Modeling of MHD instabilities in existing and future fusion devices in view of control

In this thesis, an improved version of the CarMa code is presented, called CarMa-D, for the analysis of ResistiveWall Modes (RWMs) in thermonuclear fusion devices, simultaneously considering the effects of volumetric threedimensional conducting structures and in presence of the effects associated with plasma dynamics, toroidal rotation or drift-kinetic damping. The CarMa-D code is the result of the coupling of the CARIDDI code, for the eddy current analysis in the conducting structures, with the MARS-K code, for MHD stability computations. The strength point behind CarMa-D is that the new coupling strategy does not rely on the simplifying assumptions of neglecting the plasma mass, toroidal rotation and kinetic damping physics, assumptions on which relies the CarMa code. Under these hypothesis, the plasma response to external perturbations depends on the dynamic of the perturbation itself: this behaviour is modelled through a matrix-based Padé rational function. The approximated plasma response is then combined with the equation for the eddy current induced in the metallic structures, in order to obtain a linear system of differential equations as the original CarMa version, but with a higher number of degrees of freedom to model the dynamics of the plasma. The new version overcomes the main limitations of the original computational model, in particular: (i) the massless assumption for the plasma is removed, allowing modeling of global modes growing on ideal-kink time scales; (ii) the effects of toroidal plasma flow and drift kinetic damping can be rigorously included into the new model, providing a powerful tool to study macroscopic phenomena where both plasma dynamics and 3-D conducting structures play important roles. The mathematical model has been also generalized to take into account multiple toroidal mode numbers (multi-modal CarMa-D). The code has been successfully tested with a reference equilibrium of a plasma with circular cross-section, and then used to study RWM stability analysis of the modes n = 1 and n = 2 on JT-60SA Scenario 5. Finally, additional effort has been made to write the CarMa-D mathematical model in a way suitable for a state-space representation, in order to exploit its features in a model-based feedback control strategy to actively suppress RWMs.