How significant are runaway electrons returning to the acceleration region in solar flares?

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. We then apply our model to RHESSI observations of two flares with different spectral characteristics. One flare whose X-ray spectra during the impulsive phase are well represented by a single power-law, and the other requiring strong broken power-law spectra (difference between the upper and lower energy spectral indices is greater than 0.6).