Quantum Statistical Pressure Research Articles

Stability analysis of linear ion waves leading to nonlinear shock and soliton structures in a dense quantum plasma with strongly coupled ions and degenerate electrons

In a quantum plasma with strongly coupled ions and Fermi degenerate electron fluids, features of low frequency wave dispersion and nonlinear electrostatic structure formation are explored. Dynamics of strongly coupled ions is considered through a generalized momentum balance equation over the visco-elastic relaxation time for ion correlations and viscosity of ion fluid through shear. Quantum forces associated with degenerate electron fluid include many-particle effect of exchange-correlations, quantum statistical-pressure and quantum recoil effect. The system supports dispersive shock and soliton structures regulated by the Korteweg-de Vries Burger equation and modified-Korteweg-de Varies equation, respectively which are derived and solved analytically. Only monotonic shock structures are observed for a given value of the Burger factorμ. For solitary structures, the amplitude and width depend upon quantum dispersive effects of electrons.

Electron-exchange and correlation effects on filamentation instability of a high-density current-driven plasma

The effects of exchange and correlation on the filamentation instability of a high-density current-driven plasma are theoretically investigated under diffusion conditions by applying the quantum hydrodynamic (QHD) model and the Ampère-Maxwell law. Based on the dispersion relation, a new instability condition is presented, according to which, the important characteristic quantities are identified. Moreover, the new condition reveals a red shift of the cutoff wavelength in which the instability is suppressed. As a result, the thickness of the current filaments would be greater in the presence of quantum effects. It is also proven that exchange and correlation effects on the instability growth rate and the current filament size are more significant than the other typical quantum phenomena, such as quantum diffraction and tunneling, which are included in the QHD model through the quantum statistical pressure and the Bohm potential.

Conversion efficiency of even harmonics of whistler pulse in quantum magnetoplasma

AbstractStudy of even harmonic generation resulting from propagation of whistler pulse in homogeneous high-density quantum plasma immersed in an externally applied magnetic field, using the recently developed quantum hydrodynamic model is presented. The effects of quantum Bohm potential, quantum statistical pressure, and electron spin have been taken into account. The field amplitude of even harmonic of the whistler with respect to fundamental wave and the conversion efficiency for phase-mismatch has been analyzed. The conversion efficiency of harmonic radiation depends on the plasma electron density, magnetic field strength as well as the intensity of whistler pulse. The efficiency increases significantly with an increase in plasma density, magnetic field and whistler wave intensity. Higher conversion efficiency is observed in degenerate plasma for lower values of the static magnetic field as compared with classical plasma.

Modulational and three wave decay instabilities in degenerate electron-ion dense plasmas

A formalism for nonlinear interaction of degenerate upper-hybrid waves (DUHWs) with degenerate ion-cyclotron waves (DICWs) and degenerate Alfven waves (DAWs) is revisited to account for quantum corrections owing to quantum Bohm potential, quantum exchange-correlations, and quantum statistical pressure. For this purpose, different nonlinear dispersion relations are derived with quantum settings. By using the phasor matching techniques, the growth rates of three wave decay and modulational instabilities are analyzed by identifying the nonlinear coupling of high-frequency DUHWs with low-frequency DICWs and DAWs. Numerically, it is revealed that parametric three wave decay and modulational instabilities are significantly influenced by the impact of Fermi pressure and exchange-correlation in a degenerate magnetoplasma. The present results are important to understand the dispersive properties of nonlinear waves and their mutual couplings at quantum scales in degenerate environments like white dwarfs, neutron stars, and magnetars.

Propagation of electrostatic energy through a quantum plasma

The theory of propagation of electrostatic energy through an infinite, homogeneous electron–ion quantum plasma is presented. Simple expressions for the energy flow, energy density, and energy velocity of longitudinal oscillation waves in the system are derived using the linearized quantum hydrodynamic theory for the electron fluid, which incorporates the important quantum statistical pressure and electron diffraction force, while the optical response of the ion particles is characterized by the classical frequency‐dependent dielectric function, ϵion. Both cases of plasmon (high‐frequency) and quantum ion‐acoustic (low‐frequency) waves are considered.

