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1 Introduction 1

Ⅰ Historical Developments 4

Ⅰ.1 Natural Accelerators 5

Ⅰ.2 Electrostatic Accelerators 6

Ⅰ.3 Induction Accelerators 6

Ⅰ.4 Radio-Frequency(RF)Accelerators 9

Ⅰ.5 Colliders and Storage Rings 17

Ⅰ.6 Synchrotron Radiation Storage Rings 18

Ⅱ Layout and Components of Accelerators 19

Ⅱ.1 Acceleration Cavities 19

Ⅱ.2 Accelerator Magnets 20

Ⅱ.3 Other Important Components 22

Ⅲ Accelerator Applications 23

Ⅲ.1 High Energy and Nuclear Physics 23

Ⅲ.2 Solid-State and Condensed-Matter Physics 24

Ⅲ.3 Other Applications 24

Exercise 24

2 Transverse Motion 35

Ⅰ Hamiltonian for Particle Motion in Accelerators 36

Ⅰ.1 Hamiltonian in Frenet-Serret Coordinate System 37

Ⅰ.2 Magnetic Field in Frenet-Serret Coordinate System 39

Ⅰ.3 Equation of Betatron Motion 41

Ⅰ.4 Particle Motion in Dipole and Quadrupole Magnets 41

Exercise 42

Ⅱ Linear Betatron Motion 47

Ⅱ.1 Transfer Matrix and Stability of Betatron Motion 47

Ⅱ.2 Courant-Snyder Parametrization 51

Ⅱ.3 Floquet Transformation 52

Ⅱ.4 Action-Angle Variable and Floquet Transformation 57

Ⅱ.5 Courant-Snyder Invariant and Emittance 60

Ⅱ.6 Stability of Betatron Motion:A FODO Cell Example 65

Ⅱ.7 Symplectic Condition 66

Ⅱ.8 Effect of Space-Charge Force on Betatron Motion 67

Exercise 73

Ⅲ Effect of Linear Magnet Imperfections 85

Ⅲ.1 Closed-Orbit Distortion due to Dipole Field Errors 85

Ⅲ.2 Extended Matrix Method for the Closed Orbit 91

Ⅲ.3 Application of Dipole Field Error 92

Ⅲ.4 Quadrupole Field(Gradient)Errors 101

Ⅲ.5 Basic Beam Observation of Transverse Motion 105

Ⅲ.6 Application of quadrupole field error 108

Ⅲ.7 Transverse Spectra 110

Ⅲ.8 Beam Injection and Extraction 115

Ⅲ.9 Mechanisms of emittance dilution and diffusion 117

Exercise 121

Ⅳ Off-Momentum Orbit 129

Ⅳ.1 Dispersion Function 129

Ⅳ.2 H-Function,Action,and Integral Representation 133

Ⅳ.3 Momentum Compaction Factor 136

Ⅳ.4 Dispersion Suppression and Dispersion Matching 139

Ⅳ.5 Achromat Transport Systems 141

Ⅳ.6 Transport Notation 143

Ⅳ.7 Experimental Measurements of Dispersion Function 145

Ⅳ.8 Transition Energy Manipulation 146

A．γT jump schemes 146

B．Flexible momentum compaction(FMC)lattices 149

C．Other similar FMC modules 155

D．FMC in double-bend(DB)lattices 156

Ⅳ.9 Minimum〈H〉Modules 157

Exercise 161

Ⅴ Chromatic Aberration 172

Ⅴ.1 Chromaticity Measurement and Correction 173

Ⅴ.2 Nonlinear Effects of Chromatic Sextupoles 178

Ⅴ.3 Chromatic Aberration and Correction 178

Ⅴ.4 Lattice Design Strategy 183

Exercise 184

Ⅵ Linear Coupling 186

Ⅵ.1 The Linear Coupling Hamiltonian 186

Ⅵ.2 Effects of an isolated Linear Coupling Resonance 189

Ⅵ.3 Experimental Measurement of Linear Coupling 193

Ⅵ.4 Linear Coupling Correction with Skew Quadrupoles 196

Ⅵ.5 Linear Coupling Using Transfer Matrix Formalism 197

Exercise 197

Ⅶ Nonlinear Resonances 202

Ⅶ.1 Nonlinear Resonances Driven by Sextupoles 202

