Incoherent Transverse Space Charge Effects during Injection, RF Capture and Early Acceleration in AGS

After a review of the present situation in the AGS incoherent space charge effects in respectively the just injected beam, the coasting beam and the bunched beam are considered. Numerical estimates of shifts and spreads in betatron frequencies are given. The ratio of peak to average azimuthal densities in bunched beams is calculated for parabolic and uniform initial energy distributions. It is concluded that the intensity limit of the AGS is probably set by loss of particles out of vertical betatron phase via resonances and coupling in the early bunched beam.