Geomagnetic Deviation of Relativistic Electron Beams Producing Terrestrial Gamma Ray Flashes

Abstract

In this work, we investigate the effect of the geomagnetic field on terrestrial gamma ray flashes (TGFs). Although this effect should be relatively weak for a single event, for example compared to the effect of the electric field orientation in the source region, it must be systematically present. Indeed, we show that a statistically significant excess of TGFs is detected to the east of their presumed lightning source by Fermi-Gamma-ray Burst Monitor (GBM). The corresponding eastward deviation is found to be likely greater than 0.1°in longitude, which is consistent with the expected effect of the geomagnetic field on relativistic runaway electron beams producing TGFs. Using analytical and numerical means, we show that the geomagnetic deviation can be used to estimate the magnitude of the electric field in TGF source regions. The electric field magnitudes we obtain are consistent with those necessary to drive relativistic runaway electron avalanches (RREAs).

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

“…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.…”

“…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: $$${n}_{e}^{\mathit{sat}}=\frac{{\varepsilon }_{0}}{{q}_{e}{\mu }_{e}{\nu }_{\mathit{RREA}}}\simeq 1{0}^{15}{\mathrm{m}}^{-3}\quad ;\quad {\nu }_{\mathit{RREA}}^{-1}=5.16\times 1{0}^{-7}\mathrm{s}$$$ where q e is the electron charge, μ e is the electron mobility, and ν RREA is the runaway electron production frequency. Figure 2 clearly shows that the quenching of the electric field is indeed rapidly observed for n e > 10 14 m −3 .…”

“…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).…”

“…The model is based on the one presented in Gourbin and Celestin (2023b). It is a self‐consistent, relativistic, hybrid model using both a Monte Carlo method and an electromagnetic particle‐in‐cell method coupled with a fluid model solving drift‐diffusion equations of low‐energy charged species to simulate RREAs accurately.…”

“…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.…”