Quantum Hydrodynamic Model Research Articles

Propagation Characteristics of Electrostatic Surface Plasma Waves at the Spin‐Polarized Quantum Plasma–Vacuum Interface

ABSTRACTThis investigation explores the characteristics of electrostatic surface plasma waves within the framework of a spin‐polarized quantum plasma. Utilizing the spin‐polarized quantum hydrodynamic model and incorporating essential elements like Fermi pressure and Bohm potential, we derive the dispersion relation governing surface plasma waves at a plasma–vacuum interface. Through Fourier decomposition of the hydrodynamic model, we establish the dispersion relation that outlines the behavior of surface plasmons under conditions of small amplitude. Quantum effects, encompassing degenerate pressure, and Bohm potential are considered with specific attention given to the spin polarization effect, treating spin up, and spin down electrons as distinct species. The resulting dispersion relation demonstrates that, regardless of the degree of spin matching, Bohm potential significantly alters the phase speed in the limit of a large wave vector. Increasing spin mismatch in the quantum plasma leads to a decrease in the phase speed of the surface mode for a fixed value of the plasmonic coupling parameter . Our findings bear relevance to graphene‐based plasmonic systems, aligning with some of the observations reported in Gao et al. (2013) and Guo et al. (2019).

Landau quantization effects on damping Kawahara solitons in electron–positron–ion plasma in rotating ionized medium

For the dynamics of three-dimensional electron–positron–ion plasmas, a fluid quantum hydrodynamic model is proposed by considering Landau quantization effects in dense plasma. Ion–neutral collisions in the presence of the Coriolis force are also considered. The application of the reductive perturbation technique produces a wave evolution equation represented by a damped Korteweg–de Vries equation. This equation, however, is insufficient for describing waves in our system at very low dispersion coefficients. As a result, we considered the highest-order perturbation, which resulted in the damped Kawahara equation. The effects of the magnetic field, Landau quantization, the ratio of positron density to electron density, the ratio of positron density to ion density, and the direction cosine on linear dispersion laws as well as soliton and conoidal solutions of the damped Kawahara equation are explored. The understanding from this research can contribute to the broader field of astrophysics and aid in the interpretation of observational data from white dwarfs.

The combined effects of quantum and strong coupling on the nonlinear collective excitation in quantum dusty plasmas

The quantum hydrodynamic model for electrons and ions and the generalized hydrodynamic model for the strongly coupled dust particles are proposed in the strongly coupled quantum dusty plasma, where the combined quantum effects of quantum diffraction, quantum statistic pressure, as well as electron exchange and correlation effects are all considered in the quantum hydrodynamic model. The shear and bulk viscosity effects are included in the viscoelastic relaxation, which leads to the decay of the dust-ion-acoustic waves. The approximate time-dependent solitary solution is obtained by the momentum conservation law in the presence of viscosity.

Nonlinear analysis of ion‐acoustic solitary waves in an unmagnetized highly relativistic quantum plasma

AbstractThe present paper explores the dynamics of ion‐acoustic solitary waves (IASWs) within an unmagnetized, highly relativistic quantum plasma containing positive and negative ions alongside electrons, employing the quantum hydrodynamic model. The treatment accounts for the inertial characteristics of negative and positive ions, considering electrons as inertialess. The nonlinear nature of quantum IASWs is investigated through the derivation of the Korteweg–de Vries equation using the reductive perturbation method. The investigation highlights how wave propagation characteristics, whether compressive or rarefactive, are substantially modulated by several parameters, such as the quantum diffraction parameter , relativistic effects , equilibrium density , and ion mass ratio . The analysis identifies the existence of both slow and fast wave modes, heavily influenced by the relativistic parameters involved. Our findings have significant implications for the understanding of both laboratory and space plasmas, especially in contexts where negative ions are present.

Modulation instability of magnetosonic waves in semiconducting quantum plasma considering Fermi degenerate pressure, exchange correlation potential, and Bohm potential

This study investigates the modulation instability of magnetosonic waves in a semiconducting quantum plasma system. Utilizing the quantum hydrodynamic model, we derive the nonlinear Schrödinger equation and its solution through the reductive perturbation technique. The growth rate of modulation instability for magnetosonic waves has been derived. This study incorporates various quantum corrections, including Fermi degenerate pressure, exchange-correlation potential, and Bohm potential. We study the bright soliton profiles of magnetosonic waves, and additionally, we conduct graphical analyses of the linear dispersion relation and the product of the dispersive coefficient (P) and nonlinear coefficient (Q) of the nonlinear Schrödinger equation. It has been found that magnetosonic waves exhibit modulation instability within specific parameter ranges of the semiconductor plasma and at certain wavelength regimes. Further, we present a comparative study between GaSb and InSb semiconducting plasma systems. The exchange-correlation potential and Fermi degenerate pressure have significantly impacted the modulation instability growth rate, whereas the effect of the Bohm potential is much lower.

