Warm Dense Regime Research Articles

First-principles studies on the equation of state, thermal conductivity, and opacity of deuterium-tritium (DT) and polystyrene (CH) for inertial confinement fusion applications

Using first-principles (FP) methods, we have performed ab initio compute for the equation of state (EOS), thermal conductivity, and opacity of deuterium-tritium (DT) in a wide range of densities and temperatures for inertial confinement fusion (ICF) applications. These systematic investigations have recently been expanded to accurately compute the plasma properties of CH ablators under extreme conditions. In particular, the first-principles EOS and thermal-conductivity tables of CH are self-consistently built from such FP calculations, which are benchmarked by experimental measurements. When compared with the traditional models used for these plasma properties in hydrocodes, significant differences have been identified in the warm dense plasma regime. When these FP-calculated properties of DT and CH were used in our hydrodynamic simulations of ICF implosions, we found that the target performance in terms of neutron yield and energy gain can vary by a factor of 2 to 3, relative to traditional model simulations.

First-principles study on equation of states and electronic structures of shock compressed Ar up to warm dense regime.

The equation of states (EOS) and electronic structures of argon with temperatures from 0.02 eV to 3 eV and densities from 0.5 g/cm(3) to 5.5 g/cm(3) are calculated using the pair potential and many-body potential molecular dynamics and the density functional theory (DFT) molecular dynamics with van der Waals (vdW) corrections. First-principles molecular dynamics is implemented above 2.0 g/cm(3). For the cases of low densities below 3 g/cm(3), we performed pair potential molecular dynamics in order to obtain the ionic configurations, which are used in density functional theory to calculate the EOS and electronic structures. We checked the validity of different methods at different densities and temperatures, showing their behaviors by comparing EOS. DFT without vdW correction works well above 1 eV and 3.5 g/cm(3). Below 1 eV and 2.0 g/cm(3), it overestimates the pressure apparently and results in incorrect behaviors of the internal energy. With vdW corrections, the semi-empirical force-field correction (DFT-D2) method gives consistent results in the whole density and temperature region, and the vdW density functional (vdW-DF2) method gives good results below 2.5 g/cm(3), but it overestimates the pressure at higher densities. The interactions among the atoms are overestimated by the pair potential above 1 eV, and a temperature dependent scaled pair potential can be used to correct the ionic configurations of the pair potential up to 3 eV. The comparisons between our calculations and the experimental multi-shock compression results show that the Hugoniot line of DFT-D2 and DFT tends to give larger pressure than the results of the self-consistent fluid variational theory, and the difference increases with the density. The electronic energy gap exists for all our cases up to 5.5 g/cm(3) and 1 eV. The effect of vdW interactions on the electronic structures are also discussed.

Multishock Compression Properties of Warm Dense Argon.

Warm dense argon was generated by a shock reverberation technique. The diagnostics of warm dense argon were performed by a multichannel optical pyrometer and a velocity interferometer system. The equations of state in the pressure-density range of 20–150 GPa and 1.9–5.3 g/cm3 from the first- to fourth-shock compression were presented. The single-shock temperatures in the range of 17.2–23.4 kK were obtained from the spectral radiance. Experimental results indicates that multiple shock-compression ratio (ηi = ρi/ρ0) is greatly enhanced from 3.3 to 8.8, where ρ0 is the initial density of argon and ρi (i = 1, 2, 3, 4) is the compressed density from first to fourth shock, respectively. For the relative compression ratio (ηi’ = ρi/ρi-1), an interesting finding is that a turning point occurs at the second shocked states under the conditions of different experiments, and ηi’ increases with pressure in lower density regime and reversely decreases with pressure in higher density regime. The evolution of the compression ratio is controlled by the excitation of internal degrees of freedom, which increase the compression, and by the interaction effects between particles that reduce it. A temperature-density plot shows that current multishock compression states of argon have distributed into warm dense regime.

