Threshold for the torus instability of arched, line-tied flux ropes

Coronal mass ejections occur when long-lived magnetic flux ropes anchored to the solar surface destabilize and erupt away from the Sun. One mechanism that drives this eruption is the ideal magnetohydrodynamic torus instability [1]. The torus instability has previously been considered in axisymmetric fusion devices where instability criterion is given by the decay index of the confining magnetic field, n = -∂ln(B)/∂ln(R) > n_cr, where n_cr = 1.5 in the large aspect ratio limit. In recent laboratory experiments performed on the Magnetic Reconnection Experiment (MRX), however, the critical decay index in solar-relevant, line-tied flux ropes was instead found to be n_cr ≈ 0.8 [2]. In this work, we investigate how line-tying and aspect ratio effects modify the predicted torus instability criterion. We then compare these predictions to the MRX flux rope eruption database. This work motivates future laboratory experiments in continued investigation of line-tied flux rope eruption mechanisms, including the role of magnetic self-organization in erupting and non-erupting flux ropes.
[1] B. Kliem and T. Török, Phys. Rev. Lett. 96, 255002 (2006)
[2] Myers et al., Nature 528, 526 (2015)