A stochastic method of solution of the Parker transport equation

TL;DR

This paper introduces a stochastic numerical method based on solving stochastic differential equations to model galactic cosmic ray transport in the heliosphere, accurately capturing short-term variations like Forbush decreases and 27-day cycles.

Contribution

It develops a stochastic approach to solve the Parker transport equation using SDEs, providing an alternative to finite difference methods for modeling cosmic ray variations.

Findings

The stochastic model agrees with experimental data.

The backward approach is superior to the forward approach.

The method effectively models short-term cosmic ray intensity variations.

Abstract

We present the stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. Based on the solution of the Parker transport equation we developed models of the short-time variation of the GCR intensity, i.e. the Forbush decrease (Fd) and the 27-day variation of the GCR intensity. Parker transport equation being the Fokker-Planck type equation delineates non-stationary transport of charged particles in the turbulent medium. The presented approach of the numerical solution is grounded on solving of the set of equivalent stochastic differential equations (SDEs). We demonstrate the method of deriving from Parker transport equation the corresponding SDEs in the heliocentric spherical coordinate system for the backward approach. Features indicative the preeminence of the backward approach over the forward is stressed. We compare the outcomes of the stochastic model of the Fd and 27-day variation of the GCR intensity with our former models established by the finite difference method. Both models are in an agreement with the experimental data.