Amplitude Dependence of Time of Flight and its Connection to Chromaticity

In general, the time of flight of a charged particle in an accelerator will depend on the particle’s transverse amplitude. This effect can become important in machines with large transverse emittances, such as muon accelerators. We will describe the effect, its physical origin, and the circumstances where it becomes important. We will then demonstrate that the effect is directly related to chromaticity. We will describe the effect on the longitudinal dynamics in various circumstances, including linacs and fixed field alternating gradient accelerators (FFAGs). We will describe methods for correcting the effect, particularly in FFAGs.