Saturation characteristic of electromagnetic ion cyclotron waves

Electromagnetic ion cyclotron (EMIC) waves are an integral component of the Earth's dynamic space environment. In order to quantify their effect, it is necessary to know their saturation amplitude, but in modeling studies it is usually the linear growth rate that is calculated and various assumptions need to be made in order to relate this growth rate to the final amplitude of the wave. Here, we perform a comparison of the saturation characteristics of EMIC waves using a 2.5-D electromagnetic hybrid PIC code, with the corresponding linear growth rates calculated with the hot-plasma dispersion solver of the HOTRAY code. We choose a set of values consistent with satellite observations for our nominal case, and explore the parameter space in the neighborhood of this nominal case, by varying the hot proton density and thermal anisotropy. We find that the saturation amplitudes increase monotonically, and the times to saturation decrease monotonically with increasing growth rates, independent of the values of density and anisotropy. Both the saturation amplitude and time to saturation curves can be fit by simple two-parameter models with acceptable errors. This result implies that within the limitations and caveats of the present study, the saturation amplitudes and time to saturation can be predicted with good accuracy based on the linear growth rates alone, which can be used directly in conjunctions with global ring current simulations to model the resultant effects on magnetospheric particles