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In this paper we analyse the running and asymptotic diffusion coefficients of a plasma in the case of zonal flow generation by an anisotropic stochastic electrostatic potential. Both the weak and relatively strong turbulence regimes were analysed. The analysis of the diffusion coefficients in wave vector space 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 as zonal flows. We have shown that the fragmentation of drift wave structures is strongly influenced by the anisotropy parameter, the electrostatic Kubo number and by the initial values of the wave vector.

Anisotropy in the magnetic fluctuation spectrum (stochastic anisotropy) and magnetic shear induce variations of global averaged quantities such as the running and the asymptotic diffusion tensors that can be investigated using a semi-analytical method. The study considers ranges for the anisotropy parameter, magnetic Kubo number and shear parameter leading to contrasting dynamical behaviors. In particular, the trapping of the stochastic magnetic field lines is analyzed. An asymptotic 'poloidal' velocity larger for stronger anisotropy is obtained for the wandering of the magnetic field lines for different values of the parameters.

The decorrelation trajectory method is applied to the diffusion of magnetic field lines in a perturbed sheared slab magnetic configuration. Some interesting decorrelation trajectories for several values of the magnetic Kubo number and of the shear parameter are exhibited. The asymmetry of the decorrelation trajectories appears in comparison with those obtained in the purely electrostatic case studied in earlier work. The running and asymptotic diffusion tensor components are calculated and displayed.

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