Absence of equilibrium among close-packed twisted flux tubest

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Abstract
The general absence of static equilibrium of a close-packed array of parallel twisted flux tubes in a highly conducting medium is demonstrated by showing that the solutions to the equilibrium equation V2 A+4πP'(A) = 0 do not generally preserve the flux connections around each twisted tube as the functional form of P(A) is varied. A special constraint on the variation of P(A) is introduced, then, by the requirement that the flux connections be preserved. Hence we conclude that while a particular array of twisted tubes, described by the internal circulation of flux within each tube, may have an equilibrium for some suitably chosen functional form P(A), the array is generally in a state of nonequilibrium for lack of that precise functional form in the real world.

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