Knotting Plasma

We simulated the time evolution of plasma torus knots in resistive, viscous MHD. These torus knots are stationary solutions to the ideal MHD equations, as proposed by Kedia et al. These magnetic fields are parameterised by the winding numbers np and nt and exist of several families of nested magnetic fields around a core field line. In ideal MHD, the topological structure of these solitons is conserved and these fields form stationary solutions, but these properties are not carried over to resistive MHD. We will look at the structure of the magnetic field of such a plasma. We find that a new magnetic surface family arises whose topology depends on the poloidal winding number $n_p$ of the initial magnetic field. The time evolution of the corresponding magnetic energy and helicity is strongly influenced by these np. When np > 1, the new magnetic surfaces have a non-zero Euler characteristic and depend on a zero magnetic field line along the z-axis. The toroidal winding number nt is of...Show moreWe simulated the time evolution of plasma torus knots in resistive, viscous MHD. These torus knots are stationary solutions to the ideal MHD equations, as proposed by Kedia et al. These magnetic fields are parameterised by the winding numbers np and nt and exist of several families of nested magnetic fields around a core field line. In ideal MHD, the topological structure of these solitons is conserved and these fields form stationary solutions, but these properties are not carried over to resistive MHD. We will look at the structure of the magnetic field of such a plasma. We find that a new magnetic surface family arises whose topology depends on the poloidal winding number $n_p$ of the initial magnetic field. The time evolution of the corresponding magnetic energy and helicity is strongly influenced by these np. When np > 1, the new magnetic surfaces have a non-zero Euler characteristic and depend on a zero magnetic field line along the z-axis. The toroidal winding number nt is of lesser influence, and the corresponding zero line contracts and disappears. Both the old and the new structures are preserved over time and we observe the formation of magnetic islands between magnetic surfaces.Show less

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Knotting Plasma