The mathematical theory of reduced MHD models for fusion plasmas

TL;DR

This paper rigorously derives reduced magnetohydrodynamics (MHD) models for fusion plasmas by framing them as singular limits of hyperbolic PDE systems, ensuring their validity as approximations of full MHD equations.

Contribution

It formulates the derivation of reduced MHD models within a general singular limit theory, providing a rigorous mathematical proof of their validity.

Findings

Reduced MHD models are proven to be valid approximations of full MHD equations.

Solutions of full MHD converge to solutions of reduced models.

The formulation leverages hyperbolic PDE singular limit theory for rigorous derivation.

Abstract

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.