Path integral monte carlo calculation of the deuterium hugoniot

Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations

We present a study of hydrogen at pressures higher than molecular dissociation using the coupled electron-ion Monte Carlo method. These calculations use the accurate reptation quantum Monte Carlo method to estimate the electronic energy and pressure while doing a Monte Carlo simulation of the protons. In addition to presenting simulation results for the equation of state over a large region of the phase diagram, we report the free energy obtained by thermodynamic integration. We find very good agreement with density-functional theory based molecular-dynamics calculations for pressures beyond 600 GPa and densities above rho=1.4 g/cm(3) , both for thermodynamic and structural properties. This agreement provides a strong support to the different approximations employed in the density-functional treatment of the system, specifically the approximate exchange-correlation potential and the use of pseudopotentials for the range of densities considered. We find disagreement with chemical models, which suggests that a reinvestigation of planetary models--previously constructed using the Saumon-Chabrier-Van Horn equations of state--might be needed.

Equation of State and Electrical Conductivity of Dense Fluid Hydrogen and Helium

The equation of state of fluid hydrogen, helium, and their mixtures is determined within fluid variational theory. Reactions between the constituents such as dissociation and ionization are considered. Results are given for densities and temperatures relevant for the interior of giant planets. Furthermore, the electrical conductivity is determined within linear response theory. Comparison is performed with available experiments and other theoretical work.

Structure of strongly coupled multicomponent plasmas

We investigate the short-range structure in strongly coupled fluidlike plasmas using the hypernetted chain approach generalized to multicomponent systems. Good agreement with numerical simulations validates this method for the parameters considered. We found a strong mutual impact on the spatial arrangement for systems with multiple ion species which is most clearly pronounced in the static structure factor. Quantum pseudopotentials were used to mimic diffraction and exchange effects in dense electron-ion systems. We demonstrate that the different kinds of pseudopotentials proposed lead to large differences in both the pair distributions and structure factors. Large discrepancies were also found in the predicted ion feature of the x-ray scattering signal, illustrating the need for comparison with full quantum calculations or experimental verification.

Density measurement of low- Z shocked material from monochromatic x-ray two-dimensional images

An experiment on LULI 2000 laser devoted to density determination of shocked plastic from a two-dimensional monochromatic x-ray radiography is presented. A spherical quartz crystal was set to select the He-alpha line of vanadium at 2.382 A and perform the image of the main target. Rear side diagnostics were implemented to validate the new diagnostic. The density experimental results given by radiography are in good agreement with rear side diagnostics data and hydrodynamical simulations. The pressure regime into the plastic is 2-3 Mbar, corresponding to a compression between 2.7-2.9.

Pair-distribution functions of two-temperature two-mass systems: comparison of molecular dynamics, classical-map hypernetted chain, quantum Monte Carlo, and Kohn-Sham calculations for dense hydrogen

Two-temperature, two-mass quasiequilibrium plasmas may occur in electron-ion plasmas, nuclear-matter, as well as in electron-hole condensed-matter systems. Dense two-temperature hydrogen plasmas straddle the difficult partially degenerate regime of electron densities and temperatures which are important in astrophysics, in inertial-confinement fusion research, and other areas of warm dense-matter physics. Results from quantum Monte Carlo (QMC) are used to benchmark the procedures used in classical molecular-dynamics simulations and hypernetted chain (HNC) and classical-map HNC (CHNC) methods to derive electron-electron and electron-proton pair-distribution functions. Where QMC is not available, we used Kohn-Sham results as the reference calculation. Then, nonequilibrium molecular dynamics for two-temperature, two-mass plasmas are used to obtain pair distribution functions without specifying the interspecies cross temperature. Using these results, the correct HNC and CHNC procedures for the evaluation of pair-distribution functions in two-temperature two-mass two-component charged fluids are established and results for a mass ratio of 1:5, typical of electron-hole fluids, are presented.

Excited electron dynamics modeling of warm dense matter

We present a model (the electron force field, or eFF) based on a simplified solution to the time-dependent Schrödinger equation that with a single approximate potential between nuclei and electrons correctly describes many phases relevant for warm dense hydrogen. Over a temperature range of 0 to 100,000 K and densities up to 1 g/cm(3), we find excellent agreement with experimental, path integral Monte Carlo, and linear mixing equations of state, as well as single-shock Hugoniot curves from shock compression experiments. In principle eFF should be applicable to other warm dense systems as well.

