1. Details of Equation-of-State and Opacity Models
Igor V. Sokolov, University of Michigan, and CRASH-team
The radiation is treated within the multi-group model: the radiation energy density is assumed to be integrated over some frequency range, for each group
The multi-group radiation diffusion model is coupled to the hydrodynamic motion. The following effects are accounted for in this way:
the radiation “advection”;
the effect of the radiation pressure on the plasma motion (momentum and energy sources in the hydrodynamic equations of motion);
radiation diffusion;
absorption and spontaneous emission.
The models for Equation Of State (EOS) and for opacities are needed to close the following hydrodynamic equations:
General features.
The input parameters for both inline EOS and inline opacities are
Energies of different states (of atom and ions).
The states differ with:
charge number
principal quantum number for ground and excited states
for the given state its energy is a total of the ionization energy and excitation energy. The ionization energies are all taken from databases, some of the excitation energies are approximated.
Populations and partition function ('ionization equilibrium'), which determine relative and absolute densities of different atoms/ions.
Ionization equilibrium is calculated by minimizing the Helmholtz free energy. We do this with account of:
Effects of Fermi statistics in free electron gas
The energy of electrostatic interaction ('the continuum lowering') in the approximation of the Madelung energy.
Excitation energy and its possible dependence on the plasma density ('pressure ionization')
From the properly minimized Helmholtz free energy we also derive the energy density and pressure (if the equal ion and electron temperatures are assumed), or electron pressure and electron energy density. They are used as the equation of state in out hydrodynamic simulations.
Opacities.
Free-free transitions: approximated Gaunt factor, account for Fermi statistics effects in the electron gas.
Bound-bound transitions: we use of the Kramers formula for the oscillator strengths. At the present time we neglect the transitions with no change in the principal quantum number.
Bound-free transitions: account for Fermi statistics effects in the electron gas. Neglect the absorption by core electrons from inner electron shells.
For multi-group opacities the absorption coefficients are averaged with Planckian weight function over the frequency group range, to obtain the set of Planck opacities. The inverse of the absorption coefficient is averaged with the Planckian temperature derivative, giving the inverse of the Rosseland opacities. 
The use of the same partition functions as the inputs for EOS and opacities ensures the consistency of the overall model.
Hydro equations + multi-group radiation diffusion
Bound-bound absorption in polyimide, T = 10 eV