Ambipolar Diffusion of Cosmic-Ray Muon Ionization Tracks and Their Possible Role in Atmospheric Electrical Breakdown

Cosmic-ray secondary muons continuously traverse the Earth's atmosphere and generate ionization tracks through interactions with atmospheric molecules. In this work, we investigate the transient electrodynamic effects associated with these relativistic particles. Using the Liénard–Wiechert formalism, Bethe–Bloch energy-loss calculations, and an ambipolar diffusion model, we estimate the evolution of muon-induced electron-ion channels and their impact on local atmospheric conductivity. Our results indicate that the direct electromagnetic fields of individual muons are negligible on macroscopic atmospheric scales, whereas their residual ionization tracks can temporarily enhance local conductivity by several orders of magnitude before diffusive decay. We further compare these conductivity enhancements with electric-field conditions relevant to Relativistic Runaway Electron Avalanches (RREA) in thunderstorm environments. The analysis suggests that muon-generated ionization channels may provide localized seed electrons and transient conductive pathways, potentially contributing to atmospheric discharge processes under strong pre-existing electric fields.