Impulsive phase heating by uni-directional current systems in solar flares

The thermal interpretation of solar flare impulsive phase hard X-ray emission requires rapid heating of a substantial coronal volume to very high temperatures. In this study we investigate the possibility of producing such heating by current dissipation, driven by a tearing instability associated with a single uni-directional current system. Earlier research is synthesized by coupling the energy equation, including loss terms previously neglected, with an equation describing the evolution of the growing electric field. The resistivity due to the excitation of ion-cyclotron and ion-acoustic waves is computed by assuming marginal stability.It is found, for the fast tearing mode, that for initial growth rates _f 0.3 s^-1 (corresponding to a current channel width l 3 × 10⁵ cm), the electron heating is offset by convective losses, resulting in a very slow temperature rise. Furthermore, hard X-ray emitting temperatures (2 × 10⁸ K) are never realized. For the larger growth rates corresponding to smaller current channel widths, heating from 10⁷ to 10⁸ K can be achieved in a few seconds. However, in this regime the maximum volume that can be heated is only of order 10²⁰ cm³, some three to five orders of magnitude less than the volume of heated material that is inferred from hard X-ray emission measures. These results suggest that in the case of the fast tearing mode a more complicated geometry involving multiple small-scale, oppositely-directed, current channels may be necessary to achieve the required heating.