Energy and fluxes of thermal runaway electrons produced by exponential growth of streamers during the stepping of lightning leaders and in transient luminous events

In the present paper, we demonstrate that the exponential expansion of streamers propagating in fields higher than the critical fields for stable propagation of streamers of a given polarity leads to the exponential growth of electric potential differences in streamer heads. These electric potential differences are directly related to the energy that thermal runaway electrons can gain once created. Using full energy range relativistic Monte Carlo simulations, we show that the exponential growth of potential differences in streamers gives rise to the production of runaway electrons with energies as high as similar to 100 keV, with most of electrons residing in energy range around several tens of keVs. We apply these concepts in the case of lightning stepped leaders during the stage of negative corona flash. The computation of electric field produced by stepped leaders demonstrates for the first time that those energetic electrons are capable of further acceleration up to the MeV energies. Moreover, the flux of runaway electrons produced by streamers suggests that stepped leaders produce a considerable number of energetic electrons, which is in agreement with the number of energetic photons observed from satellites in terrestrial gamma ray flashes (TGFs). The results suggest that previously proposed process of relativistic runaway electron avalanche is difficult to sustain in the low-electric fields observed in thunderclouds and is generally not needed for explanation of TGFs. The present work also gives insights on relations between physical properties of energetic electrons produced in streamers and the internal electrical properties of streamer discharges, which can further help development and interpretation of X-ray diagnostics of these discharges.