Parametric interaction of electrostatic waves in a dusty plasma

The nonlinear coupling of a low-frequency electron quasi-mode and a high fr equency electrostatic wave through a high-frequency electromagnetic pump is considered in a dusty plasma, which includes the effect of dust charging. The electron quasi-mode occurs in a dusty plasma whose electron Debye lengt h and electron temperature are much greater than, respectively, the ion Deb ye length and the ion temperature. The nonlinear dispersion relation has a structure that is much simpler than the nonlinear dispersion relation for t he parametric instability in dust-free plasmas. Only a purely growing insta bility can be excited, and the threshold and growth rate are obtained.