Microinstabilities in Advanced Tokamak and Stellarator Geometries

Doctoral thesis, 2008

The anomalous particle and heat transport observed in magnetically confined plasmas is generally attributed to plasma turbulence driven by short-scale instabilities, called microinstabilities. Understanding the stability limits of microinstabilities and their dependency on the equilibrium configuration is of paramount importance in the effort to predict the performance of future fusion devices such as the International Thermonuclear Experimental Reactor (ITER). The present thesis investigates the linear stability properties of simple electron drift waves, ion-temperature-gradient (ITG) modes, collisionless trapped electron (TE) modes and resistive edge modes in the electrostatic limit in realistic advanced toroidal geometries. The magnetic field equilibria under study are that of an ITER-like tokamak and Wendelstein 7-X (W7-X) stellarator, and are computed using the variational moments equilibrium code (VMEC). The instability-models are formulated in the ballooning mode representation and the drift wave problem is set as an eigenvalue equation along a field line. The derived eigenvalue problem is solved numerically in the magnetic field equilibria using a standard shooting code technique and applying Wentzel-Kramers-Brillouin (WKB) type boundary conditions. Correlations of the mode stability and the mode structure with various equilibrium quantities, such as density gradient, electron/ion temperature gradients, temperature ratios, wave vector, magnetic field, magnetic field line curvature, and local/global magnetic shear, are investigated. The results are also compared with earlier tokamak and stellarator studies.