Relativistic runaway electron avalanches: unified density-dependent scaling and transport

Relativistic runaway electron avalanches (RREAs) are commonly characterized by an empirical relation linking the avalanche length to the electric-field excess above the runaway threshold. In this study, CORSIKA simulations are used to examine the behavior of this parameterization under different atmospheric densities and electric-field conditions and to investigate the subsequent propagation of particles beyond the accelerating field region. Simulations are performed for four high-altitude observational sites. The effective avalanche lengths derived from the vertical electron profiles exhibit inter-station scatter when fitted with a single coefficient across the combined dataset. Incorporating an additional density-dependent term reduces this scatter and improves the fit, increasing the coefficient of determination from R ² ≈0.90 to R ² ≈0.99. Simulations of particle propagation beyond the electric-field region show different attenuation behavior for the electron and gamma-ray components. Reassessment of the empirical free path distance (FPD) formulation for a 100 m field-to-detector separation yields an electron–gamma energy coefficient of C ₁ ≈1.37, while the density dependence of electron energy losses is accounted for using stopping-power data from the National Institute of Standards and Technology (NIST) ESTAR (Stopping Powers and Range Tables for Electrons) database.