Quantum Magnetohydrodynamic Model Research Articles

Study of shear Alfve’n waves with Landau quantization effect in degenerate relativistic plasma

In a ground breaking endeavor, we investigate a fundamental quantum property of fermions, specifically electrons, within a non-uniform quantized magnetic field, unveiling novel insights into shear Alfve’n waves in the relativistic realm of quantum plasma, particularly within the context of a degenerate Fermi gas. Employing the quantum magnetohydrodynamic model, we delve into the profound implications of the Landau quantization effect. This quantum phenomenon holds paramount importance across diverse fields such as condensed matter physics, astrophysics, and quantum information. Our study focuses on a plasma composed of degenerate relativistic electrons coexisting with cold fluid ions, which are non-degenerate particles. The findings of this research reveal substantial modifications in the thermodynamic, kinetic, and dispersion relation characteristics of shear Alfve’n waves when subjected to a non-uniform quantized magnetic field. This exploration offers a pioneering perspective on the intricate interplay between quantum physics and plasma dynamics, with implications for a wide array of scientific disciplines.

Magnetoacoustic waves in spin-1/2 dense quantum degenerate plasma: nonlinear dynamics and dissipative effects

Abstract Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev’s potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments.

The impact of quantized magnetic pressure on the stimulated Brillouin scattering of electromagnetic waves

Within the frame work of Landau quantization theory of Fermi gas, we formulate here the exotic physics of magnetic stimulated Brillouin scattering instability (MSBS) arising due to the nonlinear interaction of high frequency electromagnetic waves (EMWs) with degenerate, strongly magnetized electron-ion plasma. Quantum magneto hydrodynamic model (QMHD) is followed to develop the basic differential equations of quantized magnetosonic waves (QMWs) in the presence of super strong magnetic (SSH) field, whereas Maxwell equations are used to derive the governing differential equation of pump EMWs. The nonlinear interaction of EMWs and QMWs is addressed by employing the phasor matching technique. The obtained dispersion relation of MSBS shows that for a fixed density of fermions, the SSH field alone suppresses the MSBS instability as a function of quantized magneto ion velocity (C He ) and the Alfven speed (V A ) via three-wave decay and modulational instabilities. However, for particular condition the MSBS instability is found to increase as a function of SSH field. Next, the analytical results are verified numerically and graphically for soft x-rays in the environment of neutron star. The present MSBS analysis may be critical in neutron stars, radio pulsars and magnetars having super strong magnetic field i.e. even larger than the quantum threshold value i.e, H ∼ 4.4 × 1013 G, or in any application where the enhancement or suppression of SBS may be important.

Magnetosonic waves propagation in a magnetorotating quantum plasma.

Employing the quantum magnetohydrodynamic (QMHD) model, the basic properties of magnetosonic waves were investigated in a magnetorotating quantum plasma. The contemplated system considered a combined effects of quantum tunneling and degeneracy forces, dissipation influence, spin magnetization, in addition to the Coriolis force. Fast and slow magnetosonic modes were obtained and examined in the linear regime. Their frequencies are significantly modified due to the rotating parameters (frequency and angle) in addition to quantum correction effects. The nonlinear Korteweg-de Vries-Burger equationwas derived using the reductive perturbation approach in a small amplitude limit. The aspects of magnetosonic shock profiles were explored analytically by applying the Bernoulli equationapproach and numerically using the Runge-Kutta method. The regarded plasma parameters due to the investigated effects were found to play major roles in specifying the nature of monotonic and oscillatory shock waves' structures and their features. Our results may be applicable in magnetorotating quantum plasma in astrophysical environments such as neutron stars and white dwarfs.

Density polarization effect of spin-up and spin-down electrons on magnetosonic solitons in a dense plasma with oblique magnetic field

Nonlinear wave propagation of fast and slow magnetosonic waves is investigated in a magnetized quantum plasma with spin polarization effects of degenerate electrons. The multi-fluid quantum magnetohydrodynamic model is considered and two separate fluid dynamic equations for degenerate electrons i.e. spin-up and spin-down states (Pauli paramagnetism) with their different Fermi pressures. The ions are assumed to be classical and external magnetic field lies in a plane. The magnetization energy and current density of electrons due to the spin-1/2 effects are included in the momentum equation of the degenerate electrons and Maxwell equations, respectively. A Korteweg-de-Vries (KdV) equation is derived for nonlinear magnetosonic waves in a dense magnetized plasma with the inclusion of electron spin effects and oblique external magnetic field. The electron inertial effect (which causes wave dispersion) of both spin-up and spin-down state electrons is also included in the model. It is found that electron spin polarization density has significant effects on the phase speed and soliton structures (i.e. its width and amplitude) of fast (hump) and slow (dip) magnetosonic waves in a dense magnetized plasma. The present theoretical study along with the obtained numerical results may have possible applications towards many realistic astrophysical scenarios.

