Coherent Suppression of Molecular Bremsstrahlung Radiation at GHz Frequencies in the Ionization Trail of Extensive Air Showers

Several attempts to detect extensive air showers (EAS) induced by ultrahigh-energy cosmic rays have been conducted in the last decade based on the molecular Bremsstrahlung radiation (MBR) at GHz frequencies from quasi-elastic collisions of ionisation electrons left in the atmosphere after the passage of the cascade of particles. These attempts have led to the detection of a handful of signals only, all of them forward-directed along the shower axis and hence suggestive of originating from geomagnetic and Askaryan emissions extending into GHz frequencies close to the Cherenkov angle. In this paper, the lack of detection of events is explained by the coherent suppression of the MBR in frequency ranges below the collision rate due to the destructive interferences impacting the emission amplitude of photons between the successive collisions of the electrons. The spectral intensity at the ground level is shown to be several orders of magnitude below the sensitivity of experimental setups. In particular, the spectral intensity at 10~km from the shower core for a vertical shower induced by a proton of $10^{17.5}$ eV is 7-to-8 orders of magnitude below the reference value anticipated from a scaling law converting a laboratory measurement to EAS expectations. Consequently, the MBR cannot be seen as the basis of a new detection technique of EAS for the next decades.