Hybrid simulations of protons strongly accelerated by a parallel collisionless shock

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Abstract
We present initial results from one‐dimensional hybrid simulations which directly address the problems of using such methods to simulate the acceleration of ions to high energy by parallel shocks. As particles are accelerated from the thermal population, they are repeatedly “split,” thereby ensuring statistically valid energy spectra covering a wide dynamic range. In order to model the complex foreshock, as expected if the simulation domain were large enough, and as seen in observations, we introduce a source of upstream turbulence. This turbulence produces an enhanced high energy tail in the upstream particle distribution extending to over a hundred times the plasma flow energy, and a prominent shoulder downstream.