  The reconnection rate is obtained for the simplest case of 2D symmetric
reconnection in an incompressible plasma. In the short note (Erkaev et al.,
Phys. Rev. Lett.,84, 1455 (2000)), the reconnection rate is found by matching
the outer Petschek solution and the inner diffusion region solution. Here the
details of the numerical simulation of the diffusion region are presented and
the asymptotic procedure which is used for deriving the reconnection rate is
described. The reconnection rate is obtained as a decreasing function of the
diffusion region length. For a sufficiently large diffusion region scale, the
reconnection rate becomes close to that obtained in the Sweet-Parker solution
with the inverse square root dependence on the magnetic Reynolds number,
determined for the global size of the current sheet. On the other hand, for a
small diffusion region length scale, the reconnection rate turns out to be very
similar to that obtained in the Petschek model with a logarithmic dependence on
the magnetic Reynolds number. This means that the Petschek regime seems to be
possible only in the case of a strongly localized conductivity corresponding to
a small scale of the diffusion region.