Stability analysis and applications of traveling wave solutions of three-dimensional nonlinear modified Zakharov–Kuznetsov equation in a magnetized plasma

Propagation of three-dimensional nonlinear solitary waves in a magnetized electron–positron plasma is analyzed. Modified extended mapping method is further modified and applied to three-dimensional nonlinear modified Zakharov–Kuznetsov equation to find traveling solitary wave solutions. As a result, electrostatic field potential, electric field, magnetic field and quantum statistical pressure are obtained with the aid of Mathematica. The new exact solitary wave solutions are obtained in different forms such as periodic, kink and anti-kink, dark soliton, bright soliton, bright and dark solitary waves, etc. The results are expressed in the forms of trigonometric, hyperbolic, rational and exponential functions. The electrostatic field potential and electric and magnetic fields are shown graphically. The soliton stability of these solitary wave solutions is analyzed. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems.

Quantum Space Charge Waves in a Waveguide Filled with Fermi-Dirac Plasmas Including Relativistic Wake Field and Quantum Statistical Pressure Effects

Abstract The effects of quantum statistical degeneracy pressure on the propagation of the quantum space charge wave are investigated in a cylindrically bounded plasma waveguide filled with relativistically degenerate quantum Fermi-Dirac plasmas and the relativistic ion wake field. The results show that the domain of the degenerate parameter for the resonant beam instability significantly increases with an increase of the scaled beam velocity. It is found that the instability domain of the wave number increases with an increase of the degenerate parameter. It is also found that the growth rate for the resonant beam instability decreases with an increase of the degenerate parameter. In addition, it is shown that the lowest harmonic mode provides the maximum value of the growth rates. Moreover, it is shown that the instability domain of the wave number decreases with an increase of the beam velocity.

Nonlinear quantum ion acoustic shock wave dynamics with exchange-correlation effects

The dynamics of linear and nonlinear electrostatic shock excitations is studied in homogeneous, unmagnetized, unbounded and dissipative quantum plasma consisting of electrons and ions. The dissipation in the system is taken into account by incorporating the ion kinematic viscosity. The system is modelled using the quantum hydrodynamic equations in which the electrons are significantly affected by the quantum forces, viz., the quantum statistical pressure, the quantum Bohm potential and electron exchange-correlations due to electron spin. In the weakly nonlinear limit, using reductive perturbation method deformed Korteweg-de Vries Burgers’s (KdVB) equation, which elegantly combines the effects of nonlinearity, dispersion and dissipation is derived. It is found that the present model predicts the existence of both nonlinear oscillatory and monotonic shock structures. The temporal evolution, stability and phase-space dynamics of nonlinear ion acoustic shocks are investigated numerically to elucidate the effects of quantum diffraction, electron exchange correlation and ion kinematic viscosity.

Effects of quantum statistical pressure on the Washimi-Karpman magnetization and power radiation in degenerate quantum Fermi-Dirac plasmas

The physical properties of the Washimi-Karpman ponderomotive magnetization are investigated in relativistically degenerate quantum Fermi-Dirac plasmas including the influence of quantum statistical degeneracy pressure. The induced magnetization and power radiation due to the Washimi-Karpman ponderomotive interaction are obtained in Fermi-Dirac plasmas. It is found that the ponderomotive magnetization decreases with an increase of the relativistic degeneracy parameter. It is also shown that the quantum statistical degeneracy pressure effect is more significant in small frequency and large wave number domains than that in large frequency and small wave number domains. In addition, it is found that the ponderomotive power radiation decreases with an increase of the relativistic degeneracy parameter in Fermi-Dirac plasmas. The variations of the Washimi-Karpman magnetization and power radiation due to the physical characteristics of degenerate quantum Fermi-Dirac plasmas are also discussed.

Damped electrostatic structures in quantum plasmas

In this work, we study the damped nonlinear solitary wave structures in electron ion dense collisional plasmas in the presence of exchange correlation potential. Due to high density and low temperature, these plasmas are considered as quantum plasmas. The quantum mechanical effects due to quantum statistical pressure, quantum tunnelling, and exchange correlation due to 1/2 spin of Fermions are included in a quantum hydrodynamic model. The collisions of plasmas particles with neutrals are taken into account to derive the Damped Korteweg-de Vries equation. A reductive perturbation technique is performed to study nonlinearities and dispersive effects in the plasma system. The comparative importance of the potential due to the degenerate pressure, exchange correlation potential, and the Bohm potential in the linear and nonlinear dispersion is presented. The effects of variations of different plasma parameters on propagation characteristics of damped oscillations in the context of astrophysical objects like neutron stars/pulsar are discussed.

