Diffusion tensor for Galactic cosmic rays in the interplanetary medium with a magnetic field

The Boltzmann kinetic equation is analyzed in the MHD approximation. This analysis requires an explicit expression for the collision integral F _c. In the classical theory, F _c=?vf _μ ⁽¹⁾ Ω_μ, where f _μ ⁽¹⁾ is the first spherical harmonic in the Galactic-cosmic-ray (GCR) distribution, Ω_μ are the components of a unit particle velocity vector, and the frequency ν of collisions between GCRs and interplanetary magnetic-field nonuniformities is assumed to be a scalar. The assumption that ν_ij is a tensor (which is the result of anisotropy in the interplanetary medium) distinguishes this study from others. Since the anisotropic GCR effects in the heliomagnetosphere are marginal, the nondiagonal elements of tensor ν_ij were set equal to zero. Our analysis has yielded the diffusion-tensor components D _∥, and D _A, which are expressed in terms of interplanetary parameters. The energy dependencies of D _∥, and D _A are in good agreement with the experimental data and calculations by other authors.