Higher order contribution to ion-acoustic Korteweg–de Vries (KdV) soliton in unmagnetized quantum plasmas with arbitrary degeneracy of electrons

The propagation of nonlinear ion-acoustic Korteweg–de Vries (KdV) solitons and dressed solitons (with higher order contribution term) in unmagnetized quantum plasmas with arbitrary degeneracy of electrons is investigated using quantum hydrodynamic model. The reductive perturbation method is used to derive the first order nonlinear ion-acoustic KdV equation and also higher order contribution of inhomogeneous differential equation is obtained for the dressed ion-acoustic wave soliton in arbitrary degenerate electron plasmas. Moreover, the higher order inhomogeneous differential equation is solved (nonsecular solution is obtained) using the renormalization method. The conditions for the validity of the higher order correction are also discussed in detail for ion-acoustic solitons in unmagnetized arbitrary degenerate electrons plasma case. The effects of chosen values of electron temperature, equilibrium fugacity and corresponding electron density of a physical quantum plasma system and quantum diffraction parameter H (for two conditions i.e., H < 2 or H > 2) on the amplitude and width of the KdV and dressed ion-acoustic wave solitons for both electrostatic potential hump (compressive) or dip (rarefactive) structures are investigated. The numerical plots are also presented for illustration with numerical values of a physical partially degenerate electrons plasma system exist in the astrophysical or laboratory conditions.

Nonlinear excitation of wakefields in quantum plasma channel

A detailed analytical study for wakefields excitation in a channel of quantum plasma is presented. The recently developed quantum hydrodynamic (QHD) model has been used to develop the interaction picture. Applying the perturbations in the laser fields orders, the magnetic and electric wakefields have been obtained for a Gaussian laser pulse. The electrons trapped by the wakefields are accelerated to extremely high energies. The quantum effects of Fermi statistical pressure and the quantum Bohm potential have been found to make significant changes in the nature of wakefields generated. The plasma channel helps in self-focusing and also contributes to acceleration. Both the longitudinal and transverse forces acting on the accelerating electron have been calculated.

Temperature-induced disruptive growth rate behavior due to streaming instability in semiconductor quantum plasma with nanoparticles

The nature of the growth rate due to streaming instability in a semiconductor quantum plasma implanted with nanoparticles has been analyzed using the quantum hydrodynamic model. In this study, the intriguing effect of temperature, beam electron speed, and electron-hole density on growth rate and frequency is investigated. The results show that the growth rate demonstrates a nonlinear behavior, strongly linked to the boron implantation, beam electron streaming speed and quantum correction factor. A noteworthy finding in this work is the discontinuous nature of the growth rate of streaming instability in boron implanted semiconducting plasma system. The implantation leads to a gap in the growth rate which further gets enhanced upon increase in concentration of implantation. This behavior is apparent only for a specific range of the ratio of thermal speed of the electrons to that of the holes.

Excitation of nonlinear longitudinal structures in spin‐1/2 quantum plasma in the presence of ion beam

AbstractThe formation of longitudinal, nonlinear structures in an interacting ion beam, spin‐1/2 quantum, electron‐ion plasma is reported by employing a separate spin evolution quantum hydrodynamic model (SSE‐QHD). The reductive perturbation method is followed to develop the KdV equations. In the presence of an ion beam and keeping the finite electron inertial effects, ion acoustic (IA) soliton and spin electron acoustic (SEA) soliton are found. The critical values of beam speed and spin polarization, required for the existence of solitary structures, are highlighted. It is prescribed that the present model supports rarefactive and compressive SEA soliton and compressive IA soliton. It is shown that the ion beam is essential for the existence of a compressive SEA solitary structure. We have also calculated and compared the energy densities of both solitons. Furthermore, the dependence of the nonlinear structures on the beam parameters and spin polarization are also examined. Our findings would be useful to understand the new spin‐dependent nonlinear structures as well as the features of nonlinear IA waves in ion beam–plasma interactions.

The effect of external magnetic field on the instability of THz plasma waves in nanoscale graphene field-effect transistors

Abstract The instability of plasma waves in the channel of field-effect transistors will cause the electromagnetic waves with THz frequency. Based on a self-consistent quantum hydrodynamic model, the instability of THz plasmas waves in the channel of graphene field-effect transistors has been investigated with external magnetic field and quantum effects. We analyzed the influence of weak magnetic fields, quantum effects, device size, and temperature on the instability of plasma waves under asymmetric boundary conditions numerically. The study results show that the magnetic fields, quantum effects, and the thickness of the dielectric layer between the gate and the channel can increase the radiation frequency. Additionally, we observed that increase in temperature leads to a decrease in both oscillation frequency and instability increment. The numerical results and accompanying images obtained from our simulations provide support for the above conclusions.

