| Preface |
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xi | |
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I Electromagnetism and Classical Mechanics |
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1 | (80) |
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1 Electromagnetic Fields in Accelerator Components |
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3 | (56) |
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1.1 Boundary Conditions on Electromagnetic Fields |
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7 | (5) |
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1.1.1 Surface of an infinite permeability material |
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8 | (3) |
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1.1.2 Surface of an ideal conductor |
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11 | (1) |
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1.2 Two-Dimensional Multipole Fields |
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12 | (21) |
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1.2.1 Current distribution for a pure multipole |
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18 | (4) |
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1.2.2 Geometry of iron-dominated multipole magnets |
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22 | (4) |
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1.2.3 Multipole decomposition |
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26 | (7) |
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1.3 Three-Dimensional Fields |
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33 | (10) |
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1.3.1 Cartesian and cylindrical modes |
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34 | (5) |
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1.3.2 Generalised gradients |
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39 | (4) |
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1.4 Fields in Radiofrequency Cavities |
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43 | (16) |
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1.4.1 Rectangular cavities |
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46 | (7) |
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1.4.2 Cylindrical cavities |
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53 | (6) |
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2 Hamiltonian for a Particle in an Accelerator Beam Line |
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59 | (22) |
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2.1 The Hamiltonian for a Straight Beam Line |
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61 | (7) |
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2.2 Dynamical Variables for Beam Dynamics |
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68 | (4) |
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2.3 The Hamiltonian in a Curved Co-ordinate System |
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72 | (4) |
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2.4 Symplectic Transfer Maps and Liouville's Theorem |
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76 | (5) |
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II Single-Particle Linear Dynamics |
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81 | (182) |
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3 Linear Transfer Maps for Common Components |
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83 | (44) |
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85 | (3) |
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88 | (8) |
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3.3 Dipole Fringe Fields and Edge Focusing |
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96 | (5) |
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101 | (5) |
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106 | (3) |
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3.6 Radiofrequency Cavity |
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109 | (7) |
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116 | (11) |
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4 Linear Optics in Uncoupled Beam Lines |
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127 | (30) |
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128 | (4) |
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4.2 The Courant--Snyder Parameters |
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132 | (4) |
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4.3 Action--Angle Variables |
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136 | (7) |
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4.4 Courant--Snyder Parameters in a FODO Beam Line |
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143 | (4) |
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147 | (3) |
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4.6 Courant--Snyder Parameters and Particle Distribution |
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150 | (7) |
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157 | (38) |
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5.1 Transverse--Longitudinal Coupling |
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158 | (18) |
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158 | (4) |
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5.1.2 Momentum compaction and phase slip |
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162 | (6) |
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168 | (8) |
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176 | (12) |
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188 | (2) |
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5.4 Examples of Coupled Optics |
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190 | (5) |
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5.4.1 Uniform solenoid field |
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190 | (1) |
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5.4.2 Flat-beam electron source |
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191 | (4) |
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6 Linear Imperfections in Storage Rings |
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195 | (20) |
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196 | (2) |
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198 | (5) |
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6.3 Quadrupole Alignment Errors |
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203 | (1) |
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204 | (3) |
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6.5 Beam-Based Alignment of Quadrupoles |
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207 | (3) |
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210 | (5) |
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7 Effects of Synchrotron Radiation |
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215 | (48) |
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7.1 Classical Radiation: Radiation Damping |
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217 | (13) |
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7.2 Quantum Radiation: Quantum Excitation |
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230 | (7) |
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7.3 Equilibrium Emittance and Lattice Design |
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237 | (13) |
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7.3.1 Natural emittance in a FODO storage ring |
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239 | (4) |
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7.3.2 Double-bend achromat |
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243 | (3) |
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7.3.3 TME lattices and multibend achromats |
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246 | (4) |
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7.4 Computation of Equilibrium Emittances |
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250 | (8) |
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7.5 Synchrotron Radiation and Spin Polarisation |
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258 | (5) |
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III Single-Particle Nonlinear Dynamics |
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263 | (130) |
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8 Examples of Nonlinear Effects in Accelerator Beam Lines |
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265 | (22) |
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8.1 Longitudinal Dynamics in a Bunch Compressor |
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265 | (9) |
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8.2 Chromaticity in a Linear FODO Beam Line |
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274 | (5) |
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8.3 Chromaticity in Storage Rings |
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279 | (8) |
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9 Representations of Transfer Maps |
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287 | (22) |
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289 | (7) |
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9.2 Power Series Map for a Sextupole |
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296 | (5) |
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9.3 Mixed-Variable Generating Functions |
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301 | (8) |
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10 Symplectic Integrators |
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309 | (22) |
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310 | (9) |
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10.2 Explicit Symplectic Integrator for s-dependent Fields |
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319 | (6) |
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10.3 Symplectic Runge--Kutta Integrators |
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325 | (6) |
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11 Methods for Analysis of Single-Particle Dynamics |
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331 | (62) |
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11.1 A Lie Transformation Example: the -- I Transformer |
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332 | (3) |
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11.2 Canonical Perturbation Theory |
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335 | (25) |
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11.2.1 Dipole perturbations: closed orbit distortion |
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343 | (3) |
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11.2.2 Quadrupole perturbations: focusing errors |
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346 | (2) |
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11.2.3 Skew quadrupole perturbations: coupling |
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348 | (9) |
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11.2.4 Sextupole perturbations |
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357 | (3) |
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11.3 Resonances and Dynamic Aperture |
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360 | (13) |
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11.4 Normal Form Analysis |
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373 | (11) |
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11.5 A Numerical Method: Frequency Map Analysis |
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384 | (9) |
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393 | (180) |
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395 | (50) |
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12.1 The Kapchinsky--Vladimirsky Distribution |
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397 | (5) |
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12.2 The Envelope Equations for the KV Distribution |
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402 | (5) |
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12.3 Elliptically Symmetric Non-KV Distributions |
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407 | (9) |
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12.4 Space-Charge Tune Shifts |
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416 | (9) |
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12.5 Matching a Continuous Beam to a Solenoid Field |
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425 | (4) |
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12.6 Longitudinal Dynamics with Space Charge |
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429 | (11) |
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440 | (5) |
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445 | (24) |
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446 | (10) |
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13.2 Intrabeam Scattering |
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456 | (13) |
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459 | (4) |
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13.2.2 Bjorken--Mtingwa formulae |
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463 | (2) |
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13.2.3 High energy approximation |
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465 | (4) |
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14 Wake Fields, Wake Functions and Impedance |
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469 | (42) |
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14.1 Wake Fields in a Resonant Cavity |
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471 | (8) |
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14.2 Resistive-Wall Wake Fields |
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479 | (12) |
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491 | (8) |
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499 | (12) |
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15 Coherent Instabilities |
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511 | (62) |
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15.1 Coupled-Bunch Instabilities |
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512 | (13) |
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512 | (8) |
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15.1.2 Longitudinal modes |
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520 | (5) |
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15.2 Potential-Well Distortion |
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525 | (4) |
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15.3 Coasting Beams: Microwave Instability |
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529 | (11) |
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15.4 Single-Bunch Instabilities |
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540 | (33) |
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15.4.1 Head-tail instability |
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541 | (11) |
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15.4.2 Sacherer's integral equation |
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552 | (8) |
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15.4.3 Discrete modes: Robinson instability |
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560 | (6) |
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566 | (7) |
| Bibliography |
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573 | (12) |
| Index |
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585 | |