Longitudinal dynamics in an FFAG accelerator under conditions of rapid acceleration and fixed, high rf

A signature of fixed-field acceleration is that the orbit of the beam centroid unavoidably changes with energy. The corresponding change in pathlength results in phase slip relative to the fixed-frequency accelerating waveform. Nevertheless, depending on the location of the fixed-points of the motion, synchronous or asynchronous cross-crest acceleration is possible for a limited number of turns. The possibility of asynchronous rf can be understood simply by realizing that for acceleration in a single pass, the initial cavity phases can be set to exactly compensate for the phase slip. The present work explores the influence of the path-length fixed points and of rf manipulations on the longitudinal dynamics in FFAGs.