Structurepreserving techniques in accelerator physics
Abstract
To a very good approximation, particularly for hadron machines, chargedparticle trajectories in accelerators obey Hamiltonian mechanics. During routine storage times of eight hours or more, such particles execute some $10^{8}$ revolutions about the machine, $10^{10}$ oscillations about the design orbit, and $10^{13}$ passages through various bending and focusing elements. Prior to building, or modifying, such a machine, we seek to identify accurately the longterm behavior and stability of particle orbits over such large numbers of interactions. This demanding computational effort does not yield easily to traditional methods of symplectic numerical integration, including both explicit Yoshidatype and implicit RungeKutta or Gaussian methods. As an alternative, one may compute an approximate oneturn map and then iterate that map. We describe some of the essential considerations and techniques for constructing such maps to high order and for realistic magnetic field models. Particular attention is given to preserving the symplectic condition characteristic of Hamiltonian mechanics.
 Publication:

arXiv eprints
 Pub Date:
 October 2022
 DOI:
 10.48550/arXiv.2211.00252
 arXiv:
 arXiv:2211.00252
 Bibcode:
 2022arXiv221100252A
 Keywords:

 Physics  Accelerator Physics;
 Physics  Computational Physics
 EPrint:
 28 pages, 5 figures