Anomalous diffusion of cosmic rays in magnetic field turbulence - Linkage between diffusion statistics and turbulence statistics

Anomalous diffusion of energetic charged particles (cosmic rays) is studied using a simple two-dimensional cross field diffusion model. Both super-diffusion and sub-diffusion can take place in the model. When typical Larmor radius of the particles is much less than the field correlation length, the particles essentially gradient-B drift along equi-contour lines of the magnetic field strength, and thus the diffusion in this parameter regime can essentially be understood by analyzing statistics of the magnetic field islands composed of these equi-contour lines. We numerically evaluate the statistics of the field islands such as the probability distribution function of island radius and fractal dimension of the island contour lines, as functions of the power-law index of the magnetic field turbulence. We find numerically and analytically the scaling laws of time-scale dependent diffusion coefficients using the parameters obtained by analysis of the field islands statistics.