Study of Controlled Longitudinal Emittance Blow-Up for High Intensity LHC Beams in the CERN SPS

Preventive longitudinal emittance blow-up, in addition to a fourth harmonic Landau damping RF system, is required to keep the LHC beam in the SPS stable up to extraction. The beam is blown-up in a controlled way during the acceleration ramp by using band-limited phase noise targeted to act inside the synchrotron frequency spread, which is itself modified both by the second RF system and by intensity effects (beam loading and others). For a high intensity beam these latter effects can lead to a non-uniform emittance blow-up and even loss of stability for certain bunches in the batch. In this paper we present studies of the emittance blow-up achieved with high intensity beams under different conditions of both RF and noise parameters.