(Photo and caption from
Cantarella)
This picture shows the integral curves of a certain vector field V
defined on a solid cylinder. Layers of the cylinder are cut away in order to
reveal the structure of the vector field. The field V is a solution to the
forcefree field equation V = A curl(V), where A is about 2.4. The
field is required to be tangent to the boundary of the cylinder, and horizontal
on the boundary. This solution is discussed in the paper Upper Bounds for Writhe
and Helicity by Cantarella, et. al.. It was first discovered by S. Lunquist in
1958, and is known as the "Lundquist solution". (RMK NOTE: The helicity (V . curl(V)) is not zero. Hence all force free fields have a nonzero value for the Topological Torsion 3form.)
