A Landau fluid model for warm collisionless plasmas

Abstract

A Landau fluid model for a collisionless electron-proton magnetized plasma, that accurately reproduces the dispersion relation and the Landau damping rate of all the magnetohydrodynamic waves, is presented. It is obtained by an accurate closure of the hydrodynamic hierarchy at the level of the fourth order moments, based on linear kinetic theory. It retains non-gyrotropic corrections to the pressure and heat flux tensors up to the second order in the ratio between the considered frequencies and the ion cyclotron frequency.Comment: to appear in Phys. Plasma

Fluctuation-dissipation relations for a plasma-kinetic Langevin equation

“…This material and, indeed, most of the results described above, perhaps belong to elementary textbooks, but we are not aware of any where they are adequately explained-although implicitly they underlie the thinking behind both Landau-fluid closures (Hammett & Perkins 1990;Hammett et al 1992;Hedrick & Leboeuf 1992;Snyder et al 1997;Passot & Sulem 2004;Goswami et al 2005;Passot & Sulem 2007) and Hermitespace treatments for plasma kinetics (Armstrong 1967;Grant & Feix 1967;Hammett et al 1993;Parker & Carati 1995;Ng et al 1999;Watanabe & Sugama 2004;Zocco & Schekochihin 2011;Loureiro et al 2013;Hatch et al 2013;Plunk & Parker 2014). …”

“…The simplest Landau-fluid closure Simplistically described, the idea of Landau-fluid closures is to truncate the Hermite hierarchy of equations (4.3-4.5) at some finite m and to replace in the last retained equation 36) where R m+1 , which in general depends on the complex frequency ζ (equation (4.32)), is approximated by some suitable frequency-independent expression leading to the correct recovery of the linear physics from the truncated system. A considerable level of sophistication has been achieved in making these choices and we are not proposing to improve on the existing literature (Hammett & Perkins 1990;Hammett et al 1992;Hedrick & Leboeuf 1992;Snyder et al 1997;Passot & Sulem 2004;Goswami et al 2005;Passot & Sulem 2007). It is, however, useful, in the context of the result of section 3.1 that the "fluid" version of FDR is recovered in the limit of low frequency and weak damping, to show how the same conclusion can be arrived at via what is probably the simplest possible Landau-fluid closure.…”

“…Their (free) energy is transferred to perturbations of the particle distribution function that develop ever finer structure in velocity space and are eventually removed by collisions or, in a formally collisionless limit, by some suitable coarse-graining procedure. The electrostatic potential ϕ in such systems cannot in general be rigorously shown to satisfy a "fluid" equation of the form (1.1), with γ the Landau damping rate, although the idea that equation (1.1) or a higher-order generalisation thereof is not a bad model underlies the so-called Landau-fluid closures (Hammett & Perkins 1990;Hammett et al 1992;Hedrick & Leboeuf 1992;Snyder et al 1997;Passot & Sulem 2004;Goswami et al 2005;Passot & Sulem 2007).…”

Fluid and drift-kinetic description of a magnetized plasma with low collisionality and slow dynamics orderings. I. Electron theory

“…In return, the fluid closure moments (12)(13)(14)(15) are evaluated directly without the need of a cumbersome substraction of the mean velocity. Second, the moving-frame derivation incorporates exactly the contribution of the electric field, consistent with the momentum conservation equation or generalized Ohm's law (10).…”

“…The collisional moments (14,15) that appear in the fluid (10,11) and drift-kinetic (26) equations can now be evaluated. For these, the asymptotic form (41,43) of the electron-ion collision operator for v ∼ v the yields convergent integrals and is therefore sufficient.…”