Magnetic field line curvature induced pitch angle diffusion in the inner magnetosphere

Abstract

We study magnetic field line curvature (FLC) pitch angle scattering as a detrapping mechanism in the inner magnetosphere. In this region, changes in pitch angle from individual scattering events are usually small which allows us to use the diffusion approximation. Previous studies that have used the diffusion approximation simply calculated rough decay rates which were based either on inverse diffusion coefficients or the strong diffusion limit. Here we calculate FLC diffusion coefficients for a dipole field and use eigenfunction analysis to model the long‐term behavior of particle distributions in a quiet time inner magnetosphere. The resulting pitch angle distributions are given and their decay periods are used to explore energy thresholds. Our calculations predict that the long‐term pitch angle distributions are sharply peaked near 90° when the adiabaticity parameter ε ≲ 1/3, but they broaden as ε increases. This dependence is consistent with the expectation that at large ε the pitch angle distribution will become isotropic. Because the change in pitch angle for individual particles depends strongly on ε, a threshold in ε is often used to demarcate the onset of nonadiabatic single particle motion. Although the distribution decay rates calculated here are also strongly dependent on ε, we find that a realistic description of the division between static and diffusive regimes must account for the local bounce frequency.