Wave packet simulation of dense hydrogen

Dense hydrogen is studied in the framework of wave packet molecular dynamics. In this semiquantal many-body simulation method the electrons are represented by wave packets which are suitably parametrized. The equilibrium properties and time evolution of the system are obtained with the help of a variational principle. At room temperature the results for the isotherms are in good agreement with anvil experiments. At higher densities beyond the range of the experimental data a transition from a molecular to a metallic state is predicted. The wave packets become delocalized and the electrical conductivity increases sharply. The phase diagram is calculated in a wide range of the pressure-density-temperature space. The observed transition from the molecular to metallic state is accompanied by an increase in density in agreement with recent reverberating shock wave experiments.

Low variance energy estimators for systems of quantum Drude oscillators: Treating harmonic path integrals with large separations of time scales

In the effort to develop atomistic models capable of accurately describing nanoscale systems with complex interfaces, it has become clear that simple treatments with rigid charge distributions and dispersion coefficients selected to generate bulk properties are insufficient to predict important physical properties. The quantum Drude oscillator model, a system of one-electron pseudoatoms whose "pseudoelectrons" are harmonically bound to their respective "pseudonuclei," is capable of treating many-body polarization and dispersion interactions in molecular systems on an equal footing due to the ability of the pseudoatoms to mimic the long-range interactions that characterize real materials. Using imaginary time path integration, the Drude oscillator model can, in principle, be solved in computer operation counts that scale linearly with the number of atoms in the system. In practice, however, standard expressions for the energy and pressure, including the commonly used virial estimator, have extremely large variances that require untenably long simulation times to generate converged averages. In this paper, low-variance estimators for the internal energy are derived, in which the large zero-point energy of the oscillators does not contribute to the variance. The new estimators are applicable to any system of harmonic oscillators coupled to one another (or to the environment) via an arbitrary set of anharmonic interactions. The variance of the new estimators is found to be much smaller than standard estimators in three example problems, a one-dimensional anharmonic oscillator and quantum Drude models of the xenon dimer and solid (fcc) xenon, respectively, yielding 2-3 orders of magnitude improvement in computational efficiency.

First principles calculations of shock compressed fluid helium

The properties of hot dense helium at megabar pressures are studied with two first principles computer simulation techniques: path integral Monte Carlo simulation and density functional molecular dynamics. The simulations predict that the compressibility of helium is substantially increased by electronic excitations that are present in the hot fluid at thermodynamic equilibrium. A maximum compression ratio of 5.24(4)-fold the initial density was predicted for 360 GPa and 150,000 K. This result distinguishes helium from deuterium, for which simulations predicted a maximum compression ratio of 4.3(1). Hugoniot curves for statically precompressed samples are also discussed.

Molecular dynamics simulations of optical conductivity of dense plasmas

The optical conductivity sigma (omega) for dense Coulomb systems is investigated using molecular dynamics simulations on the basis of pseudopotentials to mimic quantum effects. Starting from linear response theory, the response in the long-wavelength limit k=0 can be expressed by different types of autocorrelation functions (ACF's) such as the current ACF, the force ACF, or the charge density ACF. Consistent simulation data for transverse as well as longitudinal ACF's are shown which are based on calculations with high numerical accuracy. Results are compared with perturbation expansions which are restricted to small values of the plasma parameter. The relevance with respect to a quantum Coulomb plasma is discussed. Finally, results are presented showing a consistent description of these model plasmas in comparison to quantum statistical approaches and to experimental data.

Monte Carlo results for the hydrogen Hugoniot

We propose a theoretical Hugoniot relation obtained by combining results for the equation of state from the direct path integral Monte Carlo technique (DPIMC) and those from reaction ensemble Monte Carlo (REMC) simulations. The main idea of this proposal is based on the fact that the DPMIC technique provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically by applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson et al. [Phys. Rev. Lett. 87, 225501 (2001)] and Collins et al. [Science 281, 1178 (1998)].

