Solar and geomagnetic activity modulation of wave–particle interactions in Earth’s radiation belts

Solar forcing and geomagnetic disturbances reshape radiation-belt electron populations through a chain of coupled processes that cannot be represented adequately by a single activity index. This study introduces an activity-conditioned resonance kernel (ACRK) that links solar-wind driving, magnetic compression, cold-plasma density, and wave spectra to pitch-angle and energy diffusion. The formulation distinguishes rapid event-scale modulation from slower background recovery, yields a bounded diffusion closure, and provides a sufficient condition for the sign of local energization. Controlled numerical experiments demonstrate threshold-like changes in resonance access and lower trajectory mismatch than static-spectrum and event-driven quasi-linear models. The study is deliberately based on reproducible synthetic experiments rather than a new satellite-data reanalysis. The proposed framework clarifies the conditions under which geomagnetic activity favors local acceleration, scattering, or mixed responses in Earth’s outer radiation-belt.