  The squashing factor Q (Titov et al. 2002), 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.
