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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2017

Electric fields at finite temperature

Partial differential equations for the electric potential at finite temperature, taking into account the thermal Euler–Heisenberg contribution to the electromagnetic Lagrangian are derived. This complete temperature dependence introduces quantum corrections to several well known equations such as the Thomas–Fermi and the Poisson–Boltzmann equation. Our unified approach allows at the same time to derive other similar equations which take into account the effect of the surrounding heat bath on electric fields. We vary our approach by considering a neutral plasma as well as the screening caused by electrons only. The effects of changing the statistics from Fermi–Dirac to the Tsallis statistics and including the presence of a magnetic field are also investigated. Some useful applications of the above formalism are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Entropy density of an adiabatic relativistic Bose-Einstein condensate star

Inspired by recent works, we investigate how the thermodynamics parameters (entropy, temperature, number density, energy density, etc) of Bose-Einstein Condensate star scale with the structure of the star. Below the critical temperature in which the condensation starts to occur, we study how the entropy behaves with varying temperature till it reaches its own stability against gravitational collapse and singularity. Compared to photon gases (pressure is described by radiation) where the chemical potential, μ is zero, entropy of photon gases obeys the Stefan-Boltzmann Law for a small values of T while forming a spiral structure for a large values of T due to general relativity. The entropy density of Bose-Einstein Condensate is obtained following the similar sequence but limited under critical temperature condition. We adopt the scalar field equation of state in Thomas-Fermi limit to study the characteristics of relativistic Bose-Einstein condensate under varying temperature and entropy. Finally, we obtain the entropy density proportional to (σT{sup 3}-3T) which obeys the Stefan-Boltzmann Law in ultra-relativistic condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory

Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to leading order (–0.221 Z 5/3 and –0.021 Z ln Z respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to E x (N,Z) ≈ –0.354 N 2/3 Z (as known before only for Z >> N >> 1) and E c ≈ –0.02 N ln N . These asymptotic estimates are most correct for atomic ions with large N and Z >> N, but we find that they are qualitatively and semi- quantitatively correct even for small N and for N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely-predictive approximate density functionals should be designed to recover the correct asymptotics. Here, it is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Can “Two-” and “One-Dimensional” Multielectron Atoms Exist?

The quasi-classical Thomas–Fermi method is applied to 2D and 1D multielectron atoms. In terms of this method, such atoms are shown not to exist because of the fact that the physical boundary conditions that are analogous to the 3D version of the theory, where boundary conditions are met, cannot be fulfilled. Our theoretical results can be experimentally tested. Atomic number Z{sub 1,} {sub 2max} (~10{sup 2}?) is assumed to exist in terms of this method. At Z > Z{sub 1,2max}, low-dimensional multielectron atoms cannot exist, in contrast to oneor two-electron atoms and, e.g., an experimentally detected Bose condensate of low-dimensional atoms with Z ~ 10 (Na).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Criterion for strong localization on a semiconductor surface in the Thomas–Fermi approximation

The localization behavior of a two-dimensional electron gas confined at the surface of a heavily doped semiconductor under conditions of the “natural” size effect in the space-charge region is investigated. The scattering of low-energy electrons by the chaotic potential formed at the surface by point charges of ionized impurities is analyzed and the electron mean free path is determined. A criterion for strong localization in this two-dimensional electron system is obtained on the basis of the Ioffe–Regel criterion.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Fermi-Teller Theory of Low Velocity Ionization Losses Applied to Monopoles

Recently there has developed a renewed interest in the ionization losses of slow monopoles. An excellent summary of the literature is contained in a paper of Ahlen and Kinoshital (hereafter referred to as A.K.). A.K. have derived lower bounds for the ionization losses of a slow monopole passing through matter. However, they neglected the effects of an energy gap, in insulating materials, on the excitation of atomic electrons. Using the Thomas-Fermi statistical model of atomic wave functions, we have calculated lower bounds for ionization losses in "insulators" including effects due to an energy gap. The Fermi-Teller theory 2 (hereafter referred-to as F.T.) was originally used to predict the stopping, by ionization losses, of slow charged particles in materials. The theory is based on a calculation of the energy lost to a uniform "Fermi sea". However, the authors note that the actual "Fermi velocity" cancels out in the derivation. Therefore their calculated results also apply to a "Thomas-Fermi" atom, in which each volume element is considered to be a Fermi sea filled to the top of the potential well with atomic electrons.

