Theoretical study of simple magnetohydrodynamic models for fusion plasma stability

The subject of this thesis relates to the study of simplified Magneto-Hydro Dynamic fluid systems, also called reduced MHD systems. These systems are capable of describing the most violent instabilities that can appear in fusion plasmas. Using a scalar representation of the MHD vectorial system, a reduced MHD system in toroidal geometry is constructed and it has been demonstrated that the limits of ideal stability of the reduced system are the same as that of the complete MHD system for the given perturbations. A modular MHD code, whose structure is based on the structure of the reduced system, has been developed in parallel. This code is used to integrate and study reduced systems of different complexities up to the complete MHD system. Finally, a study of the influence (stabilizing) of the plasma rotation and of a resistive wall (destabilizing) on the linear stability of the double tearing modes has been carried out in configurations of recent interest (hollow current profiles). (author). 57 refs., 28 figs