Intrinsic and resonance space charge limits

The space charge limit in circular program accelerators has been studied using a simulation program. Results from the simulation study indicate a different model for the space charge limit than the often-presented models which emphasize resonances due to magnetic field errors. In studies of three operating accelerators, which include the Alternating Gradient Synchrotron, the Proton Synchrotron Booster, and the Fermilab Booster, it was found that the computed intrinsic space charge limit was fairly close to the experimentally observed space charge limit. This result and studies of the effects of resonances due to magnetic field errors suggest that the intrinsic space charge limit provides an upper bound for the space charge limit which is not far from what is actually achieved by operating accelerators. The resonances present due to magnetic field errors, if strong enough, can prevent the accelerator from achieving the intrinsic space charge limit. However, the effects of these resonances were found to be appreciable only when the beam intensity gets close to the intrinsic space charge limit. Well below the intrinsic space charge limit, there is little beam growth due to magnetic field error driven resonances, and the space charge forces tend to stabilize these resonances