A virtual Simons' Hour Talk: MHD Equilibria with Non-Constant Pressure in Nondegenerate Toroidal Domains
Given by: Daniel Peralta-Salas
Note the time: 8:00am EDT / 12:00 UTC. Zoom link will be sent via email.
Abstract: In this talk I will present recent results on the existence of piecewise smooth MHD equilibria in three-dimensional toroidal domains with nonconstant stepped-pressure, where the plasma current exhibits an arbitrary number of current sheets. The existence of free boundary steady states surrounded by vacuum with an external surface current will be also discussed. The toroidal domains where these equilibria are shown to exist do not need to be small perturbations of an axisymmetric domain, and in fact they can have any knotted topology. The building blocks used in our construction are analytic toroidal domains satisfying a certain nondegeneracy condition. The proof involves three main ingredients: a gluing construction of Beltrami fields, a Hamilton-Jacobi equation on the two-dimensional torus, and a KAM theorem for divergence-free fields in three dimensions.
This is based on joint work with A. Enciso and A. Luque (arXiv:2104.08149).