave Description of a Waveguide-to-Cavity Coupling 148 5.8 Microwave Power Systems for Linacs 156 5.9 Multipacting 159 5.10 Electron Field Emission 162 5.11 RF Electric Breakdown: Kilpatrick Criterion 163 5.12 Adiabatic Invariant of an Oscillator 164 5.13 Slater Perturbation Theorem 165 5.14 Quasistatic Approximation 167 5.15 Panofsky–Wenzel Theorem 168 References 173 6 Longitudinal Particle Dynamics 175 6.1 Longitudinal Focusing 175 6.2 Difference Equations of Longitudinal Motion for Standing-Wave Linacs 177 6.3 Differential Equations of Longitudinal Motion 178 6.4 Longitudinal Motion when Acceleration Rate is Small 178 6.5 Hamiltonian and Liouville’s Theorem 182 6.6 Small Amplitude Oscillations 186 6.7 Adiabatic Phase Damping 187 6.8 Longitudinal Dynamics of Ion Beams in Coupled-Cavity Linacs 189 6.9 Longitudinal Dynamics in Independent-Cavity Ion Linacs 190 6.10 Longitudinal Dynamics of Low-energy Beams Injected Into a v = c Linac 192 6.11 Rf Bunching 194 6.12 Longitudinal Beam Dynamics in H-Mode Linac Structures 196 References 199 7 Transverse Particle Dynamics 201 7.1 Transverse RF Focusing and Defocusing 201 7.2 Radial Impulse from a Synchronous Traveling Wave 203 7.3 Radial Impulse near the Axis in an Accelerating Gap 204 7.4 Including Electrostatic Focusing in the Gap 207 7.5 Coordinate Transformation through an Accelerating Gap 208 7.6 Quadrupole Focusing in a Linac 209 7.7 Transfer-Matrix Solution of Hill’s Equation 211 7.8 Phase-Amplitude Form of Solution to Hill’s Equation 213 7.9 Transfer Matrix through One Period 214 7.10 Thin-Lens FODO Periodic Lattice 215 7.11 Transverse Stability Plot in a Linac 217 7.12 Effects of Random Quadrupole Misalignment Errors 218 7.13 Ellipse Transformations 221 7.14 Beam Matching 222 7.15 Current-Independent Beam Matching 224 7.16 Solenoid Focusing 225 7.17 Smooth Approximation to Linac Periodic Focusing 226 7.18 Radial Motion for Unfocused Relativistic Beams 227 References 230 8 Radiofrequency Quadrupole Linac 232 8.1 Principles of Operation 232 8.2 General Potential Function 236 8.3 Two-Term Potential Function Description 238 8.4 Electric Fields 240 8.5 Synchronous Acceleration 241 8.6 Longitudinal Dynamics 242 8.7 Transverse Dynamics 243 8.8 Adiabatic Bunching in the RFQ 245 8.9 Four-Vane Cavity 248 8.10 Lumped-Circuit Model of Four-Vane Cavity 249 8.11 Four-Vane Cavity Eigenmodes 251 8.12 Transmission-Line Model of Quadrupole Spectrum 254 8.13 Radial-Matching Section 260 8.14 RFQ Transition Cell 265 8.15 Beam Ellipses in an RFQ 271 8.16 Tuning for the Desired Field Distribution in an RFQ 273 8.17 Four-Rod Cavity 274 8.18 Four Vane with Windows RFQ 276 References 280 9 Multiparticle Dynamics with Space Charge 282 9.1 Beam Quality, Phase Space, and Emittance 283 9.2 RMS Emittance 285 9.3 Transverse and Longitudinal Emittance 287 9.4 Emittance Conventions 288 9.5 Space-Charge Dynamics 289 9.6 Practical Methods for Numerical Space-Charge Calculations 292 9.7 RMS Envelope Equation with Space Charge 296 9.8 Continuous Elliptical Beams 297 9.9 Three-Dimensional Ellipsoidal Bunched Beams 299 9.10 Beam Dynamics Including Linear Space-Charge Field 300 9.11 Beam-Current Limits from Space Charge 302 9.12 Overview of Emittance Growth from Space Charge 303 9.13 Emittance Growth for rms Matched Beams 306 9.14 Model of Space-Charge-Induced Emittance Growth in a Linac 314 9.15 Emittance Growth for rms Mismatched Beams 316 9.16 Space-Charge Instabilities in RF Linacs from Periodic Focusing: Structure Resonances 318 9.17 Longitudinal-Transverse Coupling and Space-Charge Instabilities for Anisotropic Linac Beams 319 9.18 Beam Loss and Beam Halo 325 9.19 Los Alamos Beam Halo Experiment 329 9.20 Scaling of Emittance Growth and Halo 331 9.21 Longitudinal Beam Dynamics Constraint on the Accelerating Gradient 332 References 338 10 Beam Loading 341 10.1 Fundamental Beam-Loading Theorem 342 10.2 The Single-Bunch Loss Parameter 344 10.3 Energy Loss to Higher-Order Cavity Modes 344 10.4 Beam Loading in the Accelerating Mode 345 10.5 Equations Describing a Beam-Loaded Cavity 347 General Results 348 Optimum Detuning 350 Extreme Beam-Loaded Limit 351 Numerical Example of a Beam-Loaded Cavity 351 Example of a Heavily Beam - Loaded Superconducting Cavity with Bunches Injected on the Crest of the Accelerating Wave 352 10.6 Generator Power when the Beam Current is Less than Design Value 352 10.7 Transient Turn-On of a Beam-Loaded Cavity 354 References 360 11 Wakefields 361 11.1 Image Force for Line Charge in Round Pipe 362 11.2 Fields from a Relativistic Point Charge and Introduction to Wakefields 364 11.3 Wake Potential from a Relativistic Point Charge 367 11.4 Wake Potentials in Cylindrically Symmetric Structures 368 11.5 Scaling of Wake Potentials with Frequency 370 11.6 Bunch Wake Potentials for an Arbitrary Charge Distribution 371 11.7 Loss Parameters for a Particular Charge Distribution 376 11.8 Bunch Loss Parameters for a Gaussian Distribution 377 11.9 Beam-Coupling Impedance 378 11.10 Longitudinal- and Transverse-Impedance Definitions 380 11.11 Impedance and Wake Potential for a Single Cavity Mode 381 11.12 Short-Range Wakefields-Parasitic Losses 383 11.13 Short-Range Wakefields: Energy Spread 383 11.14 Short-Range Wakefields: Compensation of Longitudinal Wake Effect 384 11.15 Short-Range Wakefields: Single-Bunch Beam Breakup 384 11.16 Short-Range Wakefields: BNS Damping of Beam Breakup 386 11.17 Long-Range Wakefields and Multibunch Beam Breakup 389 11.18 Multipass BBU in Recirculating Electron Linacs 397 References 402 12 Special Structures and Techniques 405 12.1 Alternating-Phase Focusing 405 12.2 Accelerating Structures Using Electric Focusing 406 12.3 Coupled-Cavity Drift-Tube Linac 410 12.4 Beam Funneling 411 12.5 RF Pulse Compression 413 12.6 Superconducting RF Linacs 414 Brief History 415 Introduction to the Physics and Technology of RF Superconductivity 416 12.7 Examples of Operating Superconducting Linacs 419 Atlas 419 Cebaf 419 Spallation Neutron Source 421 12.8 Future Superconducting Linac Facilities 423 International Linear Collider 423 Next-Generation Rare Isotope Facility 426 Free-Electron Lasers 427 References 430 Index 433