Influence of Geometry on Drift Waves in Tokamaks and Stellarators

There is a general consensus that drift waves are responsible for a large amount of transport in fusion experiments and it is of importance to investigate their linear stability and nonlinear evolution. These instabilities have therefore been intensively investigated in tokamaks for the last few decades. The situation is different in stellarators, where they have only received limited attention due to the complicated 3-dimensional structure and the related high resolution requirements for a numerical treatment. In this thesis a computer code has been developed that calculates necessary magnetic field quantities of any magnetic confinement fusion devices using equilibria obtained from the VMEC code. The code solves the eigenvalue problem using the linear stability of simple i-δ drift model, dissipative two fluid model, and reactive ion-temperature gradient (ITG) instability in the electrostatic limit using the ballooning mode formalism. For all these modes, a shooting code technique is used and WKB type boundary conditions are applied. The equilibria are calculated for, the three-field-period toroidal heliac H1-NF, the five-field-period helias Wendelstein 7-X (W7-X), for different aspect ratios of circular tokamak configurations and for the Joint European Torus tokamak (JET). The dependence of the spectrum of stable and unstable modes, on various equilibrium parameters like density gradients, temperature gradients, temperature ratios, wave vectors, normal and geodesic curvature and local magnetic shear are investigated. Stellarators results are also compared and contrasted with tokamak results