Transverse coherent direct space charge: comparison between several approaches

The proton driver of a future Muon Collider complex is designed to deliver a multi-GeV, short and high-intensity proton bunch to a target in order to maximize the muon yield. In the International Muon Collider Collaboration (IMCC), two high power H- Linac configurations are studied: a 2 MW with a beam energy of 5 GeV, and a 4 MW with a beam energy of 10 GeV. The Linac is followed by an accumulator ring and a compressor ring. With a single bunch intensity of 5.0e14 protons within a transverse emittance of ~15 mm mrad, strong space-charge effects can be expected in these rings. In this framework, different simulation codes used to estimate the transverse coherent space-charge mode frequency shifts in synchrotrons have been compared: BimBim, based on the Circulant Matrix Model (CMM); the Effective impedance method for space-charge; GALACTIC based on the Vlasov equation; the boxcar model for space-charge only; and the ABS model which assumes an Air-Bag bunch distribution in a Square well.