Mathematical methods and solitary wave solutions of three-dimensional Zakharov-Kuznetsov-Burgers equation in dusty plasma and its applications

Abstract In this research article, a new technique for solving nonlinear complex physical phenomena, arising in different fields of science, is investigated, called Modified extended mapping method. The method is applied to three dimensional Zakharov-Kuznetsov-Burgers (ZKB) equation for the dust-ionacoustic waves in dusty plasmas. As a result, the exact and solitary wave solutions (which represent electric field potential), electric and magnetic fields and quantum statistical pressure for ZKB equation are obtained with the aid of Mathematica. These new exact solitary wave solutions are expressed in the forms of hyperbolic, trigonometric and rational functions. The graphical representations of the electric field potential and electric and magnetic fields are shown. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems.

Inverse Compton power and cooling time in a quantum Fermi-Dirac plasma including the quantum degeneracy pressure

The inverse Compton power is investigated in relativistically degenerate quantum Fermi-Dirac plasmas including the influence of quantum statistical degeneracy pressure. The ordinary and double Compton scattering cross sections, the inverse Compton power, and the cooling time are obtained in Fermi-Dirac plasmas. It is shown that the differential Compton scattering cross section has a maximum at the small wave number domain. However, the differential Compton scattering cross section increases with an increase of the wave number in the case of a large relativistic degeneracy parameter. It is interesting to note that the differential Compton scattering cross section in the backward scattering region is greater than that in the forward scattering region when the degeneracy pressure is large. It is also shown that the double Compton scattering process is quite suppressed in the forward scattering domain. It is also shown that the inverse Compton power increases with an increase of the relativistic degeneracy parameter. It is also shown that the influence of the relativistic degeneracy on the inverse Compton power is more significant for small plasmon energies. In addition, it is found that the cooling time due to the inverse Compton process decreases with an increase of the relativistic degeneracy parameter.

Propagation of Surface Modes in a Warm Non-Magnetized Quantum Plasma System**Supported by the National Natural Science Foundation of China under Grant No 11547137, and the Fundamental Research Funds for the Central Universities under Grant Nos JZ2015HGBZ0123 and JZ2016HGBZ0759.

The propagation of surface modes in warm non-magnetized quantum plasma is investigated. The surface modes are assumed to propagate on the plane between vacuum and warm quantum plasma. The quantum hydrodynamic model including quantum diffraction effect (the Bohm potential) and quantum statistical pressure is used to derive a new dispersion relation of surface modes. The new dispersion relation of surface modes is analyzed in some special interesting cases. It is shown that the dispersion relation can be reduced to the earlier results in some special cases. The results indicate that the quantum effects can facilitate the propagation of surface modes in such a semi-bounded plasma system. This work is helpful to understand the physical characteristics of the surface modes and the bounded quantum plasma.

Hydrodynamic theory of partially degenerate electron–hole fluids in semiconductors

A quantum hydrodynamic theory for high-frequency electron–hole Langmuir and acoustic-like oscillations as well as static charge shielding effects in arbitrarily doped semiconductors is presented. The model includes kinetic corrections to the quantum statistical pressure and to the quantum Bohm potential for partially degenerate electrons and holes at finite temperatures. The holes contribute to the oscillations and screening effects in semiconductors in a similar manner as real particles. The dielectric functions are derived in the high-frequency limit for wave excitations and in the low-frequency limit for the study of static screening. The dispersion relation for the Langmuir and acoustic-like oscillations is examined for different parameters of doped silicon (Si). Some interesting properties and differences of electron hole dynamical behavior in N- and P-type Si are pointed out. Holes are also observed to enhance an attractive charge shielding effect when the semiconductor is highly acceptor-doped.

Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma

The propagation of dust–ion-acoustic waves with high-energy electrons and positrons in three-dimensional is considered. The Zakharov–Kuznetsov–Burgers (ZKB) equations for the dust–ion-acoustic waves in dusty plasmas is obtained. The conservations laws and integrals of motion for the ZKB equation are deduced. In the present study, by applying the modified direct algebraic method, we found the electric field potential, electric field and quantum statistical pressure in form water wave solutions for three-dimensional ZKB equation. The solutions for the ZKB equation are obtained precisely and efficiency of the method can be demonstrated. The stability of the obtained solutions and the movement role of the waves by making the graphs of the exact solutions are discussed and analyzed.

