Preface page xi1 Introduction 11.1 Differences or Differentials? 11.2 Phase Space Co-ordinates 31.3 Iterations, Ancient and Modern 51.4 Accelerator History： The Two Golden Ages 6Exercises 102 Linear Motion 132.1 Stable Oscillations 132.2 Transverse Motion through Magnets 162.3 Matrix Equations of Motion 19Exercises 223 Strong Focusing Transverse Optics 243.1 Linear Stability and Twiss Functions 253.2 Turn-by-Turn Motion in Phase Space 273.3 Propagation across a Fraction of a Turn 293.4 Continuous Propagation 303.5 FODO Cell Optics 32Exercises 354 Longitudinal and Off-Momentum Motion 374.1 Constant Momentum Offset： Transverse Motion 374.2 The Dispersion Function 394.3 Oscillating Momentum： Longitudinal Motion 414.4 The Standard Map 45Exercises 485 Action and Emittance ?C One Particle or Many? 505.1 Transverse Action-Angle Co-ordinates 505.2 Unnormalised Emittances and Beam Sizes 525.3 Tune Spread and Filamentation 545.4 Linac Phase Space Area Emittances 565.5 Normalised Emittance and Adiabatic Damping 585.6 Longitudinal Phase Space Parameters 60Exercises 616 Magnets 636.1 Normal and Skew Multipole Magnets 636.2 Iron-Dominated Magnets 656.3 Conductor-Dominated Magnets 666.4 Field Quality and Errors 67Exercises 697 RF Cavities 737.1 Waveguides 737.2 Transverse Modes 747.3 Cylindrical Resonant Cavities ?C Pill-Boxes 767.4 Cavity Performance Limits 79Exercises 818 Linear Errors and Their Correction 838.1 Trajectory and Closed Orbit Errors 838.2 Linear Coupling 888.3 Tune Shifts and β-Waves 89Exercises 929 Sextupoles, Chromaticity and the Hénon Map 949.1 Chromaticity in a FODO Lattice 949.2 Chromaticity Correction 969.3 The Hénon Map ?C A Unit Strength Sextupole in 1-D 989.4 A Taxonomy of 1-D Motion 1009.5 Dynamic Aperture 103Exercises 10410 Octupoles, Detuning and Slow Extraction 10710.1 Single Octupole Lattice 10710.2 Discrete Motion in Action-Angle Space, J, φ 10910.3 Two-Turn Motion with Q ≈ 12 11010.4 Slow Extraction near the Half-Integer 111Exercises 11311 Synchrotron Radiation ?C Classical Damping 11611.1 Spectrum and Distribution Pattern 11611.2 Energy Loss Per Turn and Longitudinal Damping 11911.3 Continuous Acceleration 12411.4 Transverse Damping and Partition Numbers 126Exercises 12812 Synchrotron Radiation ?C Quantum Excitation 13112.1 Energy Spread 13212.2 Horizontal Emittance 13412.3 Vertical Emittance 138Exercises 13913 Linacs ?C Protons and Ions 14113.1 Time Structures 14213.2 Multi-Cell Synchronism 14513.3 Linear Motion 14713.4 Radio Frequency Quadrupoles 15313.5 Beam Losses and Haloes 157Exercises 15814 Linacs ?C Electrons 15914.1 Longitudinal and Transverse Focusing 15914.2 RF Capture 16114.3 Bunch Compression 16214.4 Recirculating and Energy Recovery Linacs 16414.5 Beam Breakup 166Exercises 16915 The Beam?CBeam Interaction and 1-D Resonances 17015.1 Round Beam-Beam Interaction 17015.2 First-Order Theory of 1-D Resonances 17415.3 Resonance Island Tunes and Widths 176Exercises 18016 Routes to Chaos 18116.1 Resonance Overlap 18216.2 Tune Modulation 18416.3 Dynamical Zones in Tune Modulation Space 187Exercises 190Appendix A Selected Formulae for Accelerator Design 191A.1 Matrices for Linear Motion through Accelerator Elements 191A.2 Propagation of Twiss Functions 196References 198Index 201
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