Evaluation of Monte Carlo tools for high-energy atmospheric physics II: Relativistic runaway electron avalanches

This work is distributed underthe Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/)The emerging field of high-energy atmospheric physics studies how high-energy particles are produced in thunderstorms, in the form of terrestrial γ-ray flashes and γ-ray glows (also referred to as thunderstorm ground enhancements). Understanding these phenomena requires appropriate models of the interaction of electrons, positrons and photons with air molecules and electric fields. We investigated the results of three codes used in the community-Geant4, GRanada Relativistic Runaway simulator (GRRR) and Runaway Electron Avalanche Model (REAM)-to simulate relativistic runaway electron avalanches (RREAs). This work continues the study of Rutjes et al. (2016), now also including the effects of uniform electric fields, up to the classical breakdown field, which is about 3.0 MV m at standard temperature and pressure. We first present our theoretical description of the RREA process, which is based on and incremented over previous published works. This analysis confirmed that the avalanche is mainly driven by electric fields and the ionisation and scattering processes determining the minimum energy of electrons that can run away, which was found to be above ≈ 10 keV for any fields up to the classical breakdown field. To investigate this point further, we then evaluated the probability to produce a RREA as a function of the initial electron energy and of the magnitude of the electric field. We found that the stepping methodology in the particle simulation has to be set up very carefully in Geant4. For example, a too-large step size can lead to an avalanche probability reduced by a factor of 10 or to a 40 % overestimation of the average electron energy. When properly set up, both Geant4 models show an overall good agreement (within ≈ 10 %) with REAM and GRRR. Furthermore, the probability that particles below 10 keV accelerate and participate in the high-energy radiation is found to be negligible for electric fields below the classical breakdown value. The added value of accurately tracking low-energy particles (< 10 keV) is minor and mainly visible for fields above 2 MV m. In a second simulation set-up, we compared the physical characteristics of the avalanches produced by the four models: Avalanche (time and length) scales, convergence time to a self-similar state and energy spectra of photons and electrons. The two Geant4 models and REAM showed good agreement on all parameters we tested. GRRR was also found to be consistent with the other codes, except for the electron energy spectra. That is probably because GRRR does not include straggling for the radiative and ionisation energy losses; hence, implementing these two processes is of primary importance to produce accurate RREA spectra. Including precise modelling of the interactions of particles below 10 keV (e.g. by taking into account molecular binding energy of secondary electrons for impact ionisation) also produced only small differences in the recorded spectra. © 2018 Author(s).This work was supported by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 320839 and the Research Council of Norway under contracts 208028/F50 and 223252/F50 (CoE). For part of the results of this work, it was necessary to use the Fram computer cluster of the UNINETT Sigma2 AS, under project no. NN9526K. Gabriel Diniz is supported by the Brazilian agency CAPES. Casper Rutjes acknowledges funding by FOM project no. 12PR3041, which also supported Gabriel Diniz's 12-month stay in the Netherlands. Ivan S. Ferreira thanks CNPqs grant PDE(234529/2014-08) and also FAPDF grant no. 0193.000868/2015, 03/2015. This material is based in part upon work supported by the Air Force Office of Scientific Research under award no. FA9550-16-1-0396. The authors would like to thank the two referees, Ashot Chilingarian and an anonymous referee, for their valuable comments and suggestions that helped to improve the quality of this work