Magnetoacoustics and magnetic quantization of Fermi states in relativistic plasmas

Abstract Dispersive characteristics of electromagnetic sound waves with frequencies less than the electron and ion gyro-frequencies are studied herein analytically and numerically at astrophysical scales. Magnetic quantization of Fermi states is concerned with the degenerate relativistic electrons fluid treated by quantum hydrodynamic model (QHD). The quantum features are included from Landau quantized Fermi pressure dependent upon the dc magnetic field, whereas the ions are treated as nondegenerate and classical. The numerical analysis verifies the analytical results. The phase speed of magnetosonic waves for relativistic degenerate plasma typically for white dwarf stars parameters is depicted from the graphical figures. In this manuscript, an overlooked feature of quantization, that is Landau quantization, is mainly focused for magnetoacoustics in plasmas.

The Dynamics of Electron Acoustic Solitary Waves in a Nonmagnetized Quantum Plasma with Two Temperature Electrons

In this article we have studied the linear and nonlinear properties of plasma waves using a one-dimensional quantum hydrodynamic (QHD) model specifically designed for quantum plasma with electron acoustic waves (EAWs). In particular, we use the standard reductive perturbation method to investigate the solitary structures resulting from nonlinearity. We use this method to derive and numerically analyze the Kortewegde Vries (KdV) equation relevant to the plasma system as well as the dispersion relation. Furthermore, in order to shed light on the dynamics of plasma waves under external influences, we investigate the temporal evolution of a forced KdV equation. PACS-52.20.j; 52.25.b; 52.30.d; 52.35.Mw; 52.65.Vv.

A new perspective on drift waves in self-gravitating magnetized quantum plasma

The quantum hydrodynamic model is used in this study to investigate electrostatic waves in a non-uniform, quantum magnetized dusty plasmas while accounting for dust gravitational effects. Quantum effects for dust grains are omitted, and ions and electrons are considered low-temperature Fermi gases. The generalized analytical dispersion relationship for the dust gravitation drift (DGD) wave is derived. The temperature dependence of the environment induces quantum effects which have been shown to have a significant impact on wave dispersion. In the absence of gravitational effects at high temperature, the fundamental dust drift mode has been reproduced. The criteria and the transitioning regimes are presented. Our findings apply to dense astrophysical objects such as the Enceladus encounter in the E ring of Saturn.

Lagrangian reduction and wave mean flow interaction

How does one derive models of dynamical feedback effects in multiscale, multiphysics systems such as wave mean flow interaction (WMFI)? We shall address this question for hybrid dynamical systems, defined as systems whose motion can be expressed as the composition of two or more Lie-group actions. Hybrid systems abound in fluid dynamics. Examples include: the dynamics of complex fluids such as liquid crystals; wind-driven waves propagating with the currents moving on the sea surface; turbulence modelling in fluids and plasmas; and classical–quantum hydrodynamic models in molecular chemistry. From among these examples, the motivating question here is: How do wind-driven waves produce ocean surface currents?The paper first summarises the geometric mechanics approach for deriving hybrid models of multiscale, multiphysics motions in ideal fluid dynamics. It then illustrates this approach for WMFI in the examples of 3D WKB waves and 2D wave amplitudes governed by the nonlinear Schrödinger (NLS) equation propagating in the frame of motion of an ideal incompressible inhomogeneous Euler fluid flow. The results for these examples tell us that the mean flow in WMFI does not create waves, although it does transport the waves. However, feedback in the opposite direction is possible, since the 3D WKB and 2D NLS wave dynamics discussed here do in fact create circulatory mean flow.

Quantum hydrodynamic model for noble metal nanoplasmonics

The quantum hydrodynamic model (QHDM) has become a versatile and efficient tool for plasmonics at nanometer and even subnanometer length scales, but the theory is principally applicable only to simple metals. For the most common plasmonic materials, i.e., noble metals, QHDM has not been duly justified to describe their optical responses. In particular, when noble metal structures interface with dielectric materials, electron spillover plays an important role. Although a background optical permittivity is usually invoked in Amp\`ere's law to encompass the $d$-band electrons' effect on optical responses in a direct manner, their indirect effects, e.g., acting via conduction electrons, still remain elusive. Here we identify these indirect effects and develop a near-field potential ${U}_{\mathrm{aff}}$ refined QHDM (U-QHDM), in which the $d$-band electrons' effects on the conduction electrons are recognized and the electrostatic properties of dielectric are incorporated. We report the detailed procedures of calibrating U-QHDM. Material-independent model parameters are fitted with density functional theory (DFT) calculations for simple metals. Last, the calibrated U-QHDM is benchmarked against DFT and time-dependent DFT within stabilized jellium model for Ag, Au, and Al nanostructures interfacing with dielectrics. We expect U-QHDM will be a valuable asset for the rapidly developing field of extreme nanophotonics.

