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In current research we use the effective Schrödinger-Poisson model to study a new kind of quantum level instability in an infinite-wall slab electron system. We use the Madelung fluid representation along with the conventional eigenvalue problem techniques in order to solve the linearized coupled differential equations representing the transverse collective linear excitations in the electron gas of arbitrary degree of degeneracy having a constant perpendicular momentum. It is shown that the energy levels of collective electrostatic excitations are doubly quantized due to coupled interactions between single-electron analogous to the classic problem of a particle in a box and collective Langmuir oscillations, which are modulated over single particle quantum state. We also report a new transverse electron slab current plasmon energy level instability caused by the interplay between the wave-like many-electron dispersion and the destabilizing perpendicular electron drift momentum. We further study in detail the parametric dependence of such instability versus different aspects of the quantum system. Such a quantum-level instability may have important applications in characteristic behavior the plasmonic devices and their frequency response. Parametric quantization of drifting electron fluid in a box may also have broad applications in nanoscale quantum device calibration and measurements.

In this paper, by using the effective Schrödinger–Poisson model, we investigate quantum edge plasmon excitations and electron spill-out effect in an arbitrary degenerate electron gas in the presence of perpendicular electron drift momentum. It is found that the single-electron Schrödinger equation solution produces a nonoscillatory electron number density distribution on the interface showing characteristic surface-dipole and electron spill-out effects. However, the Schrödinger–Poisson model produces large amplitude dual-tone density distribution due to both wave-like and particle-like plasmon dispersion other than surface-dipole and electron spill-out effects. The variations in the density structure are investigated in terms of different parameters such as the chemical potential, temperature, quantum electron tunneling parameter, and perpendicular electron de Broglie's wavenumber. Furthermore, we extend our study to the case of collective electron tunneling and reveal that the interface potential energy significantly differs from the case of single-electron quantum tunneling and strongly depends on the electron gas parameters. The current study reveals interesting features of the transverse plasmon excitations and electron spill-out in a current carrying narrow metal slab or metal–dielectric quantum sandwich interfaces incorporating both single-electron and collective quantum tunneling.

Small and large amplitude linear and nonlinear ion acoustic and Langmuir waves are investigated for plasma with the generalized equation of state (EoS). This EoS covers a wide range of energy-density conditions from dilute classical regime up to the relativistically degenerate matter. Investigation shows that the linear dispersion and localized excitations of ion acoustic waves are significantly affected by the plasma parameters. It is also found that the criterion for ordinary soliton existence is significantly different for fully degenerate and nondegenerate plasma regimes with given electron temperature. In the nondegenerate regime, bright solitons form only for Mach numbers above a critical value which is only a function of the fluid temperature.

In this paper we investigate the resonant electron-plasmon interactions in a drifting electron gas of arbitrary degeneracy. The kinetic corrected quantum hydrodyanmic model is transformed into the effective Schr\"{o}dinger-Poisson model and driven coupled pseudoforce system is obtained via the separation of variables from the appropriately linearized system. It is remarked that in the low phase-speed kinetic regime the characteristic particle-like plasmon branch is profoundly affected by this correction which is a function of the electron number density and temperature. We also present an alternative explanation of the quantum wave-particle duality as a direct consequence of resonant electron-plasmon interaction (electron murmuration). In this picture drifting electrons are resonantly scattered by spatial electrostatic energy distribution, characterizing them by the de Broglie's oscillations. The phase-shift and amplitude of excitations in damped driven pseudoforce system is derived and their variations in terms of normalized chemical potential and electron temperature is studied. In particular we investigate the kinetic correction effect on energy dispersion relation in the electron gas in detail. It is revealed that only the low phase-speed branch of the dispersion curve is significantly affected by the kinetic correction. It is also found that increase in the electron number density leads to increase in effective mass and consequently decrease in electron mobility while the increase in the electron temperature has the converse effect. The kinetic correction also significantly lowers the plasmon conduction band. Current model may be further elaborated to investigate the beam-plasmon interaction and energy exchange in multispecies quantum plasmas., Comment: arXiv admin note: substantial text overlap with arXiv:2002.04690

Using the asymptotic iteration method (AIM), we investigate the variation in the 1s energy levels of hydrogen and helium-like static ions in fully degenerate electron gas. The semiclassical Thomas–Fermi (TF), Shukla–Eliasson (SE), and corrected Shukla–Eliasson (cSE) models are compared. It is noted that these models merge into the vacuum level for hydrogen and helium-like ions in the dilute classical electron gas regime. While in the TF model, the hydrogen ground state level lifts monotonically toward the continuum limit with an increase in the electron concentration; in the SE and cSE models, a universal bound stabilization valley through the energy minimization occurs at a particular electron concentration range for the hydrogen-like ion which for the cSE model closely matches the electron concentrations in typical metals. The latter stabilizing mechanism appears to be due to the interaction between plasmon excitations and the Fermi length scales in the metallic density regime. In the case of helium-like ions, however, no such stability mechanism is found. The application of the cSE model with electron exchange and correlation effects reveals that the cSE model qualitatively accounts for the number density and lattice parameters of elemental metals within the framework of free electron assumption. According to the cSE model of static charge, screening a simple metal–insulator transition criterion is defined. The effect of the relativistic degeneracy effect on the ground state energy of the hydrogen atom is studied. It is shown that the ground state energy level of the hydrogen atom also undergoes a collapse at the well-known Chandrasekhar mass limit for white dwarf stars.

