Plasma with two-negative ions and immobile dust particles: planar and non-planar ion-acoustic wave propagation

Abstract

By using the hydrodynamic equations of positive and two negative ions, Boltzmann electron density distribution, and Poisson equation with immobile positive/negative dust particles, a cylindrical Korteweg-de Vries (CKdV) equation is derived for small but finite amplitude ion-acoustic waves. At the critical total negative ion concentration and/or the critical density rate of the second-negative ions, the pulses collapse at this limit as nonlinearity fails to balance dispersion. Then the CKdV equation is not appropriate to describe the system. Therefore, the modified CKdV (MCKdV) and extended CKdV (ECKdV) equations are derived at the critical plasma compositions and in the vicinity of the critical plasma compositions, respectively. The physical parameters of two plasma environments (e.g., Xe+–F-–SF\(_{6}^{-}\) and Ar+–F-–SF\(_{6}^{-}\) plasmas) are examined on the wave phase velocity and the nonlinear localized pulse profile. The latter should satisfy necessary condition to exist. The localized pulse of Ar+–F-–SF\(_{6}^{-}\) plasma is much spiky than Xe+–F-–SF\(_{6}^{-}\) plasma. Thus, the mass ratio of the negative-to-positive ions is focused upon and it emphasizes to play an important role on the pulse profile. Dependence of the geometrical divergence on the pulse profile is also investigated, which indicates that the localized pulse damps with time. The implications of our results agrees with the experimental observations.