Nonlinear interaction between ring current protons and electromagnetic ion cyclotron waves

Electromagnetic ion cyclotron (EMIC) waves have long been suggested to account for the rapid decay of ring current, which is usually described by the quasi-linear theory. We demonstrate that the interactions between ring current protons and typical EMIC waves can be highly nonlinear. A dimensionless parameter R is derived to identify the nonlinear interaction region, and a test-particle simulation is performed to analyze the motions of typical (kinetic energy E_k = 50 keV) ring current protons in detail. Nonlinear phase bunching occurs widely in the region R ∼<1, whereas nonlinear phase trapping is confined in the region R ∼ 1. The former produces the non-stochastic pitch angle decrease, probably increasing the overall loss rate predicted by the quasi-linear theory. In contrast, the latter causes the significant pitch angle increase, probably reducing the overall loss rate estimated from the quasi-linear theory. These two nonlinear mechanisms lead to complex advection and diffusion processes, and an advection-diffusion modeling is required to more accurately simulate the ring current decay induced by EMIC waves.