The role of electron inertia on jeans instability of radiative quantum plasma with the impact of rotation and resistivity

With the use of the Quantum Magnetohydrodynamic (QMHD) model, we took into account the Jeans instability of rotating magnetized radiative quantum plasma under the impact of finite electron inertia and resistivity. The issue is set up and using the linearization method and normal mode technique, we can get the general dispersion relation, which is then described in terms of various modes of propagation. Within the prescribed boundaries, we also get the Jeans instability criteria. Plotting the curves between the system's growth rate and wave number for the investigation of the stability analysis of the system, which is then thoroughly explained.

Global well-posedness of the compressible quantum magnetohydrodynamic model with small initial energy

In this paper, we investigate the three-dimensional Cauchy problem of the compressible quantum magnetohydrodynamic model. It is proved that the system admits a unique global solution, provided that the initial energy is suitably small. Furthermore, the large time behavior of the global solution is obtained.

Optimal decay rate for higher–order derivatives of solution to the 3D compressible quantum magnetohydrodynamic model

Abstract We investigate optimal decay rates for higher–order spatial derivatives of strong solutions to the 3D Cauchy problem of the compressible viscous quantum magnetohydrodynamic model in the H 5 × H 4 × H 4 framework, and the main novelty of this work is three–fold: First, we show that fourth order spatial derivative of the solution converges to zero at the L 2 - rate ( 1 + t ) - 11 4 {L^2} - {\rm{rate}}\,{(1 + t)^{- {{11} \over 4}}} , which is same as one of the heat equation, and particularly faster than the L 2 - rate ( 1 + t ) - 5 4 {L^2} - {\rm{rate}}\,{(1 + t)^{- {5 \over 4}}} in Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and the L 2 - rate ( 1 + t ) - 9 4 {L^2} - {\rm{rate}}\,{(1 + t)^{- {9 \over 4}}} , in Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. Second, we prove that fifth–order spatial derivative of density ρ converges to zero at the L 2 - rate ( 1 + t ) - 13 4 {L^2} - {\rm{rate}}\,{(1 + t)^{- {{13} \over 4}}} , which is same as that of the heat equation, and particularly faster than ones of Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019]. Third, we show that the high-frequency part of the fourth order spatial derivatives of the velocity u and magnetic B converge to zero at the L 2 - rate ( 1 + t ) - 13 4 {L^2} - {\rm{rate}}\,{(1 + t)^{- {{13} \over 4}}} , which are faster than ones of themselves, and totally new as compared to Pu–Xu [Z. Angew. Math. Phys., 68:1, 2017] and Xi–Pu–Guo [Z. Angew. Math. Phys., 70:1, 2019].

Low frequency Compressional modes in degenerate semiconductor plasmas

Properties of low frequency compressional electromagnetic wave pulse in a magnetized semiconductor hole-electron plasma, are investigated. The quantum mechanical effects such as Fermi pressure, quantum tunneling and exchange-correlation potential of inertialess electrons, inertial holes and stationary charged ion particulates are considered in the presence of the magnetic field. A new type of dispersion relation is derived for low-frequency compressional waves by employing quantum magneto-hydrodynamic model and Maxwell equations; the dispersion relation is then analyzed for parallel, perpendicular and oblique propagation of compressional electromagnetic wave pulse to the external magnetic field direction. We have analyzed the obtained dispersion relations numerically, for different semiconductor plasma such as GaAs, GaSb and, GaN, the graphs shows that the frequency of compressional electromagnetic wave pulse decreases with increase of electron-hole density concentration, whereas the frequency increases with the increase of angle of propagation compressional electromagnetic wave pulse. Our results are applicable to understanding the dynamics of semiconductor plasma to produce high power, high band-width devices in contrast to the existing gas plasma devices. Keywords: degenerate semiconductor plasma, quantum mechanical effects, compression electromagnetic wave, gas plasma device.