A hydrodynamic two fluid model encompassing inertialess electrons of arbitrary degree of degeneracy and cold ions using the quasineutrality assumption are reduced to an effective nonlinear Schr\"{o}dinger equation (NLSE) which is used to investigate driven electrostatic ion quasiparticle excitations. The quantized frequency spectrum of these quasiparticle excitations in a one-dimensional quasineutral electron-ion plasma confined in rectangular potential well is calculated. This spectrum shows a quadratic energy level increase quite similar to that of a single electron confined in a hard box with much reduced level spacings proportional to the electron to ion mass ratio. The electrostatic quasiparticle energy spectrum can be used in direct calculation of some physical properties of arbitrary degenerate plasmas such as the low-temperature specific heat capacity and thermal expansion of nanometallic compounds, semiconductors and other types of quantum plasmas. The parametrically driven NLSE is also used to study the quantum Faraday excitations in both weakly and fully nonlinear regime by employing the pseudopotential technique. The quantization criterion for fully nonlinear driven quantum Faraday excitations in an arbitrary degenerate plasma confined in a hard box of length $l$ is derived and it is shown that these excitation constitute a full spectrum frequency levels starting with those of small amplitude, high frequency sinusoidal quasiparticles up to the topmost zero-frequency level solitary quasiparticle excitations (quasisoliton level)

In this paper we study the propagation of elliptically polarized transverse electromagnetic waves in a quasineutral plasma with arbitrary degenerate electron fluid ranging from classical dilute to fully degenerate density regimes by using the appropriate collisional magnetohydrodynamics model, which incorporates the adiabatic quantum equation of states for high-frequency electron fluid compression and the Bohm quantum potential responsible for the collective quantum diffraction effect. Three distinct propagation modes are categorized corresponding to electron density regimes of dilute, intermediate, and fully degenerate plasmas. One of these modes is found to be purely of quantum mechanical origin and disappears in the absence of the quantum diffraction effect. The present generalized magnetohydrodynamics theory qualitatively describes key features of optical parameters and experimental data of dilute classical, semiconducting, and in fully degenerate plasmas. Different optical parameters, such as the refractive and absorption index of the new mode are investigated. It is shown that the optical response of the magnetized plasma with arbitrary degeneracy is essentially governed by three characteristic frequencies, namely, collision, plasmon, and cyclotron frequencies. The profound experimental minimum in the refractive index of arbitrary degenerate quantum plasmas and its dependence on the characteristic frequencies is studied in detail. Current investigation is of fundamental importance in high energy density and fusion plasma diagnostics and may provide key knowledge on the characteristics of astrophysical dense matter.

In this research, we study the traveling wave solution of an effective Schrodinger–Poisson system in the framework of quantum hydrodynamic model of a drifting electron gas with arbitrary degeneracy. It is shown that collective excitations in a quantum electron beam are characterized by two distinct particle-like and wave-like (de Broglie) wavenumbers depending on many beam parameters such as the drift speed, chemical potential, and background electromagnetic potential energies. Moreover, a new kind of beam-plasmon instability, referred to as the quantum drift instability, is found to exist in this system, which is caused by imbalance between the kinetic energy of the beam and the ambient electromagnetic and chemical potential energies. The quantum drift instability is an effect in which the energy flow from small wavelength particle-like excitations to long wavelength collective excitations occurs below a critical beam drift speed and may be characterized as the inverse of the usual Landau damping effect. We also investigate different kinds of quantum electron fluid interference effects based on generalized de Broglie wavenumbers. It is shown that in the limit of very low electron concentration and high drift the electron beam is described by the characteristic quantum de Broglie wavenumber. The fully nonlinear isothermal and adiabatic beam excitations are also numerically investigated. It is shown that quantized values of the mono-energetic electron beam speed give rise to resonant self-interference condition.

The quantum hydrodynamic model is used to investigate the arbitrary degenerate electron/hole stream instabilities in ballistic semiconductors or semiconductor plasmas (semiplasmas) for a wide range of impurity doping, number density, and temperatures. It is observed that, while the instability in classical plasma regime is always of single $k$ -range type, the double-range instability can occur in degenerate plasma regime. Different types of carrier counter-streaming instabilities are classified and parametrically studied in arbitrarily doped ballistic semiconductors. The parametric study of counter-stream instability in silicon at room temperature shows that the doping scheme has fundamental effect on electron–electron and hole–hole instabilities but no effect on electron–hole instability. Other parameters, such as the electron temperature and stream speed, have significant effects on the unstable wavenumber range and the growth rate. It is remarked that the electron stream in n-type semiconductors becomes unstable at somewhat lower limit of the stream speed than that of holes in a p-type silicon semiconductors. A description based on the energy exchange between unstable modes is given for different instability types. It is found that the instability in asymmetric doped semiconductors (electron–electron and hole–hole) is of symmetric type without energy exchange between the modes, while, for symmetric doped semiconductors (electron–hole), it is of asymmetric type with the energy exchange. Finally, it is found that the electron and hole spin exchange–correlation effects enhance the two-stream instability.

