High-frequency surface waves in quantum plasmas with electrons relativistic degenerate and exchange-correlation effects

The propagation characteristics of high-frequency surface waves are studied in spin-1/2 quantum plasmas by considering the electron relativistic degenerate and exchange-correlation effects. Using the quantum fluid equations of magnetoplasmas in the presence of the quantum Bohm potential, spin magnetization energy, relativistic degenerate pressure, and exchange-correlation effects, a generalized dispersion relation is derived. The analytical and numerical results show that the relativistic degenerate and exchange-correlation effects significantly modify the propagation properties of high-frequency surface waves. It is found that under the influence of exchange-correlation effects, the frequency spectrum of high-frequency surface waves will be down-shifted. It is also indicated that the dispersion curve shifts up with the increase of relativistic gamma factor. Furthermore, the phase speed of the high-frequency surface waves increases with increasing electron number density. The current research is helpful to understand the propagation of the high-frequency surface waves in quantum plasmas, such as those in dense astrophysical environment.     

Parametric instabilities in quantum plasmas with electron exchange-correlation effects

Parametric instabilities induced by the nonlinear interaction between high frequency quantum Langmuir waves and low frequency quantum ion-acoustic waves in quantum plasmas with the electron exchange-correlation effects are presented.By using the quantum hydrodynamic equations with the electron exchange-correlation correction,we obtain an effective quantum Zaharov model,which is then used to derive the modified dispersion relations and the growth rates of the decay and four-wave instabilities.The influences of the electron exchange-correlation effects and the quantum effects on the existence of quantum Langmuir waves and the parametric instabilities are discussed in detail.It is shown that the electron exchange-correlation effects and quantum effects are strongly coupled.The quantum Langmuir wave can propagate in quantum plasmas only when the electron exchange-correlation effects and the quantum effects satisfy a certain condition.The electron exchange-correlation effects tend to enhance the parametric instabilities,while quantum effects suppress the instabilities.     

Localized plasmons in quantum plasmas

We consider the nonlinear interactions between finite amplitude electron and ion plasma oscillations in a fermionic quantum plasma. Accounting for the quantum statistical electron pressure and the quantum Bohm potential, we derive a set of coupled nonlinear equations that govern the dynamics of modulated electron plasma oscillations (EPOs) in the presence of the nonlinear ion oscillations (NLIOs). We numerically study stationary solutions of our coupled nonlinear equations. We find that the quantum parameter H (equal to the ratio between the plasmonic and electron Fermi energy densities) introduces new features to the electron density and electric potential humps of localized NLIOs in the absence of EPOs. Furthermore, the nonlinear coupling between the EPOs and NLIOs gives rise to a new class of envelope solitons composed of bell shaped electric field envelope of the EPOs, which are trapped in the electron density hole (and an associated negative oscillatory electric potential) that is produced by the ponderomotive force of the EPOs. The knowledge of the localized plasmonic structures is of immense value for interpreting experimental observations in dense quantum plasmas.     

Arbitrary magnetosonic solitary waves in spin 1/2 degenerate quantum plasma

Linear and nonlinear compressional magnetosonic waves are studied in magnetized degenerate spin-1/2 Fermi plasmas. Starting from the basic equations of a quantum magnetoplasma we develop the system of quantum magnetohydrodynamic (QMHD) equations. Spin effects are incorporated via spin force and macroscopic spin magnetization current. Sagdeev potential approach is employed to derive the nonlinear energy integral equation which admits the rarefactive solitary structure in the subAlfvenic region. The quantum diffraction due to Bohm potential does not affect the amplitude of soliton but has a direct effect on its width. The width of soliton is broadened with the increase in the quantization of the system due to quantum diffraction. However, the nonlinear wave amplitude is reduced with the increase in the value of magnetization energy due to electron spin-1/2 effects. The degeneracy effect due to quantum plasma beta enhances the amplitude of magnetosonic soliton. The importance of the work relevant to compact astrophysical bodies is pointed out.     

Nonlinear excitation and stability analysis of ion-acoustic waves in a magnetized quantum plasma with exchange-correlation effects of degenerate electrons

The nonlinear ion-acoustic wave excitation and its stability analysis are investigated in a magnetized quantum plasma with exchange-correlation and Bohm diffraction effects of degenerate electrons in the model. Using reductive perturbation technique, the Zakharov-Kuznetsov (ZK) equation is derived for two dimensional propagation of ion-acoustic wave in a magnetized quantum plasma. It is found that the phase speed, amplitude and width of the nonlinear ion-acoustic wave structures are affected in the presence of exchange-correlation potential in the model. The stability analysis of the 2D ion-acoustic wave pulse is also presented. It is found that growth rate of the first and second order instabilities of 2D ion acoustic wave soliton is enhanced with the inclusion of exchange-correlation potential effect in the model.     

