Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Ideal MHD instabilities for coronal mass ejections: interacting current channels and particle acceleration


We review and discuss insights on ideal magnetohydrodynamic (MHD) instabilities that can play a role in destabilizing solar coronal flux rope structures. For single flux ropes, failed or actual eruptions may result from internal or external kink evolutions, or from torus unstable configurations. We highlight recent findings from 3D magnetic field reconstructions and simulations where kink and torus instabilities play a prominent role. For interacting current systems, we critically discuss different routes to coronal dynamics and global eruptions, due to current channel coalescence or to tilt-kink scenarios. These scenarios involve the presence of two nearby current channels and are clearly distinct from the popular kink or torus instability. Since the solar corona is pervaded with myriads of magnetic loops—creating interacting flux ropes typified by parallel or antiparallel current channels as exemplified in various recent observational studies—coalescence or tilt-kink evolutions must be very common for destabilizing adjacent flux rope systems. Since they also evolve on ideal MHD timescales, they may well drive many sympathetic eruptions witnessed in the solar corona. Moreover, they necessarily lead to thin current sheets that are liable to reconnection. We review findings from 2D and 3D MHD simulations for tilt and coalescence evolutions, as well as on particle acceleration aspects derived from computed charged particle motions in tilt-kink disruptions and coalescing flux ropes. The latter were recently studied in two-way coupled kinetic-fluid models, where the complete phase-space information of reconnection is incorporated.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14


  1. 1.

    E.g., the forthcoming DKIST 4-meter solar telescope targets 0.1 arc-second resolution, or about 70 km in the solar photosphere. The Visual Tunable Filtergraph (VTF) instrument on DKIST may achieve 20 km spatial resolution at 520 nm. The balloon-borne SUNRISE missions achieved 50 km resolutions.


  1. T. Amari, J.F. Luciani, Z. Mikic, J. Linker, Three-dimensional solutions of magnetohydrodynamic equations for prominence magnetic support: twisted magnetic flux rope. ApJ Lett. 518, L57–L60 (1999). https://doi.org/10.1086/312053

  2. T. Amari, A. Canou, J.J. Aly, F. Delyon, F. Alauzet, Magnetic cage and rope as the key for solar eruptions. Nature 554(7691), 211–215 (2018). https://doi.org/10.1038/nature24671

  3. S.K. Antiochos, C.R. DeVore, J.A. Klimchuk, A model for solar coronal mass ejections. ApJ 510(1), 485–493 (1999). https://doi.org/10.1086/306563

  4. A.K. Awasthi, R. Liu, H. Wang, Y. Wang, C. Shen, Pre-eruptive magnetic reconnection within a multi-flux-rope system in the solar corona. ApJ 857(2), 124 (2018). https://doi.org/10.3847/1538-4357/aab7fb

  5. A.K. Awasthi, R. Liu, Y. Wang, Double-decker filament configuration revealed by mass motions. ApJ 872(1), 109 (2019). https://doi.org/10.3847/1538-4357/aafdad

  6. G. Bateman, MHD instabilities (MIT Press, Cambridge, 1978)

  7. C. Baumgartner, J.K. Thalmann, A.M. Veronig, On the factors determining the eruptive character of solar flares. ApJ 853, 105 (2018). https://doi.org/10.3847/1538-4357/aaa243

  8. D. Biskamp, H. Welter, Coalescence of magnetic islands. PRL 44(16), 1069–1072 (1980). https://doi.org/10.1103/PhysRevLett.44.1069

  9. G.J.J. Botha, T.D. Arber, A.W. Hood, Thermal conduction effects on the kink instability in coronal loops. A & A 525, A96 (2011). https://doi.org/10.1051/0004-6361/201015534

  10. H. Carmichael, A Process for flares 50, 451 (1964)

  11. J. Chen, Theory of prominence eruption and propagation: interplanetary consequences. J. Geophys. Res. Space Phys. 101, 27499 (1996). https://doi.org/10.1029/96JA02644

  12. P.F. Chen, Coronal mass ejections: models and their observational basis. Living Rev. Solar Phys. 8(1), 1 (2011). https://doi.org/10.12942/lrsp-2011-1

  13. L.K.S. Daldorff, G. Tóth, T.I. Gombosi, G. Lapenta, J. Amaya, S. Markidis, J.U. Brackbill, Two-way coupling of a global Hall magnetohydrodynamics model with a local implicit particle-in-cell model. J. Comput. Phys. 268, 236–254 (2014). https://doi.org/10.1016/j.jcp.2014.03.009

  14. P. Démoulin, G. Aulanier, Criteria for flux rope eruption: non-equilibrium versus torus instability. ApJ 718(2), 1388–1399 (2010). https://doi.org/10.1088/0004-637X/718/2/1388

