Effect of finite ion temperature on modulational instability of ion-acoustic waves

A nonlinear Schrödinger equation for ion-acoustic waves in a collision free plasma, consisting of warm ions and hot isothermal electrons is derived using the KBM method. It is found that for finite ion temperature these waves are modulationally unstable only in a range of wave numbers. As the ratio of ion to electron temperature increases, the range of the unstable region decreases and shifts towards small wave numbers.