Particle trajectories in a four rod crab cavity

As part of the HL-LHC upgrade it is planned that crab cavities will be installed into the machine to control and increase the luminosity. Of crucial importance to the dynamics of crab cavities in the LHC machine is the modelling of the particle motion through the cavity structure, which, in some studies, has been done using thin lens kicks derived from a thin lens Hamiltonian. In this paper we study particle trajectories using field fitted vector potentials in the four rod crab cavity and make a comparison to the dynamics generated using the thin lens model