Modulation instability of lower hybrid waves leading to cusp solitons in electron–positron(hole)–ion Thomas Fermi plasma

Following the idea of three‐wave resonant interactions of lower hybrid waves, it is shown that quantum‐modified lower hybrid (QLH) wave in electron–positron–ion plasma with spatial dispersion can decay into another QLH wave (where electron and positrons are activated, whereas ions remain in the background) and another ultra‐low frequency quantum‐modified ultra‐low frequency Lower Hybrid (QULH) (where ions are mobile). Quantum effects like Bohm potential and Fermi pressure on the lower hybrid wave significantly reshaped the dispersion properties of these waves. Later, a set of non‐linear Zakharov equations were derived to consider the formation of QLH wave solitons, with the non‐linear contribution from the QLH waves. Furthermore, modulational instability of the lower hybrid wave solitons is investigated, and consequently, its growth rates are examined for different limiting cases. As the growth rate associated with the three‐wave resonant interaction is generally smaller than the growth associated with the modulational instability, only the latter have been investigated. Soliton solutions from the set of coupled Zakharov and NLS equations in the quasi‐stationary regime have been studied. Ordinary solitons are an attribute of non‐linearity, whereas a cusp soliton solution featured by nonlocal nonlinearity has also been studied. Such an approach to lower hybrid waves and cusp solitons study in Fermi gas comprising electron positron and ions is new and important. The general results obtained in this quantum plasma theory will have widespread applicability, particularly for processes in high‐energy plasma–laser interactions set for laboratory astrophysics and solid‐state plasmas.     

Lower hybrid wave instability in a spin‐polarized degenerate plasma

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

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

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

Energy transport for ion acoustic waves in a spin polarized quantum plasma

The separate spin evolution quantum hydrodynamics(SSE-QHD) model is used to investigate the energy behavior for ion acoustic waves in degenerate quantum plasma. Numerical results show that the energy flow speed decreases with spin polarization parameter. It is also shown that it decreases with the increasing rate up to a certain range of wave number and then it goes to zero asymtotically. It is observed that Bohm potential suppresses the energy flow speed. It is also noticed that the energy flow speed deviates from the group velocity even in the absence of Bohm potential effect. However, the contribution of of Bohm poential effect in spin polarized plasma reduces the extent of deviation.     

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

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

Spin magnetosonic shock-like waves in quantum plasmas

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

Solitary wave propagation in quantum electron-positron plasmas

Existence of large amplitude stationary solitary wave structures in an unmagnetized electron-positron (e-p) plasma is studied using a quantum hydrodynamic (QHD) model that includes the quantum force (tunnelling) associated with the Bohm potential and the Fermi-dirac pressure law. It is found that in a quasi-neutral pair (e-p) plasma, where the dispersion is only due to the the quantum tunnelling effects, the large amplitude stationary solitary structure exists only when the normalized Mach speed,M <√2. Such solitary structures do not exist in absence of the Bohm potential term in an unmagnetized quasineutral pair (e-p) plasma. The system is shown to support only rarefactive stationary solitary waves. For such waves the amplitude, being independent of the quantum parameter H (the ratio of the electron plasmon to electron Fermi energy), decreases with the Mach number M, whereas the width increases with both M and H. The present theory is applicable to analyze the formation of localized coherent solitary structures at quantum scales in dense astrophysical objects as well as in intense laser fields.     

Energy behavior of spin electron cyclotron wave in a spin polarized plasma

In degenerate quantum plasma the energy behavior of electrostatic modes propagating perpendicular to the external magnetic field is studied by employing the separated spin evolution quantum hydrodynamic (SSE-QHD) model. This model reveals that spin electron cyclotron wave (SECW) appears additionally with the upper hybrid wave (UHW). In case of SECW, the curves for the energy flow speed at different levels of spin polarization effect flip over at a particular value of wave number. The spin polarization effect enhances the energy flow speed before this value of wave number and then suppresses it afterward. The energy flow speed is enhanced by spin polarization effect in the entire range of wave number for the propagation of UHW. The Bohm potential effect drastically increases the energy flow speed at high wave number domain in both the waves. This study may find its applications to understand the energy behavior inspin polarized solid state plasmas     

