The spatial distribution of electron precipitation induced by VLF signals from ground‐based transmitters is determined by using a test particle computer model of the gyroresonant wave‐particle interaction (Inan et al., 1982). The results are presented as contours of energy flux on a map of the region around each transmitter. It is shown that the size of the precipitation zones is a strong function of the geographic location of the transmitter, as well as its radiated power and operating frequency. In general, the precipitation zones are much wider in longitude than in latitude and are oriented along lines of constant geomagnetic latitude. Assuming backscatter and/or wave echoing, precipitation zones around the points that are magnetically conjugate to the sources are also estimated. The results presented can be used to interpret satellite‐ or ground‐based measurements of the precipitation induced by ground‐based VLF transmitters.

No abstract

An extension of a previous test par-how to control and precipitate the energetic particle simulation model (Inan et al., 1978) of the ticles by injected waves. These experiments and gyroresonance wave-particle interaction in the others have been highly successful in identifying magnetosphere is used to compute the detailed the complex response of the magnetosphere to the time variation of the precipitated energy flux injection of coherent VLF signals [Helliwell, induced by monochormatic short-duration VLF waves. 1974; Carpenter and Miller, 1976; Inan et at., The resulting precipitation pulse is found to have 1977; Helliwell, 1977; Raghuram et al., 1977; a characteristic shape dependent on the L value, Helliwell and Katsufrakis, 1978; Dowden et al., cold plasma density, wave frequency, and duration, 1978; Chang and Helliwell, 1979; Helliwell et al., as well as the energetic particle distribution function. The role of these variables in determining the temporal variation and the magnitude of the precipitated flux is discussed for a wide range of typical magnetospheric parameters. As an example, a 400-m s wave pulse with a frequency of 6.825 kHz (equatorial half-gyrofrequency) at L = 4 and for a cold plasma density of 400 el/cc produces a 3.5-s long precipitation pulse as observed at 1000 km, with the flux reaching its peak value at approximately 3.8 s after the injection of the wave at the same point. Our findings indicate that if the predicted temporal variations can be observed, the results may be used to diagnose some of the details of the energetic particle distribution in the magnetosphere. The magnitude of the precipitated flux is a function of the trapped particle distribution. For example, for typical trapped electron distribution interacting with a 5 kHz wave of 1 pT intensity at L = 4 the peak p•recipitated energy flux is found to be 5 x 10-ergs/cm 2 s. The predicted fluxes for typical parameters are 102-103 times larger than typical background precipitation levels at these latitudes and would be detectable with presently available instruments.

The temporal and spectral shape and the absolute flux level of particle pulses precipitated by a VLF transmitter are examined from a theoretical point of view. A test‐particle model of the gyroresonant wave‐particle interaction is applied to the parameters of the observed cases for calculating the precipitation characteristics. The temporal shapes of the precipitation pulses are found to be controlled (1) by the pitch angle dependence of the particle distribution near the edge of the loss cone and (2) by the multiple interaction of the particles with the waves due to significant atmospheric backscatter.

Precipitation of radiation belt particles induced by whistlers that are generated by atmospheric lightning discharges and propagate over L shells of 2–4.5 is considered. Using a test particle model of the whistler‐particle interaction, the energy spectra and temporal profile of whistler‐induced fluxes as a function of L shell are quantitatively determined for a representative plasmaspheric cold plasma distribution. Results indicate that for higher energy electron precipitation (E > 40 keV) there exists an inner magnetospheric region (2 < L < 3) where the level of whistler‐induced precipitation can be expected to be comparatively high. Implications of this finding in terms of observational results are discussed.