Modulation of the Nonlinear Ion Acoustic Waves in a Weakly Relativistic Warm Plasma with Nonextensively Distributed Electrons

El-Labany, Salah; El-Taibany, Wael; El-Bedwehy, Nabila; El-Shafeay, Nora Ahmed

doi:10.21608/ajbas.2020.39888.1030

Modulation of the Nonlinear Ion Acoustic Waves in a Weakly Relativistic Warm Plasma with Nonextensively Distributed Electrons

Document Type : Original Article

Authors

¹ Department of Physics, Faculty of Science, Damietta University, New Damietta, Egypt

² Department of Physics, Faculty of Science, Damietta University, New Damietta, Egypt.

³ Department of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt

10.21608/ajbas.2020.39888.1030

Abstract

A reductive perturbation technique (multiple scales) is applied to a weakly relativistic warm unmagnetized adiabatic plasma system consisting of inertial ions fluid and nonextensively distributed electrons. A nonlinear Schrödinger-type (NST) equation for finite wave number at the second order is derived. Using the reductive perturbation technique we derived the corresponding Korteweg-de Vries (K-dV) equation. For small wavenumber limit the K-dV equation is transformed into NST equation. It is found that the coefficient of the NST equation obtained from the K-dV equation agree with the corresponding coefficients of NST equation obtained by the multiple scales. Moreover we investigated the effect of the physical parameters of the system namely temperature ratio of the ion temperature T_i to electron temperature T_e, the relativistic factor u_0/C as well as the nonextensive parameter (q) of the distribution on the stability/instability of the system. It is found that these parameters affect strongly on the stability/instability regions. Finally, the validity of our results in astrophysical plasma is briefly discussed.

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