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Register a new userEquation of state for dense hydrogen and plasma phase transition
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We calculate the equation of state of dense hydrogen within the chemical picture. Fluid variational theory is generalized for a multi-component system of molecules, atoms, electrons, and protons. Chemical equilibrium is supposed for the reactions dissociation and ionization. We identify the region of thermodynamic instability which is related to the plasma phase transition. The reflectivity is calculated along the Hugoniot curve and compared with experimental results. The equation-of-state data is used to calculate the pressure and temperature profiles for the interior of Jupiter.
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We present and discuss a wide-range hydrogen equation of state model based on a consistent set of ab initio simulations including quantum protons and electrons. Both the process of constructing this model and its predictions are discussed in detail. The cornerstones of this work are the specification of simple physically motivated free energy models, a general multiparameter/multiderivative fitting method, and the use of the most accurate simulation methods to date. The resulting equation of state aims for a global range of validity ($T = 1-10^9 K$ and $V_m = 10^{-9}-1 m^3/mol$), as the models are specifically constructed to reproduce exact thermodynamic and mechanical limits. Our model is for the most part analytic or semianalytic and is thermodynamically consistent by construction; the problem of interpolating between distinctly different models -often a cause for thermodynamic inconsistencies and spurious discontinuities- is avoided entirely.
We use a two-fluid model combining the quantum Greens function technique for the electrons and a classical HNC description for the ions to calculate the high-density equation of state of hydrogen. This approach allows us to describe fully ionized plasmas of any electron degeneracy and any ionic coupling strength which are important for the modeling of a variety of astrophysical objects and inertial confinement fusion targets. We have also performed density functional molecular dynamics simulations (DFT-MD) and show that the data obtained agree with our approach in the high density limit. Good agreement is also found between DFT-MD and quantum Monte Carlo simulations. The thermodynamic properties of dense hydrogen can thus be obtained for the entire density range using only calculations in the physical picture.
We develop analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasma mixtures. In the regime of strong Coulomb coupling, we use our previously developed analytic approximations for the free energy of one-component plasmas with rigid and polarizable electron background and apply the linear mixing rule (LMR). Other thermodynamic functions are obtained through analytic derivation of this free energy. In order to obtain an analytic approximation for the intermediate coupling and transition to the Debye-Hueckel limit, we perform hypernetted-chain calculations of the free energy, internal energy, and pressure for mixtures of different ion species and introduce a correction to the LMR, which allows a smooth transition from strong to weak Coulomb coupling in agreement with the numerical results.
We present a new equation of state (EOS) for dense hydrogen/helium mixtures which covers a range of densities from $10^{-8}$ to $10^6$ g.cm$^{-3}$, pressures from $10^{-9}$ to $10^{13}$ GPa and temperatures from $10^{2}$ to $10^{8}$ K. The calculations combine the EOS of Saumon, Chabrier & vanHorn (1995) in the low density, low temperature molecular/atomic domain, the EOS of Chabrier & Potekhin (1998) in the high-density, high-temperature fully ionized domain, the limits of which differ for H and He, and ab initio quantum molecular dynamics (QMD) calculations in the intermediate density and temperature regime, characteristic of pressure dissociation and ionization. The EOS for the H/He mixture is based on the so-called additive volume law and thus does not take into account the interactions between the two species. A major improvement of the present calculations over existing ones is that we calculate the entropy over the entire density-temperature domain, a necessary quantity for stellar or planetary evolution calculations. The EOS results are compared with existing experimental data, namely Hugoniot shock experiments for pure H and He, and with first principle numerical simulations for both the single elements and the mixture. This new EOS covers a wide range of physical and astrophysical conditions, from jovian planets to solar-type stars, and recovers the existing relativistic EOS at very high densities, in the domains of white dwarfs and neutron stars.
Recently developed analytic approximation for the equation of state of fully ionized nonideal electron-ion plasma mixtures [Potekhin et al., Phys. Rev. E, 79, 016411 (2009); arXiv:0812.4344], which covers the transition between the weak and strong Coulomb coupling regimes and reproduces numerical results obtained in the hypernetted chain (HNC) approximation, is modified in order to fit the small deviations from the linear mixing in the strong coupling regime, revealed by recent Monte Carlo simulations. In addition, a mixing rule is proposed for the regime of weak coupling, which generalizes post-Debye density corrections to the case of mixtures and numerically agrees with the HNC approximation in that regime.
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