Molecular Dynamics Simulation of Hydrodynamic Transport Coefficients in Plasmas

TL;DR

The paper tackles the reliability of hydrodynamic transport coefficients in a two-component plasma across a broad Coulomb coupling range by combining first-principles MD with Green-Kubo theory and comparing to Chapman-Enskog kinetic theory. It clarifies how non-equilibrium thermodynamics and kinetic theory definitions must be mapped consistently, especially for heat flux, to obtain meaningful comparisons. The results show good agreement with CE predictions in the weakly coupled regime ($\Gamma_e \lesssim 0.1$) when transport definitions are aligned, and provide strong-coupling benchmarks up to $\Gamma_e=140$ where only kinetic heat-flux contributions are physically meaningful; potential/virial terms diverge in this repulsive Coulomb model. The work also furnishes fit formulas for quick usage and offers valuable benchmarks to guide dense-plasma theories and hydrodynamic closures in regimes where strong correlations prevail.

Abstract

Molecular dynamics (MD) simulations are used to calculate transport coefficients in a two-component plasma interacting through a repulsive Coulomb potential. The thermal conductivity, electrical conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity are computed using the Green-Kubo formalism over a broad range of Coulomb coupling strength, $0.01 \leq Γ\leq 140$. Emphasis is placed on testing standard results of the Chapman-Enskog solution in the weakly coupled regime ($Γ\ll 1$) using these first-principles simulations. As expected, the results show good agreement for $Γ\lesssim 0.1$. However, this agreement is only possible if careful attention is paid to the definitions of linear constitutive relations in each of the theoretical models, a point that is often overlooked. For example, the standard Green-Kubo expression for thermal conductivity is a linear combination of thermal conductivity, electrothermal and thermoelectric coefficients computed in the Chapman-Enskog formalism. Meaningful results for electrical conductivity are obtained over the full range of coupling strengths explored, but it is shown that potential and virial components of the other transport coefficients diverge in the strongly coupled regime ($Γ\gg 1$). In this regime, only the kinetic components of the transport coefficients are meaningful for a classical plasma.

Figures (6)

• Figure 1: Current autocorrelation functions from simulations at $\Gamma_e = 0.1$ (black), $\Gamma_e = 1$ (yellow), and $\Gamma_e = 30$ (red) that are used to compute the electrical conductivity. The correlation functions are normalized to an initial value of 1.
• Figure 2: (a) Total electrical conductivity, (b) kinetic electrothermal coefficient, (c) thermal conductivity, and (d) thermoelectric coefficient as a function of $\Gamma_e$. The modified kinetic theory relations from Eq. (\ref{['eq:GK_CE_whole']}) (solid lines), and with the definitions from Eq. (\ref{['eq:CE_whole']}) (dashed lines) are also plotted for comparison. Dotted lines show the fit formulas from Eqs. (\ref{['eq:xi_wc']}) and (\ref{['eq:xi_sc']}).
• Figure 3: Thermal conductivity computed from MD as a function of $\Gamma_e$ for: the kinetic component in a two-component plasma (black circles), total in a one-component plasma (blue circles) and kinetic component in a one-component plasma (red triangles). Here the OCP data is from Ref. Scheiner_2019.
• Figure 4: Shear viscosity plotted as a function of mass ratio at $\Gamma_e = 0.1$. The modified kinetic theory relation from Eq. (\ref{['eq:GK_CE_shear']}) (solid line), and OCP MD value (dashed line) are also plotted.
• Figure 5: OCP shear viscosity plotted as a function of $\Gamma_e$. The modified kinetic theory relation from Eq. (\ref{['eq:GK_CE_shear']}) is also plotted.