Variations of muon flux in the atmosphere during thunderstorms

The variations of muon flux that are occasionally registered by ground-based scintillation detectors during thunderstorms are investigated. The variations are mainly negative (deficit) and originate due to the electric field of thunderclouds. They last from several minutes up to several hours and demonstrate minor (up to a few percent) deviations against the background. We develop an appropriate theoretical model to describe this phenomenon by investigating the two processes responsible for it: (i) the transformation of an energetic spectrum of muons in the electric field due to their acceleration or deceleration, and (ii) the decay of muons conditioned by a short life span. The change of muon flux near the ground is derived at a given altitudinal distribution (profile) of the electric field. Two possible opposite cases of an altitudinal profile of a two-layered electric field are considered: (i) upward directed in the lower layer of the cloud and downward directed in the upper layer and (ii) vice versa. We find that in case (i), the deficit of muon fluxes is observed by the detector at any threshold energy. It emerges due to a decrease of the flux of positive muons decelerated in the lower layer of a thundercloud. The corresponding increase of the flux of accelerated muons turns out to be smaller because of their partial decaying. As a result, an uncompensated decrease of total flux of muons is formed near the ground. However, in case (ii), the deficit is smaller, and it may become positive when it is observed by detectors with a threshold energy larger than ∼300 MeV. The results may help estimate the height and electric field of thunderclouds by analyzing the records of muon detectors with different energy thresholds.