Molecular Bremsstrahlung Radiation at GHz Frequencies in Air

A detection technique for ultra-high energy cosmic rays, complementary to the fluorescence technique, would be the use of the molecular Bremsstrahlung radiation emitted by low-energy ionization electrons left after the passage of the showers in the atmosphere. In this article, a detailed estimate of the spectral intensity of photons at ground level originating from this radiation is presented. The spectral intensity expected from the passage of the high-energy electrons of the cascade is also estimated. The absorption of the photons in the plasma of electrons/neutral molecules is shown to be negligible. The obtained spectral intensity is shown to be $2\times10^{-21}$W cm$^{-2}$ GHz$^{-1}$ at 10 km from the shower core for a vertical shower induced by a proton of $10^{17.5}$ eV. In addition, a recent measurement of Bremsstrahlung radiation in air at gigahertz frequencies from a beam of electrons produced at 95 keV by an electron gun is also discussed and reasonably reproduced by the model.