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

Abstract

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.

On the Self‐Quenching of Relativistic Runaway Electron Avalanches Producing Terrestrial Gamma Ray Flashes

“…Electrons still propagate over about one hundred meters before losing all their energy and eventually stop. We can also notice in this run a saturation of the low-energy (<1 keV) electron density as highlighted in Gourbin and Celestin (2023b), as well as a backward propagating field structure also discussed in the same article. This structure can be better seen in Figure 2, where the various runs stopped at different stages regarding the RREA saturation state: the cases with an injection rate below 2.94 × 10 17 electrons per second do not reach saturation before the end of the acceleration zone.…”

“…The maximum For the cases with the three highest injection rates, we see that the number of high-energy electrons stabilizes before the other cases, that is, before reaching the end of the acceleration zone. This stabilization is caused by the mechanism of saturation (Gourbin & Celestin, 2023b) and the associated collapse of the electric field, which constrains the number of electrons. An interesting feature is that, for these three cases, the number of high-energy electrons all lie between 10 17 and 10 18 , while the non-saturated cases all reached different magnitudes at the end of the simulations proportionally to the injection rate.…”

“…As a result of the flux of runaway electrons, the ion density increases linearly in time because ion recombination processes occur over a much longer timescale (see discussion in Berge et al (2022), Section 2.1). Gourbin and Celestin (2023b) showed that the electron saturation density caused by self-consistent effects occurs when the density is high enough so that the associated relaxation time is equaling the RREA characteristic growth time:…”

“…It is valid in subcritical conditions (electron density lower than saturation density) and simply comes from the assumption that the TGF quenches itself over a duration equal to the dielectric relaxation timescale caused by the production of secondary electrons. It is presumably the reason why previous works using self-consistent calculations have obtained a consistent number of TGF photons despite significant differences in the configurations, parameters, and methods employed (e.g., Dwyer, 2012;Gourbin & Celestin, 2023b;Liu & Dwyer, 2013).…”

“…In Gourbin and Celestin (2023b), we have reported the existence of a saturation of the low-energy electron density when the corresponding dielectric relaxation time (Maxwell time) becomes equal to the RREA characteristic time. This saturation was accompanied with a stabilization in the number of high-energy electrons and photons, suspiciously between 10 17 and 10 19 after a significant exponential growth in the RREA.…”