The solution of the nonlinear diffusive shock acceleration problem, where the pressure of the non-thermal population is sufficient to modify the shock hydrodynamics, is widely recognized as a key to understanding particle acceleration in a variety of astrophysical environments. We have developed a Monte Carlo technique for self-consistently calculating the hydrodynamic structure of oblique, steady state shocks, together with the first-order Fermi acceleration process and associated nonthermal particle distributions. This is the first internally consistent treatment of modified shocks that includes cross-field diffusion of particles. Our method overcomes the injection problem faced by analytic descriptions of shock acceleration and the lack of adequate dynamic range and artificial suppression of cross-field diffusion faced by plasma simulations; it currently provides the most broad and versatile description of collisionless shocks undergoing efficient particle acceleration. We present solutions for plasma quantities and particle distributions upstream and downstream of shocks, illustrating the strong differences observed between nonlinear and test particle cases. It is found that, for strong scattering, there are only marginal differences in the injection efficiency and resultant spectra for two extreme scattering modes, namely large-angle scattering and pitch-angle diffusion, for a wide range of shock parameters, i.e., for nonper-pendicular subluminal shocks with field obliquities less than or equal to 75° and de Hoffmann-Teller frame speeds much less than the speed of light.
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