Nonlinear Scattering of Relativistic Electrons by Oblique EMIC Waves

Electrons in the Earth’s outer radiation belt can experience rapid energization and pitch angle scattering through interactions with naturally generated electromagnetic waves. Cyclotron resonant interactions with large amplitude electromagnetic ion cyclotron (EMIC) emissions cause scattering and major atmospheric losses of relativistic electrons in the sub-MeV and MeV energy range. While theory and simulations in the past focused mostly on parallel propagating waves, in-situ spacecraft observations of EMIC waves commonly show quasi-parallel or moderately oblique propagation.

Here we present the results of test-particle analysis of electron interaction with helium band and hydrogen band EMIC waves parametrized by wave normal angle (WNA) and wave amplitude. It is shown that nonlinear phase trapping and the associated transport of electrons to low-pitch angles become efficient only at very large amplitudes (> 1% of the background magnetic field), especially in the helium band frequency range, making the nonlinear effects less important than in the whistler-electron interaction case. Harmonic resonant interactions with oblique waves further increase the probability of detrapping, pushing the pitch angle evolution closer to pure diffusion. We also analyze the pitch angle behavior near the loss cone and study the evolution of phase space density (PSD) through the Liouville mapping method. Despite the significant advection effects caused by force-bunching of resonant electrons at low pitch angles, the PSD in the loss cone exhibits behavior similar to strong diffusion. We argue that this is expected to be the case for any bursty precipitation caused by cyclotron resonant interactions.

The wave normal angle has only minor impact on the precipitation rate in the energy range affected by the off-equatorial fundamental resonance, except for the case of very oblique waves (WNA > 70 deg). However, since oblique EMIC waves are elliptically polarized and interact with both co-streaming and counter-streaming electrons, they can enhance the changes in the pitch angle of mirrored (trapped) relativistic electrons. The scattering efficiency for counter-streaming electrons strongly depends on the wave ellipticity, and in turn, on wave frequency, wave normal angle, and ion composition. Our simulation results support the need for accurate wave normal angle and amplitude distribution to quantify the relativistic electron precipitation to the Earth’s atmosphere.