Cosmic-Ray Distribution Function under Anisotropic Scattering of Particles by Magnetic-Field Fluctuations

Abstract

The acceleration of energetic particles and their propagation in magnetic fields of the solar wind and the Galaxy is a topical astrophysical problem. Cosmic rays (CR) affect communications and the operation of on-board spacecraft electronics and disturb the magnetosphere and the ionosphere of the Earth. The scattering of particles by magnetic-field irregularities is the primary mechanism governing the CR propagation in the interplanetary medium. If the scattering of energetic particles in the interplanetary medium is relatively inefficient (i.e., the mean free path is comparable to the heliocentric distance), a kinetic equation should be used to characterize the CR propagation. The Fokker–Planck kinetic equation is used to analyze the propagation of charged energetic particles in a magnetic field represented as a superposition of a mean uniform field and magnetic inhomogeneities of various scales. This kinetic equation corresponds to multiple small-angle scattering, and its collision integral characterizes particle diffusion in the momentum space. A system of differential equations for the spherical harmonics of the CR distribution function is obtained based on the kinetic equation. The CR transport equations are derived and solved. The evolution of the CR distribution function under anisotropic scattering of particles by magnetic-field fluctuations is examined. It is demonstrated that the angular distribution function of particles depends to a considerable extent on the degree of their scattering anisotropy. The temporal dependence of the CR distribution function is analyzed, and the parameter characterizing the scattering anisotropy is estimated.