From Tracking Code to Analysis: Generalised Courant-Snyder Theory for Any Accelerator Model

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Springer, Mar 22, 2016 - Science - 347 pages

This 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 Introduction
1
One Degree of Freedom
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
Index of Links to Useful Conceptsand Formulae
347
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About the author (2016)

Etienne Forest, the author, is a professor at KEK, the High Energy Accelerator Research Organization in Tsukuba, Japan.

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