Author: Christopher B Smiet
Requested Type: Pre-Selected Invited
Submitted: 2018-02-27 19:11:16
Princeton Plasma Physics Laboratory
100 Stellarator Road
Princeton, NJ 08540
United States of Ame
Magnetic helicity, a measure for the linking and knotting of magnetic field lines, is a conserved quantity in Ideal MHD. In the presence of resistivity, the approximate conservation of helicity constrains the rate at which magnetic energy can be dissipated. When a localized magnetic field containing helicity is set to relax in a low-resistance high-beta plasma, the magnetic pressure drives the plasma to expand whilst the helicity is still approximately conserved. Using numerical simulations I show how this interplay gives rise to a novel MHD equilibrium: the initially linked field lines self-organize to form a structure where field lines lie on nested toroidal surfaces of constant pressure. The Lorentz forces are balanced by the gradient in pressure, with a minimum in pressure on the magnetic axis. Interestingly, the rotational transform is nearly constant on all magnetic surfaces, making the structure topologically nearly identical to a famous knotted structure in topology: the Hopf fibration. I will explore the nature of this equilibrium, and how it relates geometrically to the structure of the Hopf map. Additional dynamics give rise phenomena that are well known from magnetic confinement devices; magnetic islands can occur at rational surfaces, and the finite resistivity gives rise to a Pfirsch-Schlüter type diffusion leading to growth of the structure on a resistive timescale.
Smiet, C. B., Candelaresi, S., Thompson, A., Swearngin, J., Dalhuisen, J. W., & Bouwmeester, D. (2015). Self-organizing knotted magnetic structures in plasma. Physical review letters, 115(9), 095001.