Absence of equilibrium among close-packed twisted flux tubes
The lack of equilibrium in twisted, close-packed flux tubes is demonstrated in terms of a topology of the transverse field and the necessity of defining restricted solutions for an arbitrary function in the equilibrium equation. It is shown that nearly all combinations of flux connections and functional forms have no mutual equilibrium and that the flux connections in nature are formed by footprint convection at an origin. The most close-packed twisted flux tubes are subject to dynamical nonequilibrium, with the transverse flux connections being reduced through neutral point rapid reconnection. The precise solutions which can be obtained through functional forms in the equilibrium equation do not have an analog in the real world.