Extending plasma transport theory to strong coupling through the concept of an effective interaction potential

Abstract

A method for extending traditional plasma transport theories into the strong coupling regime is presented. Like traditional theories, this is based on a binary scattering approximation, but where physics associated with many body correlations is included through the use of an effective interaction potential. The latter is simply related to the pair-distribution function. Modeling many body effects in this manner can extend traditional plasma theory to orders of magnitude stronger coupling. Theoretical predictions are tested against molecular dynamics simulations for electron-ion temperature relaxation as well as diffusion in one component systems. Emphasis is placed on the connection with traditional plasma theory, where it is stressed that the effective potential concept has precedence through the manner in which screening is imposed. The extension to strong coupling requires accounting for correlations in addition to screening. Limitations of this approach in the presence of strong caging is also discussed.

Temperature anisotropy relaxation of the one‐component plasma

“…Expectations from other transport processes, such as diffusion, suggest that the error in this approximation is on the order of 20% at weak coupling [15,20]. Some evidence for this from comparison with MD simulations will also be shown in Sec.…”

“…(1) throughout the relaxation, with only the magnitudes of T and T ⊥ evolving. It is known from other transport processes, such as self-diffusion of the OCP, that deviations from Maxwellian distributions can contribute corrections on the order of 20% in the weakly coupled limit, but are typically insignificant in the strongly coupled limit [15,20]. To the best of our knowledge, a perturbation expansion of the distribution function, such as the Chapman-Enskog [20,21] or Grad [22] expansions for hydrodynamic transport coefficients, has not yet been developed for temperature anisotropy relaxation.…”

“…Physically, this is because temperature anisotropy relaxation is a thermal processes associated with particles in the thermal part of the distribution, which do not have significant velocity-dependent components to their screening clouds. We also compare with two theories that extend these collision operators to strong coupling: effective potential theory (EPT) [14][15][16] and generalized Lenard-Balescu theory (GLB) [17][18][19]. Again, GLB includes dynamic effects in the long distance component of the linear response function, whereas EPT is based on a static description.…”

Influence of coupling on thermal forces and dynamic friction in plasmas with multiple ion species

“…7a may be explained by the same physics: assuming that the effective binary collision frequency ν αα is a proper description for the actual, many-body collisions in coupled plasmas, one should expect that ν αα cannot exceed a certain fraction of ω pα since these many-body collisions are also a collective plasma process. While one can look for alternative interpretations for the observed trend in A 12 , the very fact that within the EPT framework the role of the higher order corrections is diminished with coupling has been verified by calculating a number of different transport coefficients [38,53]. These include the OCP viscosity and heat conductivity shown in Fig.…”

“…[30]. Equation (2) reduces to the familiar expression in the weakly coupled limit, in which Ξ αβ becomes the conventional Coulomb logarithm ln Λ [38].…”