  We investigate the dynamical evolution of magnetic fields in closed regions
of solar and stellar coronae. To understand under which conditions current
sheets form, we examine dissipative and ideal reduced magnetohydrodynamic
models in cartesian geometry, where two magnetic field components are present:
the strong guide field $B_0$, extended along the axial direction, and the
dynamical orthogonal field $\mathbf{b}$. Magnetic field lines thread the system
along the axial direction, that spans the length $L$, and are line-tied at the
top and bottom plates. The magnetic field $b$ initially has only large scales,
with its gradient (current) length-scale of order $\ell_b$. We identify the
magnetic intensity threshold $b/B_0 \sim \ell_b/L$. For values of $b$ below
this threshold, field-line tension inhibits the formation of current sheets,
while above the threshold they form quickly on fast ideal timescales. In the
ideal case, above the magnetic threshold, we show that current sheets thickness
decreases in time until it becomes smaller than the grid resolution, with the
analyticity strip width $\delta$ decreasing at least exponentially, after which
the simulations become under-resolved.
