Cosmic Ray Flux in the Diffusion Approximation

The propagation of cosmic rays in the interplanetary medium is considered based on the kinetic Fokker–Planck equation. The analytical expression for the anisotropic part of the cosmic ray distribution function is derived in the approximation of small anisotropy. It is shown that, under isotropic scattering of energetic charged particles on interplanetary magnetic field fluctuations, the cosmic ray distribution function depends exponentially on the cosine of the angle between the particle velocity and radial direction. The expression for the cosmic ray flux density is obtained. It is shown that the value of the particle flux density is defined by the spatial distribution of the cosmic ray density and by the temporal dependence of the particle density. The cosmic ray transport equations have been derived (the hyperdiffusion equation and the telegraph equation). On the basis of these equations, the spatiotemporal distribution of solar cosmic ray intensity and the anisotropy of the particle angular distribution are investigated.