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

Equilibrium molecular dynamics simulations are used to calculate the thermal conductivity of the one-component plasma via the Green-Kubo formalism over a broad range of Coulomb coupling strength, $0.1\le \mathrm{\Gamma }\le 180$. These simulations address previous discrepancies between computations using equilibrium versus nonequilibrium methods. Analysis of heat flux autocorrelation functions show that very long ($6\times {10}^5{\omega }_p^{-1}$) time series are needed to reduce the noise level to allow $\lesssim 2\%$ accuracy. The simulations provide accurate data for $\mathrm{\Gamma }\lesssim 1$. This enables a test of the traditional Landau-Spitzer theory, which is found to agree with the simulations for $\mathrm{\Gamma }\lesssim 0.3$. 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 $\mathrm{\Gamma }\lesssim 10$, but none are accurate in the $\mathrm{\Gamma }\gtrsim 10$ regime where potential energy transport and coupling between mass flow and stress dominate thermal conduction.

Figure 1

Thermal conductivity (${\lambda }^{*}=\lambda /n{\omega }_p{k}_B{a}^2$) from this work compared with those calculated by Donko and Hartmann (DH) [10], Bernu, Vieillefosse, and Hansen (BVH) [28], and Salin and Caillol (SC) [29]. DH utilized a nonequilibrium method, while the remaining three used equilibrium MD.

Figure 2

(a) ACFs for $\mathrm{\Gamma }=3,10$, and 60. (b) The corresponding cumulative integral from Eq. (1) as a function of integration time $\tau$.

Figure 3

(a) The total ACF compared to the cross correlation ${\langle j_x\left(0\right)j_y\left(t\right)\rangle }_{\tau }$, used as an estimate for the noise level, for a $1\times {10}^5{\omega }_p^{-1}$ time series. (b) The same as panel (a) but with a $6\times {10}^5{\omega }_p^{-1}$ time series. (c) The variance of the cross correlation compared with the scaling of the error predicted by Eq. (4).

Figure 4

Equilibrium MD data for the total thermal conductivity and its kinetic (${\lambda }_{\mathrm{kk}}$), potential and virial (${\lambda }_{\mathrm{pp}}+{\lambda }_{\mathrm{vv}}+2{\lambda }_{\mathrm{vp}}$), and kinetic cross components ($-2{\lambda }_{\mathrm{kp}}-2{\lambda }_{\mathrm{kv}}$). Error bars are shown for the total and kinetic parts and are approximately the size of the marker. The solid lines represent fits to the separate components described in the text.

Figure 5

(a) The total ACF and its components. (b) The corresponding cumulative integral of the total ACF and its components.

Figure 6

(a) The total ACF and its components. (b) The corresponding cumulative integral of the total ACF and its components.

Figure 7

A comparison of the calculated value of ${\lambda }^{*}$ using different generalized Coulomb logarithms to the total and kinetic parts of the thermal conductivity from MD simulations.

Figure 8

The second-order Chapman-Enskog correction for EPT.

Figure 9

A comparison of the fit of Chugunov and Haensel and the MD data.