Generalized hydrodynamics model for strongly coupled plasmas

Beginning with the exact equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we obtain the density, momentum, and stress tensor-moment equations. We close the moment equations with two closures, one that guarantees an equilibrium state given by density-functional theory and another that includes collisions in the relaxation of the stress tensor. The introduction of a density functional-theory closure ensures self-consistency in the equation-of-state properties of the plasma (ideal and excess pressure, electric fields, and correlations). The resulting generalized hydrodynamics thus includes all impacts of Coulomb coupling, viscous damping, and the high-frequency (viscoelastic) response. We compare our results with those of several known models, including generalized hydrodynamic theory and models obtained using the Singwi-Tosi-Land-Sjolander approximation and the quasilocalized charge approximation. We find that the viscoelastic response, including both the high-frequency elastic generalization and viscous wave damping, is important for correctly describing ion-acoustic waves. We illustrate this result by considering three very different systems: ultracold plasmas, dusty plasmas, and dense plasmas. The new model is validated by comparing its results with those of the current autocorrelation function obtained from molecular-dynamics simulations of Yukawa plasmas, and the agreement is excellent. Generalizations of this model to mixtures and quantum systems should be straightforward.