Thundercloud high-energy radiation production by long streamers

The novel Streamer Parameter Model (SPM) [Lehtinen, 2021, doi:10.1007/s11141-021-10108-5] allows to quickly calculate the shape, velocity, and electric field of an electric streamer in air, without resorting to lengthy hydrodynamic simulations. A streamer propagates faster as its length grows. When the streamer length exceeds several meters, the velocity may become comparable to the speed of light, which necessitates correcting the model for relativistic effects. Such long streamers may describe the experimentally observed fast positive and negative breakdown. We propose that they may produce large quantities of relativistic runaway electrons, and therefore x-rays. This is facilitated by several conditions: (1) electric fields at the streamer tip may be sufficiently close to the so-called thermal runaway threshold (~30 MV/m), at which free electrons may accelerate from thermal energies up to relativistic energies; (2) in negative streamers, the energetic electrons are synchronized in velocity with the streamer front; (3) the streamer tip radius may exceed tens of centimeters, providing a large volume of the high field where the thermal runaway acceleration may take place. We apply SPM to long streamer propagation inside a thundercloud and calculate the relativistic runaway electron production, as well as radio, optical and x-ray radiation. The calculations are compared to the observations of Narrow Bipolar Events (NBE), Terrestrial Gamma Flashes (TGF), and luminous phenomena obtained during the recent ALOFT campaign.