Terrestrial gamma ray flashes with energies up to 100 MeV produced by nonequilibrium acceleration of electrons in lightning

Using Monte Carlo models simulating energetic electrons in inhomogeneous electric field and the transport of energetic photons in the Earth's atmosphere, we show that the spectrum of bremsstrahlung photons generated by nonequilibrium energetic electrons produced during stepping of lightning leaders can deviate from the typical spectrum of relativistic runaway electron avalanches (RREA) developing in weak homogeneous electric fields. This deviation is especially pronounced in the high-energy tail of the electron energy distribution for lightning leaders possessing high voltages (several hundreds of megavolts) and extremely high fields around their tips. The photon spectrum obtained accurately reproduces the recently discovered high-energy tail (up to 100 MeV) of terrestrial gamma-ray flashes (TGFs). This analysis provides the first direct evidence that TGFs are produced by lightning and not over large distances in weak thunderstorm electric fields.