The mathematical theory of reduced MHD models for fusion plasmas

Théorie mathématique des modèles de MHD r\éduite pour les plasmas de fusion

Hervé Guillard (1, 2)

1 CASTOR - Control, Analysis and Simulations for TOkamak Research
2 LJAD - Laboratoire Jean Alexandre Dieudonné

The derivation of reduced MHD models for fusion plasma is here formulated as a special instance of the general theory of singular limit of hyperbolic system of PDEs with 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

Mots clés: Tokamaks; MHD; Fusion plasma; Asymptotic analysis; hyperbolic systems; singular limit

Mots clés: Analyse asymptotique; systèmes hyperboliques; limite singulière; Plasmas de fusion

Domaines: Physique des plasmas [physics.plasm-ph]; Physique mathématique [math-ph]; Dynamique des Fluides [physics.flu-dyn]; Plasmas

Hervé Guillard. The mathematical theory of reduced MHD models for fusion plasmas. [Research Report] RR-8715, INRIA. 2015. ⟨hal-01145009⟩