Resonant Scattering of Sub-keV Electrons by Beam-Driven Electron Cyclotron Harmonic Waves

Electron cyclotron harmonic waves (ECH) play a key role in scattering and precipitation of plasma sheet electrons. Previous analysis on the resonant interaction between ECH waves and electrons assumed that these waves are generated by a loss cone distribution and propagate nearly perpendicular (similar to 88 degrees) $(\sim 88{}<^>{\circ})$ to the background magnetic field. Recent spacecraft observations, however, have demonstrated that such waves can also be generated by low energy electron beams and propagate at moderately oblique angles (similar to 70 degrees) $(\sim 70{}<^>{\circ})$. To quantify the effects of this newly observed ECH wave mode on electron dynamics in Earth's magnetosphere, we use quasi-linear theory to calculate the associated electron pitch angle diffusion coefficient. Utilizing THEMIS spacecraft measurements, we analyze in detail a few representative events of beam-driven ECH waves in the plasma sheet and the outer radiation belt. Based on the observed wave properties and the hot plasma dispersion relation of these waves, we calculate their bounce-averaged pitch angle, momentum and mixed diffusion coefficients. We find that these waves most efficiently scatter low-energy electrons (10-500 eV) toward larger pitch angles, on time scales of 102 $1{0}<^>{2}$ to 103 $1{0}<^>{3}$ seconds. In contrast, loss-cone-driven ECH waves most efficiently scatter higher-energy electrons (500 eV-5 keV) toward lower pitch-angles. Importantly, beam-driven ECH waves can effectively scatter ionospheric electron outflows out of the loss cone near the magnetic equator. As a result, these outflows become trapped in the magnetosphere, forming a near-field-aligned anisotropic electron population. Our work highlights the importance of ECH waves, particularly beam-driven modes, in regulating magnetosphere-ionosphere particle and energy coupling.