In this paper, using the generalized coupled pseudoforce model with driving elements, we develop a method to study the plasmon excitations and energy band structure in a plasmonic crystal. It is shown that the presence of the periodic ion core potential leads to pseudo-resonance condition in the plasmon wavefunction and electrostatic potential profiles, quite analogous to the frequency resonance, leading to the gap formation in the energy dispersion profiles. It is found that the dual length scale character of plasmon excitations lead to occurrence of a critical value of $a_c=2\pi\lambda_p$ for the lattice constant ($\lambda_p$ being the plasmon wavelength) above and below which the energy band structure of plasmonic crystals becomes substantially different. It is also found that energy band gap positions of parabolic free electron energy dispersion relation are slightly higher compared to that of the plasmon excitations. Here based on the plasmon definition and due to the dual length scale character of plasmons compared to that of single electrons, we provide a simplified interpretation of the wave-particle duality in quantum physics and provide the length scale regime in which both wave and particle properties can be simultaneously examined in a single experiment, where, the complementarity principle breaks down. However, the dual characteristics of electron-plasmon coupled excitations, quite analogous to starling murmuration phenomenon, strongly suggests that the long south de Broglie-Bohm pilot wave of electron is nothing but the plasmon itself. The wavefunction and electrostatic potential solution for a one dimensional plasmonic lattice with a generalized periodic potential is also derived in this research., Comment: 21 pages and 7 Figs

The one dimensional (1D) driven quantum coupled pseudoforce system governing the dynamics of collective Langmuir electron oscillations is used in order to investigate the effects of variety of space charge distributions on plasmon excitations of a nearly free electron gas with arbitrary degree of degeneracy and electron fluid temperature. A generalized closed form analytic expression for the grand wavefunction of collective excitations in presence of an arbitrary space charge distribution is presented based on the stationary solutions of the driven coupled pseudoforce system which has been derived from the Schr\"{o}dinger-Poisson model. The wavefunction and electrostatic potential profiles for some especial cases such as the Heaviside charge distribution, Dirac charge sheet, impurity charge sheet in 1D plasmonic lattice and the Kroning-Penney Dirac charge distributions with particular applications in plasmonics and condensed matter physics is investigated in this paper. It is remarkably found that two parallel Dirac charged sheets completely shield all interior plasmon excitations with any given energy value from outside electrostatic fields and charge densities. It is also found that the presence of even a weakly charged impurity layer within a perfect 1D plasmonic crystal profoundly destroys the periodic electrostatic field of the crystal lattice, hence, the Bloch character of the wavefunction considered in band gap theory of solids. Current investigation of electron excitations in arbitrary degenerate electron gas in the presence of static charge distributions may be used to develop analytic models for a variety of real physical situations. It also helps in further developments of the rapidly growing fields of nanotechnology and plasmonics., Comment: 18 pages 5 figures

In this paper we use the Schr\"{o}dinger-Poisson model to obtain a linear coupled pseudoforce system from which the wave function and the electrostatic potential of the free electron gas plasmon is deduced. It is shown that unlike for single particle wave function the plasmon wave function and corresponding electrostatic potential are characterized with two different wave numbers associated with two distinct characteristic length scales, namely, that of the single electron oscillation and of the collective Langmuir excitations. Interaction of plasmon with a rectangular potential step/well indicates features common with that of the ordinary single quantum particle. However, the two-tone oscillation character of the wave function and potential appear on the transmitted amplitude over the potential barrier/well. The plasmon propagation is found to have a distinct energy gap corresponding to the plasmon energy value of $\epsilon_g=\mu_0+2\epsilon_p$ below which no plasmon excitations occur. For instance, the zero-point plasmon excitation energy for Aluminium, is around $\epsilon_0\simeq 41.7$eV at room temperature, with the Fermi energy of $\epsilon_F\simeq 11.7$eV and plasmon energy of $\epsilon_p\simeq 15$eV. It is seen that for plasmon energies very close to the energy gap, i.e. where the two characteristic scales match ($k_1\simeq k_2$), the quantum beating effect takes place. The study of plasmon tunneling through the potential barrier indicates that the transmittivity has oscillatory behavior similar to that of a quantum particle tunneling through the potentials, but, with a characteristic two-tone oscillatory profiles. Current development can have a broad range of applications in plasmon transport through diverse free electron environments with arbitrary degeneracy and electron temperature. It also makes progress in rapidly growing nanotechnology and plasmonic fields., Comment: 21 Pages 6 Figures Submitted to Physics of Plasmas

In this paper, we investigate the electrical transport of two-terminal trilayer graphene and silicene flake (bilayer and monolayer nanoribbons) in the absence and presence of nanopores and DNA molecule by using Green’s function method. The passage of the DNA molecule through the nanopore significantly changes the transport properties. It is found that passing double-stranded DNA through trilayer graphene nanopore (tGNP) causes the metal-semiconductor quantum phase transition and in trilayer silicene nanopore (tSNP) increases the energy gap. The transport properties of DNA strands passing through nanopores depend on the thickness of the nanopores, the leads and the location of the electrodes. It has been shown that in tSNP and tGNP the energy gap with monolayer connections is larger than that of the bilayer connections. The computational results show reduction in electron transmission for both types of nanopores. These results can be useful for making a DNA sequencing devices.

