Quantum Magnetohydrodynamic Equations Research Articles

Global Existence of Weak Solutions for Quantum Magnetohydrodynamic Equations

Global Existence of Weak Solutions for Quantum Magnetohydrodynamic Equations

Quantum effects on the propagation of surface magnetoplasmon polaritons in a graphene-plasmonic structure

We investigate the properties of surface magnetoplasmon polaritons (SMPPs) in a graphene-plasmonic structure which is constructed as a graphene film sandwiched with two semi-infinite dielectrics under a perpendicular configuration. By solving Maxwell equations and quantum magneto-hydrodynamic equations with considering the quantum statistical and quantum diffraction effects, we deduce the dispersion relation of graphene SMPPs (GSMPPs) in detail. We show how the graphene electron density, the external magnetic field, and the dielectric constant, affect the features of the dispersion of GSMPPs in both classical and quantum cases. We find that the quantum effects (QEs) significantly alter the properties of GSMPPs, which are entirely different from those in a classical model. We find that the propagation speed of classical GSMPPs has small increases while the propagation speed of quantum GSMPPs has fast and sharp increases along with the increases in graphene electron density. We further find that the propagation speed decreases gradually by increasing the applied magnetic field in both classical and quantum GSMPPs. Moreover, we also find that the propagation speed of classical GSMPPs has fast decreases tending to zero at large wavenumber while the propagation speed of quantum GSMPPs has slow decreases tending to infinity with increasing the dielectric constant. Our findings elucidate that QEs play a crucial role in the properties of GSMPPs and their response to different parameters.

The propagation of linear waves in high-energy-density magnetoplasmas using a relativistic quantum magnetohydrodynamic model

The propagation characteristics of linear waves in high-energy-density magnetoplasmas are investigated using a relativistic magnetohydrodynamic model based on the framework of relativistic quantum theory. Based on the covariant Wigner function approach, a relativistic quantum magnetohydrodynamic model is established. Starting from the relativistic quantum magnetohydrodynamic equations and the Maxwell equations, the dispersion equation for relativistic quantum magnetoplasmas is derived. The contributions of both quantum effects and relativistic effects are shown in the dispersion relations for perpendicular, parallel propagation with respect to a background magnetic field. Results show that the corrections of both quantum effects and relativistic effects are significant when choosing the plasma parameters of laser-based plasma compression schemes.

Ion-acoustic dipolar vortex in degenerate magnetoplasma with ions/electrons thermal corrections.

Nonlinear evolution and propagation characteristics of an ion-acoustic (IA) dipolar vortex are examined in a magnetoplasma that comprises partially degenerate electrons and dynamic ions. The adiabatic ions reduce the quantum magnetohydrodynamic equations to a modified momentum equation. The latter admits a new solution and leads to an evolution equation for the description of a coherent IA dipolar vortex. Numerical analysis reveals that variations in the relevant plasma parameters alter the evolution condition for a stable vortex. The electron exchange-correlation enhances excitation of the vortex as it extends the parametric regime associated with the stable vortex solution. On the contrary, the ion temperature lessens the nonlinear evolution of the vortex. Importantly, a degree of enhancement in the exchange-correlation potential leads to the wave dispersion and-in return-widens the vortex potential spatially. The novel nature of the derived results stresses upon the comprehension of the ordered structures in the compact stars, the magnetic mirrors, the ionosphere, the pinch devices, etc., where thermal corrections significantly impact the waves dynamics.

Zero Mach number limit to compressible quantum magnetohydrodynamic equations with vanishing viscosity coefficients

The connection between the compressible viscous quantum magnetohydrodynamic model with low Mach number and the ideal incompressible magnetohydrodynamic equations is studied in a periodic domain. More precisely, for well‐prepared initial data, we prove the convergence of classical solutions of the compressible viscous quantum magnetohydrodynamic model to the classical solutions of the incompressible ideal magnetohydrodynamic equations with a convergence rate when the Mach number, viscosity coefficient, and magnetic diffusion coefficient simultaneously tend to zero.

Existence and blow-up of the solutions to the viscous quantum magnetohydrodynamic nematic liquid crystal model

In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the quantum effects in the two-dimensional case. We prove the existence of the global finite energy weak solutions by use of a singular pressure close to vacuum. Then we obtain the local-in-time existence of the smooth solution. In the final, the blow-up of the smooth solutions is studied. The main techniques are Faedo-Galerkin method, compactness theory, Arzela-Ascoli theorem and construction of the functional differential inequality.

Quantum and FLR effects on the Rayleigh Taylor instability of stratified plasmas

The combined effects of quantum corrections and finite Larmor radius (FLR) have been investigated on the linear hydrodynamic Rayleigh-Taylor (RT) instability of an incompressible stratified plasma. The basic quantum magnetohydrodynamic equations incorporating quantum and FLR effects are constructed and linearized under the small amplitude approximation. The general dispersion relation is derived considering appropriate magnetic field and density profiles using the normal mode analysis. It is analyzed numerically to study the effects of quantum and FLR corrections on the growth rate of RT instability in the stratified hydrodynamic fluids. It is found that the cut-off wavenumber (kmax) and critical wavenumber (kc) determining the growth rate of RT instability are modified due to the presence of FLR corrections and quantum effects. The FLR and quantum corrections have a stabilizing effect on the growth rate of RT instability of a stratified plasma.

Low Mach number limit of the viscous quantum magnetohydrodynamic model

This paper is concerned with the low Mach number limit of the magnetohydrodynamic model with periodic boundary conditions for quantum plasmas. It is justified rigorously that, for well-prepared initial data, the classical solutions of the viscous quantum magnetohydrodynamic equations converge to that of the incompressible magnetohydrodynamic equations with a sharp convergence rate as the Mach number goes to zero.

