Example of exponentially enhanced magnetic reconnection driven by a
  spatially-bounded and laminar ideal flow
  In laboratory and natural plasmas of practical interest, the spatial scale
$\Delta_d$ at which magnetic field lines lose distinguishability differs
enormously from the scale $a$ of magnetic reconnection across the field lines.
In the solar corona, plasma resistivity gives $a/\Delta_d\sim10^{12}$, which is
the magnetic Reynold number $R_m$. The traditional resolution of the paradox of
disparate scales is for the current density $j$ associated with the
reconnecting field $B_{rec}$ to be concentrated by a factor of $R_m$ by the
ideal evolution, so $ j\sim B_{rec}/\mu_0\Delta_d$. A second resolution is for
the ideal evolution to increase the ratio of the maximum to minimum separation
between pairs of arbitrarily chosen magnetic field lines,
$\Delta_{max}/\Delta_{min}$, when calculated at various points in time.
Reconnection becomes inevitable where $\Delta_{max}/\Delta_{min}\sim R_m$. A
simple model of the solar corona will be used for a numerical illustration that
the natural rate of increase in time is linear for the current density but
exponential for $\Delta_{max}/\Delta_{min}$. Reconnection occurs on a time
scale and with a current density enhanced by only $\ln(a/\Delta_d)$ from the
ideal evolution time and from the current density $B_{rec}/\mu_0a$. In both
resolutions, once a sufficiently wide region, $\Delta_r$, has undergone
reconnection, the magnetic field loses static force balance and evolves on an
Alfv\'enic time scale. The Alfv\'enic evolution is intrinsically ideal but
expands the region in which $\Delta_{max}/\Delta_{min}$ is large.
