Decay instability at the ion-ion hybrid resonance

The parametric decay of a large amplitude AC field oscillating near the ion-ion hybrid frequency is studied in a homogeneous two ion-species plasma. Two different decay modes are considered: (i) a low frequency ion acoustic wave propagating parallel to the ambient magnetic field and (ii) a 'cold' ion-Bernstein mode propagating almost perpendicular to the magnetic field. A third possibility (of decay into two ion-ion hybrid modes) is also investigated and estimates of threshold powers and growth rates are discussed in each instance