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.

References in corpus (3)

• Magnetic Helicity and the Relaxation of Fossil Fields
• The critical role of magnetic helicity in astrophysical large-scale dynamos
• Hamilton--Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity

Cited by in corpus (15)

• Weaving knotted vector fields with tunable helicity
• Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics
• Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics
• Ideal Relaxation of the Hopf Fibration
• Estimating the rate of field line braiding in the solar corona by photospheric flows
• Collision of two Hopfions
• Quantifying the Tangling of Trajectories Using the Topological Entropy
• Spin-Orbital momentum decomposition and helicity exchange in a set of non-null knotted electromagnetic fields
• Topological atom optics and beyond with knotted quantum wavefunctions
• Theoretical proposal for the experimental realisation of a monochromatic electromagnetic knot
• On the existence of the field line solutions of the Einstein-Maxwell equations
• Nonlinear dynamics of a charged particle in a strong non-null knot wave background
• Resistive evolution of toroidal field configurations and their relation to magnetic clouds
• Knots and the Maxwell Equations
• Knotted surfaces as vanishing sets of polynomials