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.

Magnetic-field-line random walk in turbulence: a two-point correlation function description

The standard theory of field-line random walk is based on the description of turbulence in the wave number space. The latter description takes into account the details of turbulence at small scales. Such details, however, are not important in the theory of random walking magnetic field lines. In the present paper we therefore use simple decorrelation models to estimate the field-line diffusion coefficient. Previous results are recovered as special limits. It is shown that a full analytical description is possible and that the only parameter controlling the field-line diffusion coefficient is the Kubo number.

Analytical description for field-line wandering in strong magnetic turbulence

We investigate analytically the random walk of magnetic field lines. In previous analytical treatments of field line wandering or random walk, it was assumed that the turbulent magnetic field is much weaker than the mean field. In the present paper, we develop an improved analytical method to describe the stochastic properties of turbulent magnetic fields. This approach is an extension of the standard theory of field line wandering and can be applied to weak as well as to strong magnetic turbulence.

Left/right brains, teammates in learning

Left/right brain research and its implications for teachers are highlighted. The medical and psychological research in asymmetry and the related attitudinal changes towards brain functioning over the last 150 years are reviewed. Strategies teachers may apply to classroom practice are abstracted from that research. Respect for the functioning of each hemisphere and the need for the “teaming” of both are emphasized.