Low-frequency plasma conductivity in the average-atom approximation

TL;DR

This paper develops a generalized average-atom model for low-frequency plasma conductivity that accurately covers all frequency regimes, incorporating many-atom collisions and aligning with established formulas and sum rules.

Contribution

It introduces a new formalism that accounts for many-atom collisions in plasma conductivity, extending the single-atom approximation to all frequency ranges.

Findings

The model reproduces the Ziman formula in the static limit.

Results align with the Kubo-Greenwood formula at high frequencies.

The approach satisfies the conductivity sum-rule precisely.

Abstract

Low-frequency properties of a plasma are examined within the average-atom approximation, which presumes that scattering of a conducting electron on each atom takes place independently of other atoms. The relaxation time tau distinguishes a high-frequency region omega tau > 1, where the single-atom approximation is applicable explicitly, from extreme low frequencies omega tau < 1, where, naively, the single-atom approximation is invalid. A proposed generalization of the formalism, which takes into account many-atom collisions, is found to be accurate in all frequency regions, from omega =0 to omega tau >1, reproducing the Ziman formula in the static limit, results based on the Kubo-Greenwood formula for high frequencies, and satisfying the conductivity sum-rule precisely. The correspondence between physical processes leading to the conventional Ohm's law and the infrared properties of QED is discussed. The suggested average-atom approach to frequency-dependent conductivity is illustrated by numerical calculations for the an aluminum plasma in the temperature range 2--10 eV.