Creation of Hollow Bunches using a Double Harmonic RF system

The main motivation for the creation of hollow bunches in the PSB is to increase the bunching factor at transfer to the PS. Due to the reduction of the peak current and direct transverse space charge forces, one expects less blow up and losses at low energy in the PS. Thus, it does not matter when the hollow distribution in longitudinal phase space is created in the PSB cycle. We propose methods involving the h=1 and h=2 RF systems available in the PSB. The first method is based on controlled blow up by recombination of the bunch in one bucket, with another empty bucket. By appropriate adjustment of the phase between the two RF systems, more empty phase space can be inserted close to the centre creating a hollow distribution. The second method is based on a redistribution of phase space. The beam is transferred from one h=2 sub-bucket to the other and, during that process, regions from the centre with high density and from the periphery are exchanged. Simulations of both methods, based on tracking of particles in he longitudinal phase space, are presented. The second method has been set up successfully at the PS Booster. A significant decrease of the peak current has been achieved, while keeping the bunch length approximately constant.