Plasmoid generation in resistive-MHD reconnection

A detailed numerical study of resistive-MHD magnetic reconnection for very large, previously inaccessible, Lundquist numbers ($10^4\le S\le 10^8$) is reported. Large-aspect-ratio Sweet-Parker current sheets are shown to be unstable to super-Alfv\'enically fast formation of plasmoid (magnetic-island) chains. The plasmoid number scales as $S^{3/8}$ and the linear growth rate of the instability as~$S^{1/4}$, in agreement with the theory by Loureiro~et~al.\ [Phys.\ Plasmas~{\bf 14}, 100703 (2007)]. In the nonlinear regime, plasmoids continue to grow faster than they are ejected and completely disrupt the reconnection layer. These results suggest that high-Lundquist-number reconnection is inherently time-dependent and thus call for a substantial revision of the standard Sweet-Parker quasi-stationary picture for~$S>10^4$.