## Particle Accelerator Physics II: Nonlinear and Higher-Order Beam DynamicsParticle Accelerator Physics II continues the discussion of particle accelerator physics beyond the introductory Particle Accelerator Physics I. Aimed at students and scientists who plan to work or are working in the field of accelerator physics. Basic principles of beam dynamics already discussed in Vol.I are expanded into the nonlinear regime in order to tackle fundamental problems encountered in present-day accelerator design and development. Nonlinear dynamics is discussed both for the transverse phase space to determine chromatic and geometric aberrations which limit the dynamic aperture as well as for the longitude phase space in connection with phase focusing at very small values of the momentum compaction. Effects derived theoretically are compared with observations made at existing accelerators. |

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### Contents

1 | |

4 | |

6 | |

General Electromagnetic Fields | 43 |

Problems | 71 |

Dynamics of Coupled Motion | 73 |

HigherOrder Perturbations | 93 |

Hamiltonian Nonlinear Beam Dynamics | 127 |

Problems | 302 |

Problems | 323 |

165 | 380 |

Insertion Device Radiation | 406 |

Appendix | 435 |

444 | |

Suggested Reading | 453 |

457 | |

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Particle Accelerator Physics II: Nonlinear and Higher-Order Beam Dynamics H. Wiedemann No preview available - 2013 |

### Common terms and phrases

aberrations accelerating cavities angle aperture beam current beam dynamics beam emittance beam line beam stability beam transport line becomes bending magnets betatron function betatron oscillations bunch length chromaticity circular accelerator coefficients coordinates coupling damping decrement defined deflection depends derived determine differential equation dipole discussion dispersion function effect electrical field energy loss energy spread equations of motion expression factor field components finite focusing FODO Fourier gaussian Hamiltonian harmonic higher-order horizontal impedance induced voltage instability integration lattice linear accelerator longitudinal magnetic field mode momentum compaction multipole nonlinear oscillation amplitude parameters particle acceleration particle beam particle density particle distribution particle energy particle trajectory path perturbation terms phase space photon polarization quadrupole radius resonance revolution frequency rotation separatrices sextupole shown in Fig solution space-charge spectrum storage ring synchrotron oscillation synchrotron radiation Touschek effect transformation tune shift vacuum chamber vanish variables vector velocity Vlasov equation wake fields wiggler wiggler magnet