Abstract
Magnetic helicity is an invariant of ideal magnetohydrodynamics (MHD) that encodes information on the topology of magnetic field lines. It has long been appreciated that magnetic topology is an important constraint for the evolution of magnetic fields in MHD. In applications to the solar atmosphere, understanding magnetic topology is crucial for following the evolution and eruption of magnetic fields. At present, magnetic helicity flux can be measured in solar observations but the interpretation of results is difficult due to the combination of confounding factors. We propose that a renormalization of helicity flux, the magnetic winding, can be used to detect more detailed topological features in magnetic fields and thus provide a more reliable signature for predicting the onset of solar eruptions.
Highlights
The evolution of magnetic fields in magnetohydrodynamics (MHD) is constrained by the underlying topology of magnetic field lines
An invariant of ideal MHD which is related to this underlying field line topology is magnetic helicity - a measure of the mean flux-weighted entanglement of the field lines
We present a renormalization of the helicity flux, which we refer to as the magnetic winding flux
Summary
The evolution of magnetic fields in magnetohydrodynamics (MHD) is constrained by the underlying topology of magnetic field lines. We discuss relative helicity flux through a planar boundary and show how it reveals that the winding of field lines can be used to describe the underlying topological structure of relative helicity (in a similar way to Gauss linkage for classical helicity). This quantity depends solely on the geometry of field lines and can detect regions of topological complexity more clearly than the helicity.
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