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

Controlled longitudinal emittance blow-up will be required to longitudinally stabilise the beams for the HighLuminosity LHC in the SPS. Bandwidth-limited noise is injected at synchrotron frequency sidebands of the RF voltage of the main accelerating system through the beam phase loop. The setup of the blow-up parameters is complicated by bunch-by-bunch differences in their phase, shape, and intensity, as well as by the interplay with the fourth harmonic Landau RF system and transient beam loading in the main RF system. During previous runs, an optimisation of the blowup had to be repeated manually at every intensity step up, requiring hours of precious machine time. With the higher beam intensity, the difficulties will be exacerbated, with bunch-by-bunch differences becoming even more important. We look at the extent of the impact of intensity effects on the controlled longitudinal blow-up by means of macro-particle tracking, as well as analytical calculations, and we derive criteria for quantifying its effectiveness. These studies are relevant to identify the parameters and observables which become key to the operational setup and exploitation of the blow-up.