Propagating Cosmic Rays with exact Solution of Fokker-Planck Equation

Abstract

Shortfalls in cosmic ray (CR) propagation models obscure the CR sources and acceleration mechanisms. This problem became particularly obvious after the Fermi, Pamela, and AMS-02 have discovered the electron/positron and p/He spectral anomalies. Most of the CR models use diffusive propagation that is inaccurate for weakly scattered energetic particles. So, some parts of the spectra affected by the heliospheric modulation, for example, cannot be interpreted. I discuss and adopt an exact solution of the Fokker-Planck equation [M. A. Malkov, Exact solution of the Fokker-Planck equation for isotropic scattering arXiv:1610.01584, doi:https://doi.org/10.1103/PhysRevD.95.023007(2017)], which gives a complete description of a ballistic, diffusive and transdiffusive (intermediate between the first two) propagation regimes. I derive a simplified version of an exact Fokker-Planck propagator that can easily be employed in place of the Gaussian propagator, currently used in major Solar modulation and other CR transport models.