Rate of steady-state reconnection in an incompressible plasma
Erkaev N. V., Semenov V. S., Alexeev H. K., Biernat H. K.
Physics of Plasmas. —
2001. — Vol. 8. — ь 11. — P. 4800–4811.
Full text of the article [pdf, 284 Kb, in english]
The reconnection rate is obtained for the simplest case of two-dimensional ~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 Re m, 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 Re m. 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. c 2001 American Institute of Physics. @DOI: 10.1063/1.1410112#