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 ν = с 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.I8 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
9.1 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
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