In this paper we develop a new method to study the plasmon energy band structure in multispecies plasmas. Using this method, we investigate plasmon dispersion band structure of different plasma systems with arbitrary degenerate electron fluid. The linearized Schr\"{o}dinger-Poisson model is used to derive appropriate coupled pseudoforce system from which the energy dispersion structure is calculated. It is shown that the introduction of ion mobility, beyond the jellium (static ion) model with a wide plasmon energy band gap, can fundamentally modify the plasmon dispersion character leading to a new form of low-level energy band, due to the electron-ion band structure mixing. The effects ionic of charge state and chemical potential of the electron fluid on the plasmonic band structure indicate many new features and reveal the fundamental role played by ions in the phonon assisted plasmon excitations in the electron-ion plasma system. Moreover, our study reveals that ion charge screening has a significant impact on the plasmon excitations in ion containing plasmas. The energy band structure of pair plasmas confirm the unique role of ions on the plasmon excitations in many all plasma environments. Current research helps to better understand the underlying mechanisms of collective excitations in charged environment and the important role of heavy species on the elementary plasmon quasiparticles. The method developed in this research may also be extended for complex multispecies and magnetized quantum plasmas as well as to investigation the surface plasmon-polariton interactions in nanometallic structures., Comment: 20 Pages 5 Figures

The shielding potential around a test charge is calculated, using the linearized quantum hydrodynamic formulation with the statistical pressure and Bohm potential derived from finite temperature kinetic theory, and the temperature effects on the force between ions is assessed. The derived screening potential covers the full range of electron degeneracy in the equation of state of the plasma electrons. An attractive force between shielded ions in an arbitrary degenerate plasma exists below a critical temperature and density. The effect of the temperature on the screening potential profile qualitatively describes the ion–ion bound interaction strength and length variations. This may be used to investigate physical properties of plasmas and in molecular-dynamics simulations of fermion plasma. It is further shown that the Bohm potential including the kinetic corrections has a profound effect on the Thomson scattering cross section in quantum plasmas with arbitrary degeneracy.

The propagation of transverse Electromagnetic (EM) waves along a high energy relativistic electron beam passing through a neutralizing heavy ion background is investigated in the presence of an external axial magnetic field. By making use of the linearized fluid equations coupled with Maxwell’s equations the dielectric tensor and the dispersion relation of excited modes are derived. Since the electron motion is considered relativistic and fluid theory of plasma is used to describe the system, the obtained results are applicable to a vast range of high energy density regime. The mutual interaction between EM and Electron Plasma Waves (EPWs) is studied numerically. In the absence of the axial magnetic field, the EPWs and the Extraordinary Electromagnetic (EOEM) waves interact due to the existence of the self-generated magnetic field. The instability caused by this interaction has already been reported [Phys. Plasma.16, 062107 (2009) ]. We found that applying an axial magnetic field will cause deflection to plasma oscillations which enables coupling between EPWs and Ordinary Electromagnetic (OEM) waves as well. The results show that increasing the external magnetic field strength suppresses the growth rate caused by the coupling of EPWs-EOEM and passes it to the growth of EPWs-OEM. Therefore by adjusting the external magnetic field strength, the growth of EOEM and OEM modes can be controlled.

In this paper, we investigate the resonant scattering of driven linear oscillations in an isothermal electron gas with an arbitrary degree of degeneracy. The coupled pseudoforce system is obtained from the quantum hydrodynamic model and is extended to include the driving pseudoforce and pseudodamping effect in order to study the quantum charge shielding on the resonant scattering, heat capacity, and Friedel oscillations around an impurity charge. It is shown that the resonant scattering phenomenon takes place when the driver wavelength matches either scale lengths of plasmon excitations, which arise due to single electron oscillations and collective electron plasma excitations. It is remarked that in the presence of a periodic density structure such as in metals, plasmon interactions with a periodic lattice structure can lead to resonant Bragg-like scattering. A generalized energy dispersion relation for pseudodamped plasmon excitations is obtained, which indicates a critical screening point beyond which the plasmon excitations behave only particlelike. It is shown that the heat capacity of plasmon excitations and the static quantum charge screening are strongly affected by interaction between the plasmon and the charge screening scale lengths.

In this paper, we investigate the energy loss of ions by arbitrarily degenerate electron fluid, in the framework of hydrodynamic model by incorporating the generalized relativistic degeneracy pressure, Wigner–Seitz cell Coulomb interactions, and electron spin-exchange pressures for a wide range of electron number-density regimes relevant to the solid density (SD), inertial confinement fusion (ICF), warm dense matter (WDM), and super-dense astrophysical objects, such as white dwarf (WD) stars. It is found that the use of non-relativistic degeneracy pressure for electron fluid, instead of the exact Chandrasekhar relativistic degeneracy pressure, for the ICF density regime and beyond can introduce significant relative error to the stopping power calculation. Therefore, current study may introduce a significant change to the ICF scheme of super-compressed fuel. It is further revealed that the relativistic degeneracy parameter, R 0, and the atomic number of constituent ions, Z, significantly affect the maximum stopping power velocity of ions. We also discover that the velocity-averaged energy loss function becomes minimal in electron number density typical of white dwarf stars, n 0≃2×1030 cm−3. It is found that the characteristic density for the minimal ion beam energy loss does not depend on the value of other plasma parameters, such as the ion–electron collision rate and the ion temperature or its atomic number. The latter finding, in particular, may help in better understanding of fusion-burning waves in dense compact stars and their cooling mechanisms.

