Cosmic ray transport in non-uniform magnetic fields: consequences of gradient and curvature drifts†

Large-scale spatial variations of the guide magnetic field of interplanetary and interstellar plasmas give rise to the mirror force -(p²/2mγB)B). The parallel component of this mirror force causes adiabatic focusing of the cosmic ray guiding center whereas the perpendicular component of the mirror force gives rise to the gradient and curvature drifts of the cosmic ray guiding center. Adiabatic focusing and the gradient and curvature drift terms additionally enter the Fokker-Planck transport equation for the gyrotropic cosmic ray particle phase space density in partially turbulent non-uniform magnetic fields. For magnetohydrodynamic turbulence with dominating magnetic fluctuations, the diffusion approximation is justified, which results in a modification of the diffusion-convection transport equation for the isotropic part of the gyrotropic phase space density from the additional focusing and drift terms. For axisymmetric undamped slab Alfvenic turbulence we show that all perpendicular spatial diffusion coefficients are caused by the non-vanishing gradient and curvature drift terms. For a specific (symmetric in μ) choice of the pitch-angle Fokker-Planck coefficients we show that the ratio of the perpendicular to parallel spatial diffusion coefficients apart from a constant is determined by the spatial first derivatives of the non-constant cosmic ray Larmor radius in the non-uniform magnetic field.