Approximate analytical formulation of radial diffusion and whistler-induced losses from a pre-existing flux peak in the plasmasphere

Modeling the spatio-temporal evolution of relativistic electron fluxes trapped in the Earth\textquoterights radiation belts in the presence of radial diffusion coupled with wave-induced losses should address one important question: how deep can relativistic electrons penetrate into the inner magnetosphere? However, a full modelling requires extensive numerical simulations solving the comprehensive quasi-linear equations describing pitch-angle and radial diffusion of the electron distribution, making it rather difficult to perform parametric studies of the flux behavior. Here, we consider the particular situation where a localized flux peak (or storage ring) has been produced at low L < 4 during a period of strong disturbances, through a combination of chorus-induced energy diffusion (or direct injection) at low L together with enhanced wave-induced losses and outward radial transport at higher L. Assuming that radial diffusion can be further described as the spatial broadening within the plasmasphere of this pre-existing flux peak, simple approximate analytical solutions for the distribution of trapped relativistic electrons are derived. Such a simplified formalism provides a convenient means for easily determining whether radial diffusion actually prevails over atmospheric losses at any particular time for given electron energy E and location L. It is further used to infer favorable conditions for relativistic electron access to the inner belt, providing an explanation for the relative scarcity of such a feat under most circumstances. Comparisons with electron flux measurements on board the Van Allen Probes show a reasonable agreement between a few weeks and four months after the formation of a flux peak.