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.     

On the formation of spin dependent double layer structure in astrophysical plasmas

Double layers (DLs) are nonlinear structures, and are thought to be responsible for particle acceleration in laboratory plasmas and astrophysical plasmas. In this paper, the existence of spin dependent DLs structure is explored using separate spin evolution quantum hydrodynamic model. Based on reductive perturbation method, we derived an extended Korteweg–de Vries (eKdV) equation to demonstrate the existence and nature of DLs. We found that spin polarization significantly enhanced the amplitude of the electrostatic potential associated with DLs. Further, spin polarization also increases the depth and width of the Sagdeev potential. It is noted that the contribution of Bohm potential effect is essential for the formation of DLs structure. Our results may be helpful to explain the phenomenon of particle acceleration in dense astrophysical environments specifically in a white dwarf.     

Extraordinary Electromagnetic Waves in Weakly Relativistic Degenerate Spin-1/2 Magnetized Quantum Plasmas

By using the relativistic quantum magnetohydrodynamic model, the extraordinary electromagnetic waves in magnetized quantum plasmas are investigated with the effects of particle dispersion associated with the quantum Bohm potential effects, the electron spin-1/2 effects, and the relativistic degenerate pressure effects. The electrons are treated as a quantum and magnetized species, while the ions are classical ones. The new general dispersion relations are derived and analyzed in some interesting special cases. Quantum effects are shown to affect the dispersion relations of the extraordinary electromagnetic waves. It is also shown that the relativistic degenerate pressure effects significantly modify the dispersive properties of the extraordinary electromagnetic waves. The present investigation should be useful for understanding the collective interactions in dense astrophysical bodies,such as the atmosphere of neutron stars and the interior of massive white dwarfs.     

Formation and dynamics of dark solitons and vortices in quantum electron plasmas

We present simulation studies of the formation and dynamics of dark solitons and vortices in quantum electron plasmas. The electron dynamics in the latter is governed by a pair of equations comprising the nonlinear Schr?dinger and Poisson system of equations, which conserves the number of electrons as well as their momentum and energy. The present governing equations in one spatial dimension admit stationary solutions in the form a dark envelope soliton. The dynamics of the latter reveals its robustness. Furthermore, we numerically demonstrate the existence of cylindrically symmetric two-dimensional quantum electron vortices, which survive during collisions. The nonlinear structures presented here may serve the purpose of transporting information at quantum scales in ultracold micromechanical systems and dense plasmas, such as those created during intense laser-matter interactions.     

Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic(DEA) shock waves and double layers in an unmagnetized,collisionless,complex or dusty plasma system are carried out.The plasma system is assumed to be composed of inertial and viscous cold electron fluids,nonextensive distributed hot electrons,Maxwellian ions,and negatively charged stationary dust grains.The standard reductive perturbation technique is used to derive the nonlinear dynamical equations,that is,the nonplanar Burgers equation and the nonplanar further Burgers equation.They are also numerically analyzed to investigate the basic features of shock waves and double layers(DLs).It is observed that the roles of the viscous cold electron fluids,nonextensivity of hot electrons,and other plasma parameters in this investigation have significantly modified the basic features(such as,polarity,amplitude and width) of the nonplanar DEA shock waves and DLs.It is also observed that the strength of the shock is maximal for the spherical geometry,intermediate for cylindrical geometry,while it is minimal for the planar geometry.The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.     

Quantum macroscopic equations from Bohm potential and propagation of waves

Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation. In the present work, moments of this kinetic equation are taken, thus deriving conservation equations. These macroscopic equations are then applied to study the propagation of longitudinal density perturbations in neutral gases and plasmas, of either fermions or bosons. The dispersion relation is derived and the effect of the Bohm potential shown; the speed of propagation calculated and the difference between fermions and bosons investigated. Pseudosonic waves in quantum plasmas are obtained including the effect of the Bohm potential.     

Cylindrical and Spherical Electron-Acoustic Shock Waves in Electron-Positron-Ion Plasmas with Nonextensive Electrons and Positrons

Electron-acoustic shock waves (EASWs) in an unmagnetized four-component plasma (containing hot electrons and positrons following the q-nonextensive distribution, cold mobile viscous electron fluid, and immobile positive ions) are studied in nonplanar (cylindrical and spherical) geometry. With the help of the reductive perturbation method, the modified Burgers equation is derived. Analytically, the effects of nonplanar geometry, nonextensivity, relative number density and temperature ratios, and cold electron kinematic viscosity on the basic properties (viz. amplitude, width, speed, etc.) of EASWs are discussed. It is examined that the EASWs in nonplanar geometry significantly differ from those in planar geometry. The results of this investigation can be helpful in understanding the nonlinear features of EASWs in various astrophysical plasmas.     

