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)].
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.
Thermodynamic properties of the equilibrium strongly coupled quantum plasmas investigated by direct path integral Monte Carlo (DPIMC) simulations within a wide region of density, temperature and positive to negative particle mass ratio. Pair distribution functions (PDF), equation of state (EOS), internal energy and Hugoniot are compared with available theoretical and experimental results. Possibilities of the phase transition in hydrogen and electron-hole plasma from neutral particle system to metallic-like state and crystal-like structures, including antiferromagnetic hole structure in semiconductors at low temperatures, are discussed.
The equation of state of hydrogen is determined theoretically in the limits of the fully ionized plasma and the neutral reacting gas mixture. Analytical results are presented for the fully ionized state and compared to data from quantum simulations. The dense hydrogen gas is dealt with using Reaction Ensemble Monte Carlo and hypernetted chain techniques. The results are compared to other theoretical methods and to experimental findings. Finally, Reaction Ensemble Monte Carlo data are combined with Path Integral Monte Carlo results to give a Hugoniot curve covering the entire pressure range.
A review is given about some selected aspects of the development of the equation of state of hydrogen. Recent results are presented for low temperature fluid hydrogen. Reaction Ensemble Monte Carlo data determined thus are combined with Path Integral Monte Carlo results to give an Hugoniot covering the entire pressure range. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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