Transverse instability of electron-acoustic solitons in a relativistic degenerate astrophysical magnetoplasma

Abstract

We study the nonlinear theory of small-amplitude electron-acoustic solitons (EASs) in a relativistic astrophysical magnetoplasma consisting of two-temperature electrons: a sparse population of relativistic nondegenerate classical electrons and a group of fully degenerate dense relativistic electrons (main constituent) immersed in a static magnetic field with a neutralizing stationary ion background. By using the multiple-scale reductive perturbation technique with the Lorentz transformation, the Zakharov-Kuznetsov (ZK) and the modified Zakharov-Kuznetsov (mZK) equations are derived to describe the evolution of EASs in two different regimes of relativistic degeneracy: $r_{d0}<50$ and $r_{d0}\gtrsim 50$. The characteristics of the plane soliton solutions of ZK and mZK equations and the soliton energy are studied. We show that the solitons moving at an angle $\alpha$ to the external magnetic field can be unstable under transverse long-wavelength perturbations. The growth rates of instabilities are obtained and analyzed with the effects of the relativity parameter ${\beta }_{\mathrm{cl}}=k_B{T}_{\mathrm{cl}}/m_e{c}^2$ and the degeneracy parameter $r_{d0}$, where $k_B$ is the Boltzmann constant and $T_{\mathrm{cl}}$ is the temperature of classical electrons. Interestingly, the ZK solitons, even if it is stable for the first-order perturbations, can be unstable in the second-order correction. Furthermore, while the first-order growth rates of perturbations for ZK solitons tend to vanish as $\alpha \to 38^{\circ }$, that for the mZK soliton goes to zero as $\alpha \to 90^{\circ }$. However, depending on the angle $\alpha$, the growth rates are found to be reduced either by increasing the values of ${\beta }_{\mathrm{cl}}$ or by decreasing the values of $r_{d0}$. The applications of our results to astrophysical plasmas, such as those in the environments of white dwarfs are discussed.

19 pages, 7 figures; the revised version appears online at https://doi.org/10.1088/1402-4896/ad9427 (Physica Scripta)

References in corpus (4)

• Current challenges in the physics of white dwarf stars
• Nonlinear Coupling of Electromagnetic and Electron Acoustic Waves in Multi-Species Degenerate Astrophysical Plasma
• Experimental study on controlled production of two-electron temperature plasma
• Stability of electromagnetic solitons]{Electromagnetic solitons and their stability in relativistic degenerate dense plasmas with two electron species

Cited by in corpus (1)

• Rayleigh-Taylor instability in inhomogeneous relativistic classical and degenerate electron-ion magnetoplasmas