There is no thermalization process in the Monte Carlo simulation in the sense of particles exchanging energy between one another because particles scatter elastically in the local frame. However, a quasi-thermal low energy distribution is created as un-shocked particles cross the shock from upstream to downstream at different angles and receive different fractions of the speed difference, uo - «2. For the parameters used here, the low-energy peak is essentially a Maxwellian when vthres = 0 •

In the semi-analytical model, the shocked thermal pressure and density are determined from the conservation relations and these are translated to a Maxwell-Boltzmann distribution.

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