Self-organizing Knotted Magnetic Structures in Plasma

Abstract

We perform full-MHD simulations on various initially helical configurations and show that they reconfigure into a state where the magnetic field lines span nested toroidal surfaces. This relaxed configuration is not a Taylor state, as is often assumed for relaxing plasma, but a state where the Lorentz force is balanced by the hydrostatic pressure, which is lowest on the central ring of the nested tori. Furthermore, the structure is characterized by a spatially slowly varying rotational transform, which leads to the formation of a few magnetic islands at rational surfaces. We then obtain analytic expressions that approximate the global structure of the quasi-stable linked and knotted plasma configurations that emerge, using maps from $S^3$ to $S^2$ of which the Hopf fibration is a special case. The knotted plasma configurations have a highly localized magnetic energy density and retain their structure on time scales much longer than the Alfvenic time scale.