Collisionless transport of energetic electrons in the solar corona at current-free double layers

Abstract

Context. Impinging electron beams in the solar chromosphere generate hard X-ray radiation (HXR) through the collisional Bremstrahlung thick target model. The deduced electron distributions usually exhibit a broken-power-law. Assuming that the initial distribution function was a drift-Maxwellian, this indicates that the distribution of energetic electrons changes in the course of their propagation, from the looptop acceleration site to the high density chromosphere, via a collisionless scattering mechanism. Aims. The formation of a broken-power-law spectrum via the particle interaction with the current-free weak double layers (DLs) in a reverse current beam plasma system. Methods. The unstable waves generated in current-free coronal plasmas are first studied by means of a linear instability analysis. For most probable coronal plasma parameters, a one-dimensional electrostatic Vlasov-code simulation is performed to understand the nonlinear evolution of the instabilities and their influences on the electron distribution. Results. DL structures cause a dissipation of low energy beam electrons and a stagnation of return-current electrons. Fast electron holes are formed, a secondary two-stream instability, caused by the DL-accelerated electrons. Electron and ion heating by DLs also takes place. Conclusions. The plasma distributions of energetic electrons in the solar corona evolve via their interactions with nonlinear largeamplitude phase-space structures. At the late stage of evolution, the low-energy electrons are slowed down while the high energy part stays uninfluenced after the appearance of DLs. A major part of the return-current electrons change their direction to that of the injected beam. As a result the distribution becomes a broken-power-law as observed by chromospheric HXR radiation.