Random ballistic interpretation of nonlinear guiding center theory

Nonlinear guiding center (NLGC) theory has been used to explain the asymptotic perpendicular diffusion coefficient κ of energetic charged particles in a turbulent magnetic field, which can be applied to better understand cosmic ray transport. Here we re-derive NLGC, replacing the assumption of diffusive decorrelation with random ballistic decorrelation (RBD), which yields an explicit formula for κ. We note that scattering processes can cause a reversal of the guiding center motion along the field line, i.e., "backtracking," leading to partial cancellation of contributions to κ, especially for low-wavenumber components of the magnetic turbulence. We therefore include a heuristic backtracking correction (BC) that can be used in combination with RBD. In comparison with computer simulation results for various cases, NLGC with RBD and BC provides a substantially improved characterization of the perpendicular diffusion coefficient for a fluctuation amplitude less than or equal to the large-scale magnetic field.