Modeling Supra-thermal Runaway Electrons Returning to the Acceleration Region in Solar Flares

Abstract:

It is well established that when an electric field is applied to a plasma, a fraction of the latter will run away. However, models describing the accelerated electron beam/return-current system have generally failed to take these runaway electrons into account, which means that the magnitude of the return-current electric field is assumed to be much less than the Dreicer field. We investigate the conditions for which runaway electrons cannot be neglected and their effect on the beam/return current system, as well as the associated bremsstrahlung spectrum. We develop a model in which an accelerated electron beam drives a steady-state co-spatial return current electric field, which locally balances the direct beam current and freely accelerates a fraction of background (return-current) electrons. The model is self-consistent, i.e. the electric field induced by the co-evolution of the direct beam and runaway current is taken into account. Main results: (1) Runaway electrons provide supra-thermal seed particles for the acceleration region and can be several tens of percent of the injected nonthermal flux, if the acceleration is ongoing in the same magnetic field lines within the time for the RC to reach the steady state. (2) The heating rate can be more than an order of magnitude lower in the corona compared to the Joule heating in the return current without runaways. (3) The model is shown to be appropriate for a flare with strong broken power-law X-ray spectra. In addition, the model is consistent with a beam streaming along a cool loop with temperatures <7MK.