Formation of Plasmoid Chains in Magnetic Reconnection

A detailed numerical study of magnetic reconnection in resistive MHD 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 $S^{3\mathrm{/}8}$ and the instability growth rate in the linear stage as $S^{1\mathrm{/}4}$, 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 hence call for a substantial revision of the standard Sweet-Parker quasi-stationary picture for $S>{10}^4$.