  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.
