Flexibility and rigidity of free boundary MHD equilibria

TL;DR

This paper investigates the conditions under which free boundary MHD equilibria are symmetric or asymmetric, revealing that without external magnetic fields, equilibria are limited to circular configurations, while external fields enable complex shapes.

Contribution

The study proves that in 2D, non-commensurate magnetic and velocity fields restrict equilibria to circular shapes, and demonstrates how external magnetic fields can produce non-symmetric equilibria.

Findings

Without external fields, equilibria are only circular.

External magnetic fields enable non-symmetric equilibria.

Some results extend to 3D axisymmetric cases.

Abstract

We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that if the magnetic field and velocity field are never commensurate, the only possible domain for any such equilibria is a disk, and the velocity and magnetic field are circular. We give examples of non-symmetric equilibria occupying a domain of any shape by imposing an external magnetic field generated by a singular current sheet charge distribution (external coils). Some results carry over to 3D axisymmetric solutions. These results highlight the importance of external magnetic fields for the existence of asymmetric equilibria.