Analysis of the Drift Instability Growth Rates in Non-Ideal inhomogeneous Dusty Plasmas

In this paper we introduce an algebraic form of the dispersion relation for a non ideal inhomogeneous dusty plasma in order to improve drastically the calculation of the drift instability growth rate. This method makes use of the multipole approximation of the Z dispersion function, previously published, and valid for the entire range. A careful analysis of the solutions spectra of this kind of polynomial equation permits us to calculate easily the growth rate of the drift instability for the ion-dust and dust acoustic mode. The value of the parallel to magnetic field wavelength for which the instability reaches the maximal value is carefully localized and discussed. The unstable dust-ion and dust acoustic mode are discriminated and analyzed in function of the density gradient, Te/Ti - ratio, and dust grain radius.