Self Consistent Modeling of Relativistic Runaway Electron Beams Giving Rise to Terrestrial Gamma-Rays Flashes

Terrestrial Gamma Ray Flashes (TGFs) are short bursts of gamma rays occurring during thunderstorms. They are believed to be produced by Relativistic Runaway Electron Avalanches (RREAs). In this paper, we present a new numerical model based on the Particle-In-Cell (PIC) method to simulate the interactions between the electromagnetic fields and the electron avalanche self-consistently. The code uses a cylindrical Yee lattice to numerically solve the electromagnetic fields, a Monte Carlo approach to simulate collisions with air molecules, and a plasma fluid model to calculate the effects of low-energy electrons and ions. The model is first tested through the reproduction of dispersion relations in a hot plasma. RREAs propagating under a homogeneous background electric field are then simulated. Owing to the self-consistent nature of this description, we report here new physical properties such as saturation processes in the electron density and in the number of high-energy electrons, detailed dynamical screening of the electric field in the ion trail of the avalanche, and the associated electric currents. We find that the saturation of RREAs is obtained when the numbers of high-energy electrons and photons is consistent with those believed to be representative of TGF sources. Development of a self-consistent model coupling a Monte Carlo code with an electromagnetic particle-in-cell code to simulate Relativistic Runaway Electron Avalanches (RREAs) We identify a saturation phenomenon of the RREA, constraining the maximum number of high-energy electrons and photons in terrestrial gamma-ray flashes Once saturation is reached, the electric field is partially screened, preventing the subsequently injected electrons from accelerating