Eigenfunction‐Based Modeling of Radiation Belt Electron Pitch‐Angle Diffusion With a Source: Formulation and Comparisons With Observations

Abstract Analyzing the dynamics of trapped electron fluxes in the Earth's outer radiation belt is a complex task, due to the presence of insufficiently known parameters and the long runtimes of multi‐dimensional radiation belt codes, preventing a thorough examination of dependencies on all parameters. Here, we present an approximate eigenfunction modeling of whistler‐mode wave‐driven electron pitch‐angle diffusion, slightly generalized compared to previous work. This new model can approximately describe, in an easy, flexible, and fast way, both the asymptotic electron pitch‐angle distribution (PAD) at all pitch angles and its temporal evolution toward this final state, in both weak and strong diffusion regimes, in the presence of a finite, time‐varying electron source. In this model, wave‐driven pitch‐angle diffusion is assumed to prevail over energy diffusion and radial diffusion, limiting its applicability to the plasmasphere or intervals of smooth decay of the electron flux outside the plasmasphere, during moderately active periods. We propose a new method, based on this model, for estimating the energy spectrum and temporal variation of the electron source. We investigate the dynamics of the electron flux measured by the Van Allen Probes and Arase spacecraft during two events in 2018 and 2022 in the outer radiation belt. We demonstrate that the new model can reproduce the evolution of the measured electron flux and of its PAD, provided that the magnitude of diffusion rates is normalized to the observed decay timescale in the 300–600 keV range and that a finite electron source term is included below 300 keV.