Thresholds of Longitudinal Single Bunch Instability in Single and Double RF systems in the CERN SPS

A fourth harmonic RF system is used in the SPS as a Landau cavity, in order to stabilize the high intensity LHC proton beam against the longitudinal instabilities. Numerous studies proved that operating the two RF systems, through the whole cycle, in bunch shortening mode is necessary to provide a good quality beam at extraction to the LHC. Furthermore, it was shown that the choice of RF parameters as voltage amplitude ratio and relative phase are critical for the beam stability. This paper presents the results of single bunch measurements performed in single and double RF systems with various RF settings and compares them with the results of macroparticle simulations for the SPS impedance model.