Self-similar solutions up to flashpoint in highly wound magnetostatics

A general theorem on force-free fields is proved and applied to highly wound field configurations. In axial symmetry such configurations expand along a cone of semi-angle 60° as the system is wound up. The self-similar field structure is determined. After 1/√3 turns the system reaches flashpoint with a discharge around this cone releasing toroidal flux loops to infinity. All poloidal flux then visits infinity

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