Nonlinear Cosmic‐Ray Diffusive Transport in Combined Two‐dimensional and Slab Magnetohydrodynamic Turbulence: A BGK‐Boltzmann Approach

Particle simulations revealed that standard quasi-linear theory cannot adequately describe the parallel and perpendicular diffusion of cosmic rays in three-dimensional magnetohydrodynamic solar wind turbulence, when the turbulence is modeled approximately as a combination of a dominant two-dimensional component and a minor slab component. Recent nonlinear theories based on a Taylor-Green-Kubo formalism, such as the nonlinear guiding center (NLGC) theory, and the weakly nonlinear theory (WNLT) proved to be much more successful. Instead, we follow a BGK-Boltzmann approach to investigate this matter. Going beyond current NLGC theory and WNLT in scope, we derived a complete cosmic-ray transport theory that includes expressions not only for parallel and perpendicular diffusion, but also for drift, convection, adiabatic energy change, and momentum diffusion. The BGK-Boltzmann approach enables one to derive tractable yet complicated expressions for the transport coefficients in both the weak and strong particle scattering limits. We show that the WNLT expressions can be recovered by combining these two limits in such a way that there is weak particle scattering along the magnetic field but strong scattering across the field. It is shown that the complex WNLT expressions can be reduced to simple analytical expressions for parallel and perpendicular diffusion that reproduce approximately the rigidity dependence of particle simulations at low to medium rigidities. These expressions also prove to be consistent with well-known expressions for perpendicular diffusion in the literature. It is discussed how large-scale gradient and curvature drifts get modified by turbulence and how stochastic particle acceleration changes when two-dimensional turbulence is dominant.