  15. S. Du, F. Guo, G.P. Zank, X. Li, A. Stanier, Plasma energization in colliding magnetic flux ropes. ApJ 867(1), 16 (2018). https://doi.org/10.3847/1538-4357/aae30e

  16. Y. Fan, On the eruption of coronal flux ropes. ApJ 719(1), 728–736 (2010). https://doi.org/10.1088/0004-637X/719/1/728

  17. J.M. Finn, P.K. Kaw, Coalescence instability of magnetic islands. Phys. Fluids 20, 72–78 (1977). https://doi.org/10.1063/1.861709

  18. J.M. Finn, W.M. Manheimer, E. Ott, Spheromak tilting instability in cylindrical geometry. Phys. Fluids 24, 1336–1341 (1981). https://doi.org/10.1063/1.863536

  19. J.P. Freidberg, Ideal magnetohydrodynamics (1987)

  20. S.E. Gibson, Solar prominences: theory and models. Fleshing out the magnetic skeleton. Living Rev. Sol. Phys. 15, 7 (2018). https://doi.org/10.1007/s41116-018-0016-2

  21. J.P. Goedbloed, R. Keppens, S. Poedts (2019) Magnetohydrodynamics of laboratory and astrophysical plasmas

  22. J.P. Goedbloed, S. Poedts, Principles of Magnetohydrodynamics (2004)

  23. T. Gou, R. Liu, B. Kliem, Y. Wang, A.M. Veronig, The birth of a coronal mass ejection. Sci. Adv. 5(3), 7004 (2019). https://doi.org/10.1126/sciadv.aau7004

  24. Y. Guo, M.D. Ding, B. Schmieder, H. Li, T. Török, T. Wiegelmann, Driving mechanism and onset condition of a confined eruption. ApJ 725(1), L38–L42 (2010). https://doi.org/10.1088/2041-8205/725/1/L38

  25. Y. Guo, C. Xia, R. Keppens, Magneto-frictional modeling of coronal nonlinear force-free fields. II. Application to observations. ApJ 828, 83 (2016). https://doi.org/10.3847/0004-637X/828/2/83

  26. Y. Guo, C. Xia, R. Keppens, G. Valori, Magneto-frictional modeling of coronal nonlinear force-free fields. I. Testing with analytic solutions. ApJ 828, 82 (2016). https://doi.org/10.3847/0004-637X/828/2/82

  27. Y. Guo, C. Xia, R. Keppens, M.D. Ding, P.F. Chen, Solar magnetic flux rope eruption simulated by a data-driven magnetohydrodynamic model. ApJ Lett. 870, L21 (2019). https://doi.org/10.3847/2041-8213/aafabf

  28. A. Hassanin, B. Kliem, Helical kink instability in a confined solar eruption. ApJ 832(2), 106 (2016). https://doi.org/10.3847/0004-637X/832/2/106

  29. T. Hirayama, Theoretical model of flares and prominences. I: Evaporating flare model. Sol. Phys. 34(2), 323–338 (1974). https://doi.org/10.1007/BF00153671

  30. A.W. Hood, E.R. Priest, Kink instability of solar coronal loops as the cause of solar flares. Sol. Phys. 64, 303–321 (1979). https://doi.org/10.1007/BF00151441

  31. Q. Hu, J. Qiu, B. Dasgupta, A. Khare, G.M. Webb, Structures of interplanetary magnetic flux ropes and comparison with their solar sources. ApJ 793, 53 (2014). https://doi.org/10.1088/0004-637X/793/1/53

  32. P.A. Isenberg, T.G. Forbes, A three-dimensional line-tied magnetic field model for solar eruptions. ApJ 670(2), 1453–1466 (2007). https://doi.org/10.1086/522025

  33. S.C. Jardin, The spheromak. Europhys. News 17, 73–76 (1986). https://doi.org/10.1051/epn/19861706073

  34. Y. Jiang, J. Yang, H. Wang, H. Ji, Y. Liu, H. Li, J. Li, Interaction and merging of two sinistral filaments. ApJ 793(1), 14 (2014). https://doi.org/10.1088/0004-637X/793/1/14

  35. J. Jing, C. Liu, J. Lee, H. Ji, N. Liu, Y. Xu, H. Wang, Statistical analysis of torus and kink instabilities in solar eruptions. ApJ 864(2), 138 (2018). https://doi.org/10.3847/1538-4357/aad6e4

  36. R. Keppens, Z. Meliani, A.J. van Marle, P. Delmont, A. Vlasis, B. van der Holst, Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics. J. Comput. Phys. 231, 718–744 (2012). https://doi.org/10.1016/j.jcp.2011.01.020

  37. R. Keppens, O. Porth, C. Xia, Interacting tilt and kink instabilities in repelling current channels. ApJ 795, 77 (2014). https://doi.org/10.1088/0004-637X/795/1/77

