Title: CRPropa 3.1 -- A low energy extension based on stochastic differential equations,
Abstract: The propagation of charged cosmic rays through the Galactic environment
influences all aspects of the observation at Earth. Energy spectrum,
composition and arrival directions are changed due to deflections in magnetic
fields and interactions with the interstellar medium. Today the transport is
simulated with different simulation methods either based on the solution of a
transport equation (multi-particle picture) or a solution of an equation of
motion (single-particle picture).
We developed a new module for the publicly available propagation software
CRPropa 3.1, where we implemented an algorithm to solve the transport equation
using stochastic differential equations. This technique allows us to use a
diffusion tensor which is anisotropic with respect to an arbitrary magnetic
background field. The source code of CRPropa is written in C++ with python
steering via SWIG which makes it easy to use and computationally fast.
In this paper, we present the new low-energy propagation code together with
validation procedures that are developed to proof the accuracy of the new
implementation. Furthermore, we show first examples of the cosmic ray density
evolution, which depends strongly on the ratio of the parallel
$\kappa_\parallel$ and perpendicular $\kappa_\perp$ diffusion coefficients.
This dependency is systematically examined as well the influence of the
particle rigidity on the diffusion process.