Twisted magnetic knots and links

Abstract

For magnetic knots and links in plasmas, we introduce an internal twist and study their dynamical behavior in numerical simulations. We use a set of helical and non-helical configurations and add an internal twist that cancels the helicity of the helical configurations or makes a non-helical system helical. These fields are then left to relax in a magnetohydrodynamic environment. In line with previous works, we confirm the importance of magnetic helicity in field relaxation. However, an internal twist, as could be observed in coronal magnetic loops, does not just add or subtract helicity, but also introduce an alignment of the magnetic field with the electric current, which is the source term for helicity. This source term is strong enough to lead to a significant change in magnetic helicity, which for some cases leads to a loss of the stabilizing properties expressed in the realizability condition. Even a relatively weak internal twist in these magnetic fields leads to a strong enough source term for magnetic helicity that for various cases even in a low diffusion environment, we observe an inversion in sign of magnetic helicity within timescales much shorter than the diffusion time. We conclude that in solar and stellar fields, an internal twist does not automatically result in a structurally stable configuration and that the alignment of the magnetic field with the electric current must be taken into account.