## From Tracking Code to Analysis: Generalised Courant-Snyder Theory for Any Accelerator ModelThis book illustrates a theory well suited to tracking codes, which the author has developed over the years. Tracking codes now play a central role in the design and operation of particle accelerators. The theory is fully explained step by step with equations and actual codes that the reader can compile and run with freely available compilers. In this book, the author pursues a detailed approach based on finite “s”-maps, since this is more natural as long as tracking codes remain at the centre of accelerator design. The hierarchical nature of software imposes a hierarchy that puts map-based perturbation theory above any other methods. The map-based approach, perhaps paradoxically, allows ultimately an implementation of the Deprit-Guignard-Schoch algorithms more faithful than anything found in the standard literature. This hierarchy of methods is not a personal choice: it follows logically from tracking codes overloaded with a truncated power series algebra package. After defining abstractly and briefly what a tracking code is, the author illustrates most of the accelerator perturbation theory using an actual code: PTC. This book may seem like a manual for PTC; however, the reader is encouraged to explore other tools as well. The presence of an actual code ensures that readers will have a tool with which they can test their understanding. Codes and examples will be available from various sites since PTC is in MAD-X (CERN) and BMAD (Cornell). |

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### Contents

1 | |

18 | |

One Degree of Freedom | 45 |

4 Classification of Linear Normal Forms | 81 |

5 Nonlinear Normal Forms | 120 |

6 Spin Normal Form | 151 |

The Mother of All Algorithms | 176 |

8 DepritGuignard Perturbation Theory Faithful to the Code | 205 |

Appendix D Program one_turn_orbital_map_phase_ad | 278 |

Appendix E Program Pendulum | 283 |

Appendix F Program standard_map | 286 |

Appendix G Program one_turn_cavity_map | 293 |

Appendix H Program radiation_map | 299 |

Appendix I Program modulated_map | 303 |

Appendix J Program modulated_map_Jordan | 307 |

Appendix K Program one_resonance_map | 311 |

9 Here Is the Conclusion of This Book | 236 |

Why Do I Reject Symplectic Phasors? | 245 |

11 The Logarithm of a Map | 247 |

12 Stroboscopic Average for the ISF Vector n | 251 |

13 Hierarchy of Analytical Methods | 254 |

Appendix A The Hardwired ALS Lattice | 269 |

Appendix B Program for one_turn_orbital_map | 273 |

Appendix C Programone_turn_orbital_map_normal_form_2d | 275 |

Appendix L Program very_damped_map | 316 |

Appendix M Program spin_phase_advance_isf | 318 |

Appendix N Program hamitonian_guignard_csf90 | 325 |

Appendix O Program hamitonian_guignardf90 | 331 |

Appendix P Program hamiltonian_guignard_1dff90 | 337 |

Appendix Q Program hamiltonian_guignard_1df_xf90 | 341 |

347 | |

### Other editions - View all

From Tracking Code to Analysis: Generalised Courant-Snyder Theory for Any ... Etienne Forest No preview available - 2018 |

From Tracking Code to Analysis: Generalised Courant-Snyder Theory for Any ... Etienne Forest No preview available - 2016 |