Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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

Nature volume 528, pages 526–529 (2015)Cite this article

Subjects

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

References

  1. Kunow, H., Crooker, N. U., Linker, J. A., Schwenn, R. & von Steiger, R. (eds) Coronal Mass Ejections Ch. 2, 12 (Springer, 2006)

  2. Kuperus, M. & Raadu, M. A. The support of prominences formed in neutral sheets. Astron. Astrophys. 31, 189–193 (1974)

    ADS  Google Scholar 

  3. Chen, J. Effects of toroidal forces in current loops embedded in a background plasma. Astrophys. J. 338, 453–470 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  4. Titov, V. S. & Démoulin, P. Basic topology of twisted magnetic configurations in solar flares. Astron. Astrophys. 351, 707–720 (1999)

    ADS  Google Scholar 

  5. Amari, T., Canou, A. & Aly, J.-J. Characterizing and predicting the magnetic environment leading to solar eruptions. Nature 514, 465–469 (2014)

    Article  CAS  ADS  Google Scholar 

  6. Ji, H., Wang, H., Schmahl, E. J., Moon, Y.-J. & Jiang, Y. Observations of the failed eruption of a filament. Astrophys. J. 595, L135–L138 (2003)

    Article  CAS  ADS  Google Scholar 

  7. Török, T. & Kliem, B. Confined and ejective eruptions of kink-unstable flux ropes. Astrophys. J. 630, L97–L100 (2005)

    Article  ADS  Google Scholar 

  8. Joshi, N. C. et al. Confined partial filament eruption and its reformation within a stable magnetic flux rope. Astrophys. J. 787, 11 (2014)

    Article  ADS  Google Scholar 

  9. Forbes, T. G. & Isenberg, P. A. A catastrophe mechanism for coronal mass ejections. Astrophys. J. 373, 294–307 (1991)

    Article  ADS  Google Scholar 

  10. Kliem, B. & Török, T. Torus instability. Phys. Rev. Lett. 96, 255002 (2006)

    Article  CAS  ADS  Google Scholar 

  11. Fan, Y. & Gibson, S. E. Onset of coronal mass ejections due to loss of confinement of coronal flux ropes. Astrophys. J. 668, 1232–1245 (2007)

    Article  CAS  ADS  Google Scholar 

  12. Liu, Y. Magnetic field overlying solar eruption regions and kink and torus instabilities. Astrophys. J. 679, L151–L154 (2008)

    Article  ADS  Google Scholar 

  13. Démoulin, P. & Aulanier, G. Criteria for flux rope eruption: non-equilibrium versus torus instability. Astrophys. J. 718, 1388–1399 (2010)

    Article  ADS  Google Scholar 

  14. Savcheva, A., Pariat, E., van Ballegooijen, A., Aulanier, G. & DeLuca, E. Sigmoidal active region on the sun: comparison of a magnetohydrodynamical simulation and a nonlinear force-free field model. Astrophys. J. 750, 15 (2012)

    Article  ADS  Google Scholar 

  15. Sun, X. et al. Why is the great solar active region 12192 flare-rich but CME-poor? Astrophys. J. 804, L28 (2015)

    Article  ADS  Google Scholar 

  16. Myers, C. E. Laboratory Study of the Equilibrium and Eruption of Line-Tied Magnetic Flux Ropes in the Solar Corona. http://arks.princeton.edu/ark:/88435/dsp01dv13zw44b, PhD thesis, Princeton Univ. (2015)

  17. Hansen, J. F. & Bellan, P. M. Experimental demonstration of how strapping fields can inhibit solar prominence eruptions. Astrophys. J. 563, L183–L186 (2001)

    Article  ADS  Google Scholar 

  18. Soltwisch, H. et al. Flarelab: early results. Plasma Phys. Contr. Fusion 52, 124030 (2010)

    Article  ADS  Google Scholar 

  19. Tripathi, S. K. P. & Gekelman, W. Laboratory simulation of arched magnetic flux rope eruptions in the solar atmosphere. Phys. Rev. Lett. 105, 075005 (2010)

    Article  CAS  ADS  Google Scholar 

  20. Gold, T. & Hoyle, F. On the origin of solar flares. Mon. Not. R. Astron. Soc. 120, 89–105 (1960)

    Article  ADS  Google Scholar 

  21. Sakurai, T. Magnetohydrodynamic interpretation of the motion of prominences. Publ. Astron. Soc. Jpn. 28, 177–198 (1976)

    ADS  Google Scholar 

  22. Hood, A. W. & Priest, E. R. Critical conditions for magnetic instabilities in force-free coronal loops. Geophys. Astrophys. Fluid Dyn. 17, 297–318 (1981)

    Article  ADS  Google Scholar 

  23. Mikic´, Z., Schnack, D. D. & van Hoven, G. Dynamical evolution of twisted magnetic flux tubes. I—Equilibrium and linear stability. Astrophys. J. 361, 690–700 (1990)

    Article  ADS  Google Scholar 

  24. Török, T., Kliem, B. & Titov, V. S. Ideal kink instability of a magnetic loop equilibrium. Astron. Astrophys. 413, L27–L30 (2004)

