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

A nonlinear Schroedinger 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 α, such that 0<α<αc, there exists an upper bound on k, i.e., kch, below which the waves would be modulationally unstable. However, when α>αc, there exists a lower bound on k, kcl, 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