Ⅶ.2 Higher-Order Resonances 209

Ⅶ.3 Nonlinear Detuning from Sextupoles 211

Ⅶ.4 Betatron Tunes and Nonlinear Resonances 212

Exercise 213

Ⅷ Collective Instabilities and Landau Damping 216

Ⅷ.1 Impedance 216

Ⅷ.2 Transverse Wave Modes 220

Ⅷ.3 Effect of Wakefield on Transverse Wave 221

Ⅷ.4 Frequency Spread and Landau Damping 225

Exercise 228

Ⅸ Synchro-Betatron Hamiltonian 232

Exercise 237

3 Synchrotron Motion 239

Ⅰ Longitudinal Equation of Motion 240

Ⅰ.1 The Synchrotron Hamiltonian 244

Ⅰ.2 The Synchrotron Mapping Equation 245

Ⅰ.3 Evolution of Synchrotron Phase-Space Ellipse 246

Ⅰ.4 Some Practical Examples 247

Ⅰ.5 Summary of Synchrotron Equations of Motion 248

Exercise 249

Ⅱ Adiabatic Synchrotron Motion 251

Ⅱ.1 Fixed Points 252

Ⅱ.2 Bucket Area 253

Ⅱ.3 Small-Amplitude Oscillations and Bunch Area 255

Ⅱ.4 Small-Amplitude Synchrotron Motion at the UFP 258

Ⅱ.5 Synchrotron Motion for Large-Amplitude Particles 259

Ⅱ.6 Experimental Tracking of Synchrotron Motion 261

Exercise 263

Ⅲ RF Phase and Voltage Modulations 268

Ⅲ.1 Normalized Phase-Space Coordinates 268

Ⅲ.2 RF Phase Modulation and Parametric Resonances 271

Ⅲ.3 Measurements of Synchrotron Phase Modulation 277

Ⅲ.4 Effects of Dipole Field Modulation 280

Ⅲ.5 RF Voltage Modulation 288

Ⅲ.6 Measurement of RF Voltage Modulation 295

Exercise 297

Ⅳ Nonadiabatic and Nonlinear Synchrotron Motion 301

Ⅳ.1 Linear Synchrotron Motion Near Transition Energy 302

Ⅳ.2 Nonlinear Synchrotron Motion at γ≈γT 305

Ⅳ.3 Beam Manipulation Near Transition Energy 308

Ⅳ.4 Synchrotron Motion with Nonlinear Phase Slip Factor 309

Ⅳ.5 The QI Dynamical Systems 312

Exercise 315

Ⅴ Beam Manipulation in Synchrotron Phase Space 317

Ⅴ.1 RF Frequency Requirements 318

Ⅴ.2 Capture and Acceleration of Proton and Ion Beams 320

Ⅴ.3 Bunch Compression and Rotation 322

Ⅴ.4 Debunching 326

Ⅴ.5 Beam Stacking and Phase Displacement Acceleration 326

Ⅴ.6 Double rf Systems 327

Ⅴ.7 The Barrier RF Bucket 334

Exercise 340

Ⅵ Fundamentals of RF Systems 343

Ⅵ.1 Pillbox Cavity 343

Ⅵ.2 Low Frequency Coaxial Cavities 345

Ⅵ.3 Beam Loading 353

Ⅵ.4 Beam Loading Compensation and Robinson Instability 356

Exercise 359

Ⅶ Longitudinal Collective Instabilities 362

Ⅶ.1 Longitudinal Spectra 363

Ⅶ.2 Collective Microwave Instability in Coasting Beams 367

Ⅶ.3 Longitudinal Impedance 369

Ⅶ.4 Microwave Single Bunch Instability 373

Exercise 381

Ⅷ Introduction to Linear Accelerators 383

Ⅷ.1 Historical Milestones 383

Ⅷ.2 Fundamental Properties of Accelerating Structures 387

A．Transit time factor 387

B．Shunt impedance 388

C．The quality factor Q 388

Ⅷ.3 Particle Acceleration by EM Waves 389

A．EM waves in a cylindrical wave guide 390

B．Phase velocity and group velocity 391

C．TM modes in a cylindrical pillbox cavity 392

D．Alvarez structure 395

E．Loaded wave guide chain and the space harmonics 396

F．Standing wave,traveling wave,and coupled cavity linacs 399

G．HOMs 401

