Quasilinear perpendicular diffusion of cosmic rays in weak dynamical turbulence

The quasilinear calculation of perpendicular diffusion of cosmic ray particles for weak dynamical magnetic turbulence of arbitrary geometry is presented. Starting from the equations of motion, a detailed point-by-point derivation of quasilinear Fokker-Planck coefficients is given. It is shown that, to have diffusive behaviour of the Fokker-Planck coefficients, the existence of a finite correlation time of the magnetic fluctuations is essential. From the perpendicular Fokker-Planck coefficient D-perpendicular to the perpendicular spatial diffusion coefficient kappa(perpendicular to) and the associated perpendicular mean free path lambda(perpendicular to) are calculated for the damping model of dynamical magnetic turbulence and three different turbulence geometries: slab, 2D and composite turbulence. Explicit analytical expressions for the perpendicular transport parameters of electrons and protons are given for realistic heliospheric plasma parameters. By comparing with our previous determination of the parallel transport parameters, the variation of the ratio of mean free paths lambda(perpendicular to)/lambda(parallel to) with particle rigidity for the three turbulence models is investigated. The comparison of these predictions with future accurate experimental determinations of the ratio of mean free paths will allow conclusions on the nature of interplanetary magnetic turbulence.