Molecular Dynamics Simulation of Hydrodynamic Transport Coefficients in Plasmas

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.