Laboratory experiments on arched, line-tied magnetic flux ropes (Myers et al. 2015, Nature) discovered a 'failed-torus' regime: torus-unstable ropes fail to erupt when the guide field (the ambient field running toroidally along the rope) is strong enough to keep them kink-stable, because internal current redistribution makes the guide field act through the rope currents to produce a dynamic toroidal-field tension force that halts the eruption — a force absent from existing eruption models. Whether this mechanism operates in the solar corona, whether it explains flare-rich but CME-poor regions such as NOAA AR 12192, and in which parameter regime internal current redistribution halts rather than disrupts an eruption, all remain open. The solar statistical counterpart built so far does not reproduce the laboratory regime map, alternative confinement mechanisms (strapping field, external reconnection, rotation/writhe, non-axisymmetry, gravity) are actively proposed, and no time-dependent three-dimensional line-tied simulation of the relaxation dynamics has been published. Myers et al. 2015 attribute the unresolved status of the question to a lack of coronal magnetic field measurements and the limitations of idealized numerical modelling; time-dependent three-dimensional line-tied MHD simulations of the relaxation dynamics and observational tests using guide-field diagnostics from coronal field reconstructions are therefore natural routes toward a resolution.

Background

Coronal mass ejections (CMEs) are explosive releases of magnetized plasma from the Sun's corona; whether a destabilized magnetic structure erupts into interplanetary space or fails, remaining confined in the low corona (a 'failed' or 'confined' eruption producing a flare without a CME), is a central question of solar eruptive physics and space-weather prediction. Much of the released energy is stored in magnetic flux ropes — twisted, arched bundles of magnetic field anchored at both ends in the dense photosphere, a condition called line-tying. Within magnetohydrodynamics (MHD, the fluid description of magnetized plasma), two ideal instabilities are the standard eruption criteria. The torus instability arises when the ambient 'strapping' field transverse to the rope falls off with height fast enough, conventionally quantified by the decay index n=−dln⁡Bp/dln⁡zn=-d\ln B_{\mathrm{p}}/d\ln z with eruption expected once nn exceeds a critical value near 1.5 for a large-aspect-ratio torus (Kliem & Török 2006). The helical kink instability occurs when the rope's twist exceeds a threshold, commonly parametrized by the edge safety factor qaq_a, and can either trigger or disrupt an eruption. A third field component — the guide field, the ambient field running along the rope axis (toroidally) — was not assigned a controlling role in eruption onset until recently.

Observations complicate the torus picture: some flux ropes that satisfy the torus criterion nevertheless fail to erupt. The archetype is active region NOAA AR 12192, the largest sunspot region of cycle 24, which produced over one hundred flares (including six of the largest, X-class) but essentially no CMEs from its core. In a laboratory experiment (Myers et al. 2015) on the Magnetic Reconnection Experiment (MRX) device at Princeton, arched, line-tied flux ropes were driven through the torus- and kink-instability parameter space. The experiment revealed a 'failed-torus' regime: when the guide field is strong enough to keep the rope kink-stable, torus-unstable ropes still fail to erupt. During the rope's internal self-organization — a redistribution of its electric current, originally described as resembling Taylor relaxation (relaxation to a lower-energy state while conserving magnetic helicity, a measure of field-line twist and linkage) — the guide field acts through the rope currents to produce a downward toroidal-field tension force that grows as the rope accelerates, halting the eruption. This 'dynamic' tension force is missing from existing eruption models, which therefore cannot explain or predict failed-torus events. Companion laboratory studies measured the full force inventory (upward hoop force from the rope current, downward strapping force, downward toroidal tension) and found that line-tied, low-aspect-ratio conditions reduce the hoop force and enhance the tension force relative to analytic expectations, implying the standard eruption criteria need modification for solar application.

Whether the mechanism operates in the Sun's corona is untested. The guide field of a coronal flux rope cannot be measured directly; it must be inferred from photospheric vector magnetograms (e.g., SDO/HMI) via potential-field extrapolation (a current-free reconstruction) or nonlinear force-free field modeling (reconstruction assuming the Lorentz force vanishes). The observational counterpart constructed so far (Jing et al. 2018: 38 major flares placed on a decay-index–twist diagram, built explicitly as the solar counterpart of the laboratory parameter map) found eruptiveness controlled mainly by the decay index, with twist playing little discriminating role — a structure that does not reproduce the laboratory regime map, with the discrepancy attributed by the authors to the role of magnetic reconnection. Case studies of torus-unstable failures propose other operative factors: large rotation (writhe) of the rope apex (Zhou et al. 2019), gravity and null-point field structure (Filippov 2020), reconnection between the rope and overlying flux (Chen et al. 2023; Ding et al. 2022), non-axisymmetric Lorentz-force components (Zhong et al. 2021), and strong surrounding 'magnetic cages' (Amari et al. 2018). The AR 12192 studies attribute that region's confinement to a strong strapping field and weak core-field nonpotentiality (Sun et al. 2015; Liu et al. 2016; Jiang et al. 2016). On the laboratory side the interpretation of the current redistribution continues to be refined (Alt et al. 2023 excluded Taylor relaxation as the redistribution mechanism, in favor of ideal-MHD effects with non-ideal layers at the electrodes). No study has demonstrated, or ruled out, the dynamic guide-field tension mechanism in the corona, and no eruption-prediction framework includes it.

Problem Statement

Determine whether the dynamic toroidal-field tension force (the failed-torus mechanism) discovered in laboratory line-tied flux-rope experiments operates in the solar corona and accounts for the observed failure of torus-unstable eruptions. Three linked open aspects bear on this single objective, and all three must be addressed for the objective to count as resolved: none is sufficient on its own. (1) Modeling: whether flux-rope internal relaxation and reconnection produce, in time-dependent three-dimensional magnetohydrodynamic simulations with line-tied boundary conditions, the downward toroidal-field tension surge that halts an eruption, and in which parameter regime — strapping-field decay index, guide-field strength (or kink safety factor), and twist — internal current redistribution prevents eruption rather than disrupting the rope or being precluded by kink instability. (2) Observation: whether a systematic comparison of confined and eruptive solar events — including flare-rich, CME-poor active regions such as NOAA AR 12192 — using quantitative guide-field proxies from coronal field reconstructions (potential-field or nonlinear force-free extrapolations) shows the failed-torus regime to be populated in the corona, and which observable diagnostics reliably indicate reduced eruptivity attributable to strong guide fields, with the confounding alternatives (strapping-field decay index, external reconnection, rotation/writhe, non-axisymmetry, gravity, mass draining) explicitly separated. (3) Transferability: how laboratory-specific conditions — external circuit inductance, boundary conditions, limited ionization fraction, finite Lundquist number, rapid post-event flux-rope reformation — affect the extrapolation of the measured relaxation and reformation dynamics to coronal conditions. The goal is a quantitative determination of whether or not the guide-field tension mechanism is operative and predictive for the Sun; if the mechanism is confirmed, identifying the eruption criterion and observational proxy by which the toroidal-tension term would enter eruption-prediction frameworks would address the fact, noted by Myers et al. 2015, that existing models cannot explain or predict failed-torus events.

References

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