Linear mhd stability studies with the starwall code

The STARWALL/CAS3D/OPTIM code package is a powerful tool to study the linear MHD stability of 3D, ideal equilibria in the presence of multiply-connected ideal and/or resistive conducting structures, and their feedback stabilization by external currents. Robust feedback stabilization of resistive wall modes can be modelled with the OPTIM code. Resistive MHD studies are possible combining STARWALL with the linear, resistive 2D CASTOR code as well as nonlinear MHD simulations combining STARWALL with the JOREK code. In the present paper, a detailed description of the STARWALL code is given and some of its applications are presented to demonstrate the methods used. Conducting structures are treated in the thin wall approximation and depending on their complexity they are discretized by a spectral method or by triangular finite elements. As an example, a configuration is considered consisting of an ideal plasma surrounded by a vacuum domain containing a resistive wall and bounded by an external wall. Ideal linear MHD modes and resistive wall modes in the presence of multiply-connected walls are studied. In order to treat the vertical mode self-consistently the STARWALL code has been completed by adding the so-called Luest-Martensen term generated by a constant normal displacement of the plasma. The appendix contains the computation of the 2D Fourier transform of singular inductance integrals, and the derivation of an asymptotic expansion for large Fourier harmonics.