Oscillations of electrons within the RF bucket formed by the potential well are stable. Electrons outside of the RF bucket slowly lose energy and eventually are lost. However, the process of radiation damping, which acts as a frictional damping to the synchrotron oscillations, provides a mechanism by which electrons outside the RF bucket have a small probability of being recaptured into a subsequent RF bucket. This is shown by a plot of the phase including radiation damping shown below. Each RF bucket has a narrow attractor which extends over previous buckets in the ring.
Electrons landing on the attractor damp into that bucket.
The diffusion process is important for a subset of synchrotron radiation users who desire a pure single bunch fill in the ring. The ordinate and coordinate are and . We've observed the diffusion process by carefully measuring the relative intensity of charge in buckets following a large bunch over the course of 20-100 minutes. In an effort to understand some anomalous results in the study of longitudinal beam transfer functions, we were led into the fascinating field of nonlinear longitudinal beam dynamics. By driving synchrotron oscillations sufficiently hard via phase modulation, longitudinal phase space can be significantly distorted, even so far as to split an electron bunch into two separate bunches within the same RF bucket.