Anomalous diffusion of cosmic rays: A geometric approach

In this work, we analyze the process leading to the occurrence of anomalous transport phenomena associated with galactic cosmic rays propagating through the interstellar space. The origin of non-conventional transport is found in the dynamics of cosmic rays dominated by long uninterrupted flights interspersed with interactions with magnetized scattering clouds. The process is analyzed via a geometric Monte Carlo model that is able to mimic the intrinsic non-local character of the investigated transport phenomena. Numerical results show the existence of ranges of density and re-emission strengths of the interstellar magnetic clouds leading to heavy-tailed (Lévy α-stable) distributions of the propagating cosmic rays denoting a marked superdiffusive character. The correspondence between the geometric Monte Carlo integration method proposed in this work and the fractional Green’s functions suggests a novel approach to efficiently performing integration in higher dimensional spaces.