Modified Enskog kinetic theory for strongly coupled plasmas

Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling ($\mathrm{\Gamma }\gtrsim 30$). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.

Figure 1

Geometry of two colliding hard spheres of diameter $\sigma$ at the point of contact.

Figure 2

(a) Pair distribution function for hard spheres calculated from the Percus-Yevick approximation. (b) Pair distribution function the OCP calculated from the HNC approximation (lines) and MD simulations (circles).

Figure 3

Geometry of a binary collision between point particles in the center of mass frame.

Figure 4

(a) Depiction of momentum vectors in a binary collision of hard spheres, and (b) in a binary collision of particles interacting through a continuous potential.

Figure 5

Solutions of Eqs. (22) and (23) obtained using MD simulations of self-diffusivity and shear viscosity of the OCP. Also shown are the maximum physical covolume of hard spheres (dashed line) and the virial expansion obtained using the ${\left(b\rho \right)}_{\mathrm{MD}}$ data in Eq. (10) (solid line).

Figure 6

Covolume ($b\rho$) and corresponding collision probability enhancement factor ($\chi$) computed (a) using the method of Sec. 4b for three values of $\alpha$ and (b) using the methods of Sec. 4c.

Figure 7

Covolume and collision enhancement factors computed from the MD method from Sec. 4a (squares), the heuristic method from Sec. 4b using $\alpha =0.87$ (circles), and from the Stroud-Ashcroft method from Sec. 4c (lines).

Figure 8

Normalized self-diffusion coefficient of the OCP computed from MD simulations (circles), the effective potential theory based on the Boltzmann-like collision operator (diamonds), and the modified Enskog method from Sec. 4b using $\alpha =0.87$ (squares).

Figure 9

Ratio of the OCP self-diffusion coefficients calculated using MD simulations and the effective potential theory based on the Boltzmann-like collision operator (diamonds) and including the Enskog correction based on the method of Sec. 4b for $\alpha =0.5,0.87$, and 0.95.

Figure 10

Self-diffusion coefficient for the Yukawa OCP at four different screening parameters calculated using MD (circles), the effective potential theory (dashed red lines), and the modified Enskog method from Sec. 4b using $\alpha =0.87$ (solid blue lines).

Figure 11

Normalized shear viscosity of the OCP computed from MD: total (circles), kinetic contribution (downward triangles), and potential contribution (upward triangles). Three theoretical evaluations are shown: ${\eta }_{\mathrm{EP}}^{*}$, ${\eta }_{\mathrm{EP}}^{*}/\chi$, and Eq. (21), for which the heuristic method with $\alpha =0.87$ was used to determine $\chi$ and $b\rho$.