Contents -- Preface -- 1 Wakes and Impedances -- 1.1 Wake Fields -- 1.1.1 Two Approximations -- 1.1.2 Panofsky-Wenzel Theorem -- 1.1.3 Cylindrically Symmetric Chamber -- 1.2 Coupling Impedances -- 1.3 Parasitic Loss -- 1.3.1 Coherent Loss -- 1.3.2 Incoherent Loss -- 1.4 Exercises -- 1.5 Appendix: A Collection of Wakes and Impedances -- References -- Bibliography -- 2 Potential-Well Distortion -- 2.1 Longitudinal Phase Space -- 2.1.1 Momentum Compaction -- 2.1.2 Equations of Motion -- 2.1.2.1 Synchrotron Oscillation -- 2.2 Mode Approach -- 2.2.1 Vlasov Equation -- 2.2.2 Coasting Beams -- 2.3 Static Solution -- 2.4 Reactive Force -- 2.4.1 Space-Charge Impedance -- 2.4.2 Other Distributions -- 2.5 Bunch-Shape Distortion -- 2.5.1 Haissinski Equation -- 2.5.2 Elliptical Phase-Space Distribution -- 2.6 Synchrotron Tune Shift -- 2.6.1 Incoherent Synchrotron Tune Shift -- 2.6.2 Coherent Synchrotron Tune Shift -- 2.7 Potential-Well Distortion Compensation -- 2.7.1 Space-Charge Cancellation -- 2.7.2 Ferrite Insertion -- 2.8 Potential-Well Distortion in Barrier RF -- 2.8.1 RF Barriers -- 2.8.2 Asymmetric Beam Profile -- 2.9 Exercises -- Bibliography -- 3 Betatron Tune Shifts -- 3.1 Static Transverse Forces -- 3.1.1 Electric Image Forces -- 3.1.2 Magnetic Image Forces -- 3.2 Space-Charge Self-Force -- 3.2.1 Incoherent Self-Force Tune Shift -- 3.2.2 Tune-Shift Distribution -- 3.2.3 Incoherence versus Coherence -- 3.3 Tune Shift for a Beam -- 3.3.1 Image Formation -- 3.3.2 Coasting Beams -- 3.3.3 Bunched Beams -- 3.4 Other Vacuum Chamber Geometries -- 3.4.1 Circular Vacuum Chamber -- 3.4.2 Elliptical Vacuum Chamber -- 3.4.3 Rectangular Vacuum Chamber -- 3.4.4 Closed Yoke -- 3.5 Connection with Impedance -- 3.5.1 Impedance from Images -- 3.5.2 Impedance from Self-Force -- 3.6 Exercises -- Bibliography -- 4 Envelope Equation -- 4.1 The Integer Resonance.

4.2 The Kapchinsky-Vladimirsky Equation -- 4.2.1 Least-Square Value -- 4.2.2 One Dimension -- 4.2.3 Two Dimensions -- 4.3 Collective Oscillations of Beams -- 4.3.1 One Dimension -- 4.3.2 Two Dimensions -- 4.3.2.1 Equivalent- Unijorm-Beam -- 4.4 Simulations -- 4.4.1 One Dimension -- 4.4.2 Two Dimensions -- 4.5 Application to Synchrotrons -- 4.6 Exercises -- Bibliography -- 5 Longitudinal Microwave Instability for Coasting Beams -- 5.1 Microwave Instability -- 5.1.1 Dispersion Relation -- 5.1.2 Stability Curve and Keil-Schnell Criterion -- 5.1.3 Landau Damping -- 5.1.4 Self-Bunching -- 5.1.5 Overshoot -- 5.2 Observation and Cure -- 5.3 Ferrite Insertion and Instability -- 5.3.1 Microwave Instability -- 5.3.2 Cause of Instability -- 5.3.3 Heating the Ferrite -- 5.3.4 Application at the PSR -- 5.4 Exercises -- Bibliography -- 6 Longitudinal Microwave Instability for Short Bunches -- 6.1 Bunch Modes -- 6.1.1 A Particle in Synchrotron Oscillation -- 6.1.2 Coherent Azimuthal Modes -- 6.1.3 Measurement of Coherent Modes -- 6.2 Collective Instability -- 6.2.1 Dispersion Relation of a Sideband -- 6.2.2 Landau Damping of a Sideband -- 6.2.2.1 Equi-Growth Contours -- 6.2.3 Stability of a Bunch -- 6.2.3.1 Higher Azimuthal Modes -- 6.2.3.2 Coherent Shift from Mean Incoherent Frequency -- 6.2.3.3 Bi- Gaussian Distribution -- 6.3 Coupling of Azimuthal Modes -- 6.4 Bunch Lengthening and Scaling Law -- 6.5 Sawtooth Instability -- 6.5.1 Possible Cure -- 6.5.1.1 Precaution at The Next Linear Collider (NLC) -- 6.6 Exercises -- Bibliography -- 7 Beam-Loading and Robinson's Instability -- 7.1 Equivalent Circuit -- 7.2 Beam-Loading in an Accelerator Ring -- 7.2.1 Steady-State Compensation -- 7.3 Robinson's Stability Criteria -- 7.3.1 Phase Stability at Low Intensity -- 7.3.2 Phase Stability at High Intensity -- 7.3.3 Robinson's Damping -- 7.4 Transient Beam-Loading.

