Bulk Energization of Electrons in Solar Flares by Alfven Waves

Bulk energization of electrons to 10-20 keV in solar flares is attributed to dissipation of Alfven waves that transport energy and potential downward to an acceleration region near the chromosphere. The acceleration involves the parallel electric field that develops in the limit of inertial Alfven waves (IAWs). A two-potential model for IAWs is used to relate the parallel potential to the cross-field potential transported by the waves. We identify a maximum parallel potential in terms of a maximum current density that corresponds to the threshold for the onset of anomalous resistivity. This maximum is of order 10 kV when the threshold is that for the Buneman instability. We argue that this restricts the cross-field potential in an Alfven wave to about 10 kV. Effective dissipation requires a large number of up-and down-current paths associated with multiple Alfven waves. The electron acceleration occurs in localized, transient, anomalously conducting regions (LTACRs) and is associated with the parallel electric field determined by Ohm's law with an anomalous resistivity. We introduce an idealized model in which the LTACRs are (upward-)current sheets, a few skin depths in thickness, separated by much larger regions of weaker return current. We show that this model can account semi-quantitatively for bulk energization.