On the electrical conductivity of plasmas and metals

TL;DR

This paper reviews and extends models for electrical conductivity in dense plasmas and metals, resolving inconsistencies and deriving formulas applicable across a wide range of conditions, including low temperatures and non-Lorentzian plasmas.

Contribution

It provides a generalized framework for conductivity calculations, incorporating ion and electron interactions, and clarifies the applicability of the Ziman and Bloch formulas under various conditions.

Findings

Derived a general conductivity formula for Lorentzian two-component plasmas.

Extended the Ziman formula to arbitrary degeneracy and temperature ranges.

Analyzed the effects of electron-electron collisions and non-Lorentzian behavior.

Abstract

Methods for modelling the electrical conductivity of dense plasmas and liquid metals, based upon the well-known Ziman formula, are reviewed from a general perspective, and some earlier inconsistencies relating to its application to finite temperature systems are resolved. A general formula for the conductivity of a Lorentzian two-component plasma in thermal equilibrium is derived from the Lenard-Balescu collision integral in which both energy and momentum exchange between ions and electrons are accounted for. This formula is used as a basis for some generalizations of the Ziman formula, which apply to plasmas of arbitrary degeneracy over a much wider range of conditions. These formulae implicitly include the collective motions of the ions, but neglect the collective motions of the electrons. Detailed consideration of the latter shows that they generally have a small effect on the conductivity. Conditions for the validity of the Ziman formula are derived. The extension of the general theory to arbitrarily low temperatures, where the ion dynamics become dominated by collective effects, in which dynamical ion correlations need to be taken into account, is shown to lead to the well-known Bloch formula. Consideration is given to non-Lorentzian plasmas by explicitly accounting for electron-electron collisions. Corrections to the Lorentzian model in the form of a power series in 1/Z are derived.