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 ${\cos }^2{\mathrm{\theta (m}}_i{\mathrm{/m}}_e\text{)\hspace{0.17em}<̃\hspace{0.17em}1}$ 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.