Stability of Chandrasekhar's nonlinear force-free fields

TL;DR

This paper proves the orbital stability of Chandrasekhar's nonlinear force-free magnetic field solution in ideal MHD, showing it remains stable under weak ideal limits and contributes to understanding magnetic field stability.

Contribution

It establishes the orbital stability of Chandrasekhar's nonlinear force-free field within the framework of ideal MHD, a novel result for this class of solutions.

Findings

Chandrasekhar's solution is orbitally stable in ideal MHD.

Stability holds regarding weak ideal limits of axisymmetric solutions.

The result applies to large coherent magnetic structures with Alfvén waves.

Abstract

Chandrasekhar's nonlinear force-free field, discovered in 1956, is a rare example of a nonlinear force-free field describing a large coherent structure of axisymmetric magnetic field lines with swirls in the presence of Alfv\'en waves. We demonstrate that his traveling wave solution is orbitally stable with the energy norm in ideal MHD regarding weak ideal limits of axisymmetric Leray-Hopf solutions.