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 characterize the competition between wave-induced and adiabatic motions, and a test-particle simulation is performed to analyze the motions of typical (kinetic energy Ek=50keV) ring current protons in detail. The nonlinear phase bunching occurs widely in the region R~<1, whereas the nonlinear phase trapping is confined in the region R~1. The former produces the deterministic 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.