Cross sections and modelling results for TGF- and positron spectrum produced by a negative stepped lightning leader

We model the energy resolved angular distribution of TGFs and of positrons produced by a negative lightning leader stepping upwards in a thundercloud. First we present our new results for doubly differential cross sections for Bremsstrahlung and pair production based on the triply differential cross-sections of Bethe and Heitler. Other cross sections in literature and databases do not cover the appropriate energy range or do not apply to the small atomic numbers of nitrogen and oxygen or do not resolve both energies and emission angles of emitted photons or positrons. Second we have extended the Monte Carlo model of Chao Li towards relativistic electron energies, and we have included the new cross sections as well as Compton scattering of photons and photo ionization. We will present the angular resolved spectrum of TGFs and positrons of stepped negative leaders and compare it with results of other authors