Longitudinal Space Charge Modeling in the CERN PS

Particles in an intense bunch will experience longitudinal self-fields due to space-charge. This space charge effect, described by geometric factors dependent on a particle's transverse position, beam size, and beam pipe aperture, is usually incorporated into longitudinal trackers on a per-turn basis by assuming particles are uniformly affected. Sampling from a 6D distribution in phase-space, a particle's transverse trajectories within a bunch will vary due to Betatron motion. A transverse tracker was developed to characterize the effective geometric factor of a given particle accounting for its transverse emittance, phase advance, and dispersion within a ring. A particle's effective geometry factor is then estimated by interpolation without the need for transverse tracking. This variance in geometric factor due to transverse motion was incorporated into the longitudinal tracker $BLonD$, systematically affecting the synchrotron frequency distribution. The filamentation rate of a mismatched or perturbed longitudinal distribution was increased, which could suggest a stabilizing space-charge phenomenon.