First Principles Calculations of Shock Compressed Fluid Helium

Abstract

The properties of hot dense helium at megabar pressures were studied with two first-principles computer simulation techniques, path integral Monte Carlo and density functional molecular dynamics. The simulations predicted 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.There has been considerable controversy in the deuterium equation of state (EOS) since laser shock wave experiments probed the megabar pressure regime for the first time and predicted that deuterium is highly compressible under shock conditions to approximately 6-fold the initial density [1,2]. Such a high compression ratio was neither reproduced with magnetic compression experiments [3,4] nor with explosively driven shocks [5,6]. Both sets of later experiments predicted compression ratios close to 4.3(1), which is in good agreement with results from first principles computer simulations [7,8,9]. When we applied the same simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), to hot dense helium, we found that helium's shock compressibility is substantially increased due to electronic excitations in the fluid.In this Letter, we make the prediction that electronic excitations in helium lead to a maximum shock compression ratio of 5.24(4), while such excitations in deuterium do not increase the compressibility ratio beyond 4.3(1). Furthermore, we show that the compression ratio is reduced when the sample is precompressed statically in a diamond anvil cell before a shock is launched. Such novel compression techniques are currently developed and data for dense helium are forthcoming [10]. The combination of static and dynamic compression techniques allows the study of materials at much higher densities, and their application to hydrogen and helium will enable a direct characterization of a much larger section of the isentrope that determines the interiors of giant planets.Present studies of giant planetary interiors [11] are based on approximate free energy models that rely on analytical thermodynamic expressions and are often fit to experimental results if available. Although these models (for helium read [12,13,14]) are very practical, their predictive capabilities for shock states and the EOS are limited because interaction and polarization effects in a dense fluid are very difficult to study analytically, which underlines the need of first principles simulations.Shock wave experiments provide us with direct information for materials' EOS at high pressure and temperature. When a shock wave passes through the sample, the thermodynamic state of the material, characterized by the internal energy, pressure, ...

Properties of Dense Fluid Hydrogen and Helium in Giant Gas Planets

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Multiphase equation of state for carbon addressing high pressures and temperatures

“…Fermionic PIMC simulations have been applied to study hydrogen [31][32][33][34][35][36][37][38][39], helium [40,41], hydrogen-helium mixtures [42], and one-component plasmas [43,44], and most recently to simulate carbon and water plasmas [14]. In PIMC simulations, electrons and nuclei are treated equally as Feynman paths in a stochastic framework for solving the full, finite-temperature, quantum many-body problem.…”

First-principles equation of state and shock compression predictions of warm dense hydrocarbons

“…1. Besides the dependence of shock velocity, the shock compression is controlled by the excitation of internal degrees of freedom, which increases the compression, and interaction effects, which decrease it [71]. With increasing temperature and pressure, polystyrene is increasingly compressed until a maximum density of 4.9 g cm −3 reached at 2.0×10 6 K, which corresponds to the excitation of K shell electrons of carbon ions, as we will explain below.…”

“…Similar to the PIMC simulations of hydrogen [57,58,[64][65][66][67][68][69][70], helium [59,71], H-He mixtures [72], carbon [60,73], nitrogen [74], oxygen [75], neon [76], and water [60], we employ a free-particle nodal structure. We enforce fermion nodes at a small imaginary time interval of 1/8192 Hartree −1 (Ha −1 ) while pair density matrices [77,78] are evaluated in larger step of 1/1024 Ha −1 [67].…”