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The criterion for infinite positron feedback in dynamics of relativistic runaway electron avalanches

Relativistic runaway electron avalanches (RREA) accelerated by thunderstorm large-scale electric fields are one of the sources of atmospheric gamma radiation. In strong electric fields, RREAs can multiply by the relativistic feedback. Infinite relativistic feedback makes avalanches self-sustainable and hypothetically can cause a terrestrial gamma-ray flash (TGF). This paper introduces a kinetic approach to study the relativistic feedback caused by positrons since positron feedback dominates for the directly observed electric field strengths. With this approach, the criterion for infinite positron feedback within thunderstorms is derived. Discovered criterion allows obtaining the thunderstorm electric field parameters required for infinite positron feedback for any altitude. The possibility of derived thunderstorm conditions is discussed.