There are no known analytic solutions to the force-free magnetic field equations in coordinates representing Dupin cyclides. Here it is shown that force-free fields can not only have solutions for toroids, as was shown in an earlier paper, but also for cyclides. The fact that the curvature lines of Dupin cyclides are all circles is used to derive a force-free magnetic field on the surface of an elliptic Dupin cyclide.
The paper is available at: http://arxiv.org/abs/2310.17673
A FORCE-FREE MAGNETIC FIELD SOLUTION IN CYCLIDAL COORDINATES