Magnetic reconnection, plasmoids and numerical resolution

Explaining fast magnetic reconnection in electrically conducting plasmas has been a theoretical challenge in plasma physics since its first description by Eugene N. Parker. In the recent years the observed reconnection rate has been shown by numerical simulations to be explained by the plasmoid instability that appears in highly conductive plasmas. In this work we show that the plasmoid instability is very sensitive to the numerical resolution used. It is shown that well resolved runs display no plasmoid instability even at Lundquist number as large as $5\cdot10^5$ achieved at resolutions of $32\,768^2$ grid points. On the contrary in simulations that are under-resolved below a threshold, the plasmoid instability manifests itself with the formation of larger plasmoids the larger the under-resolving is. The present results thus question the description of the plasmoid instability as a mechanism for fast magnetic reconnection.