Topological restrictions in magnetic field dynamics and reconnection.

Candelaresi Simon, iomsn@physto.se, Nordita, Sweden

Abstract
The dominance of the magnetic helicity as the determining topological invariant in magnetohydrodynamics is revisited for helical and non-helical field configurations. For fields with positive z-components we determine the fixed points of the field line mapping. The sum of the Poincare indices at those fixed points, the fixed pints index, gives rise to further restrictions, not captured by the magnetic helicity alone. Various braided field configurations, which correspond to helical and non-helical knots, are simulated in fully resistive magnetohydrodynamics. We observe an evolution which confirms the importance of the fixed point index as additional restricting quantity. Moreover, a topological flux function, the field line helicity, is computed at the fixed points and monitored during turbulent relaxation. Its rate of change gives a proxy for the magnetic reconnection rate.