Magnetoacoustic Nonlinear Periodic Wave and Soliton Structures in Degenerate Pair Plasmas in the Presence of Exchange-Correlation Force

By employing a two-fluid quantum magnetohydrodynamic (QMHD) model, linear and nonlinear aspects of magnetoacoustic wave propagation in dense magnetized electron–positron (e-p) plasma are examined in the presence of exchange-correlation potential as well. The degenerate plasma pressure and the Bohm potential effects are already taken in the model. The reductive perturbation method (RPM) is used, and the modified Korteweg–de Vries (modified KdV) equation (or KdV equation containing linear drift term) is derived for nonlinear magnetoacoustic wave propagation in degenerate pair plasma under periodic boundary conditions. The well-known Sagdeev potential approach is opted to obtain the analytical solution of magnetoacoustic cnoidal wave and soliton in dense pair plasmas. The numerical plots of magnetoacoustic cnoidal wave and soliton structures are also presented, and the condition of their formation in dense e-p plasma is discussed in detail. The parametric analysis in the absence and the presence of exchange-correlation potential effects of electrons and positrons is discussed. Moreover, the parametric analysis of the variations of plasma density and magnetic field intensity on the formation and propagation of nonlinear structures in dense e-p plasma in the presence of exchange-correlation force effects in the model is also done using the astrophysical plasma parameters mentioned in the literature for pulsars (or white dwarfs).

Effect of relativistically degenerate electrons on linear and nonlinear structures in ion temperature gradient driven pure drift mode

Low frequency, electrostatic, pure drift mode is investigated in dense magnetized electron-ion plasma in the presence of relativistically degenerate electrons using quantum magnetohydrodynamic model (QMHD). Ions are considered as warm classical particles. Inhomogeneities in background ion density, ion temperature and external magnetic field are taken into account. In the linear regime, dispersion relation is obtained and plotted for both non-relativistic and ultra-relativistic regimes. Parametric study shows that for both non-relativistic and ultra-relativistic cases, growth rate of the wave increases by increasing, , which is the ratio of background ion temperature to density. In the nonlinear case, solitary solutions are obtained by using the functional variable method. Graphical illustrations are used to show the effect of relativistically degenerate electrons and other parameters like electron and ion number densities, magnetic field and ion temperature on nonlinear structures in both non relativistic and relativistic regimes. This work may be helpful to understand low frequency phenomena in dense inhomogeneous plasmas like neutron stars, white dwarfs and next generation lasers.

Spin contribution to the instability of THz plasma waves

When the boundary conditions of the source and drain are asymmetric, the plasma waves may become unstable in the channel of a field effect transistor (FET). We use the quantum magnetohydrodynamic model to study the influence of the quantum Bohm potential, Fermi statistical pressure, and electron spin effects on the stability of THz plasma waves propagating perpendicular to the magnetic field in the FET. A dispersion equation governing the THz plasma oscillation is obtained. Numerical results have shown that the presence of spin effects has enlarged the instable range of β, enhanced the instability increment, and made the frequency of THz plasma waves larger. The research shows that nanometer FETs with spin effects have advantages in realizing practical terahertz radiation.

Extraordinary and upper-hybrid waves in spin quantum magnetoplasmas with vacuum polarization effect

The propagation of extraordinary and upper-hybrid waves in spin quantum magnetoplasmas with vacuum polarization effect is investigated. Based on the quantum magnetohydrodynamics model including Bohm potential, arbitrary relativistic degeneracy pressure and spin force, and Maxwell's equations modified by the spin current and vacuum polarization current, the dispersion relations of extraordinary and upper-hybrid waves are derived. The analytical and numerical results show that quantum effects (Bohm potential, degeneracy pressure and spin magnetization energy) and the vacuum polarization effect modify the propagation of the extraordinary wave. Under the action of a strong magnetic field, the plasma frequency is obviously increased by the vacuum polarization effect.

