The theory of particle diffusion in a strong random magnetic field with an allowance for higher multipole moments of the distribution function

Abstract

The kinetic equation including a small-scale collisional integral for the particles propagating in a strong random and regular magnetic field [29] is solved by expanding the distribution function into series in spherical harmonics of the particle momentum angles. Using methods of the quantum theory of the angular moment [41], the equations for higher multipole moments of the distribution function in the space of momentum angles are derived and solved in the stationary case for the galactic cosmic rays in interplanetary space. The observed amplitudes and phases of the diurnal variation harmonics can be explained using the results of measurements of the interplanetary magnetic field performed on board the Ulysses spacecraft [12–14] and other satellites [45, 46] with an allowance for redistribution of the interplanetary and interstellar magnetic field lines. The spatial structure of the convection and diffusion fluxes of the galactic cosmic rays is refined. Formulas taking into account a change in the Earth’s axis tilt relative to the direction toward the Sun are derived, which allow the annual changes in contributions to the diurnal variation harmonics to be determined. The equation of diffusion taking into account the 2nd harmonic is obtained, and the contribution of this effect to the relative particle density in the cosmic rays in a spherically symmetric case is analyzed.