Stability of Nonlinear Force-Free Magnetic Fields

Based on the magnetohydrodynamic energy principle, it is proved that Gold-Hoyle’s nonlinear force-free magnetic field is unstable. This disproves the sufficient criterion for stability of nonlinear force-free magnetic fields given by Krüger that a nonlinear force-free field is stable if the maximum absolute value of the force-free factor is smaller than the lowest eigenvalue associated with the domain of interest.