Kubo–Greenwood approach to conductivity in dense plasmas with average atom models

Abstract

A new formulation of the Kubo-Greenwood conductivity for average atom models is given. The new formulation improves upon previous by explicitly including the ionic-structure factor. Calculations based on this new expression lead to much improved agreement with ab initio results for DC conductivity of warm dense hydrogen and beryllium, and for thermal conductivity of hydrogen. We also give and test a slightly modified Ziman-Evans formula for the resistivity that includes a non-free electron density of states, thus removing an ambiguity in the original Ziman-Evans formula. Again results based on this expression are in good agreement with ab initio simulations for warm dense beryllium and hydrogen. However, for both these expressions, calculations of the electrical conductivity of warm dense aluminum lead to poor agreement at low temperatures compared to ab initio simulations.

Free-free opacity in dense plasmas with an average atom model

“…getting α(ω) from σ 1 (ω), is qualitatively the same as used in DFT-MD simulations [1,7]. The method of calculating σ 1 (ω) is described in reference [15]. In brief, we evaluate…”

“…This all seems straightforward, however, there is one complication. As discussed in reference [15] one has a choice of scattering potential in which to calculate the wavefunctions ψ. Reasonable arguments can be made for either using the average atom potential V ef f N e (r) or the so-called pseudoatom potential…”

“…xc ee [n ext e (r)]. (16) Empirically we find that V P A (r) gives better results for the dc conductivity (σ 1 (0)) compared to ab initio simulations at high temperatures and densities, whereas V N e gives better results as we approach normal (solid) densities and cold temperatures [15,30]. Without further investigation we will use the two potentials where experience suggests they should be reasonable.…”

“…(see reference [3] for an explanation of the terms in this equation). It is straightforward, if lengthy, to show that this is equal to the expression given in equation (13) above provided that 1) S(k) is set equal to 1, 2) the scattering potential (and thus the wavefunctions) are the same, 3) the chemical potential and the corresponding average electron density are the same, and 4) the photon frequency dependent collision frequency in equation 17is replaced with an energy independent collision frequency chosen so that σ 1 (ω) satisfies the conductivity sum rule equation (15).…”

“…It takes into account a realistic ionic structure factor, treats bound and free electrons equally, predicts average ionization and has no ad hoc continuum lowering model. The average atom model is first used to calculate the electronic structure of an atom in the plasma, and then the optical conductivity is calculated using the Kubo-Greenwood formalism [15][16][17][18]. The Kramers-Kronig dispersion relations are then used to calculate an index of refraction and hence the opacity.…”