Coupled electron-ion monte carlo calculations of dense metallic hydrogen

We present an efficient new Monte Carlo method which couples path integrals for finite temperature protons with quantum Monte Carlo calculations for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. We report data for the equation of state for temperatures across the melting of the proton crystal. Our data exhibit more structure and higher melting temperatures of the proton crystal than do Car-Parrinello molecular dynamics results. This method fills the gap between high temperature electron-proton path integral and ground state diffusion Monte Carlo methods and should have wide applicability.

Reaction ensemble Monte Carlo technique and hypernetted chain approximation study of dense hydrogen

In spite of the simple structure of hydrogen, up to now there is no unified theoretical and experimental description of hydrogen at high pressures. Recent results of Z-pinch experiments show a large deviation from those obtained by laser driven ones. Theoretical investigations including ab initio computer simulations show considerable differences at such extreme conditions from each other and from experimental values. We apply the reaction ensemble Monte Carlo technique on one hand and a combination of the hypernetted chain approximation with the mass action law on the other to study the behavior of dense hydrogen at such conditions. The agreement between both methods for the equation of state and for the Hugoniot curve is excellent. Comparison to other methods and experimental results is also performed.

Internal versus external conductivity of a dense plasma: many-particle theory and simulations

In the long-wavelength limit k=0, the response function has been investigated with respect to the external and internal fields which is expressed by the external and internal conductivity, respectively. Molecular dynamics simulations are performed to obtain the current-current correlation function and the dynamical collision frequency which are compared with analytical expressions. Special attention is given to the dynamical collision frequency and the description of plasma oscillations in the case of k=0. The relation between the external and internal conductivity and the current-current correlation function is analyzed.

Dense plasma effects on nuclear reaction rates

Plasma density effects can cause an exponential change in charged particle nuclear reaction rates important in stellar evolution. Reaction rates in dense plasma, with emphasis on quantum aspects, are examined here using path integral Monte Carlo calculations. Quantum mechanics causes a reduction in the many body enhancement of the reaction rate compared to the value for a classical system. This can be attributed to the "quantum smearing" of the short range Coulomb interaction resulting in reduced repulsion between the reacting pair and surrounding particles. Electron screening and ion exchange effects are also examined, with screening reducing and exchange slightly increasing the many body enhancement.

Use of a wave reverberation technique to infer the density compression of shocked liquid deuterium to 75 GPa

A novel approach was developed to probe density compression of liquid deuterium (L-D2) along the principal Hugoniot. Relative transit times of shock waves reverberating within the sample are shown to be sensitive to the compression due to the first shock. This technique has proven to be more sensitive than the conventional method of inferring density from the shock and mass velocity, at least in this high-pressure regime. Results in the range of 22-75 GPa indicate an approximately fourfold density compression, and provide data to differentiate between proposed theories for hydrogen and its isotopes.

Shock compression of deuterium near 100 GPa pressures

The shock-compression curve (Hugoniot) of D2 near 100 GPa pressures (1 Mbar) has been contro-versial because the two published measurements have limiting compressions of fourfold and sixfold. Our purpose is to examine published experimental results to decide which, if either, is probably correct. The published Hugoniot data of low-Z diatomic molecules have a universal behavior. The deuterium data of Knudson et al. (fourfold limiting compression) have this universal behavior, which suggests that Knudson et al. are correct and shows that deuterium behaves as other low-Z elements at high tem-peratures. In D2, H2, N2, CO, and O2, dissociation completes and average kinetic energy dominates average potential energy above approximately 60 GPa. Below approximately 30 GPa, D2, H2, N2, CO, and O2 are diatomic. D2 dissociation is accompanied by a temperature-driven nonmetal-metal transition at approximately 50 GPa.

Kinetic and correlation energies and distribution functions of dense plasmas

The mean value of the kinetic energy of a quantum plasma is investigated in Hartree-Fock and Montroll-Ward approximations using the method of thermodynamic Green's functions. Usually, one finds the kinetic energy to be larger than that of an ideal plasma due to the interaction between the particles in the system. However, also the opposite case is possible, i.e., a decrease of the kinetic energy compared to that of the ideal gas. This special correlation effect is found for temperatures of about 10(6) K and densities between 10(21) and 10(26) cm(-3). Here, the single-particle distribution function is shifted towards smaller momenta, and the binary distribution is changed.

