Cosmic rays propagation along solar magnetic field lines: a fractional approach

Abstract

The work is devoted to the interpretation of Ulysses and Voyager spacecrafts data on solar cosmic rays fluxes. Particles move around turbulent magnetic field lines over spiral curves. Considering only their projections on these lines, we see a one-dimensional walk with a finite speed. Taking an inverse power law for the free path distribution leads to the differential equation with partial derivatives of fractional orders. Its solution gives the propagator which provides coincidence with observed data not only in the asymptotical region as obtained by Perri and Zimbardo (2007), but in the intermediate one as well.