Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons

Nonlinear ion-acoustic waves are analyzed in a nonrelativistic magnetized quantum plasma with arbitrary degeneracy of electrons. Quantum statistics is taken into account by means of the equation of state for ideal fermions at arbitrary temperature. Quantum diffraction is described by a modified Bohm potential consistent with finite-temperature quantum kinetic theory in the long-wavelength limit. The dispersion relation of the obliquely propagating electrostatic waves in magnetized quantum plasma with arbitrary degeneracy of electrons is obtained. Using the reductive perturbation method, the corresponding Zakharov-Kuznetsov equation is derived, describing obliquely propagating two-dimensional ion-acoustic solitons in a magnetized quantum plasma with degenerate electrons having an arbitrary electron temperature. It is found that in the dilute plasma case only electrostatic potential hump structures are possible, while in dense quantum plasma, in principle, both hump and dip soliton structures are obtainable, depending on the electron plasma density and its temperature. The results are validated by comparison with the quantum hydrodynamic model including electron inertia and magnetization effects. Suitable physical parameters for observations are identified.

Figure 1

Coefficient $\alpha$ from Eq. (12), as a function of the chemical potential ${\mu }_0$. Solid line: $T=4000$ K. Dotted line: $T=6000$ K. Dashed line: $T=8000$ K.

Figure 2

Quantum diffraction parameter defined in Eq. (23), as a function of the equilibrium fugacity $z=e^{\beta {\mu }_0}$, and normalized to $H_0={\left[(2{\alpha }_F/3){(2\beta m_e{c}^2/\pi )}^{1/2}\right]}^{1/2}$.

Figure 3

Squared width of the localized structure as shown in Eq. (71), as a function of the quantum diffraction parameter $H^2$.

Figure 4

Coupling parameter defined in Eq. (77), as a function of the equilibrium fugacity $z=e^{\beta {\mu }_0}$, and normalized to $g_0=2{\alpha }_F\sqrt{2\beta m_e{c}^2}/\left[3{\left(3\sqrt{\pi }\right)}^{1/3}\right]$.

Figure 5

Ratio between the diffraction parameter $H^2$ from Eq. (23) and the coupling parameter $g$ from Eq. (77), as a function of the equilibrium fugacity $z=e^{\beta {\mu }_0}$.

Figure 6

Upper, dotted curve: Coupling parameter $g$ from Eq. (77), Lower, dashed curve: Quantum diffraction parameter $H^2$ from Eq. (23), as a function of the electronic Fermi energy $E_F$ (in $\mathrm{eV}$), for hydrogen plasma and the intermediate dilute-degenerate regime where $T=T_F$.

Figure 7

Upper, dotted curve: Maximum wavelength ${\lambda }_{\max }$. Lower, dashed curve: Minimal wavelength ${\lambda }_{\min }$, consistent with Eq. (78), as a function of the electronic Fermi energy $E_F$ (in $\mathrm{eV})$, for hydrogen plasma and the intermediate dilute-degenerate regime where $T=T_F$.

Figure 8

Cold and weakly coupled ions are below the upper, dotted straight line (where the ionic temperature $T_i$ equals the electronic Fermi temperature $T_F$) and above the lower, dashed straight line (where the ionic coupling parameter $g_i=1$).

Figure 9

Two-dimensional profile of the MIAW hump soliton structure (70), moving at supersonic speed in the laboratory frame, using normalized coordinates. Parameters: $n_0=5\times {10}^{30}{\mathrm{m}}^{-3}$, $H^2=0.10$, $g=0.22$, $T=T_F=1.24\times {10}^6$ K, $B_0={10}^3$ T, $l_x=l_y=\sqrt{2}/2$, and $\delta V=0.10$.