Conservative dielectric functions and electrical conductivities from multicomponent Bhatnagar-Gross-Krook

In high energy-density experimental campaigns, computational models are essential for designing, interpreting, and diagnosing experiments. Since experimental micro-physical data is often unavailable, macroscopic simulations rely on microscopic models to inform various properties. Important micro-physical properties include: energy loss functions, dielectric functions, dynamic structure factors, and electrical conductivities [Phys. Plasmas 25, 056306 (2018)]. Our objective is to examine these models using single species and multispecies BGK kinetic equations, particularly the recently published model by Haack et al. [J Stat. Phys., 168, 826-856 (2017)]. From the susceptibility, we utilize linear response theory to uncover the effects of conservation laws that are not readily apparent in dynamic structure function, dielectric function, and conductivity models. We establish connections between older literature, such as the classical BGK kinetic equation [Bhatnagar, Gross, and Krook, Phys. Rev. 94, 511]. Mermin's dielectric function [Phys. Rev. B 1, 2362 (1970)] and models for electrical conductivities (e.g., Drude and Drude-Smith [Smith Phys. Rev. B 64, 155106 (2001)]). Numerical calculations are performed to illustrate how microscopic models are effected by these conservative constraints. Finally, we present numerical results, which include applications to C impurities in inertial confinement fusion (ICF) targets composed of deuterium and tritium.