Effect of superthermal-trapped (\(\kappa -\beta \)) electrons on the modulational instability of ion-acoustic waves

Abstract

This research work focusses on examining the attributes of ion-acoustic waves (IA waves) in a plasma environment embodying superthermal-trapped electron distributions, characterised by the parameters \(\kappa \) and \(\beta \) representing superthermality and trapping respectively. The study utilises a modified nonlinear Schrödinger equation (m-NLSE) derived using the reductive perturbation method (RPM) to model the dynamics of modulated wave packets in this plasma framework. The study investigates the impact of superthermality (\(\kappa \)) and trapping (\(\beta \)) parameters on the envelopes of IA waves. The research explores the conditions for modulational instability (MI) of IA waves, characterised by the dispersion-nonlinearity product PQ in the m-NLSE. Bright and dark solitons are observed corresponding to different signs of PQ, i.e., \(PQ<0\) and \(PQ>0\) indicating the presence of modulationally unstable and stable regimes, respectively. The cutoff wavenumber \(k_{c}\) at which MI enters increases with decreasing superthermality (increasing \(\kappa \)). Interestingly, \(k_{c}\) is observed to be independent of the trapping parameter (\(\beta \)), suggesting that electron trapping does not significantly influence the onset of MI. Further, the effects of \(\kappa \) and \(\beta \) on the maximum growth rate (\(\Gamma _{\textrm{max}}\)) and the modulational wavenumber (\(K_{\textrm{max}}\)) associated with MI are also investigated.