New closures for more precise modeling of Landau damping in the fluid framework

TL;DR

This paper develops and maps new fluid closures that accurately incorporate Landau damping effects, demonstrating convergence between fluid and kinetic models through higher-order moment closures.

Contribution

It provides a comprehensive mapping of all plausible Landau fluid closures at the 4th-order moment level, identifying the most precise ones and showing convergence to kinetic theory.

Findings

Most precise closures identified for 4th-order moments.

Higher-order moment closures can reproduce Landau damping with arbitrary accuracy.

Fluid and kinetic models converge as higher-order moments are included.

Abstract

Incorporation of kinetic effects such as Landau damping into a fluid framework was pioneered by Hammett and Perkins PRL 1990, by obtaining closures of the fluid hierarchy, where the gyrotropic heat flux fluctuations or the deviation of the 4th-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 $Z(\zeta)$ that appears in kinetic theory or the associated plasma response function $R(\zeta)=1 + \zeta Z(\zeta)$, have to be approximated with a suitable Pad\'e approximant in such a way, that the closure is valid for all $\zeta$ 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 4th-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.