Numerical modeling of the 22‐year variation of the cosmic ray intensity and anisotropy

Abstract

We have solved the two‐dimensional time‐dependent diffusion‐convection equation numerically to obtain the distribution and anisotropy of cosmic rays in the heliosphere. We have assumed that the parallel and perpendicular mean free paths are proportional to the particle Larmor radius, and we have treated each proportionality constant (a, b) as a parameter. We have found that the set (a, b) = (4, 2) gives the steady state solution compatible with observations on the intensity and the solar diurnal anisotropy of cosmic rays in 0.5‐ to 10‐GeV range as obtained at the earth. This set of (a, b) corresponds to the ratio of the diffusion coefficients D∥/D⊥ = 10. In our solution the intensity for the (pre‐1980) interplanetary magnetic field (IMF) state where the solar magnetic dipole and the angular velocity vector are parallel is higher than for the (post‐1980) state where they are antiparallel, while the phase of the diurnal anisotropy is about 15 hours for the parallel state and about 18 hours for the antiparallel state. We have also reproduced the observed small radial gradient for each IMF state. We discuss the nature of the solution in order to understand the effect of the density gradient drift motion on the cosmic ray distribution.