Theoretical investigation of thunderstorm induced enhancements of cosmic ray fluxes

We conducted theoretical investigation of long lasting pulses of cosmic-ray electrons and gamma-ray radiation, which are often observed during thunderstorms by particle detectors at high altitude cosmic-ray stations. These thunderstorm ground enhancements (TGEs) last several minutes, during which the flux of electrons and gamma-quants can surpass a few hundred percent over background level. We developed theoretical model and derived energetic spectrums of electrons and gamma-quants at given value of thunderstorm electric field. The model considers two following mechanisms, which can change the flux of electrons in electric field: (i) transformation of the spectrum of cosmic-ray electrons and (ii) formation of electron avalanche. Due to (i) the number of low (few MeV) energy electrons decreases and small abundance (<5% of total flux of cosmic rays) of cosmic-ray electrons with energies >10 MeV emerges. The spectral fluxes of two electron components - avalanche and cosmic-ray electrons are derived, which shows that contribution of cosmic-ray electrons in total abundance of electrons is small. Consequently, the contribution of gamma ray radiation, produced by the abundance of cosmic-ray electrons is small as well. We derived the exact equations for the spectrums of these two components of gamma ray radiation and showed that spectral curve of avalanche gamma-quants can be approximated by a simple function exp(−E/E0)/E up to ∼40 MeV. At higher energies gamma-ray radiation is produced by the abundance of cosmic-ray electrons and it has approximately power-law spectrum.