Modulation instability of ion-acoustic waves in a multi-ion plasma

A nonlinear Schrödinger equation for ion-acoustic waves in a collision-free plasma, consisting of a mixture of two cold ion species and hot isothermal electrons is derived using the KBM method. It is used to discuss the modulation instability in which the effect of the light-on concentration is analysed. We find that the unstable region depends sensitively upon the fraction of light-ion concentration (α) and the ion-mass ratio. An approximate relation for α_critical is derived for a given ion species in terms of the ion-mass ratio, which governs the minimum wave number, below which the carrier wave is stable against the modulational instability.