Testing thermal conductivity models with equilibrium molecular dynamics simulations of the one component plasma

TL;DR

This study uses equilibrium molecular dynamics simulations to accurately measure the thermal conductivity of the one component plasma across a wide range of coupling strengths, testing and evaluating existing theoretical models.

Contribution

It provides the first accurate simulation data for low Coulomb coupling and critically assesses the validity of traditional and extended thermal conductivity theories.

Findings

Landau-Spitzer theory agrees for $ ext{Gamma} extless 0.3$

Two theories extend well to moderate coupling $ ext{Gamma} extless 10$

No existing models accurately predict high coupling $ ext{Gamma} extgreater 10$

Abstract

Equilibrium molecular dynamics simulations are used to calculate the thermal conductivity of the one component plasma (OCP) via the Green-Kubo formalism over a broad range of Coulomb coupling strength, $0.1\le\Gamma\le180$. These simulations address previous discrepancies between computations using equilibrium versus nonequilibrium methods. Analysis of heat flux autocorrelation functions show that very long ($6\times10^5\omega_p^{-1}$) time series are needed to reduce the noise level to allow $\lesssim2\%$ accuracy. The new simulations provide the first accurate data for $\Gamma \lesssim 1$. This enables a test of the traditional Landau-Spitzer theory, which is found to agree with the simulations for $\Gamma \lesssim 0.3$. It also enables tests of theories to address moderate and strong Coulomb coupling. Two are found to provide accurate extensions to the moderate coupling regime of $\Gamma \lesssim 10$, but none are accurate in the $\Gamma \gtrsim 10$ regime where potential energy transport and coupling between mass flow and stress dominate thermal conduction.