Phase space approach to inhomogenous incompressible 2-D MHD turbulence

Magnetohydrodynamic (MHD) turbulence can be understood as an effective plasma of Alfven waves serving as quasi-particles called alfvenons. Then, coherent structures in this turbulence can be understood as mean fields through which the alfvenons interact. Their formation can be described by kinetic theory, but classical kinetic theory does not suffice. Instead, one must account for the fact that alfvenons have polarization (``spin''), and the alfvenon wavelengths are generally nonnegligible compared to the scales of coherent structures. This means that quantum-like kinetic theory is needed to describe MHD turbulence as alfvenon plasma. We report the corresponding (Wigner-Moyal) formalism and its application to calculating quasilinear modulational instabilities in two-dimensional MHD turbulence. Comparison of this theory with numerical simulations, both quasilinear and nonlinear, will also be presented.