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One‐dimensional hybrid simulations of quasi‐parallel collisonless shocks have been performed. Alpha particles are included in the simulations self‐consistently in such a way that sufficient simulation particles are present to give reasonable statistics. It is found that a fraction of the incoming solar wind protons and alpha particles is accelerated near the shock and escapes upstream. These particles constitute a diffuse upstream particle population. The density ratio bias factor, i.e., the density ratio of diffuse alpha particles to diffuse protons normalized to the solar wind He ++ to H + density ratio varies between 0.5 and 4.0, and depends on the solar wind He ++ to H + density ratio and on the shock Mach number. The density ratio bias factor for a low Mach number shock ( M A = 4.6) is f ∼ 0.5 when the alpha particles are treated as test particles and increases to ∼1 when the solar wind ratio of alpha to protons is 0.25. For a high Mach number shock of M A = 8.9 with a very small alpha particle contribution to the solar wind we obtained a density ratio bias factor of f ∼ 4.
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Trattner et al. (1991) studied this question.
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