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Magnetohydrodynamic equilibria in a straight magnetic quadrupole field

A straight, uniform-current, elliptic-cross-section plasma maintained in equilibrium by a quadrupole field is studied. Asymptotic analysis is used to show the existence of an ‘infinity’ of bifurcation points. Numerical investigation confirms the analysis and yields examples of m = 2 (elliptical), m = 3 (‘pear-shaped’), and m = 4 configurations. Further analysis shows the possibility of multi-columnar equilibria. The role of constraints with respect to elliptic equilibria is discussed.