The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 3. The proton halo and dispersive waves

[1] The kinetic shell model seeks to test the collisionless kinetic response of coronal hole protons to the quasi-linear resonant cyclotron dissipation of outwardly directed, parallel propagating ion cyclotron waves, which is often invoked as the mechanism responsible for generating the fast solar wind. In this model, we make the approximation that the resonant cyclotron interaction proceeds much faster than any other process affecting the protons, so that the resonant portions of the distribution are maintained in a state of marginal stability with respect to this interaction. Under this approximation, the resonant protons are organized on nested shells of constant density in velocity space, defined by the condition that the proton energy is conserved in the rest frame moving with the phase speed of the resonant wave. These shells then evolve on the slower nonresonant timescale, responding to the shell-averaged forces of gravity, charge-separation electric field, mirror force, and an inertial force due to the fact that the waves are propagating in the accelerating plasma frame. Since these kinetic shell distributions are held in a marginally stable state, they cannot exchange any more energy with the waves than that taken to maintain that state. Thus their evolution corresponds to the effect of the maximum possible dissipation of outward propagating waves. Our earlier work was simplified in two major respects: we considered only dispersionless waves and we assumed that all the antisunward protons were resonantly interacting with self-generated inward propagating waves. In this paper, we first present an improved treatment of the antisunward protons which yields more plausible speeds and temperatures than obtained previously. We then incorporate the effects of ion cyclotron dispersion into the model. Dispersion creates resonant shells which are broader in upsilon(parallel to) than our previous dispersionless distributions. We find that the nonresonant forces acting on these dispersive shell distributions invariably produce only weak acceleration and result in perpendicular cooling rather than the heating that is generally required for fast solar wind speeds. These effects are attributed to the weaker inertial force on the sunward dispersive shells and are essentially independent of the behavior of the antisunward particles. Since these results correspond to the maximum possible dissipation by this mechanism, we conclude that the heating of coronal hole protons and the generation of the fast solar wind are not caused by the collisionless dissipation of parallel propagating ion cyclotron waves.