A Study of Triggered Emissions

Abstract

In this paper we present a new interpretation of Triggered V.L.F. Emissions (T.E. hereafter). Let us briefly recall the main characteristics of these emissions. Manmade morse pulses, originating in one hemisphere travel along magnetic field lines in the whistler mode and are received in the conjugate hemisphere. These signals can trigger emissions which consist of either rising or falling tones, quasi monochromatic at a given time. They are more likely to be triggered by dashes than by dots, indicating that, at a given amplitude, the duration of the triggering pulse must exceed some threshold in order to trigger an emission. These emissions are more commonly observed when the triggering wave (T.W.) frequency is near one-half of the equatorial gyrofrequency of electrons. A more detailed description can be found in the works of Helliwell (1965) and Stiles and Helliwell (and references therein), 1975. The special features of theses emissions have motivated a large amount of theoretical work (Gendrin, 1974 and references therein). The observed large frequency variations of T.E. are undoubtedly related to the inhomogeneity along field lines. Thus we feel that any work in which the inhomogeneity is deleted cannot provide a complete explanation of the observations. The fact that T.E. are only observed when the triggering wave (T.W.) duration exceeds a threshold (which seems to depend on the T.W. amplitude) indicates the nonlinear character of the process which leads to emissions. Among the possible nonlinear phenomena which could take place, trapping of particles (in the potential troughs of the T.W.) seems to be a promising candidate, since its characteristic time is smaller than that of any other non-linear process. Some authors (Helliwell and Crystal, 1973) argued that stimulated emissions can begin at a level much lower than the one at which trapping can occur. They introduce in their computations twelve sheets of resonating particles and followed their dynamics in a time dependent and spatially homogeneous situation. They found an exponentially growing wave up to a level which does not depend on the amplitude of the input wave. We have carefully looked at their results and concluded that they were studying in fact a classical beam plasma instability. The saturation and subsequent amplitude oscillations that they found are also in agreement with the predictions of the beam-plasma instability theory, namely, saturation of the amplification when the wave has reached a level sufficient to trap all the beam particles. With a realistic smooth distribution function, the results would be very different (see the discussion in the next paragraph). In any case, as long as the T.W. has a low amplitude, its rate of amplification is the same as that of the white noise of the medium. Consequently Helliwell and Crystal should explain why the white noise is not also amplified, by their process, up to an observable level.