Einstein-Smoluchowski Equation and Time-Dependent Modulation of Galactic Cosmic Rays

Physics

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Scientific paper

We develop three dimensional (3D) hybrid model of galactic cosmic ray (GCR) propagation in the heliosphere based on the Parker's transport equation. The hybrid model consists of two parts-stationary for high rigidities of GCR particles and non-stationary for relatively low rigidities. It is supposed that scattering of GCR particles in the irregularities (turbulence) of the interplanetary magnetic field (IMF) can be considered as a Brownian motion, and the Einstein-Smoluchowski relation < x2 rangle = b Ktsc is valid; < x2 rangle is the mean-square diffusion distance of the GCR particles, K is diffusion coefficient and tsc scattering time; b=2, 4 and 6 for one, two and three dimensional space, respectively. We show that a construction of the hybrid model is possible owing to the dependence of diffusion coefficient on the rigidity of GCR particles. We applied the hybrid model to describe the Forbush effect of the GCR intensity. For the assumed Forbush effect the hybrid model consists of the stationary part for rigidities > 21 GV and of the non-stationary part for rigidities < 21 GV. This model needs sim 30% less time for numerical solution than the non-stationary model.

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