Equation of State and opacities for warm dense matter
M. Cotelo1, P. Velarde2, A. G. de la Varga3
1

Instituto de Fusión Nuclear, Jose Gutierrez Abascal 2, Madrid (Spain), cotelo@din.upm.es
Instituto de Fusión Nuclear, Jose Gutierrez Abascal 2, Madrid (Spain), velarde@din.upm.es
3
Instituto de Fusión Nuclear, Jose Gutierrez Abascal 2, Madrid (Spain), agvarga@upm.es

2This work presents a study of thermodynamic and trasport properties for matter at moderateand high temperatures and densities, including warm dense matter (WDM). This data is used in theAMR radiation transport code ARWEN [1] to study laboratory astrophysics and other processes likefast ignition (related to the HiPER project) or X-ray secondary sources (related to ELI project).
A general equation of state (EOS) obtained with QEOS is corrected with a new pressure
multiplier (with density and temperature dependance) to fit the avaliable shockwave experimental
data. Ab initio molecular dynamic (MD) simulations were done to improve the fitting for states
where there is few avaliable data, as for WDM. The MD simulations uses the isokinetick esemble,
keeping temperature and density fixed during the simulation. The equation of motion of the ions incontact with a thermostat are solved using the ABINIT code [2] in the framework of finite
temperature density functional theory (DFT). The maximum temperature used in MD simulations
are limited to 500 eV because of the calculations becomes prohibitive. An accurate EOS is obtained
for a wide interval of densites and temperatures. All corrections in the EOS paid specially attention
to his thermodynamic consistency to ensure the stability of the hydrodynamic code ARWEN.
Also ARWEN code includes heat transport process. The thermal conductivity coefficient isobtained using DFT with local density approximation (LDA), averaging over several time steps of aMD simulation. A detailed electronic structure calculation of the system is needed in order to obtainaccurate results. Thermal conductivity is evaluated with the Kubo-Greenwood formulation. Great
difference between analytical models [3] and DFT data exists for low temperatures where the ion
correlation is important.
Finally, direct computation of the opacity of a mixture is compared with calculations that use
an average over the opacities of pure elements. Also a comparison of the ionization derived from
opacity calculations with the predicted ionization of the Thomas-Fermi model is done because of
his importance in radiation process.
References:[1]F. Ogando and P. Velarde, “Development of a radiation transport fluid dynamic code under AMR scheme”,
Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 71, no. 2-6, pp. 541-550, 2001.
[2] X. Gonze et al. , “ABINIT: First-principles approach to material and nanosystem properties”, ComputerPhysics Communications, vol. 180, no. 12, pp. 2582-2615, 2009.
[3] Y. T. Lee and R. M. More, “An electron conductivity model for dense plasmas”, Physics of Fluids, vol 27, no.
5, pp. 1273-1286, 1984.

8th International Conference on High Energy Density Laboratory Astrophysics
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