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Terrestrial gamma-ray flashes (TGFs) are commonly associated withrelativistic runaway electron avalanches (RREAs). However, research shows thata single RREA cannot generate observable TGF fluxes. In an attempt to settlethis issue the relativistic feedback mechanism was suggested by Joseph Dwyer.The Monte Carlo simulations and analytical descriptions of this type offeedback assume that acceleration region has a large size in a planeperpendicular to the direction of the electric field. Therefore these studiesdo not take into account transverse diffusion of RREAs starting points and thefinite transverse size of the accelerating region. Electrons created by thefeedback outside this region can not be accelerated by the electric field andform an avalanche, which may lead to a decrease in the total number of newavalanches and an increase in the requirements for self-sustaining RREAproduction by the feedback. In this article the transverse propagation ofavalanches starting points was described using a modified two-dimensionaldiffusion equation. A correction to the criterion for self-sustainingproduction of RREAs was obtained. Monte Carlo simulation was also performed tocalculate the correction for the feedback coefficient.

Influence of the finite transverse size of the accelerating region on the relativistic feedback