7.4.1 Fundamental Theorem of Beam-Loading -- 7.4.2 From Transient to Steady State -- 7.4.2.1 Limiting Case with 60 -+ 0 -- 7.4.2.2 Limiting Case with Tb >> Tf -- 7.4.3 Transient Beam-Loading of a Bunch -- 7.4.3.1 Gaussian Distribution -- 7.4.3.2 Parabolic Distribution -- 7.4.3.3 Cosine-Square Distribution -- 7.4.3.4 Cosine Distribution -- 7.4.4 Transient Compensation -- 7.4.4.1 Coupled-Bunch Instabilities -- 7.5 Examples -- 7.5.1 Fermilab Main Ring -- 7.5.2 Fermilab Booster -- 7.5.3 Fermilab Main Injector -- 7.5.4 Proposed Prebooster -- 7.5.4.1 The Ramp Curve -- 7.5.4.2 The RF System -- 7.5.4.3 Fixed-Frequency RF Cavities -- 7.6 Exercises -- Bibliography -- 8 Longitudinal Coupled-Bunch Instabilities -- 8.1 Sacherer's Integral Equation -- 8.1.1 Frequency Domain -- 8.1.2 Synchrotron Tune Shift -- 8.1.2.1 Water-Bag Model -- 8.1.3 Robinson's Instability -- 8.1.3.1 Point-Bunch Theory -- 8.2 Time Domain Derivation -- 8.3 Observation and Cures -- 8.3.1 Higher-Harmonic Cavity -- 8.3.2 Passive Landau Cavity -- 8.3.3 Rf-Voltage Modulation -- 8.3.4 Uneven Fill -- 8.3.4.1 Modulation Coupling -- 8.3.4.2 Landau Damping -- 8.3.4.3 Applications -- 8.4 Exercises -- Bibliography -- 9 Transverse Instabilities -- 9.1 Transverse Focusing and Transverse Wake -- 9.2 Betatron Fast and Slow Waves -- 9.3 Separation of Transverse and Longitudinal Motions -- 9.4 Sacherer's Integral Equation -- 9.5 Solution of Sacherer's Integral Equations for Radial Modes -- 9.5.1 Chebyshev Modes -- 9.5.2 Legendre Modes -- 9.5.3 Hermite Modes -- 9.5.4 Longitudinal Integral Equation -- 9.6 Frequency Shifts and Growth Rates -- 9.6.1 Broadband Impedance -- 9.6.2 Narrowband Impedance -- 9.7 Approximate Solutions and Effective Impedances -- 9.7.1 Sacherer's Sinusoidal Modes -- 9.8 Chromaticity Frequency Shift -- 9.9 Exercises -- Bibliography -- 10 Transverse Coupled-Bunch Instabilities.

