Decay of a lower-hybrid wave to two lower-hybrid waves

The threshold and initial evolution for the decay of a lower-hybrid wave to two lower-hybrid waves are determined. Included are the effects of convective losses in a three-dimensional lower-hybrid resonance cone geometry and the effects of inhomogeneity appropriate to lower-hybrid heating in a tokamak. It is found that the decay to two lower-hybrid waves differs from other such parametric instabilities previously studied in that its instability threshold can have a strong dependence on the minor radius of the tokamak. This is due to the quasi-absolute nature of the instability. While its threshold power is high in small devices, the instability poses a serious threat in reactor size devices.