Limits on the streaming and escape of electrons in thermal models for solar hard X-ray emission

Abstract

Upper limits on the number of fast electrons streaming through and escaping from a plasma whose electrons have been heated to approximately 100 billion K and confined by a collisionless ion-acoustic thermal conduction front are determined. It is shown that such a front is fairly transparent to fast electrons with velocities much larger than the thermal velocity because the anisotropic ion-acoustic waves cannot scatter them, making them collisionless on a scale much larger than the thickness of the front. The collisionless analog of the collisional thermoelectric field is derived self-consistently and shown to offer a significant impediment to fast electrons because they must climb over a larger potential barrier than in the collisional case. The only factors limiting the escape of electrons able to surmount this barrier are their rate of production and the requirement that they carry less heat flux than the maximum heat flux allowable. The rate of production is determined for the case of a Maxwellian whose tail is being filled collisionally.