Laboratory Study of the Torus Instability Threshold in Solar-relevant, Line-tied Magnetic Flux Ropes

Coronal mass ejections (CMEs) occur when long-lived magnetic flux ropes (MFRs) anchored to the solar surface destabilize and erupt away from the Sun. This destabilization is often described in terms of an ideal magnetohydrodynamic instability called the torus instability. It occurs when the external magnetic field decreases sufficiently fast such that its decay index, ${n}_{}=-z\,\partial (\mathrm{ln}{B}_{})/\partial z$ , is larger than a critical value, $n\gt {n}_{\mathrm{cr}}^{}$ , where ${n}_{\mathrm{cr}}^{}=1.5$ for a full, large aspect ratio torus. However, when this is applied to solar MFRs, a range of conflicting values for ${n}_{\mathrm{cr}}^{}$ is found in the literature. To investigate this discrepancy, we have conducted laboratory experiments on arched, line-tied flux ropes and applied a theoretical model of the torus instability. Our model describes an MFR as a partial torus with foot points anchored in a conducting surface and numerically calculates various magnetic forces on it. This calculation yields better predictions of ${n}_{\mathrm{cr}}^{}$ that take into account the specific parameters of the MFR. We describe a systematic methodology to properly translate laboratory results to their solar counterparts, provided that the MFRs have a sufficiently small edge safety factor or, equivalently, a large enough twist. After this translation, our model predicts that ${n}_{\mathrm{cr}}^{}$ in solar conditions falls near ${n}_{\mathrm{cr}}^{\mathrm{solar}}\sim 0.9$ and within a larger range of ${n}_{\mathrm{cr}}^{\mathrm{solar}}\sim (0.7,1.2)$ , depending on the parameters. The methodology of translating laboratory MFRs to their solar counterparts enables quantitative investigations of CME initiation through laboratory experiments. These experiments allow for new physics insights that are required for better predictions of space weather events but are difficult to obtain otherwise.