Structure formation in MHD turbulence as instability of effective quantumlike plasma*

Within the quasilinear approximation, structure formation in turbulence can be viewed as instability of effective collisionless plasma formed by linear waves, which serve as particles. These "particles" are quantumlike in the sense that their wavelengths can be nonnegligible and so is their polarization, which produces "spin" effects. The kinetic equation of this "plasma" is the Moyal equation for the Wigner tensor of the turbulent field, and the non-turbulent field governs collective interactions. We apply this formulation to MHD turbulence, where the role of effective particles is played by Alfven waves. Potentially, MHD  structure formation can be described on the same footing with standard linear instabilities of conventional plasma. The Alfven-wave Hamiltonian, which is pseudo-Hermitian, is inferred from [A. Brizard, Phys. Lett. A 168, 357 (1992)]. We seek to explicitly formulate the theory of Alfven-wave plasma stability and, as an application, to describe quasilinear turbulent dynamo from first principles.