Effective Potential Theory for Transport Coefficients across Coupling Regimes

A plasma transport theory that spans weak to strong coupling is developed from a binary collision picture, but where the interaction potential is taken to be an effective potential that includes correlation effects and screening self-consistently. This physically motivated approach provides a practical model for evaluating transport coefficients across coupling regimes. The theory is shown to compare well with classical molecular dynamics simulations of temperature relaxation in electron-ion plasmas as well as simulations and experiments of self-diffusion in one-component plasmas. The approach is versatile and can be applied to other transport coefficients as well.

Figure 1

(a) Pair distribution function for the OCP determined from classical MD (circles), HNC (solid lines), and the screened Coulomb potential (dashed lines) for $\Gamma =0.1$, 1, 10, and 100. (b) Magnitude of the effective interaction potential calculated from Eq. (2). The thick red (lower) and blue (upper) lines show the $r/a$ intervals where $\varphi <0$ for $\Gamma =10$ and 100.

Figure 2

Self-diffusion coefficient $D^{*}=D/a^2{\omega }_p$ for the OCP calculated using classical MD with Green-Kubo relations (blue circles) and using various effective potentials in the Chapman-Enskog collision integrals: from MD derived $g(r)$ data (black squares), HNC (red diamonds), and screened Coulomb (black dashed line).

Figure 3

Comparison of the velocity relaxation rate measured in Ref. 24 with theoretical predictions using HNC and screened Coulomb effective potentials. For a comparison of the experiment to other theories, see Fig. 5 of Ref. 24.

Figure 4

A comparison of classical MD simulations and theoretical predictions for the generalized Coulomb logarithm in like-charge electron-ion thermal relaxation.