Electron energy spectrum and structure deduced from analysis of VLF discrete emissions by using the Helliwell criterion

Helliwell's [1967] theory of VLF discrete emissions is based on cyclotron resonance between energetic streaming electrons and waves in a localized interaction region near the equator. Maximum wave-electron coupling requires that the emission frequency change at a rate determined by the position, relative to the equator, of the interaction region. In general the interaction region drifts along the field line; the drift velocity is determined by equilibrium between the input electron flux and the output radiation. This criterion is used in this paper to derive a method to determine the electron stream properties from ground-observed VLF emission spectrograms. This method is applied to the analysis of 75 discrete emissions from a single 3-hour event. Over the range of resonant longitudinal energies scanned by the emissions, 6–60 kev, the average energy spectrum was of the form E−2.2, in general agreement with satellite measurements in the same region (L=3.3). The relative stream density, as deduced for this energy spectrum, showed spikes similar to electron microbursts observed in satellites. A further test of Helliwell's requirement for internal consistency, that the interaction drift should never overtake either the emitted wave or the resonant electrons (−υg<υi<υ∥), was performed for about a thousand such υg, υi υ∥ triplets. With four exceptions that were within the probable error, all satisfied this test.