Calculation of a deuterium double shock Hugoniot from ab initio simulations

We calculate the equation of state of dense deuterium with two ab initio simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, in the density range of 0.67 < or = rho < or = 1.60 g cm(-3). We derive the double shock Hugoniot and compare with the recent laser-driven double shock wave experiments by Mostovych et al. [Phys. Rev. Lett. 85, 3870 (2000)]. We find excellent agreement between the two types of microscopic simulations, but a significant discrepancy with the laser-driven shock measurements.

Ab initio study of deuterium in the dissociating regime: sound speed and transport properties

The sound speed and the transport properties of dense hydrogen (deuterium) are computed from local spin-density approximation molecular-dynamics simulations in the dissociating regime. The sound speed c(s) is evaluated from the thermodynamical differentiation of the equation of state in the molecular phase and is in very good agreement with recent experiments. The diffusion constant D and the viscosity eta are extracted from simulations performed at V=6, 4, and 2.7 cm(3)/mole, corresponding, respectively, for deuterium at rho=0.672, 1.0, and 1.5 g/cm(3) in a range of temperatures 1000 K<T<50,000 K. In the dissociated regime, the diffusion coefficient is well predicted by one-component plasma formulas using a renormalized coupling parameter recently proposed by Murillo [M. S. Murillo, Phys. Rev. B 62, 4115 (2000)]. The behavior of the shear viscosity in the dissociated regime is more complex and exhibits a crossover between atomic and screened plasma formulation. A comparison with recent molecular-dynamics simulations of Yukawas systems shows that the inverse of the screening length must lie between 1 and 2, in nearest-neighbor radius units, as suggested by the results on the diffusion.

Equation of state measurements in liquid deuterium to 70 GPa

Using intense magnetic pressure, a method was developed to launch flyer plates to velocities in excess of 20 km/s. This technique was used to perform plate-impact, shock wave experiments on cryogenic liquid deuterium ( L-D(2)) to examine its high-pressure equation of state. Using an impedance matching method, Hugoniot measurements were obtained in the pressure range of 30-70 GPa. The results of these experiments disagree with previously reported Hugoniot measurements of L-D(2) in the pressure range above approximately 40 GPa, but are in good agreement with first principles, ab initio models for hydrogen and its isotopes.

Isentropes and Hugoniot curves for dense hydrogen and deuterium

Multiple-shock experiments with fluid hydrogen have shown that a transition from semiconducting behavior to metal-like conductivity occurs at pressures (p) of about 140 GPa and temperatures (T) near 3000 K. We model the p-T pathway by Hugoniot curves (initial shock) and isentropes (subsequent shocks). For the calculation of these curves we apply an expression for the free energy developed recently for dense hydrogen and deuterium plasma in the regions of partial dissociation and partial ionization. Furthermore, we discuss the relations between Hugoniot curves, isentropes and the coexistence line of the plasma phase transition.

Path integral Monte Carlo simulation of the low-density hydrogen plasma

Restricted path integral Monte Carlo simulations are used to calculate the equilibrium properties of hydrogen in the density and temperature range of 9.83 x 10(-4)</=rho</=0.153 g cm(-3) and 5000</=T</=250 000 K. We test the accuracy of the pair density matrix and analyze the dependence on the system size, on the time step of the path integral, and on the type of nodal surface. We calculate the equation of state and compare with other models for hydrogen valid in this regime. Further, we characterize the state of hydrogen and describe the changes from a plasma to an atomic and molecular liquid by analyzing the pair correlation functions and estimating the number of atoms and molecules present.

Local-spin-density-approximation molecular-dynamics simulations of dense deuterium

Local-spin-density-approximation molecular-dynamics simulations of deuterium in the dissociating regime are presented, with a particular emphasis on the molecular phase of two isochores corresponding for deuterium to V=6 cm(3)/mole, rho=0.670 g/cm(3) and V=4 cm(3)/mole, rho=1 g/cm(3). It is shown that the transition from the molecular regime, well described by the local-spin-density-approximation functional, to the dissociated regime where previous local-density-approximation results are recovered, comes with a negative curvature deltaP/deltaT<0 in the isochore. We show that this effect is not enough to explain the large compressibility measured in the laser experiments [L. B. DaSilva et al., Phys. Rev. Lett. 78, 483 (1997); G. W. Collins et al., Science 281, 1178 (1998); P. Celliers et al., Phys. Rev. Lett. 84, 5564 (2000)].