The criterion for infinite gamma feedback in the Dwyer model

Avalanches of runaway electrons accelerated by an electric field in thunderclouds are one of the sources of Terrestrial Gamma-ray Frlashes (TGF). However, electrons produced in the avalanche process are not enough to describe TGF, which experimentally observed from space. Joseph Dwyer proposed a feedback model that increases the number of particles in avalanches. One of the key mechanisms in the Dwyer model is the gamma feedback, the contribution of which increases with the electric field strength. Gamma feedback is based on the phenomenon of reversal of photons of bremsstrahlung, which is formed during the acceleration of electrons in the cloud field. These photons can give new electrons at the beginning of the avalanche formation region, which leads to the formation of secondary avalanches. In this work, a criterion for the formation of infinite feedback due to the reversal of bremsstrahlung gamma quanta was derived.