Accurate dynamics in an azimuthally-symmetric accelerating cavity

We consider beam dynamics in azimuthally-symmetric accelerating cavities, using the EMMA FFAG cavity as an example. By fitting a vector potential to the field map, we represent the linear and non-linear dynamics using truncated power series and mixed-variable generating functions. The analysis provides an accurate model for particle trajectories in the cavity, reveals potentially significant and measurable effects on the dynamics, and shows differences between cavity focusing models. The approach provides a unified treatment of transverse and longitudinal
motion, and facilitates detailed map-based studies of motion in complex machines like FFAGs.