Modulational instability of dust acoustic solitary waves for variable-charge dust grains in an ion beam–dusty plasma

Abstract

A theoretical study is presented for the nonlinear self-modulation of low-frequency electrostatic dust acoustic (DA) waves propagating in a dusty plasma exposed to an external ion beam. By employing the derivative expansion perturbation method, a nonlinear Schrödinger equation (NLSE) is derived for the electric potential wave amplitude. Both dispersion and nonlinearity coefficients of the NLSE are explicit functions of the carrier wavenumber and of relevant physical parameters background species density and temperature, and dust charging fluctuation. The modulation instability of the NLSE is investigated. It is found that the presence of the ion beam species reduces the stable domain of the DA waves and the stable DA waves are created at higher wavenumber, k. Increasing ion beam temperature results as an increment of the wave dispersion and nonlinearity and the wave frequency. Also it widens the stability domain of the DA waves. Including the dust charge fluctuations changes drastically the domain where one can find stable DA wave envelopes. A brief conclusion is provided related to the application of the current findings in laboratory plasma experiments.