Abstract
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 Schrödinger 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.
Highlights
During the last two decades, there has been great deal of interest in the study of linear and nonlinear wave phenomena in electron–positron–ion plasmas
Several authors have derived the nonlinear Schrödinger equation by either using the reductive perturbation method (Ichikawa et al 1972; Shimizu and Ichikawa 1972) or the Krylov–Bogoliubov– Mitropolosky (KBM) method (Kakutani and Sugimoto 1974) and have studied the stability of ion-acoustic waves against modulational instability in a collisional free plasma consisting of cold ions and hot electrons
Using the standard reductive perturbation technique, a nonlinear Schrödinger equation is derived by Ju-Kui et al (2002) to study the modulational instability of finite-amplitude ion-acoustic waves in a non-magnetized warm ion plasma
Summary
During the last two decades, there has been great deal of interest in the study of linear and nonlinear wave phenomena in electron–positron–ion plasmas. Several authors have derived the nonlinear Schrödinger equation by either using the reductive perturbation method (Ichikawa et al 1972; Shimizu and Ichikawa 1972) or the KBM method (Kakutani and Sugimoto 1974) and have studied the stability of ion-acoustic waves against modulational instability in a collisional free plasma consisting of cold ions and hot electrons. Using the standard reductive perturbation technique, a nonlinear Schrödinger equation is derived by Ju-Kui et al (2002) to study the modulational instability of finite-amplitude ion-acoustic waves in a non-magnetized warm ion plasma. Mahmood et al (2011) studied the nonlinear amplitude modulation of ion-acoustic wave in the presence of warm ions in unmagnetized EPI plasmas. The aim of this paper is to study the modulational instability of ion-acoustic wave in unmagnetized electron– positron–ion plasma when electron and positron species have different temperatures.
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