Minimum dissipation rates in magnetohydrodynamics

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Abstract
Minimum dissipation rate states are explored for a current-carrying channel of magnetofluid, supported by a dc magnetic field and driven by an applied electric field. The minimization is carried out subject to the constraints of constant axial (toroidal) magnetic flux and constant time-averaged rate of supply of magnetic helicity. The solutions of the resulting Euler-Lagrange equations are sensitive to boundary conditions on the current density j. One set of boundary conditions on j leads to the same consequences as Taylor’s ‘‘minimum-energy’’ theory. A different set leads to significantly different consequences, including a departure from the ‘‘force-free’’ magnetic profile and a toroidal component of current density that does not reverse at the wall when the toroidal magnetic field reverses.