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

AbstractWe present in this work, a thermodynamic perturbation theory for equation of state of hydrogen and helium in the warm dense regime. The system is modeled as a mixture of classical point ions and quantum electrons. A perturbation series for Helmholtz free energy and correlation functions of the ions and electrons as a function of density and temperature is proposed. Combining the classical thermodynamic perturbation theory and the orbitial‐free quantum hyper‐netted chain theory, a systematic procedure to obtain the terms of the perturbation series is developed. The ion‐ion correlations are treated within the hyper‐netted chain approximation and the ion‐electron correlations are treated within the Thomas‐Fermi‐Dirac‐Weizsäcker approximation. The method has been applied to obtain isotherms of hydrogen and helium in the warm dense regime. The isotherms are compared with available ab‐initio data and the results are analyzed. A good agreement with ab‐initio data has been observed for pressures greater than one Mbar. Advantages and limitations of the present method are discussed along with possible future improvements. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Interaction picture density matrix quantum Monte Carlo.

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

Molecular Dynamics Simulations of Warm Dense Carbon

AbstractWe present classical and DFT‐based molecular dynamics (MD) simulations of carbon in the warm dense matter regime (ϱ = 3.7 g/cc, 0.86 eV < T < 8.62 eV [T < 100 eV for classical MD]). Two different classical interatomic potentials are used: 1. LCBOP, designed to simulate condensed (e.g. solid) phases of C, and 2. linearly screened Coulomb (Yukawa) potentials. It is shown that LCBOP over‐predicts minima and maxima in the pair correlation functions of liquid‐C in this regime when compared to the DFT‐MD results. The screened Coulomb model, while under‐correlating at low‐T, seems to produce the correct qualitative features in the static ionic pair distributions at the highest‐T. However, both approaches predict the decay in the ionic contribution of the specific heat as T → ∞ to be much slower than that predicted by a model based on DFT‐MD. These differences in the MD‐derived equations of state in warm dense regimes could have important consequences when using classical inter‐ionic forces such as these in large‐scale MD simulations aimed at studying, for instance, processes of relevance to inertial confinement fusion when C is used as an ablator material. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Equations of state and transport properties of mixtures in the warm dense regime

We have performed average-atom molecular dynamics to simulate the CH and LiH mixtures in the warm dense regime, and obtained equations of state and the ionic transport properties. The electronic structures are calculated by using the modified average-atom model, which have included the broadening of energy levels, and the ion-ion pair potentials of mixtures are constructed based on the temperature-dependent density functional theory. The ionic transport properties, such as ionic diffusion and shear viscosity, are obtained through the ionic velocity correlation functions. The equations of state and transport properties for carbon, hydrogen and lithium, hydrogen mixtures in a wide region of density and temperature are calculated. Through our computing the average ionization degree, average ion-sphere diameter and transition properties in the mixture, it is shown that transport properties depend not only on the ionic mass but also on the average ionization degree.

Quantum molecular dynamics study of warm dense iron.

The equation of state, the self-diffusion coefficient and viscosity of fluid iron in the warm dense regime at densities from 12.5 to 25.0 g/cm(3), and temperatures from 0.5 to 15.0 eV have been calculated via quantum molecular dynamics simulations. The principal Hugoniot is in good agreement with nuclear explosive experiments up to ∼ 50 Mbar but predicts lower pressures compared with high intensity laser results. The self-diffusion coefficient and viscosity have been simulated and have been compared with the one-component plasma model. The Stokes-Einstein relationship, defined by connections between the viscosity and the self-diffusion coefficient, has been determined and has been found to be fairly well described by classical predictions.

Exchange-correlation energy for the three-dimensional homogeneous electron gas at arbitrary temperature

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r_{s} = (3/4\pi n)^{1/3} a_{B}^{-1} < 40 and \Theta = T/T_{F} > 0.0625). In doing so, we construct a Pad\'{e} approximant which collapses to Debye-H\"{u}ckel theory in the high-temperature, low-density limit. Likewise, the zero-temperature limit matches the numerical results of ground-state quantum Monte Carlo, as well as analytical results in the high-density limit.

