Jacobi equations and particle accelerator beam dynamics
Mathematical Physics
2024-11-08 v1 Dynamical Systems
math.MP
Accelerator Physics
Applied Physics
Abstract
A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi equation of an affine averaged Lorentz connection. We introduce a specific notion reference trajectory as integral curves of the main velocity vector field. A perturbation caused by the statistical nature of the bunch of particles is considered.
Cite
@article{arxiv.1203.6037,
title = {Jacobi equations and particle accelerator beam dynamics},
author = {Ricardo Gallego Torrome},
journal= {arXiv preprint arXiv:1203.6037},
year = {2024}
}
Comments
16 pages