Electron density perturbations by electrostatic wavesand their effect on plasma waves in a dusty plasma

Interaction of high-frequency electrostatic waves and a staticelectron density perturbation is considered in a dusty plasmaincluding the effect of dusty charging. The static electrondensity perturbation is created by the low-frequencyponderomotive force in the parameter regime of a dusty plasmawhere the electron Debye length and temperature are much greaterthan the ion Debye length and temperature, respectively. Theelectron momentum damping rate (νe) due to the high-frequencycharging process of the dust grains can be much greateror much smaller than the electron plasma frequency or wavefrequency (ω) under consideration, depending upon theparameters of the dusty plasma.When ω>>νe, the nonlinear high-frequency wave coupledwith the electron density perturbation is described by anonlinear Schrödinger equation, which bears a modulationallyunstable envelope. When ω<<νe, the high-frequencyelectrostatic wave reduces to a dust charge relaxation mode andthe coupled nonlinear wave equation yields a solution of envelopeshocks.