  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.
