Bifurcation, efficiency, and the role of injection in shock acceleration with the Bohm diffusion

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Abstract
The efficiency and uniqueness of the diffusive shock acceleration is studied on the basis of the novel kinetic solutions. These solutions obtained earlier (paper I, astro-ph/9707152) selfconsistently describe a strong coupling of cosmic rays with the gas flow. They show that the dependence of the acceleration efficiency upon physical parameters is critical in nature. In this paper we investigate a steady acceleration in the parameter space formed by the injection rate (\nu ), the upper cut-off momentum p_1 and the Mach number M while the flow compression R serves as an order parameter. We determine a manifold of all possible solutions in this parameter space.

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