Bulk Energization of Electrons in Solar Flares by Alfv\'en Waves

TL;DR

This paper proposes a model where Alfvén waves in solar flares generate parallel electric fields in localized regions, leading to electron acceleration up to 20 keV, with a maximum potential around 10 kV constrained by plasma instabilities.

Contribution

It introduces a two-potential model linking wave potentials to electron acceleration, highlighting the role of anomalous resistivity and localized current sheets in bulk energization.

Findings

Maximum parallel potential is about 10 kV due to instability thresholds.

Electron acceleration occurs in transient, localized regions called LTACRs.

The model semi-quantitatively explains bulk energization in solar flares.

Abstract

Bulk energization of electrons to $10\,-\,20\,$keV in solar flares is attributed to dissipation of Alfv\'en 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 Alfv\'en 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 Alfv\'en wave to about $10\,$kV. Effective dissipation requires a large number of up- and down-current paths associated with multiple Alfv\'en 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.