Electron pitch-angle scattering by magnetic waves

Fluxes of relativistic electrons are trapped in the earth's radiation belts and exhausted by loss-cone pitch-angle scattering through interaction with various magnetospheric plasma waves. The high temporal variability of the fluxes is poorly understood and routinely modeled using quasi-linear pitch-angle diffusion theory, which is strictly only applicable for rather low ratios $\epsilon$ of the wave energy to the earth's magnetic field energy. Here, we present a novel electron pitch-angle scattering theory valid for arbitrary $\epsilon$. We concentrate on the simplest case of electromagnetic ion cyclotron (EMIC) waves, approximated with a set of time-independent transverse magnetic fluctuations, and obtain a general integro-differential evolution equation for a pitch-angle distribution $f$. If $f$ evolves weakly on the correlation time scales, the equation reduces to a Fokker-Planck diffusion equation with a {\it time-dependent} diffusion coefficient $D$. Quasi-linear theory is recovered as a first-order truncation of the asymptotic expansion in $\epsilon$ of electron equations of motion and breaks down for $\epsilon \geq 10^{-4}$ [1]. In particular, $D$ changes scaling around this point from $D \propto \epsilon$ to $D \propto \sqrt{\epsilon}$ and is found to be 16 times smaller that the quasi-linear result for $\epsilon = 10^{-2}$ at time $t=30$ electron gyroperiods. [1] K. Liu {\it et al.}, J. Geophys. Res. {\bf 115} A04204 (2010).