Radial evolution of intermittent heat flux in solar coronal holes

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. 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 intermittent heat flux produced by the microflares was modeled as electron beams with constant speed and temperature for simplicity. In this paper, we consider a more sophisticated model of the heat flux taking into account the action of the mirror force and the charge separation electric field on the beam particles. We show that the radial evolution of the heat flux is determined mainly by the beam expansion along the magnetic field roughly at the root mean square velocity of the beam particles, while the variation of the beam bulk speed and thermal energy is less important.