VLF emission produced by a rarefied electron beam during active experiments in the Earth ionosphere: Conditions of observation of the emission

Abstract

The peculiarities of whistler waves spontaneously radiated by an electron beam artificially injected into the Earth ionosphere are discussed. The conditions of registration of the whistler wave packets by a remote on board VLF receiver have been analyzed; they depend on mutual disposition of the electron gun and the VLF receiver as well as on the pitch angle of the injected electrons. It is shown that the internal frequency width of the whistler signal, connected with ray representation of a wave field, depends on the distance between the emitting region of the beam and the receiver and determines the lowest bandwidth of the VLF receiver in use. In the case of a dense plasma (when the plasma frequency ωp is much greater than the electron gyrofrequency ωc) the main results are obtained analytically. The effective value of the electron collision frequency for the background plasma can be estimated through measurements of the maximum value of the injection pitch angle of the beam's electrons, which leads to a steep drop in the level of the whistler signal. It is shown that double‐pole singularity in the single electron Cherenkov energy loss near the Gendrin's velocity appears only at a single frequency depending on the beam and the background plasma parameters. Thus the total growth of the energy loss in this case reveals an increase by a factor of the order of ωp/ωc compared to the usual single‐pole contribution. The Cherenkov radiation from the sharp leading front of the beam does not reveal any Mach cone structure. The peculiarities of the spectral parameters of the whistler emission at the Doppler‐shifted resonances are also discussed; the Mach cone exists in these cases. Thus this feature can be responsible for the crucial difference between the registration pattern of high‐frequency and whistler frequency emission in active experiments similar to ARAKS.