A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves

TL;DR

This paper derives a self-consistent model for marginally stable parallel ion cyclotron waves in a proton-electron plasma, revealing new wave behaviors and stability thresholds that differ from traditional bi-Maxwellian assumptions.

Contribution

It introduces a novel equation describing self-consistent marginal stability states with explicit solutions, advancing understanding of wave-particle interactions in plasmas.

Findings

Wave phase speeds exceed cold plasma predictions.

Characteristic resonant surfaces are more peaked in perpendicular velocity.

Threshold anisotropy for wave generation is higher than bi-Maxwellian estimates.

Abstract

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating through this marginally stable plasma will neither grow nor damp. The dispersion relation of these waves, {\omega} (k), smoothly rises from the usual MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow \pm\infty. The proton distribution function has constant phase-space density along the characteristic resonant surfaces defined by this dispersion relation. Our equation contains a free function describing the variation of the proton phase-space density across these surfaces. Taking this free function to be a simple "box function", we obtain specific solutions of the marginally stable state for a range of proton parallel betas. The phase speeds of these waves are larger than those given by the cold plasma dispersion relation, and the characteristic surfaces are more sharply peaked in the v\bot direction. The threshold anisotropy for generation of ion cyclotron waves is also larger than that given by estimates which assume bi-Maxwellian proton distributions.