Drift wave turbulence in a plasma is analyzed on the basis of the Wave Liouville Equation, describing the evolution of the wave action, i.e., the distribution function of wave packets (quasiparticles) characterized by position x and wave vector k. A closed kinetic equation is derived for the ensemble-average part of this function by the methods of non-equilibrium statistical mechanics. It has the form of a non-Markovian advection-diffusion equation describing coupled diffusion processes in x- and k-spaces.

General forms of the diffusion coefficients are obtained in terms of Lagrangian velocity correlations.

These coefficients are evaluated in the Decorrelation Trajectory (DCT) approximation. This technique was recently developed in order to treat Lagrangian correlations beyond the classical quasilinear approximation. It duly takes into account the important trapping phenomena of particles in a rugged electrostatic potential. The method requires a non-trivial extension in order to deal with the zonal flow problem.

The analysis of individual decorrelation trajectories provides an illustration of the fragmentation of drift wave structures in the radial direction and the generation of long-wavelength structures in the poloidal direction, that are identified with zonal flows.

The sixteen components of the four 2×2 diffusion tensors (D_xx, D_kk , D_xk, D_kx) are evaluated numerically for different values of the Kubo number (measuring the strength of the turbulence) and of the initial values of the wave number. They will be discussed in relation to the zonal flow generation.