Fermi Plasma Research Articles

Nonlinear quantum fluid equations for a finite temperature Fermi plasma

Nonlinear quantum electron fluid equations are derived, taking into account the moments of the Wigner equation and by using the Fermi–Dirac equilibrium distribution for electrons with an arbitrary temperature. A simplified formalism with the assumptions of incompressibility of the distribution function is used to close the moments in velocity space. The nonlinear quantum diffraction effects into the fluid equations are incorporated. In the high-temperature limit, we retain the nonlinear fluid equations for a dense hot plasma and in the low-temperature limit, we retain the correct fluid equations for a fully degenerate plasma.

Localized electrostatic excitations in a Thomas–Fermi plasma containing degenerate electrons

By using the Thomas–Fermi electron density distribution for quantum degenerate electrons, the hydrodynamic equations for ions, and the Poisson equation, planar and nonplanar ion-acoustic solitary waves in an unmagnetized collisionless plasma are investigated. The reductive perturbation method is used to derive cylindrical and spherical Korteweg–de Vries equations. Numerical solutions of the latter are presented. The present results can be useful in understanding the features of small but finite amplitude localized ion-acoustic solitary pulses in a degenerate plasma.

Ion-temperature-gradient driven modes in very dense magnetoplasmas

By employing the quantum magnetohydrodynamic-Poisson model, a general dispersion relation for low-frequency electrostatic ion-temperature-gradient (ITG) modes in a very dense Fermi plasma is derived. The growth rate is found to be higher in the presence of ion-temperature gradients and electron corrections due to quantum fluctuations. Two new ITG driven modes in the Fermi plasma are found. These ITG modes are associated with an electron density response that differs from the Boltzmann law. It is expected that newly found ITG modes can play an important role in anomalous cross-field ion energy transport in the next-generation laser-solid density plasma experiments as well as in dense astrophysical bodies (e.g., neutron stars and the interior of white dwarfs).

Neutrino induced charge in a superdense two-electron Fermi plasma

Using plasma physics methods, the effective neutrino charge in a superdense two-electron Fermi plasma is determined. The Fermi plasma has distinct groups of hot and cold electrons. Accounting for the quantum statistical pressure for the hot electron component and the quantum force associated with the quantum Bohm potential, the neutrino induced charge produced by the neutrino driving force is estimated. The influence of the quantum-mechanical effects on the neutrino effective electric charge has been investigated.

Neutrino effective charge in a dense Fermi plasma

By using a plasma physics approach, the neutrino effective charge in a dense Fermi plasma is determined here. Its value is determined by the collective quantum plasma processes. It is found that the contribution of the ion motion can be important even in Fermi plasmas, despite the negligible weak interaction between neutrinos and ions. This results from the electron–ion couplings, which are dominant in the low-frequency limit of the equivalent charge spectrum.

Fluid Turbulence in Quantum Plasmas

Nonlinear fluid simulations are developed by us to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a very dense Fermi (quantum) plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations (EPO) is determined critically by a ratio of the energy density of the EPOs and the electron kinetic energy density of quantum plasmas. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory.

Fully nonlinear ion-sound waves in a dense Fermi magnetoplasma

The nonlinear propagation of ion-sound waves in a collisionless dense electron-ion magnetoplasma is investigated. The inertialess electrons are assumed to follow a non-Boltzmann distribution due to the pressure for the Fermi plasma and the ions are described by the hydrodynamic (HD) equations. An energy balance-like equation involving a new Sagdeev-type pseudo-potential is derived in the presence of the quantum statistical effects. Numerical calculations reveal that the profiles of the Sagdeev-like potential and the ion-sound density excitations are significantly affected by the wave direction cosine and the Mach number. The present studies might be helpful to understand the excitation of nonlinear ion-sound waves in dense plasmas such as those in superdense white dwarfs and neutron stars as well as in intense laser-solid density plasma experiments.

Two-dimensional Fermi plasma in a magnetic field.

We investigate the dielectric response of a planar Fermi plasma in the presence of a constant external magnetic field. The conductivity tensor is derived in the random-phase approximation taking into account the effects of the spin of the electron. This proper inclusion of spin makes a significant difference to the results compared with all previous studies, which ignored the intrinsic spin of the electron. In studying the dispersion relations for the electrodynamic modes of the plasma in an external magnetic field, it is necessary to observe that the longitudinal and transverse modes are coupled. These coupled modes are investigated in some detail.

Electron liquid at any degeneracy.

A unified theory is presented that describes the thermodynamic and dielectric properties of the electron liquid throughout the full range of thermal degeneracy: from the zero-temperature fully degenerate Fermi plasma to the high-temperature classical one-component plasma. Through an approximate inclusion of local-field corrections in the polarizability, results are obtained that are accurate up to intermediate values of the coupling strength. For future applications, closed-form parametrizations are presented for the thermodynamic and dielectric functions, as functions of density and temperature. The consequences of an increase in temperature on the plasmon dispersion and damping, on the energy-loss function, and on the pair-correlation function are also studied. We find that quantum effects can be observed in the short-range behavior of the pair-correlation function even for some plasmas that are conventionally classified as classical.

Electron correlations. II. Ground-state results at low and metallic densities

In this second work in a series of papers the coupled-cluster or $\mathrm{exp}(S)$ formalism is applied to the problem of ground-state correlations in the one-component Fermi plasma. The main approximation employed is the so-called SUB2 approximation for the two-body subsystem correlation operator ${S}_{2}$ which provides a measure of the two-particle---two-hole component in the true ground-state wave function, and in which the coupling to larger subsystems is neglected. The SUB2 equations for Fermi systems are brought into tractable form by a "state-averaging" procedure which we develop by analogy with the comparable Bose equations, and which is shown by comparison with earlier exact results to be accurate in the metallic density regime at about the 1% level. Our final results for metallic densities include the completely integrated and self-consistent effects of the terms which by themselves generate (i) the random-phase approximation (RPA) and its associated exact long-range screening effects, (ii) the extra random-phase approximation exchange terms necessary to keep the RPA explicitly antisymmetric, (iii) the self-consistent particle-particle ladders (LAD) that describe two-particle scattering within the many-body medium and which describe the exact short-range behavior, (iv) a class of particle-hole ladder terms, and (v) the self-consistent hole-potential terms. Particular attention is paid to the important effects caused by the interference at intermediate separations of the long-range RPA and the short-range LAD effects. By comparison with recent and essentially exact stochastic simulations of the many-body Schr\"odinger equation, our results are seen to be accurate to about 1% for metallic densities, and hence to provide what is probably the currently best microscopic description available for this system. We show also that even in the low-density limit the SUB2 approximation provides a good "translationally-invariant-solid" description of both charged Fermi and Bose systems in this exact Wigner crystal regime.