A theory of discrete VLF emissions from the magnetosphere


  • R. A. Helliwell


Some of the spectral forms (e.g. ‘inverted’ hook) of discrete VLF emissions are not explained satisfactorily by present theories of generation based simply on gyroresonance between energetic streaming electrons and whistler-mode waves traveling in the opposite direction. An extension of the gyroresonance idea is proposed in which the spatial variations of the electron gyrofrequency and the Doppler-shifted wave frequency are matched. The coupling time between a resonant electron and the wave is then maximized, and hence the output wave intensity is maximized. Application of this condition leads directly to an expression for the time rate of change of emission frequency in terms of the location of the interaction region. An approximate analysis of the postulated interaction process leads to a theorem that states: The magnetic field intensity is limited to a value less than that at which the bunching time approximately equals the resonance time. When the input particle flux exceeds the value required to account for this limiting value of wave intensity, the interaction region drifts downstream. If the interaction begins on the falling-tone or ‘upstream’ side of the equator, positive drift carries the interaction across the equator into the rising-tone region, giving rise to the well known ‘hook’ shape. Reversal of the drift, resulting from wave damping or other factors, carries the interaction back across the equator, giving rise to the inverted hook, a shape not explained by previous theories. Combinations of positive and negative drifts can explain the principal emission forms. The triggering delay and offset frequency of artificially triggered discrete VLF emissions can be explained by the theory.