## Accelerator PhysicsThe development of high energy accelerators began in 1911, when Rutherford discovered the atomic nuclei inside the atom. Since then, progress has been made in the following (1) development of high voltage dc and rf accelerators, (2) achievement of high field magnets with excellent field quality, (3) discovery of transverse and longitudinal beam focusing principles, (4) invention of high power rf sources, (5) improvement of high vacuum technology, (6) attainment of high brightness (polarized/unpolarized) electron/ion sources, (7) advancement of beam dynamics and beam manipulation schemes, such as beam injection, accumulation, slow and fast extraction, beam damping and beam cooling, instability feedback, etc.The impacts of the accelerator development are evidenced by the many ground-breaking discoveries in particle and nuclear physics, atomic and molecular physics, condensed matter physics, biomedical physics, medicine, biology, and industrial processing.This book is intended to be used as a graduate or senior undergraduate textbook in accelerator physics and science. It can be used as preparatory course material for graduate accelerator physics students doing thesis research. The text covers historical accelerator development, transverse betatron motion, synchrotron motion, an introduction to linear accelerators, and synchrotron radiation phenomena in low emittance electron storage rings, introduction to special topics such as the free electron laser and the beam-beam interaction. Attention is paid to derivation of the action-angle variables of the phase space, because the transformation is important for understanding advanced topics such as the collective instability and nonlinear beam dynamics. Each section is followed by exercises, which are designed to reinforce the concept discussed and to solve a realistic accelerator design problem. |

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### Contents

Introduction | 1 |

Layout and Components of Accelerators | 19 |

Transverse Motion | 35 |

Linear Betatron Motion | 47 |

Effect of Linear Magnet Imperfections | 85 |

OffMomentum Orbit | 129 |

Chromatic Aberration | 172 |

Linear Coupling | 186 |

Longitudinal Collective Instabilities | 362 |

Introduction to Linear Accelerators | 383 |

Physics of Electron Storage Rings | 417 |

Radiation Damping and Excitation | 437 |

Special Topics in Beam Physics | 497 |

Basics of Classical Mechanics | 533 |

Numerical Methods and Physical Constants | 543 |

Useful Handy Formulas | 551 |

Synchrotron Motion | 239 |

Nonadiabatic and Nonlinear Synchrotron Motion | 301 |

Beam Manipulation in Synchrotron Phase Space | 317 |

Fundamentals of RF Systems | 343 |

Physical Properties and Constants | 557 |

Symbols and Notations | 571 |

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### Common terms and phrases

accelerator action-angle variables angular antiproton approximation beam bunch beam distribution beam-beam interaction becomes bending angle betatron amplitude function betatron motion betatron oscillations betatron tune bunch length chromatic closed orbit coherent colliders cyclotron damping partition defocussing dipole field dispersion function distribution function electric field electron beam electron storage rings ellipse emittance equation of motion Fermilab fixed points focusing FODO cell Fourier gradient Hamilton's equations Hamiltonian harmonic high energy horizontal injection IUCF Cooler kicker Landau damping lattice linac linear coupling located longitudinal luminosity magnetic field mode momentum spread nonlinear normalized obtain off-momentum parameter parametric resonance particle motion perturbation phase-space area phase-space coordinates Phys proton resonance revolution frequency rf cavity rf phase rf system rf voltage separatrix sextupole Show space space-charge standing wave stopband stopband integral storage rings synchrotron motion synchrotron radiation synchrotron tune transfer matrix transition energy transverse tune shift vector velocity wiggler zero