Electrical Resistivity in Warm Dense Plasmas Beyond the Average‐Atom Model

Abstract

The exploration of atomic properties of strongly coupled partially degenerate plasmas, also referred to as warm dense matter, is important in astrophysics, since this thermodynamic regime is encountered for instance in Jovian planets' interior. One of the most important issues is the need for accurate equations of state and transport coefficients. The Ziman formula has been widely used for the computation of the static (DC) electrical resistivity. Usually, the calculations are based on the continuum wavefunctions computed in the temperatureand density-dependent self-consistent potential of a fictive atom, representing the average ionization state of the plasma (average-atom model). We present calculations of the electrical resistivity of a plasma based on the superconfiguration (SC) formalism. In this modeling, the contributions of all the electronic configurations are taken into account. It is possible to obtain all the situations between the two limiting cases: detailed configurations (a super-orbital is a single orbital) and detailed ions (all orbitals are gathered in the same superorbital). The ingredients necessary for the calculation are computed in a self-consistent manner for each SC, using a density-functional description of the electrons. Electron exchange-correlation is handled in the localdensity approximation. The momentum transfer cross-sections are calculated by using the phase shifts of the continuum electron wavefunctions computed, in the potential of each SC, by the Schrödinger equation with relativistic corrections (Pauli approximation). Comparisons with experimental data are also presented.

Comparison of electron transport calculations in warm dense matter using the Ziman formula

“…The average atom potential leads to surprisingly poor agreement in magnitude for many cases. This is surprising because it has been used frequently in the past [19,23,24], and because it is consistent with Evans' [30] original formulation. The failing may be due to the muffin-tin approximation.…”

“…The screened potential (25) and the average atom potential (26) have been widely used with the Ziman-Evans formula to calculate conductivities [13,23,24,40,41]. A third type of potential, that of a single pseudo-atom, has also been used [1,13].…”

“…Average atom models have also been used to generate electronic transport coefficients. Broadly speaking, there are to two main approaches: on the one hand are Kubo-Greenwood based calculations [7,[20][21][22] that are qualitatively similar to the QMD calculations; and on the other hand are Ziman-type methods that estimate conductivity on the basis of electron-ion scattering cross sections [1,13,19,[23][24][25].…”

A Model of Electron Transport in Dense Plasmas Spanning Temperature Regimes

“…One cause of the predicted minimum in the electrical conductivity is the onset of spatial ordering in the ions; the plasma begins to take on characteristics of a liquid metal. In liquid metals, the standard theory of conduction is based on the Ziman formula, which has been applied to warm and hot dense plasmas by many authors [62][63][64][65][66]. In particular, Burrill et al demonstrated that the electrical conductivity minimum can only be captured by a Ziman-type theory when ionic correlations are accounted for.…”

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

“…Average atom models have been used successfully for many years for equation of state calculations [8][9][10][11][12][13]. They have also been used for electrical conductivity calculations, primarily by coupling to the Ziman-Evans (ZE) formula [14][15][16][17][18][19][20]. Recently, a systemic comparison of calculations of electrical conductivity using this method against Kubo-Greenwood KS-DFT-MD calculations [14] showed generally very good agreement between the methods provided that a judicious choice was made when coupling the average atom model to the ZE formula.…”