Quantization of plasma density irregularities under the action of a powerful electromagnetic wave: spectrum of upper hybrid oscillations self consistently trapped in the density cavities

A theoretical model of the self localization of upper hybrid (UH) oscillations in plasma density depletions, due to thermal nonlinearities driven by a homogeneous and monochromatic pump electric field is presented. The Bohr-Sommerfeld condition for the trapped UH oscillations demands that the parameters of the density cavity are quantized. The depth and square of the width of the depletion across the magnetic field is proportional to an integer. For a parabolically shaped cavity, the cavity depth is proportional to the square of the width. The characteristic relative value of the density minimum is a few percents and the width is of the order of one meter, for the pump wave amplitudes used in ionospheric F-region experiments. We consider also the parametric decay of the primary localized UH oscillations trapped in the quantized plasma density depletions into secondary UH oscillations and lower hybrid waves. We have calculated the spectrum of the nonlinear stabilized secondary UH oscillations, which are also trapped self consistently in the same density cavity. The spectrum of the UH oscillations is consistent with the observed spectrum of the downshifted (DM) and upshifted (UM) maximum in stimulated electromagnetic emissions (SEE).