Equation of state of fully ionized electron-ion plasmas

Introduction

We present the equation of state (EOS) of fully ionized nonideal electron-ion plasmas (EIP). Here EOS means not only the dependence of pressure P on mass density ρ, but more generally the behavior of most important thermodynamic functions. At this site we release Fortran codes, which implement the analytic approximations for the EOS based on the references listed below.


1. Nonmagnetized plasmas

For the ideal gas of fermions, appropriate fitting formulae from Blinnikov et al. (1996) were selected. For nonideal one-component plasmas (OCP) of ions, analytic formulae were constructed to accurately reproduce Monte Carlo (MC) results for a strongly coupled Coulomb liquid (DeWitt & Slattery, 1999; Caillol, 1999), as well as our HNC results for the classical Coulomb liquid with the ion coupling parameter 0.01<Γ<160, and analytic corrections by Cohen & Murphy (19 (valid at Γ<0.3) to the Debye-Hueckel formula (valid at Γ<0.01). The quantum effects in the Coulomb liquids are included using the fitting formulae from Baiko & Chugunov (2022). For the harmonic quantum Coulomb crystal, the formulae of Baiko et al. (2001) have been used. Anharmonic corrections for a Coulomb crystal are included following Baiko & Chugunov (2022). For the nonideal (exchange-correlation) contributions to the thermodynamic functions of electron fluid, the formula given by Ichimaru et al. (1987) has been adopted. The ion-electron (ie) interaction has been taken into account by HNC calculations based on a linear response theory with finite-temperature and local-field corrections in the liquid state both for nonrelativistic and relativistic electron background. In the solid state, the ie contribution to the free energy has been calculated and fitted using the perturbation theory of Galam & Hansen (1976) with an approximate form of the ion structure factor. For mixtures of different ion species, the EOS was calculated beyond the linear mixing rule (LMR), using the finite-temperature corrections to the LMR from Potekhin et al. (2009) in the liquid/gaseous phases. In the solid regime, the corrections to the LMR are described by fitting formulae for zero-temperature random crystals.

Uncertainties still persist in the theory related to the strong quantum effects in the liquid (in the "quantum melting" regime), to the electron response in the Coulomb crystals and in the regime where the quantum effects for the ions are substantial, as well as to the solid mixtures. In view of the sensitivity of the solid-liquid transition (the melting line) to these uncertainties, this transition is imposed in the present code by default at the classical OCP value of Γ=175. This ensures the robustness of the code in the astrophysical applications. (The user can modify this melting criterion whenever needed.)

An alternative numerical realization of the same analytic fitting formulae describing thermodynamics of the electron-ion plasmas is Skye (Jermin et al. 2021).


2. Strongly magnetized plasmas

A sufficiently strong magnetic field can affect plasma thermodynamics due to the Landau quantization of the motion of charged particles. This effect can be important, for example, in strongly magnetized stars, such as magnetic white dwarfs, whose magnetic fields B reach up to 109 G, pulsars with typical B∼1012-1013 G, and magnetars with B∼1014-1015 G (e.g., Haensel et al. 2007, and references therein). Formulae for the EOS of the ideal EIP in the magnetic field and magnetically induced modifications of the nonideal contributions to the EOS have been discussed, e.g., by Blandford & Hernquist (1982), Broderick et al. (2000), Haensel et al. (2007) (see also references therein).

We have collected available analytic formulae for the EOS of nonideal EIP at any temperatures and densities and implemented them in the Fortran routines presented at this site.

References

1. Basic references
to be cited in a publication using the results or subroutines presented at this Web site

2. Our previous papers behind the present EOS implementation
  1. Chabrier G., Potekhin A.Y. Equation of state of fully ionized electron-ion plasmas. Phys. Rev. E, 58, 4941 (1998) [PDF file (200 kB)] [physics/9807042]
  2. Potekhin A.Y., Chabrier G. Equation of state of fully ionized electron-ion plasmas. II. Extension to relativistic densities and to the solid phase. Phys. Rev. E, 62, 8554 (2000) [PDF file (170 kB)] [astro-ph/0009261]
  3. Potekhin A.Y., Chabrier G., Rogers F.J. Equation of state of classical Coulomb plasma mixtures. Phys. Rev. E, 79, 016411 (2009) [PDF file (199 kB)] [arXiv:0812.4344]
  4. Potekhin A.Y., Chabrier G., Chugunov A.I., DeWitt H.E., Rogers F.J. Addendum to `Equation of state of classical Coulomb plasma mixtures'. Phys. Rev. E, 80, 047401 (2009) [PDF file (130 kB)] [arXiv:0909.3990]
  5. Potekhin A.Y., Chabrier G. Thermodynamic functions of dense plasmas: analytic approximations for astrophysical applications. Contrib. Plasma Phys., 50, 82-87 (2010) [PDF file (131 kB)] [arXiv:1001.0690]

3. Other cited references

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Page created on November 28, 2008; last updated on June 10, 2022 by Alexander Potekhin.
Last revision of the programs: June 15, 2022