The Inherently Three-Dimensional Nature of Magnetized Plasma Turbulence

摘要

It is often asserted or implicitly assumed, without justification, that theresults of two-dimensional investigations of plasma turbulence are applicableto the three-dimensional plasma environments of interest. A projection methodis applied to derive two scalar equations that govern the nonlinear evolutionof the Alfvenic and pseudo-Alfvenic components of ideal incompressiblemagnetohydrodynamic (MHD) plasma turbulence. The mathematical form of theseequations makes clear the inherently three-dimensional nature of plasmaturbulence, enabling an analysis of the nonlinear properties of two-dimensionallimits often used to study plasma turbulence. In the anisotropic limit k_perp>>k_parallel that naturally arises in magnetized plasma systems, theperpendicular 2D limit retains the dominant nonlinearities that are mediatedonly by the Alfvenic fluctuations but lacks the wave physics associated withthe linear term that is necessary to capture the anisotropic cascade ofturbulent energy. In the in-plane 2D limit, the nonlinear energy transfer iscontrolled instead by the pseudo-Alfven waves, with the Alfven waves relegatedto a passive role. In the oblique 2D limit, an unavoidable azimuthal dependenceconnecting the wavevector components will likely cause artificial azimuthalasymmetries in the resulting turbulent dynamics. Therefore, none of these 2Dlimits is sufficient to capture fully the rich three-dimensional nonlineardynamics critical to the evolution of plasma turbulence.