Ⅷ.4 Longitudinal Particle Dynamics in a Linac 402

Ⅷ.5 Transverse Beam Dynamics in a Linac 407

Exercise 410

4 Physics of Electron Storage Rings 417

Ⅰ Fields of a Moving Charged Particle 422

Ⅰ.1 Non-relativistic Reduction 424

Ⅰ.2 Radiation Field for Particles at Relativistic Velocities 424

Ⅰ.3 Frequency and Angular Distribution 427

Ⅰ.4 Quantum Fluctuation 433

Exercise 435

Ⅱ Radiation Damping and Excitation 437

Ⅱ.1 Damping of Synchrotron Motion 438

Ⅱ.2 Damping of Betatron Motion 441

Ⅱ.3 Damping Rate Adjustment 445

Ⅱ.4 Radiation Excitation and Equilibrium Energy Spread 448

Ⅱ.5 Radial Bunch Width and Distribution Function 453

Ⅱ.6 Vertical Beam Width 455

Ⅱ.7 Radiation Integrals 456

Ⅱ.8 Beam Lifetime 456

Exercise 462

Ⅲ Emittance in Electron Storage Rings 466

Ⅲ.1 Emittance of Synchrotron Radiation Lattices 467

A．FODO cell lattice 467

B．Double-bend achromat(Chasman-Green lattice) 469

C．Minimum〈H〉-function lattice 473

D．Minimizing emittance in a combined function DBA 475

E．Three-bend achromat 476

Ⅲ.2 Insertion Devices 478

Ⅲ.3 Beam Physics of High Brightness Storage Rings 486

Exercise 489

5 Special Topics in Beam Physics 497

Ⅰ Free Electron Laser(FEL) 498

Ⅰ.1 Small Signal Regime 500

Ⅰ.2 Interaction of the Radiation Field with the Beam 506

Ⅰ.3 Experiments on High Gain FEL Generation 509

Exercise 510

Ⅱ Beam-Beam Interaction 513

Ⅱ.1 The beam-beam force 517

Ⅱ.2 The Coherent Beam-Beam Effects 519

Ⅱ.3 Nonlinear Beam-Beam Effects 521

Ⅱ.4 Experimental Observations and Numerical Simulations 522

Ⅱ.5 Beam-Beam Interaction in Linear Colliders 525

Exercise 527

A Basics of Classical Mechanics 533

Ⅰ Hamiltonian Dynamics 533

Ⅰ.1 Canonical Transformations 533

Ⅰ.2 Fixed Points 534

Ⅰ.3 Poisson Bracket 534

Ⅰ.4 Liouville Theorem 535

Ⅰ.5 Floquet Theorem 536

Ⅱ Stochastic Beam Dynamics 537

Ⅱ.1 Central Limit Theorem 537

Ⅱ.2 Langevin Equation of Motion 538

Ⅱ.3 Stochastic Integration Methods 539

Ⅱ.4 Fokker-Planck Equation 541

B Numerical Methods and Physical Constants 543

Ⅰ Fourier Transform 543

Ⅰ.1 Nyquist Sampling Theorem 544

Ⅰ.2 Discrete Fourier Transform 544

Ⅰ.3 Digital Filtering 545

Ⅰ.4 Some Simple Fourier Transforms 546

Ⅱ Model Independent Analysis 546

Ⅱ.1 Model Independent Analysis 547

Ⅱ.2 Independent Component Analysis 548

Ⅱ.3 Accelerator Modeling 549

Ⅲ Cauchy Theorem and the Dispersion Relation 549

Ⅲ.1 Cauchy Integral Formula 549

Ⅲ.2 Dispersion Relation 550

Ⅳ Useful Handy Formulas 551

Ⅳ.1 Generating functions for the Bessel functions 551

Ⅳ.2 The Hankel transform 551

Ⅳ.3 The complex error function 551

Ⅳ.4 A multipole expansion formula 552

Ⅳ.5 Cylindrical Coordinates 552

Ⅳ.6 Gauss'and Stokes'theorems 553

Ⅳ.7 Vector Operation 553

Ⅴ Maxwell's equations 553

Ⅴ.1 Lorentz Transformation of EM fields 554

Ⅴ.2 Cylindrical waveguides 554

Ⅴ.3 Voltage Standing Wave Ratio 556

Ⅵ Physical Properties and Constants 557

Bibliography 561

Index 563

Symbols and Notations 571