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A sixth-order system of ordinary differntial equations along field lines is shown to have lower energy than the full magnetohydrodynamic system and thus offers a sufficient condition for stability. The two energies agree for all modes localized on field lines so that our criterion appears to be not overly restrictive. It is indeed the most optimistic sufficient condition in the literature. The criterion can be reduced to an eigenvalue problem of a single second-order integro-differential equation.
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Eliezer Hameiri (1980) studied this question.
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