Longitudinal dynamics with RF phase modulation in the LNLS electron   storage ring
  In the Brazilian synchrotron light source, we observed that modulating the phase of the accelerating fields at approximately twice the synchrotron frequency suppressed remarkably well a longitudinal coupled-bunch mode of the beam driven by a higher order mode (HOM) in one of the radiofrequency (RF) cavities. In this work, we present the results of a set of systematic measurements, in single and multibunch mode, aimed at characterizing the effects of RF phase modulation on the beam. We compare those experiments with the results of tracking simulations and of a theoretical model in which Landau damping is the stabilizing mechanism that explains the suppression of the longitudinal coupled bunch instability. We also measure the frequency of the stable islands created in longitudinal phase space by phase modulation and the longitudinal beam transfer function (BTF) as a function of the modulation frequency and amplitude. The experimental results are in good agreement with theoretical expectations. 
N. P. Abreu, P. F. Tavares and R. H. A. Farias