Visco-Elastic Density Functional Theory Approach to Strongly Coupled Plasmas: Computational Challenges

We generate a generalized hydrodynamic model for strongly coupled plasmas using density functional theory closures of BBGKY hierarchies via hypernetted chain theory. We formulate these equations in the form of a balance law, thereby providing a “memory” effect, facilitating correlation. This isothermal “single fluid” form of the electrostatic limit is modelled in a fluid context with an exact form of the functional term that is a non-local integral term rising out of hypernetted chain theory. These models, dubbed the Visco-Elastic Density functional (VEDF) equations, provide the first continuum models that match the dispersion of waves in electrostatic ultra-cold correlated plasmas. This class of models is important because they provide a path forward that does not require a fully kinetic solution for including the impact of long range correlation on the system. Hence these models represents a key step in being able to understand heterogeneous strongly coupled plasmas. We discuss the computational challenges and first steps of solving such equations.