Reduction of the Downward Energy Flux of Nonthermal Electrons in the Solar Flare Corona due to Cospatial Return-current Losses

Abstract High-energy electrons carry much of a solar flare’s energy. Therefore, understanding changes in electron beam distributions during their propagation is crucial. A key focus of this paper is how the cospatial return current reduces the energy flux carried by these accelerated electrons. We systematically compute this reduction for various beam and plasma parameters relevant to solar flares. Our 1D model accounts for collisions between beam and plasma electrons, return-current electric-field deceleration, thermalization in a warm target approximation, and runaway electron contributions. The results focus on the classical (Spitzer) regime, offering a valuable benchmark for energy flux reduction and its extent. Return-current losses are only negligible for the lowest nonthermal fluxes. We calculate the conditions for return-current losses to become significant and estimate the extent of the modification to the beam’s energy flux density. We also calculate two additional conditions that occur for higher injected fluxes: (1) where runaway electrons become significant, and (2) where current-driven instabilities might become significant, requiring a model that self-consistently accounts for them. Condition 2 is relaxed and the energy flux losses are reduced in the presence of runaway electrons. All results are dependent on beam and cospatial plasma parameters. We also examine the importance of the reflection of beam electrons by the return-current electric field. We show that the interpretation of a number of flares needs to be reviewed to account for the effects of return currents.