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 Δd 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 / Δ d ∼ 10 12, which is the magnetic Reynolds number Rm. The traditional resolution of the paradox of disparate scales is for the current density j associated with the reconnecting field Brec to be concentrated by a factor of Rm by the ideal evolution, so j ∼ B rec / μ 0 Δ d. A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrary chosen magnetic field lines, Δ max / Δ min, when calculated at various points in time. Reconnection becomes inevitable where Δ max / Δ min ∼ 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 Δ max / Δ min. Reconnection occurs on a timescale and with a current density enhanced by only ln ( a / Δ d ) from the ideal evolution time and from the current density B rec / μ 0 a. In both resolutions, once a sufficiently wide region, Δr, has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfvenic timescale. The Alfvenic evolution is intrinsically ideal but expands the region in which Δ max / Δ min is large.