Analysis of the critical electron temperature gradient in Tore Supra

Abstract

The Tore Supra [Equipe Tore Supra presented by R. Aymar in Plasma Physics and Controlled Nuclear Fusion Research, Proc. 12th Int. Conf., Nice, 1988 (IAEA, Vienna, 1989), Vol. 1, p. 9] database of fast wave electron heating discharges is analyzed with respect to the role of the critical electron temperature gradient. The experimental evidence for the critical gradient is presented from power balance thermal flux qe(∇Te) relation extrapolated to zero in the measured gradient ∇Te. The fluctuation spectra are also known to extrapolate to low levels versus ∇Te. The inferred critical gradient (∇Te)c is defined by the offset linear extrapolation of the thermal flux to zero values. Histograms of the anomalous fluxes before and after being normalized to the theoretical models are constructed. For a wide range of heating powers, the electron power balance radial heat flux is shown to be well described by Te3/2 (1/LTe−1/Lc), where Lc=(Te/∇Te)c is the gradient scale length from linear eigenmodes in a sheared magnetic field. The relative deviations of the normalized heat fluxes as a function of the excess of the temperature gradient beyond the critical gradient give one method of assessing the agreement between the models and the data. A second method is the predictive studies in which the transport codes are used to investigate the impact of the critical gradient at low and high radio frequency power levels with the model thermal diffusivities. The dominant dependence of the inferred critical temperature gradient is its proportionality to the magnetic shear as expected from the robust electron Landau damping on thermal electrons in electron temperature gradient turbulence. The evidence for the electrostatic density independent thermal diffusivity scaling versus the finite beta electromagnetic density dependent thermal diffusivity is shown in some detail. The results strongly favor the electromagnetic turbulent diffusivity formula.