Drift wave turbulence in a dense semi-classical magnetoplasma

A semi-classical nonlinear collisional drift wave model for dense magnetized plasmas is developed and solved numerically. The effects of fluid electron density fluctuations associated with quantum statistical pressure and quantum Bohm force are included, and their influences on the collisional drift wave instability and the resulting fully developed nanoscale drift wave turbulence are discussed. It is found that the quantum effects increase the growth rate of the collisional drift wave instability, and introduce a finite de Broglie length screening on the drift wave turbulent density perturbations. The relevance to nanoscale turbulence in nonuniform dense magnetoplasmas is discussed.     

Spin magnetosonic shock-like waves in quantum plasmas

The propagation of one-dimensional shock-like waves (SLWs) in a dissipative quantum magnetoplasma medium is studied. A quantum magnetohydrodynamic (QMHD) model is used to take into account the effects of quantum force associated with the Bohm potential and the pressure-like spin force for electrons. It is shown that the nonlinear evolution equation [Korteweg-de-Vries-Burger (KdVB)], which describes the dynamics of small but finite amplitude magnetosonic waves (MSWs) (where the dissipation is provided by the plasma resistivity) exhibits both oscillatory and monotonic shock-like perturbations (SLPs) by the effects of collective tunneling and spin alignment. Both the quantum and spin force significantly modify the shock-like structures and the strength of SLPs. The theoretical results could be of important for strongly magnetized astrophysical (e.g., pulsars, magnetars) plasmas.     

Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

The nonlinear propagation of modified electron‐acoustic (mEA) shock waves in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non‐relativistic degenerate inertial cold electrons, both nonrelativistic and ultra‐relativistic degenerate hot electron and inertial positron fluids, and positively charged static ions) has been investigated theoretically. The well‐known Burgers type equation has been derived for both planar and nonplanar geometry by employing the reductive perturbation method. The shock wave solution has also been obtained and numerically analyzed. It has been observed that the mEA shock waves are significantly modified due to the effects of degenerate pressure and other plasma parameters arised in this investigation. The properties of planar Burgers shocks are quite different from those of nonplanar Burgers shocks. The basic features and the underlying physics of shock waves, which are relevant to some astrophysical compact objects (viz. non‐rotating white dwarfs, neutron stars, etc.), are briefly discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lower hybrid wave instability in a spin‐polarized degenerate plasma

Lower hybrid (LH) wave instability excited due to an electron beam in a spin‐polarized degenerate plasma is studied. Using the Separate Spin Evolution quantum hydrodynamic model, incorporating Coulomb exchange interaction and Bohm potential, the general dispersion relation of nearly perpendicular propagating electrostatic waves is derived. Furthermore, in the low‐frequency limit, the dispersion of LH wave is obtained. It is found that the electron spin polarization and beam streaming speed reduce the growth rate as well as the k‐domain. However, the beam density and the propagation angle enhance both the growth rate and k‐domain of LH instability. In addition, the contribution of the Bohm potential term increases the intensity of the growth rate. All these effects may have a strong bearing on the wave and instability phenomena in spin‐polarized plasmas.     

Cylindrical and spherical dust ion-acoustic solitary waves in quantum plasmas

Dust ion-acoustic solitary waves in unmagnetized quantum plasmas are studied in spherical and cylindrical geometries. Using quantum hydrodynamic model, the electrostatic waves are investigated in the weakly nonlinear limit. A deformed Korteweg-de Vries (dKdV) equation is derived by using the reductive perturbation method and its numerical solutions are also presented. The quantum diffraction and quantum statistical effects incorporated in the system modifies the characteristics of dust ion-acoustic waves in cylindrical and spherical geometries. The role of stationary dust particles in quantum plasmas are also discussed. It is shown that the cylindrical and spherical dust ion-acoustic solitary waves behave quite differently from one-dimensional planar solitary waves in quantum plasmas.     

On the theory of Langmuir waves in a quantum plasma

Nonlinear quantum-mechanical equations are derived for Langmuir waves in an isotropic electron collisionless plasma. A general analysis of dispersion relations is carried out for complex spectra of Langmuir waves and van Kampen waves in a quantum plasma with an arbitrary electron momentum distribution. Quantum nonlinear collisionless Landau damping in Maxwellian and degenerate plasmas is studied. It is shown that collisionless damping of Langmuir waves (including zero sound) occurs in collisionless plasmas due to quantum correction in the Cherenkov absorption condition, which is a purely quantum effect. Solutions to the quantum dispersion equation are obtained for a degenerate plasma.