Plasma hydrodynamics from mean force kinetic theory

TL;DR

This work tackles the challenge of predicting transport in dense plasmas where strong correlations render traditional weakly coupled theories inadequate. It applies mean force kinetic theory (MFKT), which uses the potential of mean force in the collision operator and a Chapman-Enskog expansion to derive expressions for electrical conductivity, thermal conductivity, electrothermal and thermoelectric coefficients, and shear viscosity, all expressed via generalized Coulomb logarithms and Omega integrals. The results show excellent agreement with first-principles MD data for a two-component ion–electron plasma up to Coulomb coupling strengths of $Γ \approx 20$, demonstrating that MFKT captures strong-correlation effects and extends hydrodynamic descriptions into the dense-plasma regime. The study also clarifies the relationship between kinetic and virial contributions and discusses the limitations of a purely repulsive model, outlining future quantum generalizations to incorporate degeneracy and dense-matter effects relevant to warm dense matter and inertial confinement fusion contexts.

Abstract

Mean force kinetic theory is used to evaluate the electrical conductivity, thermal conductivity, electrothermal coefficient, thermoelectric coefficient, and shear viscosity of a two-component (ion-electron) plasma. Results are compared with molecular dynamics simulations. These simulations are made possible by assuming a repulsive Coulomb force for all interactions. Good agreement is found for all coefficients up to a Coulomb coupling strength of $Γ\approx 20$. This is over 100-times larger than the coupling strength at which traditional theories break down. It is concluded that mean force kinetic theory provides a means to extend hydrodynamics to dense plasmas.

Figures (6)

• Figure 1: Mean force kinetic theory in the $n = 2$ approximation (solid line) and the weakly coupled plasma theory result (dashed line) for electrical conductivity compared with MD results from Ref. Damman_2025.
• Figure 2: Mean force kinetic theory in the $n = 2$ approximation (solid line) and the weakly coupled plasma theory result (dashed line) for the electrothermal coefficient compared with MD results from Ref. Damman_2025.
• Figure 3: Mean force kinetic theory in the $n = 2$ (solid line) and the weakly coupled plasma theory result (dashed line) for the thermoelectric coefficient compared with MD results from Ref. Damman_2025.
• Figure 4: Mean force kinetic theory in the $n = 2$ (solid line) and the weakly coupled plasma theory result (dashed line) for the thermal conductivity compared with MD results from Ref. Damman_2025.
• Figure 5: Mean force kinetic theory in the $n=2$ approximation (solid line) and weakly coupled plasma theory result (dashed line) for the shear viscosity compared to MD of the one-component plasma from Ref. Daligault_2014