An introductory guide to fluid models with anisotropic temperatures. Part 2. Kinetic theory, Padé approximants and Landau fluid closures
Abstract
In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the longwavelength lowfrequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function Z(ζ), and the associated plasma response function R(ζ)=1+ζZ(ζ)=Z^' }(ζ)/2. We then consider a onedimensional (1D) (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the fourthorder moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ionacoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1D closures at higherorder moments than the fourth order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3D (electromagnetic) geometry in the gyrotropic (longwavelength lowfrequency) limit and map all closures that are available at the fourthorder moment level. In appendix Ae provide comprehensive tables with Padé approximants of R(ζ) up to the eighthpole order, with many given in an analytic form.
 Publication:

Journal of Plasma Physics
 Pub Date:
 December 2019
 DOI:
 10.1017/S0022377819000850
 arXiv:
 arXiv:1901.09360
 Bibcode:
 2019JPlPh..85f2003H
 Keywords:

 astrophysical plasmas;
 space plasma physics;
 plasma waves;
 Physics  Plasma Physics
 EPrint:
 Improved version, now accepted to JPP Lecture Notes. Some parts were shortened and some parts were expanded. The text now contains Conclusions