Equations of state and transport properties of warm dense beryllium: A quantum molecular dynamics study

We have calculated the equations of state, the viscosity and self-diffusion coefficients, and electronic transport coefficients of beryllium in the warm dense regime for densities from 4.0 to 6.0 g/cm(3) and temperatures from 1.0 to 10.0 eV by using quantum molecular dynamics simulations. The principal Hugoniot curve is in agreement with underground nuclear explosive and high-power laser experimental results up to ~20 Mbar. The calculated viscosity and self-diffusion coefficients are compared with the one-component plasma model, using effective charges given by the average-atom model. The Stokes-Einstein relationship, which connects viscosity and self-diffusion coefficients, is found to hold fairly well in the strong coupling regime. The Lorenz number, which is the ratio between thermal and electrical conductivities, is computed via Kubo-Greenwood formula and compared to the well-known Wiedemann-Franz law in the warm dense region.

Path-integral Monte Carlo simulation of the warm dense homogeneous electron gas.

We perform calculations of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r(s) ≡ (3/4πn)(1/3)a(0)(-1) = 1.0-40.0 and Θ ≡ T/T(F) = 0.0625-8.0) using restricted path-integral Monte Carlo simulations. Precise energies, pair correlation functions, and structure factors are obtained. For all densities, we find a significant discrepancy between the ground state parametrized local density approximation and our results around T(F). These results can be used as a benchmark for developing finite-temperature density functionals, as well as input for orbital-free density function theory formulations.

Mach stem hysteresis: Experiments addressing a novel explanation of clumpy astrophysical jet emission

Recent time-series observations of shock waves in stellar jets taken with the Hubble Space Telescope reveal localized bright knots that persist over nearly 15 years. While some of these features represent shock fronts caused by variable velocities in the flow, others appear at the intersection points between distinct bow shocks. Theoretically, when the angle between two intersecting shocks exceeds a certain critical value, a third shock (Mach stem) should form. Because Mach stems form perpendicular to the direction of flow, incoming particles encounter a normal shock instead of an oblique one, which results in brighter emission at this location. To study this phenomenon in a controlled laboratory setting, we have carried out experiments on the Omega laser aimed at understanding the formation, growth, and destruction of Mach stems in the warm dense plasma regime. Our experimental results indicate how the growth rate depends upon included angle, and numerical simulations indicate that it may be possible to stabilize an already-formed Mach stem below the critical angle when certain conditions are satisfied.

Properties of Hot Dense Plasmas by Orbital‐Free Molecular Dynamics

AbstractQuantum Molecular Dynamics simulations (QMD) based on Density Functional Theory (DFT) are now the tool of choice for describing the properties of matter in the warm dense regime (WDM). Thermodynamic and transport properties can be computed for pure phases and mixtures for a wide range of densities ρ0/10 &lt; ρ &lt; 2 – 5ρ0 (where ρ0 is the normal material density) and temperatures 0 &lt; T &lt; 10 eV. The existence of upper bounds in density and temperature is mainly due to the introduction of orbitals for evaluating the electron kinetic energy in the Kohn‐Sham equations. To get rid of this time consuming part of the computation, we propose a model combining, in a consistent way an Orbital Free Density Functional approach based on the Thomas‐Fermi approximation of the electron kinetic energy coupled with classical Molecular Dynamics for the ions (referred as OFMD model).Thanks to an efficient numerical scheme, up to thousand of particles can be propagated leading to accurate static and dynamical properties. Simulations on iron up to 5 keV and boron up to 10 times the normal density were performed. A comparison with linear screening theories using Yukawa's potentials was also done. This method bridges the gap between quantum and classical molecular dynamics in the field of hot‐dense plasmas. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)