Linear, Quasi-Linear and Nonlinear Radial Transport in the Earth's Radiation Belts

Abstract

Observational studies of the Earth's radiation belts indicate that Alfv\'enic fluctuations in the frequency range of 2-25 mHz accelerate magnetically trapped electrons to relativistic energies. For decades, statistical models of the Earth's radiation belts have quantified the impact of Alfv\'enic waves in terms of quasi-linear diffusive models. However, quasi-linear models are inadequate to quantify Alfv\'enic radial transport occurring on timescales comparable to the azimuthal drift period of $0.1- 10$ MeV electrons. With recent advances in observational methodologies offering spatial and temporal coverage of the Earth's radiation belts on fast timescales, a theoretical framework that distinguishes between fast and diffusive radial transport can also be tested for the first time with in situ measurements. In this report, we present a drift kinetic description of radial transport for planetary radiation belts. We characterize linear processes that are too fast to be modelled by quasi-linear models and determine the conditions under which nonlinearities become dynamically significant. In the linear regime, wave-particle interactions are categorized in terms of resonant and non-resonant responses. We demonstrate that the phenomenon of zebra stripes is non-resonant and can originate from the injection of particles in the inner radiation belts. We derive a radial diffusion coefficient for a field model that satisfies Faraday's law and that contains two terms: one scaling as $L^{10}$ independent of the azimuthal number $m$, and a second one scaling as $m^2 L^6$. In the nonlinear regime, we show that azimuthally symmetric waves with properties consistent with in situ measurements can energize 10-100 keV electrons in less than a drift period. This coherent process provides new evidence that acceleration by Alfv\'enic waves in radiation belts cannot be fully contained within diffusive models.