New Closures for More Precise Modeling of Landau Damping in the Fluid Framework

Incorporation of kinetic effects such as Landau damping into a fluid framework was pioneered by Hammett and Perkins, by obtaining closures of the fluid hierarchy, where the gyrotropic heat flux fluctuations or the deviation of the fourth-order gyrotropic fluid moment are expressed through lower-order fluid moments. To obtain a closure of a fluid model expanded around a bi-Maxwellian distribution function, the usual plasma dispersion function Z(ζ) that appears in kinetic theory or the associated plasma response function R(ζ)=1+ζZ(ζ) has to be approximated with a suitable Padé approximant in such a way that the closure is valid for all ζ values. Such closures are rare, and the original closures of Hammett and Perkins are often employed. Here we present a complete mapping of all plausible Landau fluid closures that can be constructed at the level of fourth-order moments in the gyrotropic limit and we identify the most precise closures. Furthermore, by considering 1D closures at higher-order moments, we show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing convergence of the fluid and collisionless kinetic descriptions.