  Several attempts to detect extensive air showers (EAS) induced by ultra-high
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 contribution to
ARENA2022, 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 interference 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. Consequently the MBR cannot be seen as the basis of a
new detection technique of EAS for the next decades. The formalism developed to
get at this conclusion allowed the key role of the two-point correlation
function of the ionisation electron velocities to be highlighted. This can
serve to study the intensity of the re-radiation of these ionization electrons
subject to the passage of an incoming coherent wave from a radar transmitter.
Some hints on this will be presented.
