The Kinetic Shell Model of Coronal Heating and Acceleration by Ion Cyclotron Waves: Dispersive Waves

The kinetic shell model of resonant cyclotron heating and acceleration results from taking this wave-particle interaction to be much faster than the non-resonant response to the gravity, electric field and mirror force in coronal holes. Under these conditions, the coronal protons are distributed on constant-density shells in velocity space along surfaces which conserve their energy in the reference frame moving with the phase speed of the resonant wave. In previous work, we considered the resonant waves to be dispersionless, so this phase speed was the same for all protons at a given position. In that case, we obtained shells which were spherical sections centered at that speed, either toward or away from the Sun along the radial magnetic field. However, when wave dispersion is included, the phase speed varies with wavenumber, and protons with different parallel speeds resonate with waves of different phase speeds. In this work, we apply the formalism of Isenberg and Lee [JGR, 101, 11055, 1996] to calculate the shape of the dispersive shells, and we incorporate this new shell structure into our kinetic model for the generation of the fast solar wind. We find a pronounced improvement in the proton anisotropies obtained by the model. We will present additional results for the solar wind speeds and temperatures, along with the model evolution of the coronal hole proton distribution and the wave intensities for inward and outward propagating ion cyclotron waves.