A self-consistent marginally stable state for parallel ion cyclotron waves

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron (IC) 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 vertical bar k vertical bar to reach omega = Omega(p) as k -> +/-infinity. 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 nu(perpendicular to) direction. The threshold anisotropy for generation of ion cyclotron waves is also larger than that given by estimates which assume bi-Maxwellian proton distributions. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3697721]