In this work we study the modulational instability of plasmas with q-entropy electrons and warm ions, using the hydrodynamic approach. A nonlinear Schrodinger equation (NLSE), governing the dynamics of envelope excitations in the plasma, is obtained by using the conventional multiscales method. Investigation of the modulational instability of the nonextensive plasmas reveals that the criteria for propagation of bright/dark envelope excitations in such plasmas are significantly affected by value of the nonextensivity parameter, q, and the fractional ion-temperature, σ. In particular, by setting σ ≠ 0 , a new region of modulational instability appears, indicating that the study of modulation instability in the cold-ion limit ( σ = 0 ) is completely different from that of warm ions. The study of the growth-rate and rogue-wave amplitudes in terms of different plasma parameters, reveals that their magnitude is of different scales for two ranges of the nonextensivity parameters, q > 1 and q 1 .

In this research, we calculate the heat capacity and electrical conductivity of plasmon excitations in an arbitrary degenerate electron gas by using the linearized Schrodinger-Poisson model. It is shown that the large heat capacity of electron fluid such as in metals can be attributed to the collective excitations. These excitations unlike those for low energy fermion excitations dominant at low temperatures follow the Bose-Einstein statistics and contribute significantly at higher temperatures where a significant number of electrons excite to energy levels beyond twice the plasmon energy of electron fluid. The current density and electrical conductivity of plasmon excitations in the current model show unique features for characteristic current-voltage and their temperature dependence. It is found that a single electron fermion excitation model such as the one used in free electron assumption is not appropriate for a full description of electron contribution to the physical properties of metals and plasmas at very high temperatures. The coupled pseudoforce system with a periodic density structure in the presence of a uniform electric field is also considered with appropriate boundary conditions to evaluate the characteristic aspects of collective excitations in a one dimensional plasmonic crystal. The application of the lattice periodicity on the wavefunction and the electrostatic potential results in singularities for the probability current due to plasmon excitations. It is shown that such an effect persists with an arbitrary ion core potential function which obeys the lattice periodicity. The current model clearly demonstrates the importance of collective electronic excitation in the physical properties of electron gas with an arbitrary degree of degeneracy.

The quantum coupled pseudoforce model with the damping term is used to study the plasmon excitations in a variety of systems. Damped plasmon excitations can be used to model different physical situations such as the plasmon penetration into insulating environments and surface plasmon excitations in semiconductors. The application of the pseudoforce model with damping around a charged Dirac sheet reveals that such pseudoforce system can also be used to model the charge shielding. It is also observed that quantum charge shielding possesses two-tone field-density variations due to both single-particle oscillations and collective electrostatic excitations. The effect of uniform electric field on the damped plasmon excitations is also considered in this paper. We further report new findings concerning the effect of collective quantum excitations which may provide further insight into the theory of bandgap structure in crystals. It is remarked that the presence of charge screening in a periodic lattice can lead to Fano resonance. Finally, a new expression for the charge-particle continuity equation in the presence of shielding effect is presented. Current investigation can have fundamental results for better understanding of the quantum transport phenomenon and optical properties of semiconductors, metallic compounds, nanoclusters, and plasmonic crystals.

In this paper, the quantum interference of plasmon excitations in the presence of charges or multipolar sources/sinks is investigated. The effective Schrodinger-Poisson system for dynamical description of the arbitrary degenerate fermi gas is reduced to a set of coupled linear pseudoforce system, and it is shown that this system admits a general multipolar solution in the 3D Cartesian coordinate. The obtained solution is then used to study well-known problems such as the double and quadruple charge interference effects. The double source interference produces patterns quite reminiscent of that of the double slit interference with the corresponding matter-wavelength matching that of the de Broglie wavelength of the electrons. It is found that the collective electrostatic interactions of quantum electron gas leads to the electrostatic energy depletion around the pole which causes electrostatic polar binding in the electron fluid. The later effect which has also been previously reported in some research seems to be an appropriate description of attractive metallic bindings. The current model is then extended to electronic interference effects in a crystal lattice with the quasiperiodic electronic states. The periodic arrangement of ionic cores in a crystal is shown to produce different density and electrostatic potential patterns for given energy eigenvalues of the fermi gas. Moreover, a generalized expression is obtained for electron probability current in the Schrodinger-Poisson model. The current model may provide a better platform for studying the quantum interference phenomenon in complex environments such as nanocompounds and plasmonic crystals.

In this work we investigate the effect of relativistic degeneracy on different properties of low-dimensional quantum plasmas. Using the dielectric response from the conventional quantum hydrodynamic model, including the quantum diffraction effect (Bohm potential) on free electrons, we explore the existence of the Shukla–Eliasson attractive screening and possibility of the ion structure formation in low-dimensional, completely degenerate electron–ion plasmas. A generalized degeneracy pressure expression for arbitrary relativity parameter in two-dimensional case is derived, indicating that change in the polytropic index (change in the equation of state) for the two-dimensional quantum fluid takes place at the electron number-density of n0 ≃ 1.1 × 1020cm−2 whereas this is known to occur for the three-dimensional case in the electron density of n0 ≃ 5.9 × 1029cm−3. Also, a generalized dielectric function valid for all dimensionalities and densities of a degenerate electron gas is calculated, and distinct properties of electron–ion plasmas, such as static screening, structure factor and Thomson scattering, are investigated in terms of plasma dimensionality.