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

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

Two-tone ion-acoustic waves in degenerate quantum plasma

Ion-acoustic waves (IAWs) in a quantum electron-ion plasma with degenerate components are theoretically investigated using a system of quantum equations of gas dynamics that allow for the quantum-size character of the object (Bohm’s quantum force is included in the equation of motion) and the Pauli exclusion principle (equations of state for degenerate Fermi gases of electrons and ions are used). Linear analysis and numerical solution of equations yielded an identical qualitative result: periodic IAWs in a quantum electron-ion plasma are always a superposition of two waves with equal phase velocities but different wavelengths. The high-frequency component of the IAW is identified with free quantum oscillations of ions. A solution in the form of an ion-sound soliton with free quantum oscillations of ions superposed on its profile is also found.     

Quantum macroscopic equations from Bohm potential and propagation of waves

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

Relativistic Magnetosonic Solitary Wave in Magnetized Multi-Ion Plasma

In the presence of an applied uniform magnetic field Bo, the properties of 2-dimensional （2D） magnetosonic solitary waves of relativistic amplitude in the plasma containing electron, light ions He^＋, and heavy ions O＋ are presented. In the weakly relativistic limit, a Kadomtsev Petviashvili （KP） equation is derived by reductive perturbation method. We give the N-soliton solution of the KP equation and find dromion solutions of a potential of the physical field. The interaction law of the dromions is obtained, which shows there is no exchange of energy, momentum, and angular momentum before and after interaction of the dromions except for phase shifts.     

Nonlocality in Relativistic Dynamics

Recent experiments have renewed interest in nonlocal interpretations of quantum mechanics. The experimental observation of the violation of Bell's inequalities implies the existence of nonlocality. Bohm expressed the nonlocal connection between quantum particles through the wave function and the quantum potential. This paper shows that a similar connection exists in a relativistic dynamical theory known as parametrized relativistic quantum theory (PRQT). We present an introduction to PRQT, derive the quantum potential for a system of relativistic scalar particles, and discuss alternative interpretations of nonlocality.     

Relativistic Boltzmann theory for a plasma: IX. Attenuation of hydromagnetic waves

Expressions are given for the space attenuation coefficient of hydromagnetic waves in a relativistic plasma. By taking into account all transport processes known from the Chapman-Enskog procedure a hitherto unnoticed dissipative effect is found. A comparison is made with the attenuation of sound waves in relativistic neutral gases.     

核力介子交换理论的新进展

本文评述了核力介子交换理论的研究进展,内容包括相对论单玻色交换势,核力介子交换的非协变微扰理论,能量无关N-N介子交换势和巴黎势的一些最新进展。     

The influence of electron exchange and relativistic corrections on elastic low energy electron diffraction from compound semiconductors

The model of the electron-solid interaction used for dynamical low energy electron diffraction (LEED) calculations is extended to include both an energy dependent local exchange interaction and relativistically computed ion-core charge densities. These extensions of earlier work based on non-relativistic, local exchange models are tested for the (110) surfaces of InP, ZnTe and InSb. Calculations reveal discernible differences between LEED intensities computed using the energy dependent exchange force and those obtained using energy independent local exchange forces. The replacement of the non-relativistic ion-core potential with a relativistic one produces smaller changes which are most apparent when the energy dependent exchange force is used for compound semiconductors containing one or more components from the fifth row or lower in the periodic table (e.g., Cd, In, Sb or Te).     

Deriving relativistic Bohmian quantum potential using variational method and conformal transformations

In this paper we shall argue that conformal transformations give some new aspects to a metric and changes the physics that arises from the classical metric. It is equivalent to adding a new potential to relativistic Hamilton–Jacobi equation. We start by using conformal transformations on a metric and obtain modified geodesics. Then, we try to show that extra terms in the modified geodesics are indications of a background force. We obtain this potential by using variational method. Then, we see that this background potential is the same as the Bohmian non-local quantum potential. This approach gives a method stronger than Bohm’s original method in deriving Bohmian quantum potential. We do not use any quantum mechanical postulates in this approach.     

Nonlinear interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schr?dinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.