From Tracking Code to Analysis: Generalised Courant-Snyder Theory for Any Accelerator Model
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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Appendix D Program one_turn_orbital_map_phase_ad
Appendix E Program Pendulum
Appendix F Program standard_map
Appendix G Program one_turn_cavity_map
Appendix H Program radiation_map
Appendix I Program modulated_map
Appendix J Program modulated_map_Jordan
Appendix K Program one_resonance_map
9 Here Is the Conclusion of This Book
Why Do I Reject Symplectic Phasors?
11 The Logarithm of a Map
12 Stroboscopic Average for the ISF Vector n
13 Hierarchy of Analytical Methods
Appendix A The Hardwired ALS Lattice
Appendix B Program for one_turn_orbital_map
Appendix C Programone_turn_orbital_map_normal_form_2d
Appendix L Program very_damped_map
Appendix M Program spin_phase_advance_isf
Appendix N Program hamitonian_guignard_csf90
Appendix O Program hamitonian_guignardf90
Appendix P Program hamiltonian_guignard_1dff90
Appendix Q Program hamiltonian_guignard_1df_xf90
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