Relativistic runaway electron avalanches (RREAs) are generally accepted as a source of thunderstorms gamma-ray radiation. Avalanches can multiply in the electric field via the relativistic feedback mechanism based on processes with gamma-rays and positrons. This paper shows that a non-uniform electric field geometry can lead to the new RREAs multiplication mechanism - “reactor feedback’, due to the exchange of high-energy particles between different accelerating regions within a thundercloud. A new method for the numerical simulation of RREA dynamics within heterogeneous electric field structures is proposed. The developed analytical description and the numerical simulation enables us to derive necessary conditions for TGF occurrence in the system with the reactor feedback Observable properties of TGFs influenced by the proposed mechanism are discussed.