  38. B. Kliem, T. Török, Torus instability. Phys. Rev. Lett. 96(25), 255002 (2006). https://doi.org/10.1103/PhysRevLett.96.255002

  39. B. Kliem, T. Török, V.S. Titov, R. Lionello, J.A. Linker, R. Liu, C. Liu, H. Wang, Slow rise and partial eruption of a double-decker filament. II. A double flux rope model. ApJ 792(2), 107 (2014)

  40. R.A. Kopp, G.W. Pneuman, Magnetic reconnection in the corona and the loop prominence phenomenon. Sol. Phys. 50(1), 85–98 (1976). https://doi.org/10.1007/BF00206193

  41. M. Kruskal, J.L. Tuck, The instability of a pinched fluid with a longitudinal magnetic field. Proc. R. Soc. A 245, 222–237 (1958). https://doi.org/10.1098/rspa.1958.0079

  42. P. Kumar, P.K. Manoharan, W. Uddin, Evolution of solar magnetic field and associated multiwavelength phenomena: flare events on 2003 November 20. ApJ 710, 1195–1204 (2010). https://doi.org/10.1088/0004-637X/710/2/1195

  43. S. Lankalapalli, J.E. Flaherty, M.S. Shephard, H. Strauss, An adaptive finite element method for magnetohydrodynamics. J. Comput. Phys. 225, 363–381 (2007). https://doi.org/10.1016/j.jcp.2006.12.010

  44. M.G. Linton, Reconnection of nonidentical flux tubes. J. Geophys. Res. 111, A12–A12S09 (2006)

  45. M.G. Linton, R.B. Dahlburg, S.K. Antiochos, Reconnection of twisted flux tubes as a function of contact angle. ApJ 553, 905–921 (2001). https://doi.org/10.1086/320974

  46. Y. Liu, Magnetic field overlying solar eruption regions and kink and torus instabilities. ApJ Lett. 679(2), L151 (2008). https://doi.org/10.1086/589282

  47. R. Liu, C. Liu, S.H. Park, H. Wang, Gradual inflation of active-region coronal arcades building up to coronal mass ejections. ApJ 723(1), 229–240 (2010). https://doi.org/10.1088/0004-637X/723/1/229

  48. R. Liu, B. Kliem, T. Török, C. Liu, V.S. Titov, R. Lionello, J.A. Linker, H. Wang, Slow rise and partial eruption of a double-decker filament. I. Observations and interpretation. ApJ 756(1), 59 (2012). https://doi.org/10.1088/0004-637X/756/1/59

  49. R. Liu, B. Kliem, V.S. Titov, J. Chen, Y. Wang, H. Wang, C. Liu, Y. Xu, T. Wiegelmann, Structure, stability, and evolution of magnetic flux ropes from the perspective of magnetic twist. ApJ 818(2), 148 (2016). https://doi.org/10.3847/0004-637X/818/2/148

  50. D.W. Longcope, H.R. Strauss, The coalescence instability and the development of current sheets in two-dimensional magnetohydrodynamics. Phys. Fluids B 5, 2858–2869 (1993). https://doi.org/10.1063/1.860673

  51. D.W. Longcope, H.R. Strauss, Spontaneous reconnection of line-tied flux tubes. ApJ 426, 742–757 (1994). https://doi.org/10.1086/174111

  52. M. Lyutikov, L. Sironi, S. Komissarov, O. Porth, Particle acceleration in relativistic magnetic flux-merging events. J. Plasma Phys. 83, 6 (2017). https://doi.org/10.1017/S002237781700071X

  53. K.D. Makwana, R. Keppens, G. Lapenta, Two-way coupling of magnetohydrodynamic simulations with embedded particle-in-cell simulations. Comput. Phys. Commun. 221, 81–94 (2017). https://doi.org/10.1016/j.cpc.2017.08.003

  54. K.D. Makwana, R. Keppens, G. Lapenta, Study of magnetic reconnection in large-scale magnetic island coalescence via spatially coupled MHD and PIC simulations. Phys. Plasmas 25(8), 082904 (2018). https://doi.org/10.1063/1.5037774

  55. P.C.H. Martens, N.P.M. Kuin, A circuit model for filament eruptions and two-ribbon flares. Sol. Phys. 122, 263–302 (1989). https://doi.org/10.1007/BF00912996

  56. Z.X. Mei, R. Keppens, I.I. Roussev, J. Lin, Magnetic reconnection during eruptive magnetic flux ropes. A&A 604, L7 (2017). https://doi.org/10.1051/0004-6361/201731146

  57. Z.X. Mei, R. Keppens, I.I. Roussev, J. Lin, Parametric study on kink instabilities of twisted magnetic flux ropes in the solar atmosphere. A&A 609, A2 (2018). https://doi.org/10.1051/0004-6361/201730395

