Envelope excitations in electronegative plasmas with electrons featuring the Tsallis distribution

Abstract: We examine the modulational instability (MI) of ion-acoustic waves (IAWs) in an electronegative plasma containing positive and negative ions as well as electrons that follow the nonextensive statistics proposed by Tsallis [J. Stat. Phys. 52, 479 (1988)]. Using the reductive perturbation method (RPM), the nonlinear Schr\"{o}dinger equation (NLSE) that governs the modulational instability of the IAWs is obtained. Inspired by the experimental work of Ichiki \emph{et al.} [Phys. Plasmas 8, 4275 (2001)], three types of electronegative plasmas are investigated. The effects of various parameters on the propagation of IAWs are discussed in detail numerically. We find that the plasma supports both bright and dark solutions. The presence of the non-extensively distributed electrons is found to play a crucial role in the formation of envelope excitations. The region in the parameter space where the MI exists depends sensitively on the positive to negative ion mass ratio (M) and negative to positive ion density ratio ($\nu$). An extensive range of the nonextensive $q$-parameters {$(-1<q<3)$} is considered and in each case the MI sets in under different conditions. The finding of this investigation is useful for understanding stable wave propagation of envelope ion-acoustic solitary waves in space and laboratory plasmas comprising ions with both positive and negative charges as well as non-Maxwellian electrons.