Intermittent Heating of the Solar Corona by Heat Flux-generated Ion Cyclotron Waves

Recently, we suggested that the source of ion heating in solar coronal holes is small-scale reconnection events (microflares) at the coronal base. The microflares launch intermittent heat flux up into the corona exciting ion cyclotron waves through a plasma microinstability. The ions are heated by these waves during the microflare bursts and then evolve with no energy input between the bursts. In this paper, we show that the structure of the proton distribution in the relatively long time periods between the microflares is determined by collisions at small heliocentric distances. At greater distances, the collisional processes can be replaced by similar processes due to secondary instabilities. These are excited by the distortion of the distribution under the action of the mirror force. At the same time, the heating during the microflare bursts is not affected by either the collisions or the secondary instabilities because of the short duration of the bursts. We demonstrate that in each intermittent heating event the protons diffuse approximately along one-dimensional curves in the phase space and can develop a quasi-plateau. The corresponding temperature increase can then be calculated without solving the diffusion equations. The overall coronal heating by this mechanism is a summed effect of all microflare bursts during the expansion time of the solar wind and adiabatic cooling between the microflares. The calculations for the collision-dominated region suggest that the overall heating is efficient enough to account for the acceleration of the fast solar wind in this region.