Linearly perturbed MHD equilibria and 3D eddy current coupling via the control surface method

In this paper, a coupling strategy based on the control surface concept is used to self-consistently couple linear MHD solvers to 3D codes for the eddy current computation of eddy currents in the metallic structures surrounding the plasma. The coupling is performed by assuming that the plasma inertia (and, with it, all Alfven wave-like phenomena) can be neglected on the time scale of interest, which is dictated by the relevant electromagnetic time of the metallic structures. As is shown, plasma coupling with the metallic structures results in perturbations to the inductance matrix operator. In particular, by adopting the Fourier decomposition in poloidal and toroidal modes, it turns out that each toroidal mode can be associated with a matrix (additively) perturbing the inductance matrix that commonly describes the magnetic coupling of currents in vacuum. In this way, the treatment of resistive wall modes instabilities of various toroidal mode numbers and their possible cross-talk through the currents induced in the metallic structures can be easily studied.