Onset of fast reconnection in forming coronal current sheets

For a current sheet of length $L$ and thickness a forming under external driving in resistive or Hall MHD at Lundquist number $S = L v_A/\eta$ of $10^{12}$ to $10^{14}$ (solar corona), determine the aspect ratio $a/L$ and the time at which tearing growth outpaces sheet thinning and fast (plasmoid-mediated or collisionless) reconnection begins; the ideal-tearing proposal gives $a/L \sim S^{-1/3}$. Determine how the criterion depends on the thinning rate and on the approach to kinetic scales ($a \sim d_i$), and predict the stored magnetic energy at onset. An answer is a criterion confirmed by driven-sheet simulations over a range of $S$ and consistent with flare-onset observations.

Driven-sheet MHD and kinetic simulations over a range of S that confirm the predicted onset aspect ratio and time, with a laboratory test at the highest attainable S.