Negative energy dust acoustic waves evolution in a dense magnetized quantum Thomas-Fermi plasma

Abstract

Propagation of nonlinear waves in the magnetized quantum Thomas-Fermi dense plasma is analyzed. The Zakharov-Kuznetsov-Burgers equation is derived by using the theory of reductive perturbation. The exact solution contains both solitary and shock terms. Also, it is shown that rarefactive waves propagate in most cases. Both the associated electric field and the wave energy have been derived. The effects of dust and electrons temperature, dust density, magnetic field magnitude, and direction besides the effect of the kinematic viscosity on the amplitude, width, and energy of the formed waves are discussed. It is shown that the negative energy wave is formed and its value is enhanced due to the increase of the kinematic viscosity and the ambient magnetic field which lead to an increase in the instability. The present results are helpful in controlling the stabilization of confined Thomas-Fermi dense magnetoplasma that are found in white dwarfs and in the high-intensity laser-solid matter interaction experiments.

Figure 1

The variation of the phase speed $v_0$, represented by Eq. (5) against ${\sigma }_d$ for different values of ${\sigma }_i$ at ${\mu }_e=18$.

Figure 2

The variation of (a) the nonlinear term A, (b) the dispersive term B, (c) the transverse term C against ${\sigma }_d$ for different values of ${\sigma }_i$, at ${\mu }_e=18$, and (d) the transverse term C against ${\mu }_e$ for different values of $\mathrm{\Omega }$ at ${\sigma }_i=0.5$, and ${\sigma }_d=0.3$ that are represented by Eq. (9).

Figure 3

The evolution of the potential ${\varphi }^{(1)}$ of the DA waves that represented by Eq. (11) with $\chi$ at ${\mu }_e=18$, for different values of (a) ${\sigma }_i$, ${\sigma }_d$, and $\eta$ with $n=0.3$, and $\mathrm{\Omega }=0.4$, (b) n, and $\mathrm{\Omega }=$ with ${\sigma }_i=0.2$, ${\sigma }_d=0.1$, and $\eta =0.3$.

Figure 4

The evolution of the associated electric field, $E^{(1)}$of DA waves that represented by Eq. (12) with $\chi$ for the potentials those represented by Fig. 1, for different values of (a) ${\sigma }_i$, ${\sigma }_d$, and $\eta$ with $n=0.3$, and $\mathrm{\Omega }=0.4$, (b) n, and $\mathrm{\Omega }=$ with ${\sigma }_i=0.2$, ${\sigma }_d=0.1$, and $\eta =0.3$.

Figure 5

The evolution of the energy $E_n$ of the DA waves that represented by Eq. (13), (a) against ${\sigma }_i$ for different values of ${\sigma }_d$ with $\eta =0.8$, $n=0.4$, $\mathrm{\Omega }=0.5$, and ${\mu }_e=12$, (b) against ${\mu }_e$ for different values of $\mathrm{\Omega }$ with $\eta =0.8$, $n=0.4$, ${\sigma }_i=0.5$ and ${\sigma }_d=0.5$, (c) against n for different values of $\eta$ with ${\sigma }_i=0.5$, ${\sigma }_d=0.5$, $\mathrm{\Omega }=0.5$, and ${\mu }_e=18$.