Surface electromagnetic wave equations in a warm magnetized quantum plasma

Based on the single-fluid plasma model, a theoretical investigation of surface electromagnetic waves in a warm quantum magnetized inhomogeneous plasma is presented. The surface electromagnetic waves are assumed to propagate on the plane between a vacuum and a warm quantum magnetized plasma. The quantum magnetohydrodynamic model includes quantum diffraction effect (Bohm potential), and quantum statistical pressure is used to derive the new dispersion relation of surface electromagnetic waves. And the general dispersion relation is analyzed in some special cases of interest. It is shown that surface plasma oscillations can be propagated due to quantum effects, and the propagation velocity is enhanced. Furthermore, the external magnetic field has a significant effect on surface wave's dispersion equation. Our work should be of a useful tool for investigating the physical characteristic of surface waves and physical properties of the bounded quantum plasmas.

New nonlinear structures in a degenerate one-dimensional electron gas

The collective dynamics of nonlinear electron waves in an one-dimensional degenerate electron gas is treated using the Lagrangian fluid approach. A new class of solutions with a nontrivial space and time dependence is derived. Both analytical and numerical results demonstrate the formation of stable, breather-like modes, provided certain conditions are met. For large amplitudes of the initial density perturbation, a catastrophic collapse of the plasma density is predicted, even in the presence of the quantum statistical pressure and quantum diffraction dispersive effects. The results are useful for the understanding of the properties of general nonlinear structures in dense plasmas.

Density effects on bremsstrahlung radiation in quantum plasmas

In this paper, we investigate the effects of plasma number-density and quantum shielding of ions by degenerate electrons on the free-free and electron-atom bremsstrahlung radiation spectra in dense quantum plasmas for a wide range of plasma number-density and atomic-number of the constituent ions. We use previously reported results from the extended Shukla-Eliasson quantum-dressed ionic potential, which takes into account the relativistic degeneracy effect, the quantum statistical pressure, the electron-exchange correlations, the Wigner-Seitz cell interaction feature, as well as the important collective quantum diffraction of electrons. It is observed that the electron number-density has fundamental effect on the free-free and bound-bound bremsstrahlung radiation spectra over the whole frequency range of radiation. By comparing the radiation spectra for the quantum plasmas with ions of bare Coulomb, Thomas-Fermi, and extended quantum potentials, many important features of the bremsstrahlung radiation is highlighted. Current investigation can provide important information on plasma diagnostics for atomic processes in dense plasmas, such as the inertial-confinement fusion, warm dense matter, and the planetary cores. The results can also help in better understanding of the cooling processes in completely degenerate hot compact stellar objects such as white dwarfs.

Quantum Bohm correction to polarization spectrum of graphene

In this paper, by using a quantum hydrodynamic plasma model which incorporates the important quantum statistical pressure and electron diffraction force, we present the corrected plasmon dispersion relation for graphene which includes a k4 quantum term arising from the collective electron density wave interference effects. This correction may well describe the shortcoming of the previous results based on the classical hydrodynamics and confirms that the quantum hydrodynamic model may be as effective as the random phase approximation in successful description of the collective density excitations in quantum plasmas. It is clearly observed that the quantum correction due to the collective interaction of electron waves gives rise to significant contribution in the dispersion behavior of the collective plasmon density waves in a wide range of wavelength, as a fundamental property of the monolayer atom-thick graphene. It is revealed that the plasmon density-perturbation linear phase-speed in graphene possesses some universal minimum characteristic value, in the absence of an external magnetic field. It is further remarked that such correction also has important effect on the dielectric function, hence on the impurity screening, in graphene.

Self-similar expansion of a warm dense plasma

The properties of an expanding plasma composed of degenerate electron fluid and non-degenerate ions are studied. For our purposes, we use fluid equations for ions together with the electron momentum equation that include quantum forces (e.g., the quantum statistical pressure, forces due to the electron-exchange and electron correlations effects) and the quasi-neutrality condition. The governing equation is written in a tractable form by using a self-similar transformation. Numerical results for typical beryllium plasma parameters revealed that, during the expansion, the ion acoustic speed decreases for both isothermal and adiabatic ion pressure. When compared with classical hydrodynamic plasma expansion model, the electrons and ions are found to initially escape faster in vacuum creating thus an intense electric field that accelerates most of the particles into the vacuum ahead of the plasma expansion. The relevancy of the present model to beryllium plasma produced by a femto-second laser is highlighted