Theory of parametric instability near the lower-hybrid frequency

The dispersion relation for parametric instabilities near the lower-hybrid frequency is derived and analyzed. It is found that for propagation angles cos2θ(mi/me) <̃ 1 resonant decay into ion acoustic (ion-cyclotron) waves does not occur; rather, decay into nonresonant quasi-ion modes and lower-hybrid waves occurs. The driving mechanism for this instability is shown to be analogous to nonlinear Landau damping in perturbation theory. The large amplitude dispersion relation is analyzed numerically for a number of typical experimental regimes, and growth rates and thresholds are obtained for both the purely growing mode and the newly found quasi-ion modes.