We investigate the existence of magnetohydrostatic equilibria for topologically complex magnetic fields. The approach employed is to perform ideal numerical relaxation experiments. We use a newly-developed Lagrangian relaxation scheme that exactly pr
eserves the magnetic field topology during the relaxation. Our configurations include both twisted and sheared fields, of which some fall into the category for which Parker (1972) predicted no force-free equilibrium. The first class of field considered contains no magnetic null points, and field lines connect between two perfectly conducting plates. In these cases we observe only resolved current layers of finite thickness. In further numerical experiments we confirm that magnetic null points are loci of singular currents.
Magnetic helicity fluxes in turbulently driven alpha^2 dynamos are studied to demonstrate their ability to alleviate catastrophic quenching. A one-dimensional mean-field formalism is used to achieve magnetic Reynolds numbers of the order of 10^5. We
study both diffusive magnetic helicity fluxes through the mid-plane as well as those resulting from the recently proposed alternate dynamic quenching formalism. By adding shear we make a parameter scan for the critical values of the shear and forcing parameters for which dynamo action occurs. For this $alphaOmega$ dynamo we find that the preferred mode is antisymmetric about the mid-plane. This is also verified in 3-D direct numerical simulations.
The resistive decay of chains of three interlocked magnetic flux rings is considered. Depending on the relative orientation of the magnetic field in the three rings, the late-time decay can be either fast or slow. Thus, the qualitative degree of tang
ledness is less important than the actual value of the linking number or, equivalently, the net magnetic helicity. Our results do not suggest that invariants of higher order than that of the magnetic helicity need to be considered to characterize the decay of the field.
