Electronic Equation Of State Research Articles

On quasineutral plasma flow in the magnetic nozzle

Exact solutions for quasineutral plasma acceleration of magnetized plasma in the paraxial magnetic nozzle are obtained. It is shown that the non-monotonic magnetic field with a local maximum of the magnetic field is a necessary condition for the formation of the quasineutral accelerating potential structure. A global nature of the accelerating potential that occurs as a result of the constraint due to the regularity condition at the sonic point is emphasized, and properties of such solutions are discussed for the case of general polytropic equation of state for electrons.

Exchange-correlation contributions to thermodynamic properties of the homogeneous electron gas from a cumulant Green's function approach

Thermodynamic properties of the interacting homogeneous electron gas are calculated using a finite-temperature cumulant Green's function approach over a broad range of densities and temperatures up to the warm dense matter regime $T\ensuremath{\sim}{T}_{F}$, where ${T}_{F}$ is the Fermi degeneracy temperature. These properties can be separated into independent particle and exchange-correlation contributions, and our focus here is on the latter. Our approach is based on the Galitskii-Migdal-Koltun and electron number sum rules from the finite temperature many-body Green's function formalism, together with an extension of the cumulant Green's function to finite temperature. Previously this approach yielded exchange-correlation energies and potentials in good agreement with quantum Monte-Carlo calculations. Here the method is extended for various thermodynamic quantities including the chemical potential, total energy, Helmholtz free-energy, electronic equation of state, specific heat, and isothermal compressibility, which optionally include spin dependence. We find that the exchange-correlation contributions are weakly varying at low temperature but exhibit significant temperature dependence in the WDM regime, as well as a crossover from exchange- to correlation-dominated behavior. In contrast to the $T={0}^{+}$ limit, we also find that renormalization effects are largely but not completely suppressed at finite temperature. Comparisons with other approaches at various levels of approximation are also discussed.

On the effect of fractional statistics on quantum ion acoustic waves

In this paper, I study the effect of a small deviation from the Fermi–Dirac statistics on the quantum ion acoustic waves. For this purpose, a quantum hydrodynamic model is developed based on the Polychronakos statistics, which allows for a smooth interpolation between the Fermi and Bose limits, passing through the case of classical particles. The model includes the effect of pressure as well as quantum diffraction effects through the Bohm potential. The equation of state for electrons obeying fractional statistics is obtained and the effect of fractional statistics on the kinetic energy and the coupling parameter is analyzed. Through the model, the effect of fractional statistics on the quantum ion acoustic waves is highlighted, exploring both linear and weakly nonlinear regimes. It is found that fractional statistics enhance the amplitude and diminish the width of the quantum ion acoustic waves. Furthermore, it is shown that a small deviation from the Fermi–Dirac statistics can modify the type structures, from bright to dark soliton. All known results of fully degenerate and non-degenerate cases are reproduced in the proper limits.

Effects of magnetic fields and slow rotation in white dwarfs

In this work we use Hartle’s formalism to study the effects of rotation in the structure of magnetized white dwarfs within the framework of general relativity. We describe the inner matter by means of an equation of state for electrons under the action of a constant magnetic field, which introduces an anisotropy in the pressures. Solutions correspond to typical densities of white dwarfs and values of magnetic field below [Formula: see text][Formula: see text]G considering perpendicular and parallel pressures independently, as if associated to two different equations of state. Rotation effects obtained account for an increase of the maximum mass for both magnetized and nonmagnetized stable configurations, up to about [Formula: see text]. Further effects studied include the deformation of the stars, which become oblate spheroids and the solutions for other quantities of interest, such as the moment of inertia, quadrupolar momentum and eccentricity. In all cases, rotation effects are dominant with respect to those of the magnetic field.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy.

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

The role of electron equation of state in heating partition of protons in a collisionless plasma

One of the outstanding questions related to the solar wind is the heating of solar wind plasma. Addressing this question requires a self consistent treatment of the kinetic physics of a collisionless plasma. A hybrid code (with particle ions and fluid electrons) is one of the most convenient computational tools, which allows us to explore self consistent ion kinetics, while saving us computational time as compared to the full particle in cell codes. A common assumption used in hybrid codes is that of isothermal electrons. In this paper, we discuss the role that the equation of state for electrons could potentially play in determining the ion kinetics.

