## Relativistic Runaway Electron Avalanches Inside the High Field Regions of Thunderclouds

##### Abstract

In this dissertation, simplified equations describing the transport and energy spectrum of runaway electrons are derived from the basic kinematics of the continuity
equations. These equations are useful in modeling the energy distribution of energetic electrons in strong electric fields, such as those found inside thunderstorms.
Dwyer and Babich [2011] investigated the generation of low-energy electrons in
relativistic runaway electron avalanches. The paper also developed simple analytical expressions to describe the detailed physics of Monte Carlo simulations of
relativistic runaway electrons in air. In this work, the energy spectra of the runaway electron population are studied in detail. Dependence of electron avalanche
development on properties such as the avalanche length, radiation length, and the
effective Møller scattering efficiency factor, are discussed in detail. To describe the
shapes of the electron energy spectra for a wide range of electric field strengths,
the random deviation of electron energy loss from the mean value is added to the
solutions. We find that this effect helps maintain an exponential energy spectrum
for electric fields that approach the runaway electron threshold field.
We also investigate the source mechanisms of Terrestrial Gamma-ray Flashes,
which are a result of relativistic runaway electron avalanches in air. In this study,
the bremsstrahlung photons are propagated through the atmosphere, where they
undergo Compton scattering, pair production, and photoelectric absorption. We
model these interactions with a Monte Carlo simulation from the TGF source location (assumed to vary between 8 and 20 km) and the edge of the atmosphere
(≈ 100 km). We then propagate these photons to a satellite plane at 568 km in
order to compare with measurements. In collaboration with the GBM instrument
team in Huntsville, AL, we were able to model spectral and temporal properties
of observed TGFs. Although the analysis of individual TGF photon spectra was
qualitative, we were able to put some constraints, i.e. source altitude and beaming
angle, on a sample of observed GBM TGFs. However, assuming a height of 15
km, we were able to model the softening in the spectrum observed as the satellite moves off-axis from the TGF source location [Fitzpatrick et al., 2014]. The
conclusion of this analysis shows that Compton scattering alone can not explain
the temporal dispersion observed. This suggests that an intrinsic time variation
exists at the source of the TGF.