Parametric instabilities due to lower-hybrid radio frequency heating of tokamak plasmas

The linear theory of parametric instabilities relevant to radiofrequency heating near the lower-hybrid frequency of tokamak-type plasmas is presented. The dispersion relations are analyzed numerically to all orders of the ion Larmor radius. The complete range of unstable spectra is obtained for 1<ω0/ωlh<5, for both deuterium and hydrogen plasmas. As the pump wave propagates from the edge of the plasma toward its interior, the transition from resonant decay to decay into quasi-modes is demonstrated. The effects of inhomogeneities upon the threshold for parametric decay, such as density gradients, finite pump width, and magnetic shear, are obtained. The relevance of these results to recent tokamak experiments is discussed briefly.