Monte Carlo results for the hydrogen Hugoniot

Equation of state of partially ionized hydrogen and deuterium plasma revisited

We present improved first-principle fermionic path integral Monte Carlo (PIMC) simulation results for a dense partially ionized hydrogen (deuterium) plasma, for temperatures in the range 15000K≤T≤400000K and densities 7×10^{-7}g/cm^{3}≤ρ_{H}≤0.085g/cm^{3} (1.4×10^{-6}g/cm^{3}≤ρ_{D}≤0.17g/cm^{3}), corresponding to 100≥r_{s}≥2, where r_{s}=r[over ¯]/a_{B} is the ratio of the mean interparticle distance to the Bohr radius. These simulations are based on the fermionic propagator PIMC (FP-PIMC) approach in the grand canonical ensemble [Filinov et al., Contrib. Plasma Phys. 61, e202100112 (2021)0863-104210.1002/ctpp.202100112] and fully account for correlation and quantum degeneracy and spin effects. For the application to hydrogen and deuterium, we develop a combination of the fourth-order factorization and the pair product ansatz for the density matrix. Moreover, we avoid the fixed node approximation that may lead to uncontrolled errors in restricted PIMC (RPIMC). Our results allow us to critically reevaluate the accuracy of the RPIMC simulations for hydrogen by Hu et al. [Phys. Rev. B 84, 224109 (2011)1098-012110.1103/PhysRevB.84.224109] and of various chemical models. The deviations are generally found to be small, but for the lowest temperature, T=15640 K they reach several percent. We present detailed tables with our first principles results for the pressure and energy isotherms. We expect our updated results will serve as a valuable benchmark for comparison with other methods.

Development of a new quantum trajectory molecular dynamics framework

An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Momentum distribution function and short-range correlations of the warm dense electron gas: Ab initio quantum Monte Carlo results

In a classical plasma the momentum distribution, n(k), decays exponentially, for large k, and the same is observed for an ideal Fermi gas. However, when quantum and correlation effects are relevant simultaneously, an algebraic decay, n_{∞}(k)∼k^{-8} has been predicted. This is of relevance for cross sections and threshold processes in dense plasmas that depend on the number of energetic particles. Here we present extensive ab initio results for the momentum distribution of the nonideal uniform electron gas at warm dense matter conditions. Our results are based on first principle fermionic path integral Monte Carlo (CPIMC) simulations and clearly confirm the k^{-8} asymptotic. This asymptotic behavior is directly linked to short-range correlations which are analyzed via the on-top pair distribution function (on-top PDF), i.e., the PDF of electrons with opposite spin. We present extensive results for the density and temperature dependence of the on-top PDF and for the momentum distribution in the entire momentum range.

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.

Equation of state for partially ionized carbon and oxygen mixtures at high temperatures

The equation of state (EOS) for partially ionized carbon, oxygen, and carbon-oxygen mixtures at temperatures 3×10(5)K is less than or approximately equal to T is less than or approximately equal to 3×10(6) K is calculated over a wide range of densities, using the method of free energy minimization in the framework of the chemical picture of plasmas. The free energy model is an improved extension of our model previously developed for pure carbon [Potekhin, Massacrier, and Chabrier, Phys. Rev. E 72, 046402 (2005)]. The internal partition functions of bound species are calculated by a self-consistent treatment of each ionization stage in the plasma environment taking into account pressure ionization. The long-range Coulomb interactions between ions and screening of the ions by free electrons are included using our previously published analytical model, recently improved, in particular for the case of mixtures. We also propose a simple but accurate method of calculation of the EOS of partially ionized binary mixtures based on detailed ionization balance calculations for pure substances.

Strong coupling and degeneracy effects in inertial confinement fusion implosions

Accurate knowledge about the equation of state (EOS) of deuterium is critical to inertial confinement fusion (ICF). Low-adiabat ICF implosions routinely access strongly coupled and degenerate plasma conditions. Using the path integral Monte Carlo method, we have derived a first-principles EOS (FPEOS) table of deuterium. It is the first ab initio EOS table which completely covers typical ICF implosion trajectory in the density and temperature ranges of ρ=0.002-1596  g/cm3 and T=1.35  eV-5.5  keV. Discrepancies in internal energy and pressure have been found in strongly coupled and degenerate regimes with respect to SESAME EOS. Hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table have indicated significant differences in peak density, areal density (ρR), and neutron yield relative to SESAME simulations.

Ionization and equation of state of dense xenon at high pressures and high temperatures

The ionization degree and equation of state of dense xenon plasma were calculated by using self-consistent fluid variational theory for temperature of 4-30kK and density of 0.01-8.5gcm;{3} . The dense fluid xenon will be ionized at high pressures and temperatures. The ionization energy of xenon will be lowered due to the interactions among all particles of Xe, Xe+ , Xe2+ , and e . The ionization degree is obtained from nonideal ionization equilibrium, taking into account the correlative contributions to the chemical potential which is determined self-consistently by the free energy function. The composition of xenon has been calculated with given densities and temperatures in the region of partial ionization. The calculated results show a pressure softening regime at the onset of ionization. Comparison is performed with available shock-wave experiments and other theoretical calculations.

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.

Equation of state for partially ionized carbon at high temperatures

Equation of state for partially ionized carbon at temperatures T approximately > or = 10(5) K is calculated in a wide range of densities, using the method of free energy minimization in the framework of the chemical picture of plasmas. The free energy model includes the internal partition functions of bound species. The latter are calculated by a self-consistent treatment of each ionization stage in the plasma environment taking into account pressure ionization. The long-range Coulomb interactions between ions and screening of the ions by free electrons are included using our previously published analytical model.