Modulational instability of ion-acoustic waves in electron-positron-ion plasmas

The stability of modulation of ion-acoustic waves in a collisionless electron-positron-ion plasma with warm adiabatic ions is studied. Using the Krylov-Bogoliubov-Mitropolosky (KBM) perturbation technique a nonlinear Schrodinger equation governing the slow modulation of the wave amplitude is derived for the system. It is found that for given set of parameters having finite ion temperature ratio (T (i) /T (e) ) the waves are unstable for the values of k lying in the range k (min)< k < k (max). On increasing the ion temperature ratio (T (i) /T (e) ), it is found that k (min) and k (max), both decreases and product PQ increases. The range of unstable region shifts towards the small wave number k, as temperature ratio (T (i) /T (e) ) increases. The positron concentration and temperature ratio of positron to electron, change the unstable region slightly. As positron concentration increases both k (min) and k (max) for modulational instability increases and maximum value of the product PQ shifts towards the larger value of k.