Modulational instability of ion-acoustic waves in a plasma with negative ions.

Abstract

A nonlinear Schr\"odinger equation that governs the nonlinear interaction of a quasistatic plasma slow response with ion-acoustic waves for a warm-ion, hot-electron plasma composed of positive ions, electrons, and negative ions is derived. It is found that the negative-ion species render these waves unstable in a wave-number (k) range that is perfectly stable in the absence of negative-ion species. It is also found that for a given value of negative-ion concentration \ensuremath{\alpha}, such that 0${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$, there exists an upper bound on k, i.e., ${\mathit{k}}_{\mathit{c}\mathit{h}}$, below which the waves would be modulationally unstable. However, when \ensuremath{\alpha}>${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$, there exists a lower bound on k, ${\mathit{k}}_{\mathit{c}\mathit{l}}$, above which the waves are modulationally unstable. The variation of the wave-number range over which the ion-acoustic wave is unstable with the negative-ion concentration, charge-multiplicity ratio, and relative mass of the two ion species is discussed. The predictions of the theory are found to be in substantial agreement with experimental observations of modulational instability.