Calculation of beams of positrons, neutrons and protons associated with terrestrial gamma-ray flashes

Positron beams have been observed by the Fermi satellite to be correlated with lightning leaders, and neutron emissions have been attributed to lightning and to laboratory sparks as well. Here we discuss the cross sections to be used for modeling these emissions, and we calculate the emissions of positrons, neutrons, and also protons from lightning leaders. Neutrons were first erroneously attributed to fusion reactions, but the photonuclear reaction responsible for neutrons should create protons as well. We predict them here; they have not been observed yet. In the paper, we first revisit the model for stepped lightning leaders of Xu, Celestin, and Pasko with updated cross sections, we analyze the spatial and energetic structure of the electron beam, and we calculate the spectrum of the generated gamma ray beam at 16 km altitude. Then we review the scattering processes of photons with emphasis on the processes above 5 MeV, in particular the photon energy losses in Compton scattering events and the generation of leptons and hadrons. We provide simple approximations for photon energy loss and lepton and hadronproduction for any photon with energy above 5 MeV passing through an arbitrary air layer. Finally, we launch a gamma ray beam with the earlier calculated spectrum of the negative stepped lightning leader from 16 km upward and calculate the production and energy of positrons, neutrons, and protons as well as the propagation of positrons.