Nonlinear effects of phase modulation in an electron storage ring

We present results of experimental studies of the nonlinear dynamics of synchrotron oscillations in the presence of phase modulation in an electron storage ring. A streak camera is used to observe the longitudinal distribution of an electron bunch directly as it forms two stable resonant islands. The positions of the fixed points as a function of modulation frequency agree well with theory. We also present measurements of the diffusion rate from one stable island to the ether for a fixed modulation frequency, which show agreement with the diffusion rates expected from large-angle intrabeam (Touschek) scattering. These results also explain anomalous results of beam transfer function diagnostic measurements obtained at other electron storage rings.