Energy-Momentum Diffusion Effects on Energy Spectra of Relativistic Runaway Electron Avalanches in Air

Abstract:

Simple kinetic equations for runaway electrons inside the high electric field regions of thunderstorms have been developed. These equations are useful in modeling the energy distribution of energetic electrons responsible for Terrestrial Gamma-ray Flashes (TGFs). To describe the shapes of the electron energy spectra for a wide range of electric field strengths, the diffusion term responsible for random deviation of electron energy ionization loss from the mean value is added to the kinetic equation. Previous work has shown that the runaway electron energy spectrum can be described by a power-law when the electric field strength is just above threshold. However, the runaway electron spectrum only approaches tens of MeV before being cut off by energy losses from bremsstrahlung emissions, and thus does not offer an explanation of the photon spectrum observed by the AGILE satellite [Tavani et al., 2011]. We find that the diffusion in energy space helps maintain an exponential energy spectrum for electric fields that approach the runaway electron threshold field and allows the possibility for electrons to be accelerated to energies exceeding the electrostatic potential (minus the average drag force) inside the thundercloud. Since this diffusion process depends on the applied electric field strength, we may also gain insight into the typical values that would be found inside thunderclouds. In this presentation, we first show the effects of diffusion on the relativistic runaway electron energy spectrum for several values of the electric field strength. We then demonstrate an analytical method for solving the momentum diffusion-convection transport equation for relativistic runaway electrons. Finally, we will compare the results of this method to our Monte Carlo simulation developed at Florida Institute of Technology [Dwyer, 2003, 2004, 2007]. Using these detailed simulation results, the diffusion coefficients in momentum space for relativistic runaway electron avalanches in air are found for the range of electric field strengths applicable to thunderstorm environments.