Reconnection rate at very high Lundquist number in three dimensions
In plain words
In very large, highly conducting plasmas the reconnecting layer breaks into a chain of magnetic bubbles called plasmoids, which speeds reconnection up. In two-dimensional simulations the resulting rate is known, but real systems are three-dimensional, where the bubbles become twisted tubes and turbulence develops.
Precise statement
In resistive (and Hall) MHD reconnection with Lundquist number S = L v_A/eta far above the critical $S_c\sim1e4$, $2\mathrm{D}$ simulations give a rate ~0.01 v_A B_0/c independent of $S$ and a power-law plasmoid size distribution. Determine in $3\mathrm{D}$ the asymptotic rate as $S$ goes to $\infty$, the critical $S_c$, the flux-rope size distribution and whether self-generated turbulence makes the $3\mathrm{D}$ rate differ from the 2D value. An answer is converged $3\mathrm{D}$ values with error bars.
What would settle it
3D MHD simulations converged in S and resolution, cross-checked against a high-S laboratory experiment.
Status in the literature
Unverified note
The 2D plasmoid-mediated rate of about 0.01 was established around 2009-2012; the 3D asymptotic regime is still under study in 2025-2026.