Space-charge calculations in synchrotrons

One obvious bottleneck of achieving high luminosity in hadron colliders, such as the Superconducting Super Collider (SSC), is the beam emittance growth, due to space charge effects in low energy injector synchrotrons. Although space-charge effects have been recognized since the alternating-gradient synchrotron was invented, and the Laslett tune shift usually calculated to quantify these effects, our understanding of the effects is limited, especially when the Laslett tune shift becomes a large fraction of the integer. Using the Simpsons tracking code, which we developed to study emittance preservation issues in proton synchrotrons, we investigated space-charge effects in the SSC Low Energy Booster (LEB). We observed detailed dependence on parameters such as beam intensity, initial emittance, injection energy, lattice function, and longitudinal motion. A summary of those findings, as well as the tracking technique we developed for the study, are presented