In order to gain reliable predictions on turbulent fluxes in tokamak plasmas, physics based transport models are required. Nonlinear gyrokinetic electromagnetic simulations for all species are still too costly in terms of computing time. On the other hand, interestingly, the quasi-linear approximation seems to retain the relevant physics for fairly reproducing both experimental results and nonlinear gyrokinetic simulations. Quasi-linear fluxes are made of two parts: (1) the quasi-linear response of the transported quantities and (2) the saturated fluctuating electrostatic potential. The first one is shown to follow well nonlinear numerical predictions; the second one is based on both nonlinear simulations and turbulence measurements. The resulting quasi-linear fluxes computed by QuaLiKiz (Bourdelle et al 2007 Phys. Plasmas 14 112501) are shown to agree with the nonlinear predictions when varying various dimensionless parameters, such as the temperature gradients, the ion to electron temperature ratio, the dimensionless collisionality, the effective charge and ranging from ion temperature gradient to trapped electron modes turbulence.

This letter reports on quasi-coherent (QC) modes observed in fluctuation spectra from Tore Supra and TEXTOR reflectometers. QC modes have characteristics in between coherent and broad-band fluctuations as they oscillate around a given frequency but have a wide spectrum. They are ballooned at the LFS midplane and appear usually on a frequency ranging from 30 to 120 kHz. In ohmic plasmas from both tokamaks, QC modes are detected only in linear ohmic confinement (LOC) regime and disappear in saturated ohmic confinement (SOC) regime. Linear simulations from Tore Supra predict that the LOC and SOC regimes are dominated by electron and ion modes respectively. Measurements of the perpendicular velocity of density fluctuations have been made from the top of TEXTOR by poloidal correlation reflectometry. They suggest that QC modes have a phase velocity ∼400 m s−1 higher in the electron diamagnetic direction than lower frequency fluctuations. Additionally, the onset of QC modes during electron cyclotron resonance heating has been observed in a Tore Supra region where turbulence is suspected to be driven by electron modes. These experimental results and instability calculations show a correlation between onsets of QC modes and predictions of trapped electron modes.

A simple model for the evolution of turbulence fluctuation spectra, which includes neighboring interactions leading to the usual dual cascade as well as disparate scale interactions corresponding to refraction by large scale structures, is derived. The model recovers the usual Kraichnan-Kolmogorov picture in the case of exclusively local interactions and midrange drive. On the other hand, when disparate scale interactions are dominant, a simple spectrum for the density fluctuations of the form |nk|2 proportional to k(-3)/(1+k2)2 is obtained. This simple prediction is then compared to, and found to be in fair agreement with, Tore Supra CO2 laser scattering data.