Multiparticle tracking simulations which proceed by iterating a single-turn for map for phase space coordiates are a mainstay of accelerator design and diagnosis. When short range wake fields or high frequency impedances are essential in the problem, many macroparticles are usually required and simulation may take days to run. A simple scaling will be shown which can reduce computer times by a factor of ten or more in practical applications in longitudinal phase space modeling of synchrotrons. The same scaling should be applicable in transverse coordinate tracking also.

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