The Kolmogorov's spectrum in the ηe-turbulence

In order to explain the anomalous transport of electrons in tokamaks, a set of reduced nonlinear equations that describe the coupling of linearly unstable short wavelength (ρe) electrostatic fluctuations driven by the electron temperature gradient (ηe) to the longer wavelength (c/ωpe) electromagnetic fluctuations was proposed. Since the system of the reduced equations is weakly 3D, the possibility of an inverse cascade in the energy spectrum, as in the 2D Navier-Stokes turbulence, could be considered. Such an inverse cascade may explain the free energy source of the magnetic fluctuations. It was showed numerically that the k-spectrum is peaked in the skin depth wavelength region at the mixing length amplitude. This suggests that the level of magnetic turbulence is sufficient to produce the empirical neo-Alcator type of confinement formula. The attention was focused on a spectral structure which indicates the nonlinear interaction between the electrostatic and electromagnetic vortices at the saturation level, in the ηe-turbulence. (M.T.)