Jacobi equations and particle accelerator beam dynamics

Details Jacobi equations and particle accelerator beam dynamics Jacobi equations and particle accelerator beam dynamics

2012-03-27

arxiv.org/abs/1203.6037v1

Physics

Mathematical Physics

16 pages

Scientific paper

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.

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