Ritson, D.↗
DOE OSTI2017

A Model for the Characterization of the Polarizability of Thin Films Independently of the Thickness of the Film

It is known that the dielectric properties of thin films can be modified relative to the bulk material because the interaction between film and substrate influences the mobility of the atoms or molecules in the first layers. Here we show that a strong scale effect occurs in nanometer size octadecylammine thin films. Here, this effect is attributed to the different distribution of molecules depending on the size of the film. To accurately describe this effect, we have developed a model which is a reinterpretation of the linearized Thomas-Fermi approximation. Within this model, we have been able to characterize the polarizability of thin films independently of the thickness of the film.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Extending and Smoothing Two-dimension Equation of State Simulation Data

The Multiphase Equation of State (MEOS) project works to produce high quality equation of state tables which are used in computationally intensive simulations of materials in different conditions. An equation of state table describes the state of matter under certain physical conditions such as pressure, volume, temperature, or internal energy. MEOS uses many different models and combinations thereof to produce accurate tables consisting of continuous smooth data, derivatives, and higher-order derivatives. Accurate and smooth data are important factors in producing precise simulations. This report focuses on improving the electron tables produced from Purgatorio and Thomas-Fermi data. Purgatorio data is extremely accurate but often jagged and discontinuous in the lower temperature and density region. Thomas-Fermi is a model that provides smooth data throughout. Together, this produces an EOS data table that is both accurate and smooth. This report describes the implementation of a new feature that allows users to define more detailed regions in the Purgatorio table to be replaced with Thomas-Fermi. As a result, MEOS can generate a table that is both more smooth and still accurate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Path integral Monte Carlo simulations of warm dense aluminum

Here, we perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of $0.1-32.4$~g$\,$cm$^{-3}$ and $10^4-10^8$~K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multi-shock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multi-shock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and Z to reveal the evolution of the plasma structure and ionization behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1974

The Apsidal-motion test for models of main-sequence stars

Apsidal-motion constants, k2, have been determined for models of homogeneous main-sequence stars constructed with the new 'Thomas-Fermi' opacities of Carson. These models are similar to those constructed with the 'hydrogenic' opacities of Cox and Stewart up to about 7 solar masses, but yield smaller values of k2 at higher masses. Nevertheless, the new theoretical constants are still systematically too large compared with most of the empirical constants known for members of well-observed binary systems. Uniform rotation is found to lower the theoretical constants only slightly. The effect of normal evolution during core hydrogen burning, however, produces good detailed agreement with observations. The primary of alpha Vir is probably evolving normally if Carson's opacities are adopted.

Stothers, R.↗
DOE OSTI2019

Equation of state of boron nitride combining computation, modeling, and experiment

The equation of state (EOS) of materials at warm dense conditions poses significant challenges to both theory and experiment. We report a combined computational, modeling, and experimental investigation leveraging new theoretical and experimental capabilities to investigate warm-dense boron nitride (BN). The simulation methodologies include path integral Monte Carlo (PIMC), several density functional theory (DFT) molecular dynamics methods [plane-wave pseudopotential, Fermi operator expansion (FOE), and spectral quadrature (SQ)], activity expansion (actex), and all-electron Green's function Korringa-Kohn-Rostoker (mecca), and compute the pressure and internal energy of BN over a broad range of densities and temperatures. Our experiments were conducted at the Omega laser facility and the Hugoniot response of BN to unprecedented pressures (1200–2650 GPa). The EOSs computed using different methods cross validate one another in the warm-dense matter regime, and the experimental Hugoniot data are in good agreement with our theoretical predictions. By comparing the EOS results from different methods, we assess that the largest discrepancies between theoretical predictions are ≲ 4% in pressure and ≲ 3% in energy and occur at 10 6 K, slightly below the peak compression that corresponds to the K -shell ionization regime. At these conditions, we find remarkable consistency between the EOS from DFT calculations performed on different platforms and using different exchange-correlation functionals and those from PIMC using free-particle nodes. This provides strong evidence for the accuracy of both PIMC and DFT in the high-pressure, high-temperature regime. Moreover, the recently developed SQ and FOE methods produce EOS data that have significantly smaller statistical error bars than PIMC, and so represent significant advances for efficient computation at high temperatures. The shock Hugoniot predicted by PIMC, actex, and mecca shows a maximum compression ratio of 4.55 ± 0.05 for an initial density of 2.26 g/cm 3 , higher than the Thomas-Fermi predictions by about 5%. In addition, we construct tabular EOS models that are consistent with the first-principles simulations and the experimental data. Our findings clarify the ionic and electronic structure of BN over a broad range of temperatures and densities and quantify their roles in the EOS and properties of this material. The tabular models may be utilized for future simulations of laser-driven experiments that include BN as a candidate ablator material.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quantum Scales of Galaxies from Self-interacting Ultralight Dark Matter

We derive the characteristic scales for physical quantities of dwarf galaxies, such as mass, size, acceleration, and angular momentum, within the self-interacting ultralight dark matter (ULDM) model. Due to the small mass of ULDM, even minor self-interactions can drastically alter these scales in the Thomas-Fermi limit. We suggest that these characteristic scales are connected to mysteries of observed galaxies. Oscillation of ULDM field can explain the current cosmological density of dark matter. Many cosmological constraints suggest that the energy scale $\tilde{m}$ for self-interacting ULDM is typically of the order $10~eV$, whereas the mass $m$ for the non-interacting case is around $10^{-21}~eV$. Self-interacting ULDM provides the better explanation for cosmological observations than the non-interacting case.

