Diffusive shock acceleration of cosmic rays with non-Gaussian transport

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The diffusive shock acceleration (DSA) is recognized as the most likely acceleration process to produce the observed power law spectrum of cosmic rays. One of the key elements of the DSA is the scattering of the cosmic rays by MHD turbulence, which is believed to exist both shock upstream and downstream. While the majority of past studies on the DSA adopt quasi-linear type model for the cosmic ray spatial diffusion, actual transport of the cosmic rays in a plasma with MHD turbulence can be qualitatively different. We studied the DSA process via test particle simulations by specifying non-Gaussian type scattering statistics to cosmic rays. The cosmic ray spectrum, spatial profile, and the acceleration time scale are evaluated, and are compared with observational data. In addition, fractal diffusion equation including the shock wave is numerically evaluated and the results are compared with the test particle simulations.