We discuss the space- and time-dependent Monte Carlo code we have developed to simulate the relativistic radiation output from compact astrophysical objects, coupled to a Fokker-Planck code to determine the self-consistent lepton populations. We have applied this code to model the emission from a magnetized neutron star accretion shell near the Alfvén radius, reprocessing the radiation from the neutron star surface. We explore the parameter space defined by the accretion rate, stellar surface field, and level of wave turbulence in the shell. Our results are relevant to the emission from atoll sources, soft X-ray-transients containing weakly magnetized neutron stars, and recently suggested models of accretion-powered emission from anomalous X-ray pulsars.
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