MHD equilibria with nonconstant pressure in nondegenerate toroidal domains

  • Alberto Enciso

    Consejo Superior de Investigaciones Científicas, Madrid, Spain
  • Alejandro Luque

    Uppsala University, Sweden
  • Daniel Peralta-Salas

    Consejo Superior de Investigaciones Científicas, Madrid, Spain
MHD   equilibria with nonconstant pressure in nondegenerate toroidal   domains cover

A subscription is required to access this article.

Abstract

We prove the existence of piecewise smooth MHD equilibria in three-dimensional toroidal domains of where the pressure is constant on the boundary but not in the interior. The pressure is piecewise constant and the plasma current exhibits an arbitrary number of current sheets. We also establish the existence of free boundary steady states surrounded by vacuum with an external surface current. The toroidal domains where these equilibria are shown to exist need not be small perturbations of an axisymmetric domain, and in fact they can have any knotted topology. The building blocks we use in our construction are analytic toroidal domains satisfying a certain nondegeneracy condition, which roughly states that there exists a force-free field that is ergodic on the surface of the domain. The proof involves three main ingredients: a gluing construction of piecewise smooth MHD equilibria, a Hamilton–Jacobi equation on the two-dimensional torus that can be understood as a nonlinear deformation of the cohomological equation (so the nondegeneracy assumption plays a major role in the corresponding analysis), and a new KAM theorem tailored for the study of divergence-free fields in three dimensions whose Poincaré map cannot be computed explicitly.

Cite this article

Alberto Enciso, Alejandro Luque, Daniel Peralta-Salas, MHD equilibria with nonconstant pressure in nondegenerate toroidal domains. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1410