Numerical Analysis of the 2D Newcomb Equations for the Resistive Wall Modes (RWMs)

Stabilization of the RWM is one of the most important design issues for future reactors operated in the advanced tokamak regime. The MARG2D [1] stability code, which solves the 2D Newcomb equations [2], is extended to study the stability of the RWM. The linear dynamics of the perturbations in RWM obeys the functional [3] $\delta $W$_{r}=\delta $W$_{p}+\delta $W$_{IV}+\delta $W$_{OV}$+D$_{w}$=0, where $\delta $W$_{p}$ is the plasma potential energy, $\delta $W$_{IV(OV)}$ the vacuum magnetic energy inside (outside) the resistive wall, and D$_{w}$ the energy dissipated in the resistive wall. In MARG2D, $\delta $W$_{p}$ and $\delta $W$_{OV}$ are given by bilinear functionals of the displacements and the perturbed magnetic field. $\delta $W$_{IV}$ is described by a scalar potential and solved by the finite element method. Results from the MARG2D code are compared with those given in [3]. The solutions of the eddy current on the resistive wall will also be compared with new WKB solutions. [1] N. Aiba, \textit{et al.,} Plasma Phys. Control. Fusion \textbf{46}, 1699 (2004). [2] S. Tokuda and T. Watanabe, Phys. Plasmas \textbf{6}, 3012 (1999). [3] M.S. Chu, \textit{et al.,} Nucl. Fusion \textbf{43}, 441 (2003).