Magnetosonics with Landau levels in GaAs semiconductor systems

The propagation of low frequency electromagnetic magnetosonic waves in a quantum magneto electron–hole plasma is investigated. Both of the semiconductor plasma species are magnetically quantized at equilibrium. The quantization is included through recoil effect and Landau effects on applying quantum hydrodynamic model (QHD). Analytical results of quantum hydrodynamical model are then verified numerically for GaAs plasma system.

Acoustic stability of a self-gravitating cylinder leading to astrostructure formation

We employ a quantum hydrodynamic model to investigate the cylindrical acoustic waves excitable in a gyromagnetoactive self-gravitating viscous cylinder comprised of two-component (electron–ion) plasma. The electronic equation of state incorporates the effect of temperature degeneracy. It reveals an expression for the generalized pressure capable of reproducing a completely degenerate (CD) quantum (Fermi) pressure and a completely non-degenerate (CND) classical (thermal) pressure. A standard cylindrical wave analysis, moderated by the Hankel function, yields a generalized linear (sextic) dispersion relation. The low-frequency analysis is carried out procedurally in four distinct parametric special cases of astronomical importance. It includes the quantum (CD) non-planar (cylindrical), quantum (CD) planar, classical (CND) non-planar (cylindrical), and classical (CND) planar. We examine the multi-parametric influences on the instability dynamics, such as the plasma equilibrium concentration, kinematic viscosity, and so forth. It is found that, in the quantum regime, the concentration plays a major role in the system destabilization. In the classical regime, the plasma temperature plays an important role in both the stabilization and destabilization. It is further seen that the embedded magnetic field influences the instability growth dynamics in different multiparametric regimes extensively, and so forth. The presented analysis can hopefully be applicable to understand the cylindrical acoustic wave dynamics leading actively to the formation of astrophysical gyromagnetic (filamentary) structures in diverse astronomical circumstances in both the classical and quantum regimes of astronomical relevance.

Ion acoustic solitons collision in spin-polarized relativistic quantum plasma

The dynamics of electrostatic ion acoustic solitons collision in relativistic magnetized spin-polarized plasma is studied using a Magnetized Relativistic Quantum Hydrodynamics model. The plasmas components are relativistic degenerate electron with spin-up (n e↑) and spin-down (n e↓) concentrations, and relativistic inertial classical ions. In two-dimensional plasma geometry, a homogeneous external magnetic field is provided along the z-direction, i.e. . The extended Poincare Lighthill Kuo (PLK) approach is used to calculate the Kortewegde Vries equations for oppositely moving ion-acoustic solitons. Before and after collision, their trajectories and associated phase shifts are computed. Only negative polarity pulses of ion acoustic solitons are observed in our stated relativistic magnetized plasma. The spin density popularization ratio κ is shown to have a significant impact on the phase shifts of colliding solitons. It is found that when κ increases, one soliton's phase shift increases while the other soliton's phase shift decreases. The relativistic effects are also analyzed numerically and found that the phase shift of colliding ions acoustic solitons grows as the relativistic component rises from weakly to ultra-relativistic. It is observed that the phase shift of both solitons is to be dependent on their phase velocity with each other. Our research is noteworthy in that it focuses on, the astrophysical systems such as white dwarf, neutron star and pulsar.

Propagation of surface plasmons in a quantum collisional semiconductor plasma

In this work, the propagation of surface plasmons in a quantum collisional semiconductor plasma is theoretically investigated using the quantum hydrodynamic model. The general dispersion equation of surface plasmons is deduced and solved in the presence of collisional effects and quantum tunneling of electrons and holes. It is shown that collisions play a significant role in the decay or growth of surface plasmons. Moreover, it is found that the quantum tunneling of electrons and holes increases the phase velocity, the group velocity, and the growth rate of instability. It is also indicated that the growth rate of instability is decreased with the increase of the ratio of hole density to electron density and the ratio of electron effective mass to hole effective mass.

Semiconductor full quantum hydrodynamic model with non-flat doping profile: I) Stability of steady state

Semiconductor full quantum hydrodynamic model with non-flat doping profile: I) Stability of steady state