Theory of Ion Temperature Gradient Driven Instabilities: Threshold and Transport

Doctoral thesis, 1994

The object of this thesis is the theory of the ion temperature gradient driven (ITGD) mode, including instabilities, thresholds and associated anomalous transport. The linear threshold has been investigated both analytically and numerically in various parameter domains. The effects of the parallel dynamics, of the magnetic curvature and of trapped electrons and ions are all studied carefully. The expressions for the thresholds have been obtained in both the sheared-slab and toroidal geometries. The non-circularity effect on the stability of the ITGD mode for the long wave length toroidal branch has also been analyzed. It is found that new branches can be induced. The corresponding threshold values have been evaluated. The anomalous transport associated with the ITGD mode has been studied on the basis of the mixing-length argument. In a tokamak, the anomalous ion thermal conductivity is calculated in the flat density limit according to the results of the mode stability analysis. A similar procedure has been used for a reversed field pinch, in order to calculate the ion anomalous viscosity which heats the ions through the dissipation of the velocity fluctuations related to the resistive MHD activity.