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A dynamic magnetic tension force as the cause of failed solar eruptions


Coronal mass ejections are solar eruptions driven by a sudden release of magnetic energy stored in the Sun’s corona1. In many cases, this magnetic energy is stored in long-lived, arched structures called magnetic flux ropes2,3,4,5. When a flux rope destabilizes, it can either erupt and produce a coronal mass ejection or fail and collapse back towards the Sun6,7,8. The prevailing belief is that the outcome of a given event is determined by a magnetohydrodynamic force imbalance called the torus instability9,10,11,12,13,14. This belief is challenged, however, by observations indicating that torus-unstable flux ropes sometimes fail to erupt15. This contradiction has not yet been resolved because of a lack of coronal magnetic field measurements and the limitations of idealized numerical modelling. Here we report the results of a laboratory experiment16 that reveal a previously unknown eruption criterion below which torus-unstable flux ropes fail to erupt. We find that such ‘failed torus’ events occur when the guide magnetic field (that is, the ambient field that runs toroidally along the flux rope) is strong enough to prevent the flux rope from kinking. Under these conditions, the guide field interacts with electric currents in the flux rope to produce a dynamic toroidal field tension force that halts the eruption. This magnetic tension force is missing from existing eruption models, which is why such models cannot explain or predict failed torus events.

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Figure 1: Representative stable and erupting flux rope discharges.
Figure 2: The experimentally measured torus versus kink instability parameter space.
Figure 3: Magnetic analysis of a characteristic failed torus event.

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We thank R. Cutler for constructing the flux rope experiment and for myriad technical contributions. We also thank F. Scotti and P. Sloboda for additional technical contributions and R. M. Kulsrud for theoretical discussions. This research is supported by Department of Energy (DoE) contract number DE-AC02-09CH11466 and by the National Science Foundation/DoE Center for Magnetic Self-Organization (CMSO).

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Authors and Affiliations



C.E.M., M.Y. and H.J. designed the laboratory experiments. C.E.M., J.Y. and J.J.-A. carried out the experiments and processed the data. C.E.M., M.Y., H.J., J.Y., W.F. and J.J.-A. interpreted the laboratory results. A.S. and E.E.DeL. placed the laboratory results in the context of solar observations and modelling. C.E.M. analysed the laboratory data, prepared the figures, and wrote the manuscript. All authors contributed to the revision of the manuscript.

Corresponding author

Correspondence to Clayton E. Myers.

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The authors declare no competing financial interests.

Additional information

The digital data for this paper can be found at

Extended data figures and tables

Extended Data Figure 1 Experimental setup.

A plasma arc (pink) is maintained between two electrodes that are mounted on a glass substrate. The electrodes, which serve as the flux rope footpoints, are horizontally separated by 2xf = 36 cm, and they have a minor radius of af = 7.5 cm. The vertical distance from these footpoints to the vessel wall is zw ≈ 70 cm. Four magnetic field coil sets (two inside the vessel, two outside) work in concert to produce a variety of potential magnetic field configurations. More specifically, the two orange coil sets are used to produce the guide potential field, while the two blue coil sets are used to produce the strapping potential field.

Extended Data Figure 2 Components of the potential magnetic field configuration.

The strapping field runs perpendicular to the flux rope axis and produces the well known strapping force, whose rapid spatial decay can trigger the torus instability. The guide field, on the other hand, runs toroidally along the flux rope axis. It stabilizes the kink instability and generates a confining magnetic tension force. The total potential magnetic field, which is the superposition of the guide and strapping field contributions, is obliquely aligned to the flux rope.

Extended Data Figure 3 Magnetic field analysis of a characteristic eruptive event.

a, The spatial evolution of the eruptive perturbation (red), with the failed torus event from Fig. 3a for comparison (black). b, Evolution of the poloidal and toroidal magnetic fluxes. Note the monotonic evolution of both fluxes. c, Hoop (Fh), strapping (Fs), and tension (Ft) force evolution, which are also strictly monotonic. d, e, Sequenced JT and BTi evolution. Note that the current profile remains uniform and rises steadily towards the wall of the machine. A new flux rope is forming at low altitude in the final frame.

Extended Data Figure 4 Sample in situ magnetic field measurements.

Seven linear magnetic field probes (yellow) are inserted vertically into the flux rope plasma. The alignment of the two-dimensional probe plane is either (a) parallel to the footpoint axis or (b) perpendicular to it. In the sample data, the colour represents the out-of-plane field, while the vectors represent the in-plane field. The position of the magnetic axis in the toroidal cross-section (the solid black line) is determined by the reversal in the out-of-plane poloidal magnetic field, By. The position of the magnetic axis in the poloidal cross-section is defined as the O-point in the circulating in-plane field (By, Bz). The out-of-plane field in the latter case is the ‘internal’ toroidal field of the flux rope BTi, which is paramagnetic in nature.

Extended Data Figure 5 Height–time plots from four representative flux rope discharges.

a, Mean toroidal plasma current waveform showing that the plasma current is nearly the same in all four cases (the light green band is the standard deviation). b, Four sample height–time plots, one from each of the four stability regimes identified in Fig. 2. The magnetic axis position (the black line) is defined by the zero-crossing in the By(t, z) data, which is shown in colour. The red line in each frame is the time-averaged height of the flux rope apex . This waveform provides the height at which qa and n are measured in each discharge. c, Table of extracted flux rope parameters for each discharge.

Extended Data Figure 6 Magnetic field and current density data for computing flux rope forces.

The probe array is aligned as shown in Extended Data Fig. 4b. In the left panel, the colour is the toroidal current density, JT, and the vectors are the poloidal magnetic field, BP. In the right panel, the colour is the internal toroidal field BTi, and the vectors are the poloidal current density JP. With all components of J and B measured, the force densities listed in Extended Data Table 3 can be readily computed. The contours in the left panel are contours of the poloidal flux function ψ(y, z) (see equation (4)). The minor radius of the rope a(θ) is defined by the poloidal flux contour shown in red (see Methods).

Extended Data Table 1 Laboratory flux rope parameters
Extended Data Table 2 Comparison of solar and laboratory dimensionless parameters
Extended Data Table 3 Decomposition of magnetic field, current density, and force terms

Supplementary information

Representative stable and erupting flux rope discharges.

Top left: Experimental setup showing the pink arched flux rope attached to two conducting footpoints. The yellow vertical lines represent the in situ magnetic probes (see Methods). Bottom left: Height-time histories of the two flux rope discharges. Right: Frame sequences with the measured out-of-plane magnetic field overlaid on corresponding fast camera visible light images. The measured magnetic axis locations (the solid lines) are defined by the reversal of the out-of-plane magnetic field (see Methods). See Fig. 1 for a breakout of individual frames from this video. (MOV 1098 kb)

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Myers, C., Yamada, M., Ji, H. et al. A dynamic magnetic tension force as the cause of failed solar eruptions. Nature 528, 526–529 (2015).

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