Force Free Plasmas - Lundquist Solution


(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 force-free 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 non-zero value for the Topological Torsion 3-form.)

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Last update 01/23/2009
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