In this paper the electrostatic two-stream instability is investigated for a large range of plasma number-density using the quantum hydrodynamic model by incorporating the relativistic degeneracy, electron-exchange, quantum diffraction and strong parallel quantizing magnetic field effects. It is found that the electron diffraction effect significantly alters the instability growth rate in a wide range of plasma number density. Two cases of classical and quantum Landau quantization limits are compared and the parametric instability condition is closely inspected. It is remarked that for a given streaming speed the instability is bounded by an upper plasma number-density limit. It is also shown that for a given stream speed there is a maximal growth rate corresponding to specific plasma number-density and perturbation wavelength. Current study can help in better understanding of electron-beam plasma interactions and energy exchange for a wide area of number densities ranging from solid density, inertial confined plasmas, big planetary cores and compact stars. It may also be useful in understanding of electrostatic beam-plasma interactions and origin of large magnitude sustainable electrical currents in super-intense plasmas with critically high magnetic fields such as, pulsars, white dwarf interiors and neutron star crusts.

In this paper, the quantum hydrodynamics (QHD) model is used to study the propagation of small- but finite-amplitude quantum electrostatic shock-wave in an inertial-less symmetric pair (ion) plasma with immobile background positive constituents. The dispersion due to the quantum tunneling and inertial effects as well as dissipation caused by particle collisions leading to the shock-like or double-layer structures are considered. Investigation of both the stationary and traveling-wave solutions to Kortewege-de Veries-Burgers evolution equation show that critical values exist which govern the type of collective plasma structures. Current analysis apply to diverse kind of symmetric plasmas such as laboratory inertially confined or astrophysical pair-ion or electron-positron degenerate plasmas.

Using the extended Poincar\'{e}-Lighthill-Kuo (PLK) reductive perturbation method, which incorporates the phase-shift variations, it is shown that common features on propagation and head-on collisions of ion-acoustic waves exist for a magnetized plasmas of different inertial-less particle distributions. For instance it is remarked that, the soliton amplitude is always independent of magnetic field strength while strictly depends on its angle regarding the propagation direction. Both types of solitons (compressive or rarefactive) are shown to exist which are defined through the critical angle $\gamma=\pi/2$ or other critical values depending on plasma fractional parameters. These critical plasma parameter values also define the sign of head-on collision phase shift. Furthermore, it is proved that for a given set of plasma parameters there is always a relative angle of propagation regarding to that of the magnetic-field for which the soliton width is maximum. Current findings applies to a wide range of magnetized plasmas including those containing background dust ingredients or two-temperature inertial-less particles and may be used to study laboratory or astrophysical magnetoplasmas., Comment: To appear in Astrophys. & Space Science

A coupled nonlinear pseudoforce system is derived from hydrodynamic equations for the nonlinear electron plasma oscillations in an electron-ion plasma with arbitrarily degenerate electron fluid in a background fixed ion potential. The dynamics of the fully nonlinear electron plasma excitations are studied using this generalized coupled pseudoforce model including the damping and driving pseudoforce elements. The fully nonlinear plasma oscillations are shown to be of quite different nature in the extreme classical and quantum limits. In particular, high frequency quantum oscillations due to electron tunneling effect modulates the ordinary large amplitude low frequency periodic Langmuir excitations in the quantum plasma regime. It is shown that such characteristic quantum oscillations appear due to the electron wavefunction overlap which also appear on the quantum shock wave structures. It is found that the stimulation of dense plasmas with the driving frequency matching that of characteristic quantum oscillations leads to the chaotic behavior of the electron fluid. The presented coupled pseudoforce theory can be used to investigate a large number of interesting nonlinear phenomena such as the quantum electron fluid chaos and turbulence, autoresonance phenomenon, quantum harmonic generation, nonlinear resonances, and bistability of quantum electron plasma oscillations.

The oblique interaction of small- but finite-amplitude KdV-type electrostatic–acoustic solitary structures is examined in an unmagnetized three-component pair-plasma using extended Poincare–Lighthill–Kuo (PLK) perturbation method. The nonlinear evolution equations along with other coupled differential equations describing the phase variation of colliding waves were derived from the basic equations. Based on numerical analysis, we found that small changes in fractional pair-temperature, their fractional density-number or collision angle between solitary waves can significantly alter the phase shifts of colliding solitons. Numerical findings also reveal that the collisional phase-shifts in soliton trajectories changes the sign for some colliding angle (depending on plasma fractional parameters) in the range 0 θ π .

The amplitude modulation of ion-acoustic waves is investigated in a plasma consisting of adiabatic warm ions, and two different populations of thermal electrons at different temperatures. The fluid equations are reduced to nonlinear Schrödinger equation by employing a multi-scale perturbation technique. A linear stability analysis for the wave packet amplitude reveals that long wavelengths are always stable, while modulational instability sets in for shorter wavelengths. It is shown that increasing the value of the hot-to-cold electron temperature ratio (μ), for a given value of the hot-to-cold electron density ratio (ν), favors instability. The role of the ion temperature is also discussed. In the limiting case ν = 0 (or ν → ∞), which correspond(s) to an ordinary (single) electron-ion plasma, the results of previous works are recovered.

