Laboratory identification of MHD eruption criteria in the solar corona

Ideal magnetohydrodynamic (MHD) instabilities such as the kink\footnote{Hood \& Priest, \textit{Geophys. Astrophys. Fluid Dynamics} \textbf{17}, 297 (1981)} and torus\footnote{Kliem \& T\"or\"ok, \textit{Phys. Rev. Lett.} \textbf{96}, 255002 (2006)} instabilities are believed to play an important role in driving ``storage-and-release" eruptions in the solar corona. These instabilities act on long-lived, arched magnetic flux ropes that are ``line-tied" to the solar surface. In spite of numerous observational and computational studies, the conditions under which these instabilities produce an eruption remain a subject of intense debate. In this paper, we use a line-tied, arched flux rope experiment to study storage-and-release eruptions in the laboratory\footnote{Myers, Ph.D. Thesis, Princeton University (2015).}. An \textit{in situ} array of miniature magnetic probes is used to assess the equilibrium and stability of the laboratory flux ropes. Two major results are reported here: First, a new stability regime is identified where torus-unstable flux ropes fail to erupt. In this ``failed torus" regime, the flux rope is torus-\textit{unstable} but kink-\textit{stable}. Under these conditions, a dynamic ``toroidal field tension force" surges in magnitude, causing the flux rope to contract. This tension force, which is missing from existing eruption models, is the $\mathbf{J}\!\times\!\mathbf{B}$ force between self-generated poloidal currents in the flux rope and the toroidal (guide) component of the vacuum field. Secondly, a clear torus instability threshold is observed in the kink-\textit{unstable} regime. This latter result, which is consistent with existing theoretical\footnote{Olmedo \& Zhang, \textit{Astrophys. J.} \textbf{718}, 433 (2010)} and numerical\footnote{T\"or\"ok \& Kliem, \textit{Astrophys. J.} \textbf{630}, L97 (2005)} results, verifies the key role of the torus instability in driving solar eruptions.