Whistler emissions produced by modulated electron beams injected into the ionosphere

Abstract

The electric and magnetic fields emitted by semi‐infinite, modulated electron beams artificially injected into the Earth ionosphere are calculated. For whistler mode waves recorded by a remote VLF receiver the spectrum of the signal depends crucially on the time from the beginning of the injection. The amplitude of a transient signal from the beam front is controlled by the difference between the modulation frequency and the frequency determined from the stationary phase point in the corresponding integral (the latter varies with time due to the beam front motion). Far from the beam front, only the forced oscillations due to the modulation of the beam density will be registered. The intrinsic frequency width of the whistler signal δf connected with the ray representation of a wave field determines the optimal frequency bandwidth of the receiver in use. The value of δf ∼ (1/R)1/2 (R is the transverse distance between the beam axis and the receiver) also determines the beam domain, ∼ R1/2 along its axis which gives the main contribution to the registered signal (Fresnel zone). The interference of waves emitted by electrons with different parallel velocities u can reduce the amplitude of the registered wave field significantly. This problem is discussed in connection with the existence of a stationary phase point (SPP) over u. It is shown that this SPP condition can be satisfied only for the wave packets emitted in the near zone of the electron gun. The amplitudes of the coherent and incoherent beam emissions are compared. In the case of a dense plasma (where the plasma frequency ωp is much greater than the electron gyrofrequency ωc) the main results are obtained analytically.