Drift phase resolved diffusive radiation belt model: 1. Theoretical framework

Most physics-based models provide a coarse three-dimensional representation of radiation belt dynamics at low time resolution, of the order of a few drift periods. The description of the effect of trapped particle transport on radiation belt intensity is based on the random phase approximation, and it is in one dimension only: the third adiabatic invariant coordinate, akin to a phase-averaged radial distance. This means that these radiation belt models do not resolve the drift phase or, equivalently, the magnetic local time. Yet, in situ measurements suggest that radiation belt intensity frequently depends on magnetic local time, at least transiently, such as during active times. To include processes generating azimuthal variations in trapped particle fluxes and to quantify their relative importance in radiation belt energization, an improvement in the spatiotemporal resolution of the radiation belt models is required. The objective of this study is to pave the way for a new generation of diffusive radiation belt models capable of retaining drift phase information. Specifically, we highlight a two-dimensional equation for the effects of trapped particle transport on radiation belt intensity. With a theoretical framework that goes beyond the radial diffusion paradigm, the effects of trapped particle bulk motion, as well as diffusion, are quantified in terms of Euler potentials, (alpha, beta), quantities akin to the radial and azimuthal directions. This work provides the theoretical foundations underlying the drift phase resolved transport equation for radiation belt dynamics. It also brings forward the concept of azimuthal diffusion as a phase-mixing agent.