Evaluation of Monte Carlo tools for high-energy atmospheric physics II: relativistic runaway electron avalanches
Authors: Sarria David , Rutjes Casper , Diniz Gabriel , Luque Alejandro , Ihaddadene Kevin M. A. , Dwyer Joseph R. , Østgaard Nikolai , Skeltved Alexander B. , Ferreira Ivan S. , Ebert Ute 
Published: November 2018

Abstract. 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−1 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−1. 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.