Nonlinear Effects of Ring Current Protons: Impacts of EMIC Wave Amplitude, Frequency, and Propagation Angle

Abstract

Nonlinear cyclotron resonance is known to cause the scattering of ring current protons to deviate from the predictions of quasi-linear theory, when wave-induced motion dominates over adiabatic motion. This study employed a test-particle simulation to investigate the nonlinear processes of ring current protons and their dependence on the amplitude, frequency, and wave normal angle ψ of electromagnetic ion cyclotron (EMIC) waves. As the equatorial pitch angle α_eq increases, proton motion becomes dominated by the wave's electromagnetic force and responds nonlinearly. When wave-induced motion and adiabatic motion become comparable, the superposition of nonlinear phase trapping and phase bunching leads to complex oscillations in both the test-particle advection and diffusion coefficients. The nonlinear behavior becomes pronounced when the wave amplitude increases significantly. As the wave frequency increases, EMIC waves can nonlinearly interact with lower energy protons (i.e., E_k < 10 keV). Furthermore, oblique EMIC waves tend to produce less significant nonlinear behavior compared to parallel EMIC waves. Increasing the wave normal angle causes the nonlinear regime (i.e., the number of protons responding nonlinearly) in the E_k−α_eq plane to shrink, and the regime changes discontinuously with respect to α_eq. We propose that the characteristics of EMIC waves significantly influence the nonlinear behavior of ring current protons and should be considered in the wave-particle interacting processes.