Space-charge effects in low-energy proton synchrotrons

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We have studied space-charge effects in low-energy proton synchrotrons using a simulation code developed specifically for supercomputers. The tracking of the beam with a few thousand macro particles is completely self-consistent, thus making it possible to follow the charge distribution as well as the beam size as a function of time. A proper substitution of the kick for the continuous space-charge force has been considered. The simulation is performed for a model lattice (similar to the SSC low energy booster) with and without half-integer resonances. In the lattice with the resonances, the rms emittance growth often observed in experiments occurs and the phase space density limit appears. The limiting value is, however, not directly related to the Laslett formula as expected. If we look at individual particles, there is a bare tune region where the real tune of some particles modified by space charge is within the resonance width. In the lattice without half-integer resonances, the rms emittance growth also occurs. It is associated with higher-order resonances driven by the beam itself. Only the tail of the beam is affected by the resonance, and the phase space density at the core remains almost unchanged.