Magnetosonic Shocks in Ultra-Relativistic Dissipative Degenerate Plasmas

Magnetosonic shock structures in dissipative magnetized degenerate electron ion plasma are studied. The two fluid quantum magnetohydrodynamic equations for non-degenerate ions and ultra-relativistic degenerate electron fluids with the Maxwell equations are presented. Using the reductive perturbation technique the Korteweg de Vries Burgers (KdVB) equation is derived and its solution is presented with the tanh method. Astrophysical plasma parameters are used to study the effects of variation of plasma density, magnetic field intensity and kinematic viscosity on the propagation characteristics of nonlinear shock structures in such plasma systems.

Electrostatic surface waves on a magnetized quantum plasma half-space

A theory of electrostatic surface waves on a quantum plasma half-space is developed with the inclusion of external magnetic field effects for the geometry in which the magnetic field is parallel to the surface and the direction of propagation is perpendicular to the magnetic field. A general analytical expression for dispersion relation of surface waves is obtained by solving Poisson and quantum magnetohydrodynamic equations with appropriate quantum boundary conditions.

Rayleigh–Taylor instability of a stratified magnetized quantum Plasma in a porous and incompressible medium

Rayleigh–Taylor instability of stratified magnetized quantum plasma in a porous medium has been investigated. Medium is assumed to be highly conducting and incompressible. The relevant quantum magnetohydrodynamic equations are solved by using appropriate boundary conditions and a dispersion relation is obtained. The dispersion relation is derived for the case, where plasma is bounded by two rigid planes. The growth rate of unstable Rayleigh–Taylor mode and stability conditions of the medium are evaluated analytically with the parameters quantum effect, magnetic field, porosity and permeability in the stratified fluids. It is found that the magnetic field and quantum effect have more stabilizing influence on Rayleigh–Taylor instability in presence of porous media. We have also found that the porosity has stabilizing influence, while permeability has destabilizing influence on Rayleigh–Taylor instability in presence of quantum effect.

Global existence of the three-dimensional viscous quantum magnetohydrodynamic model

The global-in-time existence of weak solutions to the viscous quantum Magnetohydrodynamic equations in a three-dimensional torus with large data is proved. The global existence of weak solutions to the viscous quantum Magnetohydrodynamic equations is shown by using the Faedo-Galerkin method and weak compactness techniques.

Modulation of drift-wave envelopes in a nonuniform quantum magnetoplasma

We study the amplitude modulation of low-frequency, long-wavelength electrostatic drift-wave envelopes in a nonuniform quantum magnetoplasma consisting of cold ions and degenerate electrons. The effects of tunneling associated with the quantum Bohm potential and the Fermi pressure for nonrelativistic degenerate electrons, as well as the equilibrium density and magnetic field inhomogeneities are taken into account. Starting from a set of quantum magnetohydrodynamic equations, we derive a nonlinear Schrödinger equation (NLSE) that governs the dynamics of the modulated quantum drift-wave packets. The NLSE is used to study the modulational instability (MI) of a Stoke's wave train to a small plane wave perturbation. It is shown that the quantum tunneling effect as well as the scale length of inhomogeneity plays crucial roles for the MI of the drift-wave packets. Thus, the latter can propagate in the form of bright and dark envelope solitons or as drift-wave rogons in degenerate dense magnetoplasmas.

A stability analysis of a self-gravitating optically thick magnetized quantum plasma including the effects of black body radiation

We have discussed the effect of black body radiation on self-gravitational instability of infinite homogeneous, optically thick quantum plasma carrying a uniform magnetic field. With the help of relevant linearized perturbation quantum magneto-hydrodynamic equations of the problem, using normal mode technique, a general dispersion relation is obtained with black body radiation, quantum correction and magnetic field. Discussed when propagation vectors are longitudinal and transverse to the magnetic field, separately. The new Jeans condition of instability due to quantum correction, magnetic field and black body radiation is discussed. We find that in transverse mode of propagation the condition of Jeans instability of gaseous plasma is modified by quantum correction, magnetic field and black body radiation. In the case of longitudinal mode, it is unaffected by a magnetic field, as this mode provides the Alfven mode separately with the gravitational mode. From the curves we found that the effects of quantum correction, black body radiation and magnetic field have a stabilizing influence.

Parametric studies of nonlinear magnetosonic waves in two-dimensional quantum magnetoplasmas

Using the effective one fluid quantum magnetohydrodynamic (QMHD) model, magnetosonic waves propagating obliquely to an external magnetic field are studied in an electron-ion (e-i) Fermi plasma. In the linear approximation, the effect of quantum corrections on the fast and slow magnetosonic waves are discussed. It is shown that the system of QMHD equations admit the Kadomstev–Petviashvilli soliton due to the balance between nonlinearity and dispersion caused by the obliqueness and quantum diffraction effects. It is observed that for both modes, the angle θ, the electron quantum diffraction, and statistic effects modify the shape of the solitary structure. It is also found that the results obtained for the quantum plasma differ significantly from the classical e-i plasmas.

Magnetosonic solitons in a fermionic quantum plasma

Starting from the governing equations for a quantum magnetoplasma including the quantum Bohm potential and electron spin- 12 effects, we show that the system of quantum magnetohydrodynamic (QMHD) equations admits rarefactive solitons due to the balance between nonlinearities and quantum diffraction and tunneling effects. It is found that the electron spin- 12 effect introduces a pressurelike term with negative sign in the QMHD equations, which modifies the shape of the solitary magnetosonic waves and makes them wider and shallower. Numerical simulations of the time-dependent system shows the development of rarefactive QMHD solitary waves that are modified by the spin effects.