Modulational instability of ion-acoustic waves in multicomponent plasma using \(\kappa \)-deformed Kaniadakis distribution

The present investigation focusses on studying the modulational instability of ion-acoustic waves in a multicomponent plasma system comprising positive ions, negative ions and electrons. The electron component is described by the \(\kappa \) $\kappa$ -deformed Kaniadakis distribution, with the deformation parameter \(\kappa \) $\kappa$ ranging from \(-\) $-$  0.4 to 0.4. Using the standard perturbation method, the dispersion relation is derived from the governing equations. It is found that the dispersion relation is independent of \(\kappa \) $\kappa$ but depends on other factors, such as the density ratio ( \(\alpha \) $\alpha$ ), mass ratio ( \(\eta \) $\eta$ ) and ion temperatures ( \(\sigma _{\pm }\) ${\sigma }_{\pm }$ ). Two distinct ion-acoustic modes, namely the slow mode and the fast mode, are analysed in detail based on the phase velocity. The nonlinear Schrödinger equation is derived from the governing equations, whose dispersion and nonlinearity coefficients significantly impact the stability characteristics of ion-acoustic waves. Three plasma systems, namely H \(^{+}\) ${}^{+}$ H \(^{-}\) ${}^{-}$ , Ar \(^{+}\) ${}^{+}$ F \(^{-}\) ${}^{-}$ and H \(^{+}\) ${}^{+}$ O \(_2^{-}\) ${}_2^{-}$ , which exist in the D-region of the atmosphere, are considered in this study. A comprehensive analysis is conducted for both slow and fast modes, taking into account the influence of the deformation parameter \(\kappa \) $\kappa$ , mass ratios and ion temperatures. This investigation is relevant for understanding the behaviour of ion-acoustic waves in space and laboratory plasmas where multiple ion species coexist.