Rate of steady-state reconnection in an incompressible plasma

The reconnection rate is obtained for the simplest case of two-dimensional (2D) symmetric reconnection in an incompressible plasma. In the short note [Erkaev , Phys. Rev. Lett. 84, 1455 (2000)], the reconnection rate is found by matching the outer Petschek solution and the inner diffusion region sol ution. 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 decr easing function of the diffusion region length. For a sufficiently large di ffusion 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 Re-m, determined for the global size of the curre nt 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 Pet schek model with a logarithmic dependence on the magnetic Reynolds number R e-m. This means that the Petschek regime seems to be possible only in the c ase of a strongly localized conductivity corresponding to a small scale of the diffusion region. (C) 2001 American Institute of Physics.