Instabilities in magnetized inhomogeneous dusty plasmas with the effect of recombination

Abstract

An analytical formalism to understand the impact of various parameters on evolving instabilities in inhomogeneous collisional dusty plasmas is presented here under the effect of recombination. The basic fluid dynamics for electrons and singly charged cold ions is carried out including recombination and collision at constant rate at the surface of dust particles. Dust particles are considered to be static with unperturbed density. Normal mode analysis method has been used along with linear approximation to get perturbed densities (n i1, n e1) which are used along with quasi-neutrality condition to get perturbed potential (φ1), using Poisson’s equation to obtain dispersion relation. While other authors have detected instabilities in unmagnetized plasmas, here this method has been successfully realized in presence of static magnetic field at various propagation angle and allowed the straightforward calculation of growth rates of observed instability. An extensive study of the unstable modes has been done which are well discriminated and plotted with respect to different plasma parameters like dust charge, dust density, propagation angle, magnetic field, electrostatic potential along with plasma oscillation wavelength to Debye wavelength ratio. We have observed in the said model that the presence of dust particles and propagation angle of applied magnetic field are affecting significantly the growth rate of instability as compared to magnetic field and recombination.