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

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