10.1 Resistive-Wall Instabilities -- 10.1.1 Resistive-Wall Impedance at Low Frequencies -- 10.1.2 Bypass Inductance -- 10.2 Derivation of Resistive-Wall Impedance -- 10.2.1 Wave Equations -- 10.2.2 Source Fields -- 10.2.3 Thin-Wall Model -- 10.2.4 Thick-Wall Model -- 10.2.5 Layered Wall -- 10.2.6 Laminations -- 10.3 Applications -- 10.3.1 Fermilab Booster -- 10.3.1.1 Transverse Coupled-Bunch Instabilities -- 10.3.1.2 Tune-Shift Measurement -- 10.3.2 Bench Measurement -- 10.4 Narrow Resonances -- 10.5 Exercises -- Bibliography -- 11 Mode-Coupling Instabilities -- 11.1 Transverse Mode-Coupling -- 11.2 Space-Charge and Mode-Coupling -- 11.3 Two-Particle Model -- 11.4 Longitudinal Mode-Coupling -- 11.4.1 Long Bunches -- 11.4.2 Short Bunches -- 11.5 TMCI for Long Bunches -- 11.5.1 High Energy Accelerators -- 11.5.2 TMCI Threshold for Present Proton Machines -- 11.5.3 Possible Observation -- 11.6 Exercises -- Bibliography -- 12 Head-Tail Instabilities -- 12.1 Transverse Head-Tail -- 12.1.1 Two-Particle Model -- 12.1.2 For a Bunch -- 12.1.3 Application to the Tevatron -- 12.1.3.1 Measurements by Ivanov, Burov, and Tan -- 12.2 Longitudinal Head-Tail -- 12.3 Exercises -- Bibliography -- 13 Landau Damping -- 13.1 Harmonic Beam Response -- 13.2 Shock Response -- 13.3 Landau Damping -- 13.4 Transverse Bunched Beam Instabilities -- 13.5 Longitudinal Bunched Beam Instabilities -- 13.6 Transverse Unbunched Beam Instabilities -- 13.6.1 Resistive-Wall Instabilities -- 13.6.1.1 Instability of Proton Beam -- 13.6.1.2 Instabilities of Antiproton Beam -- 13.7 Longitudinal Unbunched Beam Instabilities -- 13.8 Beam Transfer Function and Impedance Measurements -- 13.9 Decoherence versus Landau damping -- 13.9.1 Landau damping of a beam -- 13.9.2 Longitudinal Decoherence -- 13.10 Exercises -- Bibliography -- 14 Beam Breakup -- 14.1 Two-Particle Model -- 14.2 Long Bunch.

14.2.1 Balakin-Novokhatsky-Smirnov Damping -- 14.2.2 Autophasing -- 14.3 Linac -- 14.3.1 Adiabatic Damping -- 14.3.2 Detuned Cavity Structure -- 14.3.3 Multi-Bunch Breakup -- 14.3.4 Analytic Treatment -- 14.3.4.1 Amount of Energy Chirp -- 14.3.4.2 Emittance Growth -- 14.3.4.3 The Quality Factor -- 14.3.5 Misaligned Linac -- 14.3.5.1 Comparison with Simulations -- 14.3.5.2 Application -- 14.4 Quadrupole Wake -- 14.4.1 Two-Particle Model -- 14.4.2 Observation -- 14.5 Exercises -- Bibliography -- 15 Two-Stream Instabilities -- 15.1 Trapped Electrons -- 15.1.1 Single-Electron Mechanics -- 15.1.2 Electron Bounce Frequency -- 15.1.2.1 Long bunches -- 15.1.2.2 Beam Leaked into Gap -- 15.1.2.3 A Train of Short Bunches -- 15.1.3 Coupled-Centroid Oscillation -- 15.1.3.1 Landau Damping -- 15.1.4 Production of Electrons -- 15.1.4.1 Primary Electrons -- 15.1.4.2 Secondary-Electron Yield -- 15.1.4.3 Electron-Cloud Build-up and Multipactoring -- 15.1.4.4 Simulations -- 15.1.4.5 Betatron Tune Shifts -- 15.1.5 Discussion and Conclusion -- 15.2 Fast Beam-Ion Instability -- 15.2.1 The Linear Theory -- 15.2.1.1 The Ion Equation of motion -- 15.2.1.2 The Trapped-Ion Distribution -- 15.2.1.3 The Electron Equation of Motion -- 15.2.1.4 Coupled- Ion- Beam Solution -- 15.2.1.5 A Train of Bunches -- 15.2.1.6 Spectrum of Electron Beam -- 15.2.1.7 Possible Cures -- 15.2.2 Application to Electron/Positron Rings -- 15.2.2.1 Observation at ALS -- 15.2.3 Application to Fermilab Linac -- 15.2.3.1 Ionization Cross section -- 15.2.3.2 Ion Bounce Frequencies -- 15.2.3.3 Growth Times -- 15.2.3.4 Comments -- 15.2.4 Application to Fermilab Designed Damping Ring -- 15.3 Half-Integer Stopband -- 15.4 Exercises -- Bibliography -- 16 Instabilities Near and Across Transition -- 16.1 Bunch Shape Near Transition -- 16.1.1 Nonadiabatic Time -- 16.1.2 Simple Estimation.

16.1.3 More Sophisticated Approximation.