Landau-fluid closures and numerical implementation in BOUT++

Abstract

Fluid models are used to quantitatively describe many phenomena in plasmas, providing a reduced description of the lower dimensionality in comparison to kinetic models. Often, fluid models are more amenable to numerical and analytical analysis including nonlinear effects. The principal drawback of fluid models is the inability to describe kinetic effects which are important in the long mean free path regimes. However, a linear closure can be introduced to model kinetic effects, such as Landau damping. Such closures for three- and four-moment fluid model [G.W. Hammett and F.W. Perkins, Physical Review Letters 64, 3019(1990)] are known to be able to model plasma response function (with the decent accuracy) and kinetic effects of plasma microinstabilities (such as ion-temperature gradient instability). One of the results of this work is the derivation of the exact linear closure for the set of one-dimensional plasma fluid equations. The exact linear expression for the heat flux is obtained thus replacing the infinite hierarchy of fluid moments with a finite set of equations that incorporate kinetic effects of thermal motion into a fluid model. It is shown that the obtained exact closure in the limit case is reduced to the closure derived previously by Hammett and Perkins. Another goal of this work is to show how such fluid model with the kinetic closure can be modeled numerically using a recently developed non-Fourier method [A. Dimits, et. al., Phys Plasmas, 21 (5) 2014]. The method is based on the approximation of a Fourier image by a sum of Lorentzian functions allowing fast conversion into the configuration (real) space. With this approach, the one-dimensional model which includes evolution equation for the energy was implemented using the BOUT++ framework. The numerical implementation was verified in the series of test simulations of the plasma response function. Additionally, a self-consistent model of the ion Landau damping was implemented. It is shown that the damping rate for the ion Landau damping model agrees well with the exact kinetic result.