A stochastic method of solution of the Parker transport equation

• Published in: Journal of physics. Conference series Vol. 632; no. 1; pp. 12084 - 12091
• Main Authors: Wawrzynczak, A, Modzelewska, R, Gil, A
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 13.08.2015
• Subjects: Charged particles; Cosmic rays; Differential equations; Finite difference method; Galactic cosmic rays; Heliosphere; Mathematical analysis; Physics; Spherical coordinates; Stochastic models; Transport equations
• ISSN: 1742-6588; 1742-6596; 1742-6596
• DOI: 10.1088/1742-6596/632/1/012084

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