Influence of Transverse Motion on Longitudinal Space Charge in the CERN PS

Particles in an intense bunch experience longitudinal self-fields due to space charge. This effect, conveniently described by geometric factors dependent on a particle’s transverse position, beam size, and beam pipe aperture, is usually incorporated into longitudinal particle tracking on a per-turn basis. The influence of transverse betatron motion on longitudinal space charge forces is, however, usually neglected in pure longitudinal tracking codes. A dedicated tracking code was developed to characterize the CERN PS such that an effective geometric factor of a given particle could be derived from its transverse emittance, betatron phase advance, and momentum spread. The effective geometry factor is then estimated per particle by interpolation without the need for full transverse tracking and incorporated into the longitudinal tracker BLonD. The paper evaluates this effect under conditions representative of the PS, where space charge is dominant at low energy and progressively becomes negligible along the acceleration ramp. The synchrotron frequency distribution is modified and the filamentation rate is moreover increased, which could suggest a stabilizing space charge phenomenon.