Electron exchange-correlation effects on dispersion properties of electrostatic waves in degenerate quantum plasmas

Based on the quantum Magnetohydrodynamic (QMHD) model, the obliquely propagation of electrostatic waves in degenerate magnetized quantum plasmas with electron exchange-correlation effects are theoretically investigated. The modified linear dispersion relations of electrostatic waves are obtained and discussed in some specific cases. The analytical results clearly show that the dispersion properties of the high frequency electron waves (including the Langmuir wave and upper-hybrid wave) and the low frequency ion acoustic wave are modified by the quantum effects together with the electron exchange-correlation effects. The numerical results depict that the Langmuir wave and upper-hybrid wave can be unstable in the presence of the electron exchange-correlation effects, and it is also evidently indicated that the electron exchange-correlation effects can reduce the phase velocity of the waves, especially in the high wave number region. The corresponding results should be of relevance for identifying electrostatic fluctuations which transport in an inhomogeneous and magnetized quantum plasmas.

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.

Influence of FLR correction on Jeans instability in rotating radiative QMHD fluid model

ABSTRACT The descriptive exploration of Jeans instability under the QMHD fluid model for magnetized radiative plasma, preserving the consequences of rotation and finite ion Larmor radius. The problem of equations is formulated by using the quantum magnetohydrodynamic fluid model. The general dispersion relations were achieved using a standard mode analysis by formulating a linearized equation set and the dispersion relations are explained in the transverse and parallel propagations of the magnetic field. Those latter particular situations are discussed in the light of the axis of rotation in the longitudinal and transverse magnetic field. From the numerical calculation, we observe that Jean's criteria are changed due to the existence of FLR corrections, the feature of radiation, quantum correction, and magnetic field. From the graphical presentation, we find that the effect of FLR correction with rotation, quantum correction, and the magnetic field is a more stabilizing impact on comparing the system than the simple gaseous plasma medium. The result demonstrates that the system's growth rate is affected by FLR, rotation, magnetic field, and quantum correction.

Effect of rotation and quantum correction on the ionstreaming instability in the magnetized dusty plasma

The present work illustrated the modified streaming instability of the dust acoustic wave under the presence of rotation and quantum parameters. The governing equations of the problem have been demonstrated by using Quantum Magneto-hydrodynamic (QMHD) model along with the Poisson equation for the electrostatic potential. In this work, the growth rate of electrostatic waves has been studied which shows the stabilized condition of magnetized dusty plasma due to rotation and quantum parameters. In addition, the threshold condition of ion-dust drift waves is also investigated.

Influence of quantum correction on the Jeans instability of strongly coupled magnetized plasma

It is shown that the Jeans instability condition of strongly coupled finitely conducting gaseous plasma is reduced in the presence of magnetic field and quantum correction. The linearized equations are constructed by using the Quantum magneto-hydrodynamic (QMHD) model. With the help of the normal mode analysis method, a general dispersion relation is obtained. This dispersion relation is discussed by a different mode of propagation. In this paper, it has been found that, quantum correction stabilizes the growth rate of the organization but the relaxation time and electrical resistivity destabilize the growth rate in the transverse mode of propagation. Further, the modified Jeans criterion of the instability of the magnetized plasma system has been also found.

Lower bound of decay rate for higher order derivatives of solution to the compressible quantum magnetohydrodynamic model

The lower bounds of decay rates for global solution to the compressible viscous quantum magnetohydrodynamic model in three‐dimensional whole space under the H5 × H4 × H4 framework are investigated in this paper. We first show that the lower bound of decay rate for the solution converging to constant equilibrium state (1, 0, 0) in L2‐norm is when the initial data satisfy some low‐frequency assumption. Moreover, we prove that the lower bound of decay rate of k(k ∈ [1, 3]) order spatial derivative for the solution converging to constant equilibrium state (1, 0, 0) in L2‐norm is . Then, we show that the lower bound of decay rate for the time derivatives of density and velocity is , but the lower bound of decay rate for the time derivative of magnetic field converging to zero in L2‐norm is .

Coupled Drift Ion Acoustic Shock waves with trapped electrons in Quantum Magnetoplasma

Coupled drift ion acoustic shock waves are studied in inhomogeneous, dissipative quantum magnetoplasmas in the presence of adiabatically trapped electrons. We have derived a nonlinear Burgers like evolution equation having a fractional nonlinearity. The quantum magnetohydrodynamics model (QMHD) has been employed to derive this nonlinear equation (2 + 1) (two spatial and one temporal) dimensions. Nonlinear analysis of the equation is carried out to show that it admits shock solutions. These shock structures are numerically investigated by using parameters of neutron stars where quantum effects are expected to dominate the dynamics of the system. These results show significant dependence on the physical parameters namely inhomogeneity, number density, ambient magnetic field, collisional frequency and the angle of propagation.