In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrodinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the curr...

In this paper, we study the nonlinear harmonic generation effect in different oscillator models. For weakly nonlinear systems, we use the generalized forced Korteweg de Vries Burgers (KdVB) and modified KdVB (mKdVB) models in order to classify three fundamentally different harmonic structures in a nonlinear dynamical system. The first is called the internal harmonic structure which exists due to the self oscillation of the system in the absence of dissipation effect and is shown to follow either relations of nf or (2n – 1)f depending on the symmetry of oscillator potential in which n is an integer number and f is the fundamental frequency which is exactly obtained for the Helmholtz oscillator. The second structure is the resonant harmonics which appears in the presence of damping and follows the harmonic structure nf0 in which f0 is the linear resonance frequency. Finally, the last harmonic structure appears in the presence of dissipation and external periodic forcing effects which we call the external harmonic pattern. It is shown that the external harmonic pattern, in which f1 is the driving frequency, always follows the nf1 rule regardless of the potential symmetry. We then extend our analysis to study the harmonic generation in the fully nonlinear generalized Sagdeev potential for real plasmas with isothermal and adiabatic ion fluids and investigate the effects of different plasma parameters such as the fractional ion temperature and normalized ion acoustic speed on all three kinds of harmonic generation.

The traveling solitary and cnoidal wave solutions of the one dimensional driven nonlinear Schrodinger equation with a generalized form of nonlinearity are presented in this paper. We examine the modulation of nonlinear solitary excitations in two known weakly nonlinear models of classic oscillators, namely, the Helmholtz and Duffing oscillators and envelope structure formations for different oscillator and driver parameters. It is shown that two distinct regimes of subcritical and supercritical modulations may occur for nonlinear excitations with propagation speeds v 4F0, respectively, in which F0 is the driver force strength. The envelope soliton and cnoidal waves in these regimes are observed to be fundamentally different. The effect of pseudoenergy on the structure of the modulated envelope excitations is studied in detail for both sub- and supercritical modulation types. The current model for traveling envelope excitations may be easily extended to pseudopotentials with full nonlinearity rel...

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger com...

In this paper, we develop a technique to study the dynamic structure of oscillations in plasmas. We consider the hydrodynamic model and reduce the system of closed equations to the system of differential equations with integrable Hamiltonian. Then, using the analogy of pseudoparticle oscillation in the pseudoforce field, we generalize the Hamiltonian to include the dissipation and external driving force effects. The developed method is used to study various features of electron-ion plasmas with different equations of state for ions. It is shown that this method can be used in the analysis of superposed fully nonlinear oscillations and even the sheath structure of plasmas. The generalized pseudoforce equation is then used to study the dynamics of damped periodically forced nonlinear ion acoustic oscillations in plasmas with adiabatic and isothermal ion fluids. We found striking differences in dynamics of oscillations in these plasmas. The fundamental difference in the dynamic character of oscillations betw...

In this paper, a theoretical model of the autoresonance effect based on the pseudoparticle oscillation in a classical potential well is presented. The underlying connection between the autoresonance effect and the shock wave generation in fluid dynamics is revealed and effects of different parameters such as the potential, damping, external force amplitude, and frequency variation on the phase-locking effect are examined. We use the full nonlinear energy spectrum of oscillations in order to selectively choose our start frequency for the autoresonance effect to occur. We also use an exponential chirping mechanism instead of the linear one which is usually employed. We believe that the former chirping mechanism is a more natural way of energy injection into the dynamical system and provides a more effective approach with sufficient control on the phase locking stability and duration. It is shown that the double sweeping of both driving force magnitude and frequency leads to dense large amplitude wave packet...

In this paper, the full energy spectrum of nonlinear oscillations, known as the cnoidal waves, is studied in the framework of small-amplitude Korteweg de Vries and modified Korteweg de Vries (mKdV) theories based on the pseudoparticle motion in Helmholtz and Duffing potentials by employing the newly introduced pseudoenergy concept. The pseudoenergy dependence of various cnoidal oscillation parameters is then studied, and it is shown that superposition of cnoidal waves leads to familiar beating and Lissajous profiles. One of the most important aspects of the nonlinear oscillation is found to be the frequency dependence of the oscillation amplitude which mainly characterizes the nature of oscillations. It is shown that the developed method can be used to study the spectrum of oscillations and shock waves in the fully nonlinear Sagdeev pseudopotential and to directly calculate many dynamic parameters of the given nonlinear system. Current research may be helpful in understanding of basic excitations and inte...

The characteristics of a plasma sheath consisting of nonextensive electrons and thermal ions in the presence of a monoenergetic electron beam is studied in the framework of a one dimensional hydrodynamic model. Because of the electron beam, bulk electron distribution of plasma is assumed to be non-Maxwellian in general. Using the Sagdeev pseudopotential method, a modified Bohm criterion is obtained. It is shown that the criterion is significantly affected by the nonextensivity degree (q) and the beam parameters. The criterion is reduced to the standard form of the Bohm criterion when (i) the electrons have Maxwellian distribution ( q → 1), and (ii) the beam density is taken to be zero. A small amplitude analytical solution is also given for the potential in the sheath region. Moreover, assuming the total current on the electrode surface to be negligible, the floating potential is derived. The set of nonlinear hydrodynamic equations is solved numerically and the effects of many parameters such as nonextens...

