Eur. Phys. J. Plus (2021) 136: 942
https://doi.org/10.1140/epjp/s13360-021-01935-6

Regular Article

Dynamics of electrostatic waves in relativistic electron–positron-ion degenerate plasma

¹ Department of Physics, Faculty of Science, Damietta University, 34517, New Damietta, Egypt
² Department of Physics, College of Sciences, United Arab Emirates University, 15551, Al-Ain, UAE
³ Center of Space Research and Its Application, Damietta University, 34517, New Damietta, Egypt

^b m.zaghloul@uaeu.ac.ae

Received: 5 November 2020
Accepted: 1 September 2021
Published online: 14 September 2021

Abstract

Based on quantum hydrodynamics, a rigorous two-fluid model is applied to investigate the 3-dimensional propagation characteristics of linear and nonlinear electrostatic waves in a magnetized electron–positron-ion degenerate plasma. Chandrasekhar’s equation of state (EOS) is used for the degenerate relativistic electron and positron fluids while ions are treated as fixed and uniform in space. A dispersion relation for the electronic-scale waves is obtained using the linear mode analysis. A nonlinear analysis has been performed using a reductive perturbation technique, and the corresponding Zakharov–Kuznetsov (ZK) equation is derived for the evaluation of the nonlinear model. The small$-k$ expansion perturbation method is employed to examine the instability criteria of the nonlinear waves obliquely propagating into the external magnetic field. The heading result of the present study is that the main characteristics of both linear and nonlinear modes are influenced clearly by the variations in concentrations of degenerate electrons and positrons. Also, the growth rate of the wave instability is found to increase as both the electron density and the positron concentration increase. The present results are helpful in understanding the characteristics and stability conditions of electrostatic waves in many ultra-dense systems generated in laboratory experiments of laser-irradiated solids and found in celestial environments, such as magnetar coronas, pulsar magnetospheres and black holes.