Relativistic Runaway Electron Avalanche Development Near the Electric Field Threshold in Inhomogeneous Air

Relativistic Runaway Electrons Avalanches (RREAs) development depends on the applied electric field and the environment's air density. This dependency controls the RREA exponential growth length scale. The RREA development affects the bremsstrahlung excess occurring due to the passage of charged particles through the thundercloud's electric fields, the gamma-ray glow. We used Monte Carlo simulations to develop an empirical model showing the RREA behavior in a realistic atmospheric density profile. The new formulation shows how the density variation modulates the electron population under electric field strengths near the RREA electric field threshold. The model limits the initial RREA altitude range as a function of the electric field strength. The new model is valid between similar to 0.6 and similar to 18 km, covering the relevant heights to investigate the generation of ground-detected gamma-ray glows. Thunderclouds are energy sources for trespassing charged particles from cosmic rays. This extra energy gain may induce electron avalanches, known as Relativistic Runaway Electron Avalanches (RREAs), resulting in an enhanced gamma-ray flux via bremsstrahlung, the gamma-ray glow. Recent studies relate this enhancement to electric field strengths close to the RREA requirement. The atmospheric density variations affect avalanche development by modifying the RREA requirement, resulting in isolated avalanches by imposing limits to the avalanche's initial altitude. We show how RREAs develop in a realistic atmospheric density profile. We present a modification on the characteristic avalanche length under this condition. The initial avalanche altitude is crucial because it completely modifies the density profile trespassed by a downward electron shower. Finally, we discuss the consequences of isolated RREAs for high-energy emissions and show that the electric field strength constrains the possible initial altitudes for the gamma-ray glow. A new empirical model quantifies how electron avalanches vanish because of atmospheric density variations with similar to 10% accuracyThe model limits the initial altitude of electron avalanche development for electric field strengths near the avalanche thresholdWe narrow the possible gamma-ray glow source height range with the new model which is valid through similar to 0.6-18 km