Comparison study of the energy and instability of ion-acoustic solitary waves in magnetized electron-positron-ion quantum plasma

Abstract

Notably, solitary waves that emerge from the nonlinear properties of plasmas are the main focus of many current studies of localized disturbances in both laboratory and astrophysical plasmas. By applying the reductive perturbation method, we derive the nonlinear homogeneous quantum Zakharov-Kuznetsov (QZK) equation in three-component collisionless quantum plasma consisting of electrons, positrons, and ions in the presence of an external static magnetic field. The solitary wave structures are dependent on the Bohm potential, magnetic field, obliqueness, species Fermi temperatures, and densities. The soliton's electric field and energy are also derived and investigated, which were found to be reduced as the magnetic field increases. The instability growth rate is also derived by using the small-k perturbation expansion method. The previous parameters affect the instability growth rate as well. A comparison of the energy and instability growth rate behaviour against system parameters is carried out. Large energy and large instability growth rate occur at large values of positron density or lower values of ion density. At zero or small rotation angle, both decrease as the magnetic field increases. Our findings could help us understand the dynamics of magnetic white dwarfs, pulsar magnetospheres, semiconductor plasma, and high-intensity laser-solid matter interaction experiments where e-p-i plasma exists.

Figure 1

The phase velocity $\mathrm{\lambda }$, variation against p at different values of $\sigma$.

Figure 2

(A) The variation of the nonlinear term A, (B) The longitudinal dispersive term B, (C) The transverse dispersive term C represented by equation $\left(11\right)$ against p for different values of $\sigma$ at $\omega =0.5$, $\theta =20$, $H_e=0.2$, and $H_p=0.4$.

Figure 3

The variation of the QIASWs (A) the amplitude ${\varphi }_m$ against p for different values of $\sigma$ at $\omega =0.5$, $\theta =20$, (B) the width W against p for different values of $\sigma$ at $\omega =0.5$, $\theta =20$, (C) the width W against $\theta$ for different values of $\omega$ at $\sigma =0.5$, $p=0.7$ with all at $H_e=0.4$, and $H_p=0.6$.

Figure 4

The variation of the QIASWs potential ${\varphi }_0$ that represented by equation $\left(16\right)$ against $\rho$ at $\omega =0.5$, M $=0.4$, (A) for different values of $\sigma$ with $p=0.1$, $\theta$ $=1$, $H_e=0.1$, and $H_p=0.6$, (B) for different values of p with $\sigma =0.4$, $\theta$ $=1$, $H_e=0.1$, and $H_p=0.6$, (C) for different values of $\theta$ with $p=0.7$, $\sigma$ $=0.4$, $H_e=0.1$, and $H_p=0.6$, (D) for different values of $H_e$ with $p=0.7$, $\sigma =0.4$, $\theta$ $=1$, and $H_p=0.6$, (E) for different values of $H_p$ with $p=0.7$, $\sigma =0.4$, $\theta$ $=1$, and $H_e=0.6$.

Figure 4

The variation of the QIASWs potential ${\varphi }_0$ that represented by equation $\left(16\right)$ against $\rho$ at $\omega =0.5$, M $=0.4$, (A) for different values of $\sigma$ with $p=0.1$, $\theta$ $=1$, $H_e=0.1$, and $H_p=0.6$, (B) for different values of p with $\sigma =0.4$, $\theta$ $=1$, $H_e=0.1$, and $H_p=0.6$, (C) for different values of $\theta$ with $p=0.7$, $\sigma$ $=0.4$, $H_e=0.1$, and $H_p=0.6$, (D) for different values of $H_e$ with $p=0.7$, $\sigma =0.4$, $\theta$ $=1$, and $H_p=0.6$, (E) for different values of $H_p$ with $p=0.7$, $\sigma =0.4$, $\theta$ $=1$, and $H_e=0.6$.

Figure 5

The evolution of the associated electric field, $E_0$ of QIASWs that represented by equation $\left(18\right)$ with $\rho$ for the potentials those represented by Fig. 5, (A) for different values of $\sigma$ with $p=0.1$, $\theta$ $=1$, $H_e=0.1$, and $H_p=0.6$, (B) for different values of p with $\sigma =0.4$, $\theta$ $=1$, $H_e=0.1$, and $H_p=0.6$, (C) for different values of $\theta$ with $p=0.7$, $\sigma$ $=0.4$, $H_e=0.1$, and $H_p=0.6$, (D) for different values of $H_e$ with $p=0.7$, $\sigma =0.4$, $\theta$ $=1$, and $H_p=0.6$, (E) for different values of $H_p$ with $p=0.7$, $\sigma =0.4$, $\theta$ $=1$, and $H_e=0.6$.

Figure 5

The evolution of the associated electric field, $E_0$ of QIASWs that represented by equation $\left(18\right)$ with $\rho$ for the potentials those represented by Fig. 5, (A) for different values of $\sigma$ with $p=0.1$, $\theta$ $=1$, $H_e=0.1$, and $H_p=0.6$, (B) for different values of p with $\sigma =0.4$, $\theta$ $=1$, $H_e=0.1$, and $H_p=0.6$, (C) for different values of $\theta$ with $p=0.7$, $\sigma$ $=0.4$, $H_e=0.1$, and $H_p=0.6$, (D) for different values of $H_e$ with $p=0.7$, $\sigma =0.4$, $\theta$ $=1$, and $H_p=0.6$, (E) for different values of $H_p$ with $p=0.7$, $\sigma =0.4$, $\theta$ $=1$, and $H_e=0.6$.

Figure 6

The evolution of the energy $E_n$ of the QIASWs that represented by equation $\left(19\right)$ at M $=0.4$, $H_e=0.4$, and $H_p=0.6$, (A) against p for different values of $\sigma$ at $\omega =0.5$, $\theta =20$, (B) against $\theta$ for different values of $\omega$ at $\sigma =0.5$, $p=0.7$.

Figure 7

The variation of the growth rate, Gr, that represented by equation $\left(30\right)$ at $l_{\xi }=0.7,l_{\eta }=0.4,M$ $=0.4$, $H_e=0.4$, and $H_p=0.6$, (A) against $\theta$ for different values of $\omega$ at $\sigma =0.2$, $p=0.4$, (B) against p for different values of $\sigma$ at $\omega =0.5$, $\theta =20$.