Section: New Results
Asymptotic theory of reduced MHD models
Participant : Hervé Guillard.
In the study of fusion plasma, one of the fundamental model used for stability studies is the magnetohydrodynamic (MHD) model. Many theoretical and numerical works in this field use specific approximations of this model known as reduced MHD models. The derivation of these reduced MHD models has been formulated as a special instance of the theory of singular limit of hyperbolic system of partial differential equations with a large operator. This formulation allows to use the general results of this theory and to prove rigorously that reduced MHD models are valid approximations of the full MHD equations  . In particular, it is proven that the solutions of the full MHD system converge to the solutions of an appropriate reduced model. These results substantiate the intuitive physical idea that in the presence of a strong magnetic field, motion in the plane perpendicular to the plasma is nearly incompressible.