Variability in fluence and spectrum of high-energy photon bursts produced by lightning leaders

In this paper, we model the production and acceleration of thermal runaway electrons during negative corona flash stages of stepping lightning leaders and the corresponding terrestrial gamma ray flashes (TGFs) or negative cloud-to-ground (-CG) lightning-produced X-ray bursts in a unified fashion. We show how the source photon spectrum and fluence depend on the potential drop formed in the lightning leader tip region during corona flash and how the X-ray burst spectrum progressively converges toward typical TGF spectrum as the potential drop increases. Additionally, we show that the number of streamers produced in a negative corona flash, the source electron energy distribution function, the corresponding number of photons, and the photon energy distribution and transport through the atmosphere up to low-orbit satellite altitudes exhibit a very strong dependence on this potential drop. This leads to a threshold effect causing X-rays produced by leaders with potentials lower than those producing typical TGFs extremely unlikely to be detected by low-orbit satellites. Moreover, from the number of photons in X-ray bursts produced by -CGs estimated from ground observations, we show that the proportionality between the number of thermal runaway electrons and the square of the potential drop in the leader tip region during negative corona flash proposed earlier leads to typical photon fluences on the order of 1 ph/cm² at an altitude of 500 km and a radial distance of 200 km for intracloud lightning discharges producing 300 MV potential drops, which is consistent with observations of TGF fluences and spectra from satellites.