Abstract
Supernova explosions and powerful stellar winds with strong shocks can convert a sizeable part of the kinetic energy release into energetic particles. The starforming regions are argued as a favorable site of energetic particle acceleration and could be efficient sources of nonthermal emission. We present the analytic solution for the time-dependent diffusion-convection equation for the case of two approaching shocks. We also present here time-dependent model of particle acceleration in the vicinity of two closely approaching fast magnetohydrodynamic (MHD) shocks. Such MHD flows are expected to occur in rich young stellar cluster where a supernova is exploding in the vicinity of a strong stellar wind of a nearby massive star. We find that the spectrum of the high energy particles accelerated at the stage of two closely approaching shocks can be harder than that formed at a forward shock of an isolated supernova remnant. The presented method can be applied to model particle acceleration in a variety of systems with colliding MHD flows.
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