Monte Carlo simulations of anomalous diffusion of cosmic rays

The anomalous diffusion model for cosmic rays transport in fractal-like galactic medium developed by the authors allows to describe main features of the observed spectrum of charged particles arriving in the Solar system. Anomalous diffusion equation underlying the model contains fractional derivative operators and do not take into account the finite speed of particles transport. In this regard, we conducted a Monte Carlo simulation of uncoupled continuous-time random walks of particles in this model. The particles can perform an anomalously large jumps between scattering centers (Levy flights) and also can stay a long time in the inhomogeneities of the medium (Levy traps). The probability of such behavior of particles is described by power-law distributions for the jumps length and for the residence time in the inhomogeneity. In this paper, we present the spatial distribution of particles obtained from the direct simulations of particle trajectories in the framework of our model for two versions: considering finite particle speed and the case of an instantaneous jump.