Rotation and rotation shear effects on the stability of resistive wall mode

Full text: Stabilization of the Resistive Wall Modes (RWMs) by the plasma rotation is one of the most important physical issues for future reactors operated in the advanced tokamak regime. The linear stability of rotating ideal magnetofluid is governed by the Frieman-Rotenberg equation. The Frieman-Rotenberg equation contains the convective derivative term, which is the origin of the non-self-adjointness. It is well known that the non-self-adjointness implies that the normal mode decomposition of the perturbation in the form ∝ exp(iωt) is not complete. Therefore, in this study, we invoke the initial value approach. Since the recent tokamak experiments show that the rotation and rotation shear effects at rational surface are essential for the RWM stability, we employ the new matching method, which enables us to extract the rotation effects on the mode resonance with high numerical accuracy. The effectiveness of the method has been verified for the ideal kink mode analysis without rotation in cylindrical tokamak. In this study, the method is generalized to study the external modes such as RWMs and to include the rotation effects. The present method divides the plasma region into outer regions and inner layers as in the conventional asymptotic matching method. The essential difference is that the inner layers of the new method have finite width, thus, the Newcomb equation generalized to include rotation effects, which governs the outer regions, has no singularity. The matching condition is numerically satisfied such that the normal components of the Lagrangian displacement are smooth. As for the external modes, one inner layer can be allocated at the plasma surface. Then, that inner layer enables us to utilize the matching analysis, which is impossible for the asymptotic matching scheme. Furthermore, for the reversed shear profile, an additional inner layer can be located at the rational surface. The detailed numerical analysis of rotation and rotations shear effects on RWM stability will be presented. (author)