Saturation of parametric instabilities in lower hybrid heating of tokamak plasmas

A non-linear analysis of parametric instabilities in lower hybrid heating of tokamak plasmas is presented. Harmonic generation of the low frequency mode and its effect on the evolution of the parametric decay of a lower hybrid pump to another lower hybrid wave and a low frequency mode is investigated, and numerical calculations of the relevant wave system are carried out. It is found that the coupling of the low frequency wave to its harmonic may effectively suppress the spatial growth of the primary instability. This may be particularly true at the plasma edge of the tokamak, where electron and ion temperatures are low and the primary instability is strong at high pump intensity. The spectral dependence of the harmonic generation strength is compared with that of the primary instability, and the effect on pump depletion with relevant tokamak parameters is discussed.