  The thickness of current sheets is extremely important, especially as it
relates to the onset of fast magnetic reconnection. Onset determines how much
magnetic free energy can build up in a field before it is explosively released.
This has implications for many phenomena on the Sun and throughout the
universe, including the heating of the solar corona. Significant effort has
been devoted to the question of whether equilibrium current sheets in realistic
geometries have finite or zero thickness. Using a simple force balance
analysis, we show why current sheets without a guide field (2D) and with a
guide field that is invariant in the guide field direction (2.5D) cannot be in
equilibrium if they have both finite thickness and finite length. We then
estimate the conditions under which the tension of a curved line-tied guide
field can facilitate equilibrium in 3D sheets that are finite in all
dimensions. Finally, we argue that some quasi-statically evolving current
sheets undergoing slow stressing (e.g., when the coronal magnetic field is
subjected to photospheric boundary driving) may reach a critical shear, at
which point they lose equilibrium, spontaneously collapse, and reconnect. The
critical shear is generally consistent with the heating requirements of solar
active regions.