Astrophysics of Galaxies (astro-ph.GA)↗
DOE OSTI2015

Unified description of linear screening in dense plasmas

Electron screening of ions is among the most fundamental properties of plasmas, determining the effective ionic interactions that impact all properties of a plasma. With the development of new experimental facilities that probe high-energy-density physics regimes ranging from warm dense matter to hot dense matter, a unified framework for describing dense plasma screening has become essential. Such a unified framework is presented here based on finite-temperature orbital-free density functional theory, including gradient corrections and exchange-correlation effects. We find a new analytic pair potential for the ion-ion interaction that incorporates moderate electronic coupling, quantum degeneracy, gradient corrections to the free energy, and finite temperatures. This potential can be used in large-scale “classical” molecular dynamics simulations, as well as in simpler theoretical models (e.g., integral equations and Monte Carlo), with no additional computational complexity. The new potential theoretically connects limits of Debye-Hückel–Yukawa, Lindhard, Thomas-Fermi, and Bohmian quantum hydrodynamics descriptions. In conclusion, based on this new potential, we predict ionic static structure factors that can be validated using x-ray Thomson scattering data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1977

Thermodynamics of Thomas-Fermi screened Coulomb systems

We obtain in closed analytic form, estimates for the thermodynamic properties of classical fluids with pair potentials of Yukawa type, with special reference to dense fully ionized plasmas with Thomas-Fermi or Debye-Hueckel screening. We further generalize the hard-sphere perturbative approach used for similarly screened two-component mixtures, and demonstrate phase separation in this simple model of a liquid mixture of metallic helium and hydrogen.

Firey, B.↗
DOE OSTI2022

Hybrid Kohn-Sham+Thomas-Fermi scheme for high-temperature density functional theory

We report density functional theory has revolutionised our understanding of dense, strongly coupled systems in the condensed-matter limit. At elevated temperatures, such as those found in warm dense matter and dense plasma, the computational cost of calculating enough states to accurately describe a thermal ensemble of electrons is a major obstacle to practical Kohn-Sham calculations. This problem has recently been tackled from a number of approaches, including a plane-wave approximation for electrons at high energy. In this work, we demonstrate how the Thomas-Fermi density of states, equivalent to a local plane-wave approximation, can yield improved results for thermodynamic quantities, electron density profiles, and interatomic forces while requiring fewer states than existing methods.

36 MATERIALS SCIENCE↗
NASA NTRS1981

Structure and screening in molecular and metallic hydrogen at high pressure

A variational wavefunction is used to express the (spin restricted) Hartree-Fock energy as reciprocal lattice sums for static lattice FCC monatomic hydrogen and diatomic Pa3 molecular hydrogen. In the monatomic phase the hydrogenic orbital range closely parallels the inverse Thomas-Fermi wavevector; the corresponding energy E has a minimum of -0.929 Ryd/electron at r sub s = 1.67. For the diatomic phase E(r sub s) is similar, but the constituent energies, screening, and bond length reflect a qualitative change in the nature of the solid at r sub s = 2.8. This change is interpreted in terms of a transition from protons as structural units (at high density) to weakly interacting models (at low density). Insensitivity of the total energy to a rapid fall in the bond length suggests association with the rotational transition where the rapid molecular orientations characteristic of high pressures disappear and the molecules rotate freely at low pressure.

Wood, D. M.↗
DOE OSTI2019

Atom-in-jellium equations of state in the high-energy-density regime

Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that computationally efficient average-atom models can predict thermodynamic states in warm dense matter to within a few percent. One such atom-in-jellium model has typically been used to predict the electron-thermal behavior only, although it was previously developed to predict the entire equation of state (EOS). In this work, we report completely atom-in-jellium EOS calculations for Be, Al, Si, Fe, and Mo, as elements representative of a range of atomic number and low-pressure electronic structure. Comparing the more recent method of pseudoatom molecular dynamics, atom-in-jellium results were similar: sometimes less accurate, sometimes more. All these techniques exhibited pronounced effects of electronic shell structure in the shock Hugoniot which are not captured by Thomas-Fermi based EOS. These results demonstrate the value of a hierarchical approach to EOS construction, using average-atom techniques with shell structure to populate a wide-range EOS surface efficiently, complemented by more rigorous three-dimensional multiatom calculations to validate and adjust the EOS.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