Calculation of electronic equation of state(EOS) of gold at arbitrary temperature and matter density in improved atomic model

Based on the improved atomic model with considering temperature and density, the density distribution of the free electrons is dealt with by partial wave method based on the central field approximation. By an average of approximate treatment, the energy band split is given. In the atomic structure of the self-consistent calculation the band overlap is used as the free electron dynamic criterion. Electronic pressure, energy, heat capacity and other thermodynamic factors of gold are calculated

Quasi‐random integration in quantum chemistry: Efficiency, stability, and application to the study of small atoms and molecules constrained in spherical boxes

AbstractThis project consists of two parts. In the first part, a series of test calculations is performed to verify that the integrals involved in the determination of atomic and molecular properties by standard self‐consistent field (SCF) methods can be obtained through Halton, Korobov, or Hammersley quasi‐random integration procedures. Through these calculations, we confirm that all three methods lead to results that meet the levels of precision required for their use in the calculation of properties of small atoms or molecules at least at a Hartree–Fock level. Moreover, we have ensured that the efficiency of quasi‐random integration methods that we have tested is Halton=Korobov>Hammersley≫pseudo‐random. We also find that these results are comparable to those yielded by ordinary Monte Carlo (pseudo‐random) integration, with a calculation effort of two orders of smaller magnitude. The second part, which would not have been possible without the integration method previously analyzed, contains a first study of atoms constrained in spherical boxes through SCF calculations with basis functions adapted to the features of the problem: Slater‐type orbitals (STOs) trimmed by multiplying them by a function that yields 1 for 0 < r < (R‐δ), polynomial values for (R‐δ) < r < R and null for r > R, R being the radius of the box and δ a variationally determined interval. As a result, we obtain a equation of state for electrons of small systems, valid just in the limit of low temperatures, but fairly simple. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Shell effects in the equation of state of metals

A simple quasiclassical Z-scaling model (QMT) is proposed to calculate the electron equation of state (EOS) for matter with a high energy concentration. This model may be employed over a wide range of densities and temperatures from the Saha model region of application to the corrected Thomas-Fermi model model (TFC) area of use. The treated model describes ab initio typical step behavior of the ionization state and energy as a result of successive shell ionization with increased temperature. The model naturally includes the effects of electron-ion interaction with increased density. This EOS model may be interesting for gas dynamics, energetics, astrophysics, etc.

Electrostatic potential jump across fast‐mode collisionless shocks

The electrostatic potential jump across fast‐mode collisionless shocks is examined by comparing published observations, hybrid simulations, and a simple model in order to better characterize its dependence on the various shock parameters. In all three, it is assumed that the electrons can be described by an isotropic power law equation of state. The observations show that the cross‐shock potential jump correlates well with the shock strength but shows very little correlation with other shock parameters. Assuming that the electrons obey an isotropic power law equation of state, the correlation of the potential jump with the shock strength follows naturally from the increased shock compression (Δn) and an apparent dependence of the power law exponent on the Mach number which the observations indicate. We find that including a Mach number dependence for the power law exponent in the electron equation of state in our simple model, as suggested by the observations, produces a potential jump which better fits the observations. On the basis of the simulation results and theoretical estimates of the cross‐shock potential, we also discuss how the cross‐shock potential might be expected to depend on the other shock parameters, namely, βe, and θBn Given the broad range of parameters lumped together in the observational results, we feel that the qualitative agreement between them and the simulations is quite good and can be used to better elucidate the nature of the discrepancies.

Theory of weak ion acoustic double layers

We present a theory of small amplitude ion acoustic double layers in a homogeneous unmagnetized plasma. Using fluid equations for ions and a general equation of state for electrons, we show that such double layers exist when the free and reflected electron distributions are different from maxwellians.