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Several attempts to detect extensive air showers (EAS) induced by ultra-highenergy cosmic rays have been conducted in the last decade based on themolecular Bremsstrahlung radiation (MBR) at GHz frequencies from quasi-elasticcollisions of ionisation electrons left in the atmosphere after the passage ofthe cascade of particles. These attempts have led to the detection of a handfulof signals only, all of them forward-directed along the shower axis and hencesuggestive of originating from geomagnetic and Askaryan emissions extendinginto GHz frequencies close to the Cherenkov angle. In this contribution toARENA2022, the lack of detection of events is explained by the coherentsuppression of the MBR in frequency ranges below the collision rate due to thedestructive interference impacting the emission amplitude of photons betweenthe successive collisions of the electrons. The spectral intensity at theground level is shown to be several orders of magnitude below the sensitivityof experimental setups. Consequently the MBR cannot be seen as the basis of anew detection technique of EAS for the next decades. The formalism developed toget at this conclusion allowed the key role of the two-point correlationfunction of the ionisation electron velocities to be highlighted. This canserve to study the intensity of the re-radiation of these ionization electronssubject to the passage of an incoming coherent wave from a radar transmitter.Some hints on this will be presented.

Radiation of ionization electrons: the key role of their 2-pt function of velocities