Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas

A numerical study of magnetic reconnection in the large-Lundquist-number ($S$), plasmoid-dominated regime is carried out for $S$ up to $10^7$. The theoretical model of Uzdensky {\it et al.} [Phys. Rev. Lett. {\bf 105}, 235002 (2010)] is confirmed and partially amended. The normalized reconnection rate is $\normEeff\sim 0.02$ independently of $S$ for $S\gg10^4$. The plasmoid flux ($\Psi$) and half-width ($w_x$) distribution functions scale as $f(\Psi)\sim \Psi^{-2}$ and $f(w_x)\sim w_x^{-2}$. The joint distribution of $\Psi$ and $w_x$ shows that plasmoids populate a triangular region $w_x\gtrsim\Psi/B_0$, where $B_0$ is the reconnecting field. It is argued that this feature is due to plasmoid coalescence. Macroscopic "monster" plasmoids with $w_x\sim 10$% of the system size are shown to emerge in just a few Alfv\'en times, independently of $S$, suggesting that large disruptive events are an inevitable feature of large-$S$ reconnection.