Three dimensional electrostatic solitary waves in a dense magnetoplasma with relativistically degenerate electrons

Abstract

In this paper, small but finite amplitude electrostatic solitary waves in a relativistic degenerate magnetoplasma, consisting of relativistically degenerate electrons and non-degenerate cold ions, are investigated. The Zakharov-Kuznetsov equation is derived employing the reductive perturbation technique and its solitary wave solution is analyzed. It is shown that only compressive electrostatic solitary structures can propagate in such a degenerate plasma system. The effects of plasma number density, ion cyclotron frequency, and direction cosines on the profiles of ion acoustic solitary waves are investigated and discussed at length. The relevance of the present investigation vis-a-vis pulsating white dwarfs is also pointed out

Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma

“…For illustration, parameters are chosen that are representative of the relativistic plasmas found in white dwarfs. Consider n (0) e ≈ 10 30 -10 31 cm 3 and B 0 ≈ 10 10 G [11]. Figure 1 represents the variation in the Sagdeev potential V ( ) with respect to potential using Eq.…”

“…The lack of observations, however, does not necessarily imply the absence of acoustic mode oscillations, but may be associated with the motion below the detection limit [15]. The possibility of the formation of finite amplitude acoustic waves is also suggested in the case of extreme events such as supernova explosions and pulsating white dwarf stars [11]. Therefore, our objective here is to develop a nonlinear theory of nonlinear periodic ion-acoustic waves (i.e., ion-acoustic cnoidal waves), in a dense magnetoplasma with relativistic degenerate electrons.…”

“…For simplicity, let us assume that Z = 1. The dynamic of the nonlinear electrostatic waves propagating in such a degenerate plasma system is governed by [11,25] …”

“…(1)-(4) have been appropriately normalized: , which is the normalized relativistic parameter and p F e the momentum on the Fermi surface [12]. The relativistic degenerate pressure for electrons P erd is given by [5,6,11]…”

“…The average bulk densities of white dwarf stars are typically 10 30 cm 3 . The number density of the degenerate electrons can be order of 10 30 cm 3 or more in compact objects such as white dwarfs, which is very high [11]. Therefore, one of the most interesting quantum phenomena is the structure of white dwarf stars, which couple the degeneracy of electrons due to the Pauli exclusion principle and Heisenberg's uncertainty principle to the stability of the white dwarf star on macroscopic scales via the balance between the gravitational pull and the degeneracy * emadel_shamy@hotmail.com pressure of the electrons.…”