Generation of large-scale structures by strong drift turbulence

The previously existing quasilinear theory of the generation of a large-scale radial electric field by small-scale drift turbulence in a plasma is generalized for the case of strong turbulence which is usually observed in experiments. The geostrophic equation (i.e., the reduced Charney-Hasegawa-Mima equation) is used to construct a systematic theory in the two-scale direct interaction approximation. It is shown that, as in the quasilinear case, drift turbulence results in a turbulent viscosity effect and leads to the renormalization of the Poisson bracket in the Charney-Hasegawa-Mima equation. It is found that, for strong drift turbulence, the viscosity coefficient is represented as a sum of two parts, which are comparable in magnitude. As in quasilinear theory, the first part is determined by the second-order correlation functions of the turbulent field and is always negative. The second part is proportional to the third-order correlation functions, and the sign of its contribution to the turbulent viscosity coefficient depends strongly on the turbulence spectrum. The turbulent viscosity coefficient is calculated numerically for the Kolmogorov spectra, which characterize the inertial interval of the drift turbulence.