Coulomb Log for Conductivity of Dense Plasmas

TL;DR

This paper evaluates the accuracy of the Coulomb log approximation for electrical conductivity in dense plasmas by comparing it to quantum mechanical calculations, finding it reliable when log Λ exceeds 3.

Contribution

It provides a quantitative assessment of the Coulomb log approximation's accuracy across different plasma conditions and materials, highlighting its validity range.

Findings

Coulomb log approximation is accurate within ±10% when log Λ > 3.

Accuracy is consistent across different plasma species for log Λ > 3.

Higher Z materials require higher temperatures and lower densities for log Λ > 3.

Abstract

The Coulomb log (log {\Lambda}) approximation is widely used to approximate electron transport coefficients in dense plasmas. It is a classical approximation to the momentum transport cross section. The accuracy of this approximation for electrical conductivity in dense plasmas is assessed by comparing to fully quantum mechanical calculations for realistic scattering potentials. It is found that the classical approximation is accurate to +/-10% when log {\Lambda} > 3, irrespective of the plasma species. The thermodynamic regime (density and temperature) for which log {\Lambda} > 3 corresponds to does, however, strongly depend on the material. For increasing Z, log {\Lambda} is greater than 3 for increasingly high temperatures and lower densities.