Abstract
The runaway electron mechanism is of great importance for the understanding of the generation of x- and gamma rays in atmospheric discharges. In 1991, terrestrial gamma-ray flashes (TGFs) were discovered by the Compton Gamma-Ray Observatory. Those emissions are bremsstrahlung from high energy electrons that run away in electric fields associated with thunderstorms. In this paper, we discuss the runaway threshold definition with a particular interest in the influence of the angular scattering for electron energy close to the threshold. In order to understand the mechanism of runaway, we compare the outcome of different Fokker–Planck and Monte Carlo models with increasing complexity in the description of the scattering. The results show that the inclusion of the stochastic nature of collisions smooths the probability to run away around the threshold. Furthermore, we observe that a significant number of electrons diffuse out of the runaway regime when we take into account the diffusion in angle due to the scattering. Those results suggest using a runaway threshold energy based on the Fokker–Planck model assuming the angular equilibrium that is 1.6 to 1.8 times higher than the one proposed by [, ], depending on the magnitude of the ambient electric field. The threshold also is found to be 5 to 26 times higher than the one assuming forward scattering. We give a fitted formula for the threshold field valid over a large range of electric fields. Furthermore, we have shown that the assumption of forward scattering is not valid below 1 MeV where the runaway threshold usually is defined. These results are important for the thermal runaway and the runaway electron avalanche discharge mechanisms suggested to participate in the TGF generation.
Highlights
In 1991, terrestrial gamma-ray flashes (TGFs) were discovered by the Compton Gamma-Ray Observatory. Those emissions are bremsstrahlung from high energy electrons that run away in electric fields associated with thunderstorms
These results are important for the thermal runaway and the runaway electron avalanche discharge mechanisms suggested to participate in the TGF generation
The two most accepted theories to justify TGF observations are the acceleration of cold electrons in the high field surrounding leaders [13,14,15,16,17,18,19,20] and the relativistic feedback mechanism enhancing the flow of electrons in relativistic runaway electron avalanches (RREAs) associated with the storm electric field [21, 22]
Summary
Modeling associated with TGFs and RREA has started with the works of [23,24,25,26] mostly looking at the generation of RREA from cosmic rays using a Fokker–Planck approach to solve the evolution of relativistic electrons. Carlo model in N2 and He, they have defined a stochastic runaway threshold ε sto th for large electric fields higher than the one corresponding to the maximum of the friction force, and they give the rate of the runaway electron in the absence of ionization These authors took into account the influence of the angular scattering of electrons. We investigate the influence of the angular scattering of electrons in air on the definition of the runaway energy threshold for a large range of electric fields from 0.3 to 15Ek with Fokker–Planck and Monte Carlo models
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