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The integrated forces acting on a slender noncircular loop having magnetic field line twist are investigated. The loop-aligned electric current, which gives the field line twist, generates a magnetic field accoding to the Biot-Savart law. Thus, the Lorentz forces acting on each segment of the loop depend upon the explicit shape of the entire loop. To date, solutions in the integrated form exist only for the geometry of a section of a circular toroidal loop [Chen, Ap. J., 338 , 453, 1989.] The inclusion of gravity makes it necessary to consider noncircular loops. If the local minor radius along the length of the loop is much smaller than the local radius of curvature of the loop, then a reduced expression for the local Lorentz forces can be found. In this formulation, the magnetic field and thus the Lorentz force acting on any segment of the loop are due to the loop-aligned electric current from the entire loop. We carry out a detailed study of the equilibrium and dynamics of slender twisted magnetic flux loops which are not constrained to be circular.
Work sponsored by ONR. Garren is an ONR Postdoctoral Fellow.
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