In this paper, we develop an innovative approach to study the shock wave propagation using the Sagdeev potential method. We also present an analytical solution for Korteweg de Vries Burgers (KdVB) and modified KdVB equation families with a generalized form of the nonlinearity term which agrees well with the numerical one. The novelty of the current approach is that it is based on a simple analogy of the particle in a classical potential with the variable particle energy providing one with a deeper physical insight into the problem and can easily be extended to more complex physical situations. We find that the current method well describes both monotonic and oscillatory natures of the dispersive-diffusive shock structures in different viscous fluid configurations. It is particularly important that all essential parameters of the shock structure can be deduced directly from the Sagdeev potential in small and large potential approximation regimes. Using the new method, we find that supercnoidal waves can de...

In this research, we study the generalized sheath criterion for plasmas with an arbitrary degree of electron degeneracy and temperature, ranging from the classical dilute regime to the fully degenerate quantum plasmas. The latter may be relevant to warm dense matter and/or laboratory high energy density matter or even astrophysical stellar plasmas. The hydrostatic one dimensional model is used to establish the generalized Bohm's criterion for sheath entrance ion speed limits, and the small amplitude theory of the sheath problem, which accurately describes the sheath parameters for lower ion acoustic Mach numbers, is developed. Our results indicate that the sheath characteristic parameters such as electrostatic potential and density profiles, as well as the wall potential and the sheath length, are significantly affected by plasma parameters such as the ion and electron temperature and number densities in the plasma region. In particular, there are fundamental differences between sheath structures of the d...

We present a theory for the dynamical ion structure factor (DISF) and ion stopping power in an unmagnetized collisional quantum plasma with degenerate electron fluids and nondegenerate strongly correlated ion fluids. Our theory is based on the fluctuation dissipation theorem and the quantum plasma dielectric constant that is deduced from a linearized viscoelastic quantum hydrodynamical (LVQHD) model. The latter incorporates the essential physics of quantum forces, which are associated with the quantum statistical pressure, electron-exchange, and electron-correlation effects, the quantum electron recoil effect caused by the dispersion of overlapping electron wave functions that control the dynamics of degenerate electron fluids, and the viscoelastic properties of strongly correlated ion fluids. Both degenerate electrons and nondegenerate strongly correlated ions are coupled with each other via the space charge electric force. Thus, our LVQHD theory is valid for a collisional quantum plasma at atomic scales with a wide range of the ion coupling parameter, the plasma composition, and plasma number densities that are relevant for compressed plasmas in laboratories (inertial confinement fusion schemes) and in astrophysical environments (e.g., warm dense matter and the cores of white dwarf stars). It is found that quantum electron effects and viscoelastic properties of strongly correlated ions significantly affect the features of the DISF and the ion stopping power (ISP). Unlike previous theories, which have studied ion correlations in terms of the ion coupling parameter, by neglecting the essential physics of collective effects that are competing among each other, we have here developed a method to evaluate the dependence of the plasma static and dynamical features in terms of individual parameters, like the Wigner-Seitz radius, the ion atomic number, and the ion temperature. It is found that due to the complex nature of charge screening in quantum plasmas, the ion coupling parameter alone cannot be a good measure for determining ion correlation effects in a collisional quantum plasma, and such a characteristic of a dense quantum plasma should be evaluated against each of the plasma parameters involved. The present investigation thus provides testable predictions for the DISF and ISP and is henceforth applicable to a wide range of compressed plasma categories ranging from laboratory to astrophysical warm dense matter.

Propagation of electromagnetic wave through an inhomogeneous magnetized nonextensive plasma sheath is numerically examined for a realistic density profile of a reentry problem around a hypersonic vehicle. The effect of nonextensivity and inhomogeneity on radio wave communication is studied parametrically. Variation of reflection and transmission coefficients, total attenuation, and total phase shift over the plasma sheath with respect to the strength of applied magnetic field are derived and compared for different values of q-nonextensive parameter. The obtained results for inhomogeneous plasma sheath are compared with previously obtained results of authors for homogeneous plasma sheath. The comparison shows that radio communication in the inhomogeneous plasma sheath is more advantageous than that in the homogeneous case. The transmission coefficient of a plasma sheath with superthermal electrons ( 13 1. Moreover, for ωce>ω, the minimum value of total attenu...

Using the generalized hydrodynamic model, the possibility of variety of large amplitude nonlinear excitations is examined in electron-ion plasma with arbitrary electron degeneracy considering also the ion temperature effect. A new energy-density relation is proposed for plasmas with arbitrary electron degeneracy which reduces to the classical Boltzmann and quantum Thomas-Fermi counterparts in the extreme limits. The pseudopotential method is employed to find the criteria for existence of nonlinear structures such as solitons, periodic nonlinear structures, and double-layers for different cases of adiabatic and isothermal ion fluids for a whole range of normalized electron chemical potential, η0, ranging from dilute classical to completely degenerate electron fluids. It is observed that there is a Mach-speed gap in which no large amplitude localized or periodic nonlinear excitations can propagate in the plasma under consideration. It is further revealed that the plasma under investigation supports propagat...