Dynamics of ion-acoustic waves in nonrelativistic magnetized multi-ion quantum plasma: the role of trapped electrons

Abstract

The presented work provides a new perspective of quantum nonlinear propagation of ion-acoustic (IA) waves in a magnetized collisionless and dissipative multi-ion plasma system, composed of cold positive and negative charged nonrelativistic ions, negatively charged immobile heavy ions and trapped electrons; all existed in a quantizing magnetic field. We address the reductive perturbation method to derive the Korteweg-de Vries- Burgers (KdV-Burgers) and modified KdV-Burgers equations. The bifurcation theory of planar dynamical systems is applied to investigate the existence of the solitary wave and the periodic traveling wave solutions of the resulting mKdV-Burgers equation. Accordingly, the phase portrait topology is illustrated for this equation. To study the nonlinear waves in case of mKdV- Burgers, we obtain some interesting physical solutions for mKdV- Burgers. These solutions are in the form of soliton, a combination between the shock and the soliton, and finally monotonic and oscillatory shock waves. Only rarefactive IA waves are obtained for the slow mode of phase velocity. It is found that the IA solitons, IA shocks are affected by the plasma system parameters. The presented theoretical research can be successfully implemented to understanding the solitary and shocks structures in dense magnetized quantum plasmas such as those existing in white dwarfs and in the intense-laser plasma interactions.