The importance of electron-electron Bremsstrahlung for terrestrial gamma-ray flashes and electron-positron beams

Thunderstorms emit terrestrial gamma-ray flashes with single photon energies of up to tens of MeV, and electron positron beams that are created by photons with energies above 1.022 MeV. Current theories of the processes within thunderstorms (like relativistic run-away electron avalanches or lightning leaders) provide distributions of high electron energies. But how and how efficiently are the high electron energies converted into high photon energies? It is generally accepted that these photons are produced through Bremsstrahlung when energetic electrons collide with air molecules. However, presently used cross-sections for Bremsstrahlung in the geophysical literature treat only the interaction of the energetic electrons with the nuclei of molecules, as appropriate for high atomic numbers Z. On the contrary we show that for light molecules like nitrogen and oxygen the Bremsstrahlung of electrons scattered at the electrons of the atomic shell dominates the photon spectrum above hundreds of keV. We simulate the production of Bremsstrahlung photons in a constant electric field and in the field of a negative stepped leader; we find that the photon number in the energy range of 20 keV - 2 MeV increases by a factor 150, and that the photon spectrum is much flatter than without electron-electron Bremsstrahlung which is in better accordance with satellite measurements.