A straight plasma current quadrupole equilibrium, a doublet, with a free boundary and outer conducting walls is examined by means of the static magnetohydrodynamic equations. Analytic expressions for the flux surfaces are obtained for the plasma and the vacuum regions when the axial current density is uniform in the plasma cross section. An internal figure-eight separatrix is obtained when position of the plasma-vacuum interface and the outer conducting wall is appropriately chosen.
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Chu et al. (1973) studied this question.
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