Parametric instabilities of trapped upper-hybrid oscillations

Parametric instabilities of upper-hybrid oscillations trapped in a plasma density depletion across an ambient magnetic field are investigated. Approximate dispersion relations are derived, which lead to the identification of two parametric instabilities of the localized upper-hybrid bounded wave structure. Both are related to trapped upper-hybrid oscillation resonances. The first is a decay to a frequency of a trapped ware resonance, downshifted from the applied frequency, where the downshift must be slightly larger than the lower-hybrid frequency. The second instability can exist when the applied frequency is slightly below the arithmetic mean of the frequencies of two trapped oscillation resonances; then the antiStokes component of one is in resonance with the Stokes component of the other. Both slab and two-dimensional geometries are considered.