Limiting processes in the non-linear and non-diffusive acceleration of radiation belt electrons by whistler-mode waves

The acceleration of radiation belt electrons through resonant interactions with whistler-mode waves is typically analyzed using quasilinear theory, which treats phase space density spreading across energy and pitch angle as a diffusive process. However, nonlinear resonant interactions can result in distinctly non-diffusive transport, accelerating seed electron populations to several MeV within minutes under idealized scenarios. This rapid energization contrasts with spacecraft observations, which are generally well explained by Fokker-Planck models using quasilinear diffusion coefficients.

We investigate conditions under which nonlinear acceleration can be approximated as diffusion. Test-particle simulations with increasingly complex wave field models reveal two principal types of resonant electron motion. First, for single-frequency, high-amplitude waves, electrons move along resonant diffusion curves, or analogous curves in inhomogeneous magnetic fields, spreading uniformly along these curves within a few tens of seconds. Above ~500 keV, relativistic turning acceleration (RTA) and ultra-relativistic acceleration (URA) mechanisms can increase particle energies by several MeV within a few seconds.

Second, with realistic wave models including finite bandwidth and amplitude modulations, electrons can move across diffusion curves corresponding to different wave frequencies. This process, orders of magnitude slower than the idealized motion along diffusion curves, can be accurately described as diffusion. In addition, wave incoherence significantly disrupts phase trapping, slowing down nonlinear acceleration along the curves. On the time scale of several consecutive resonant interactions, electron dynamics become stochastic, and the acceleration along the curves can be effectively described as inhomogeneous diffusion with negligible advection.

We conclude that, under realistic conditions, electron acceleration happening over multiple bounce periods and longer timescales can be modeled by the Fokker-Planck equation with energy-dependent corrections to quasilinear diffusion coefficients. Efficient modeling approaches that avoid computationally expensive kinetic simulations are critical for advancing radiation belt numerical models.