Terrestrial Gamma-ray Flashes produced by complex thunderstorm electric structures

One of the possible sources of Terrestrial Gamma-ray Flashes (TGF) is Relativistic Runaway Electron Avalanches (RREA) accelerated in large-scale thunderstorm electric fields. In order to produce short and bright gamma-ray flash, a huge number of RREAs must exist simultaneously. This can be obtained through positive feedback mechanisms in RREA dynamics. At quasi-uniform thunderstorm electric fields, relativistic feedback provides RREAs multiplication via positrons and reversed gamma-rays. A significant disadvantage of relativistic feedback is that it requires high electric field strength in order to produce a TGF.

In complex thunderstorm electric structures, an additional feedback mechanism appears, the reactor feedback. Reactor feedback emerges if a thunderstorm consists of several RREA-producing regions, cells. A RREA developed in a cell radiates bremsstrahlung gamma-rays. Gamma-rays have high penetrative power and propagate through semi-critical electric field regions, where runaway electrons can stop, reaching other cells. There gamma-rays interact with air molecules, producing RREAs. Therefore, cells amplify each other by the gamma-ray exchange. The amplification rate can be strong enough to make RREAs self-sustainable, that is infinite reactor feedback. Infinite reactor feedback requires lower electric field strength compared to infinite relativistic feedback. Moreover, such RREA multiplication can cause a TGF.

In this report, a theoretical technique is developed to describe relativistic runaway electron avalanches dynamics in complex electric structures. Cells' interaction via high-energy particles exchange can be described with the Feedback Matrix, which is a matrix consisting of feedback operators. A feedback matrix action on RREA starting point distribution in i-th feedback generation creates RREAs starting point distribution in the next (i+1)-th generation. Matrix elements depend on thunderstorm electric field parameters and include RREA development physics and gamma-ray propagation physics. Diagonal matrix elements describe the self-action of cells, which is the relativistic feedback. The proposed approach includes all the feedback mechanisms and reduces the problem of avalanche dynamics to finding eigenvalues and eigenfunctions of the feedback matrix, as the eigenvalues are feedback coefficients.

With the feedback matrix solutions for RREA dynamics in different electric field geometries are obtained. Thunderstorm conditions required for TGF development are found. It is shown that the more complex the electric structure is the lower the electric field strength is required to produce a TGF.