  58. R.L. Moore, B.J. Labonte, The filament eruption in the 3B flare of July 29, 1973 - Onset and magnetic field configuration. In: M. Dryer, E. Tandberg-Hanssen (eds.) Solar and Interplanetary Dynamics, IAU Symposium, vol. 91, pp. 207–210 (1980)

  59. C.E. Myers, M. Yamada, H. Ji, J. Yoo, W. Fox, J. Jara-Almonte, A. Savcheva, E.E. Deluca, A dynamic magnetic tension force as the cause of failed solar eruptions. Nature 528(7583), 526–529 (2015). https://doi.org/10.1038/nature16188

  60. S. Parenti, Solar prominences: observations. Living Rev. Sol. Phys. 11, 1 (2014). https://doi.org/10.12942/lrsp-2014-1

  61. H.E. Petschek, Magnetic field annihilation. 50, 425 (1964)

  62. R.F. Pinto, M. Gordovskyy, P.K. Browning, N. Vilmer, Thermal and non-thermal emission from reconnecting twisted coronal loops. A&A 585, A159 (2016). https://doi.org/10.1051/0004-6361/201526633

  63. O. Porth, C. Xia, T. Hendrix, S.P. Moschou, R. Keppens, MPI-AMRVAC for solar and astrophysics. ApJ Suppl. Ser. 214, 4 (2014). https://doi.org/10.1088/0067-0049/214/1/4

  64. R.L. Richard, R.D. Sydora, M. Ashour-Abdalla, Magnetic reconnection driven by current repulsion. Phys. Fluids B 2, 488–494 (1990). https://doi.org/10.1063/1.859338

  65. B. Ripperda, O. Porth, C. Xia, R. Keppens, Reconnection and particle acceleration in interacting flux ropes. I. Magnetohydrodynamics and test particles in 2.5D. MNRAS 467, 3279–3298 (2017). https://doi.org/10.1093/mnras/stx379

  66. B. Ripperda, O. Porth, C. Xia, R. Keppens, Reconnection and particle acceleration in interacting flux ropes. II. 3D effects on test particles in magnetically dominated plasmas. MNRAS 471, 3465–3482 (2017). https://doi.org/10.1093/mnras/stx1875

  67. B. Ripperda, O. Porth, L. Sironi, R. Keppens, Relativistic resistive magnetohydrodynamic reconnection and plasmoid formation in merging flux tubes. MNRAS 485, 299–314 (2019). https://doi.org/10.1093/mnras/stz387

  68. V.D. Shafranov, The stability of a cylindrical gaseous conductor in a magnetic field. Sov. J. Atomic Energy 1, 709 (1956). https://doi.org/10.1077/BF01480907

  69. V.D. Shafranov, Plasma equilibrium in a magnetic field. Rev. Plasma Phys. 2, 103 (1966)

  70. K. Shibata, T. Magara, Solar flares: magnetohydrodynamic processes. Living Rev. Sol. Phys. 8(1), 6 (2011). https://doi.org/10.12942/lrsp-2011-6

  71. B. Snow, G.J.J. Botha, S. Régnier, R.J. Morton, E. Verwichte, P.R. Young, Observational signatures of a kink-unstable coronal flux rope using hinode/EIS. ApJ 842(1), 16 (2017). https://doi.org/10.3847/1538-4357/aa6d0e

  72. A.K. Srivastava, T.V. Zaqarashvili, P. Kumar, M.L. Khodachenko, Observation of kink instability during small B5.0 solar flare on 2007 June 4. ApJ 715(1), 292–299 (2010). https://doi.org/10.1088/0004-637X/715/1/292

  73. P.A. Sturrock, Model of the high-energy phase of solar flares. Nature 211(5050), 695–697 (1966). https://doi.org/10.1038/211695a0

  74. Y. Su, R. Liu, S. Li, W. Cao, K. Ahn, H. Ji, High-resolution observations of flares in an arch filament system. ApJ 855(2), 77 (2018). https://doi.org/10.3847/1538-4357/aaac31

  75. B.R. Suydam, Stability of a linear pinch. Proc. Second Int. Conf. Peaceful Uses Atomic Energy 31, 157 (1958)

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

  77. T. Török, B. Kliem, Confined and ejective eruptions of kink-unstable flux ropes. ApJ Lett. 630, L97–L100 (2005). https://doi.org/10.1086/462412

  78. T. Török, R. Chandra, E. Pariat, P. Démoulin, B. Schmieder, G. Aulanier, M.G. Linton, C.H. Mandrini, Filament interaction modeled by flux rope reconnection. ApJ 728, 65 (2011). https://doi.org/10.1088/0004-637X/728/1/65

  79. T. