Magnetic braiding and quasi-separatrix layers

The squashing factor Q, a property of the magnetic field line mapping, has been suggested as an indicator for the formation of current sheets, and subsequently magnetic reconnection, in astrophysical plasmas. Here, we test this hypothesis for a particular class of braided magnetic fields which serve as a model for solar coronal loops. We explore the relationship between quasi-separatrix layers (QSLs), that is, layer-like structures with high Q value, electric currents, and integrated parallel currents; the latter being a quantity closely related to the reconnection rate. It is found that as the degree of braiding of the magnetic field is increased, the maximum values of Q increase exponentially. At the same time, the distribution of Q becomes increasingly filamentary, with the width of the high-Q layers exponentially decreasing. This is accompanied by an increase in the number of layers so that as the field is increasingly braided the volume becomes occupied by a myriad of thin QSLs. QSLs are not found to be good predictors of current features in this class of braided fields. Indeed, despite the presence of multiple QSLs, the current associated with the field remains smooth and large scale under ideal relaxation; the field dynamically adjusts to a smooth equilibrium. Regions of high Q are found to be better related to regions of high integrated parallel current than to actual current sheets.