    Article  ADS  Google Scholar 

  25. Kruskal, M. & Schwarzschild, M. Some instabilities of a completely ionized plasma. Proc. R. Soc. Lond. A 223, 348–360 (1954)

    Article  ADS  MathSciNet  Google Scholar 

  26. Shafranov, V. The stability of a cylindrical gaseous conductor in a magnetic field. Sov. J . At. Energy 1, 709–713 (1956)

    Article  Google Scholar 

  27. Ryutov, D. D., Furno, I., Intrator, T. P., Abbate, S. & Madziwa-Nussinov, T. Phenomenological theory of the kink instability in a slender plasma column. Phys. Plasmas 13, 032105 (2006)

    Article  ADS  Google Scholar 

  28. Olmedo, O. & Zhang, J. Partial torus instability. Astrophys. J. 718, 433–440 (2010)

    Article  ADS  Google Scholar 

  29. Ji, H., Prager, S. C. & Sarff, J. S. Conservation of magnetic helicity during plasma relaxation. Phys. Rev. Lett. 74, 2945–2948 (1995)

    Article  CAS  ADS  Google Scholar 

  30. Taylor, J. B. Relaxation and magnetic reconnection in plasmas. Rev. Mod. Phys. 58, 741–763 (1986)

    Article  CAS  ADS  Google Scholar 

  31. Moore, R. L., Sterling, A. C., Hudson, H. S. & Lemen, J. R. Onset of the magnetic explosion in solar flares and coronal mass ejections. Astrophys. J. 552, 833–848 (2001)

    Article  ADS  Google Scholar 

  32. Antiochos, S. K., DeVore, C. R. & Klimchuk, J. A. A model for solar coronal mass ejections. Astrophys. J. 510, 485–493 (1999)

    Article  ADS  Google Scholar 

  33. Shafranov, V. Plasma equilibrium in a magnetic field. Rev. Plasma Phys. (ed. Leontovich, M. A. ) 2, 103–152 (1966)

    ADS  Google Scholar 

  34. Bateman, G. MHD Instabilities (MIT Press, 1978)

  35. Kliem, B., Lin, J., Forbes, T. G., Priest, E. R. & Török, T. Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope. Astrophys. J. 789, 46 (2014)

    Article  ADS  Google Scholar 

  36. Hsu, S. C. & Bellan, P. M. Experimental identification of the kink instability as a poloidal flux amplification mechanism for coaxial gun spheromak formation. Phys. Rev. Lett. 90, 215002 (2003)

    Article  CAS  ADS  Google Scholar 

  37. Furno, I. et al. Current-driven rotating-kink mode in a plasma column with a non-line-tied free end. Phys. Rev. Lett. 97, 015002 (2006)

    Article  CAS  ADS  Google Scholar 

  38. Bergerson, W. F. et al. Onset and saturation of the kink instability in a current-carrying line-tied plasma. Phys. Rev. Lett. 96, 015004 (2006)

    Article  CAS  ADS  Google Scholar 

  39. Oz, E. et al. Experimental verification of the Kruskal-Shafranov stability limit in line-tied partial-toroidal plasmas. Phys. Plasmas 18, 102107 (2011)

    Article  ADS  Google Scholar 

  40. Yamada, M. et al. Study of driven magnetic reconnection in a laboratory plasma. Phys. Plasmas 4, 1936–1944 (1997)

    Article  CAS  ADS  Google Scholar 

  41. Bellan, P. M. & Hansen, J. F. Laboratory simulations of solar prominence eruptions. Phys. Plasmas 5, 1991–2000 (1998)

    Article  CAS  ADS  Google Scholar 

  42. Lemen, J. R. et al. The Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Sol. Phys. 275, 17–40 (2012)

    Article  ADS  Google Scholar 

  43. Yoo, J., Yamada, M., Ji, H. & Myers, C. E. Observation of ion acceleration and heating during collisionless magnetic reconnection in a laboratory plasma. Phys. Rev. Lett. 110, 215007 (2013)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

  1. Department of Astrophysical Sciences, Princeton University, Princeton, 08544, New Jersey, USA

    Clayton E. Myers, Hantao Ji & Jonathan Jara-Almonte

  2. Princeton Plasma Physics Laboratory, Princeton, 08543, New Jersey, USA

    Clayton E. Myers, Masaaki Yamada, Hantao Ji, Jongsoo Yoo, William Fox & Jonathan Jara-Almonte

  3. Laboratory for Space Environment and Physical Sciences, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, China

    Hantao Ji

  4. Harvard–Smithsonian Center for Astrophysics, Cambridge, 02138, Massachusetts, USA

    Antonia Savcheva & Edward E. DeLuca

Authors
  1. Clayton E. Myers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masaaki Yamada
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hantao Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jongsoo Yoo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. William Fox
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jonathan Jara-Almonte
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Antonia Savcheva
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Edward E. DeLuca
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

The digital data for this paper can be found at http://arks.princeton.edu/ark:/88435/dsp01j3860933c.

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
Full size table
Extended Data Table 2 Comparison of solar and laboratory dimensionless parameters
Full size table
Extended Data Table 3 Decomposition of magnetic field, current density, and force terms
Full size table

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)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1038/nature16188

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature16188

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing