Stability of Chandrasekhar's nonlinear force-free fields

Abstract: Chandrasekhar's nonlinear force-free field is an axisymmetric magnetic field with a swirl whose current field is supported on a ball in a uniform magnetic field at infinity. We prove its orbital stability in ideal MHD for axisymmetric disturbances in terms of the existence of weak ideal limits of Leray--Hopf solutions introduced by Faraco and Lindberg. The proof is based on a derivation of Taylor's relaxation theory for nonlinear force-free fields under axisymmetry: Woltjer's principle and Taylor's conjecture with generalized magnetic helicity. The main result demonstrates the stability of axisymmetric magnetic fields with swirls in ideal MHD even though blow-up occurs.

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