Saturation effects in VLF triggered emissions

The phenomenon of artificially triggered VLF emissions was first reported in 1964. Caused by a plasma instability in the Earth's radiations belts, VLF triggered emissions occur when an externally imposed VLF wave, propagating through the magnetosphere in the whistler mode, engages in a cyclotron resonance interaction with energetic electrons trapped in the Earth's magnetic field. Salient characteristics of VLF triggered emissions include exponential temporal growth of the triggering wave and generation of free-running plasma emissions, whose frequency can differ significantly from that of the input signal. The explanation of this phenomenon has proven to be analytically intractable, primarily due to its nonlinear nature and the complicating inhomogeneity of the Earth's magnetic field. This study focuses specifically on the saturation characteristic of the phenomenon, that is, the phase of the instability associated with the termination of exponential growth. From the analysis of data from the Siple Station, Antarctica, VLF wave injection experiment recorded in 1986, three characteristics of the instability have been related to saturation: (1) Long-period oscillations, characterized by a cycle of exponential growth of the input wave to saturation, followed by suppression of the input wave, then followed by renewed exponential growth, (2) Short-period oscillations, previously associated with sidebands, and (3) Generation of incoherent off-frequency wave energy. Exploration of this instability requires the use of a numerical simulation. To that end, a simple model is developed from first-principle considerations and applied to the problem. Given realistic inputs, the model reproduces the observed characteristics of the instability during the growth and saturation phases. An analysis of the modeling results reveals that the nonlinear effects of the instability are driven by wave amplitude gradients, specifically those gradients that reflect a transition from a condition where the wave can trap electrons in its potential well in the presence of the magnetic inhomogeneity, to a condition where such trapping cannot occur