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
wave 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.