Higher Order Mode Beam Breakup Limits in the Superconducting Cavities of the SPL

The Superconducting Proton Linac (SPL) at CERN is part of the planned injector upgrade of the LHC. Initially used at low duty cycle as LHC injector it has the potential to be upgraded as a high power proton driver for neutrino physics and/or radioactive ion beams. In this paper the influence of the beam parameters on the build-up of Higher Order Mode (HOM) voltages is studied together with their interaction on the beam. For this purpose we use bunch tracking simulations in the longitudinal and transverse plane in order to define Beam Break-Up (BBU) limits. These simulations take into account changing values for the HOM frequency spread and are carried out using various distances between the HOM frequencies and the main machine lines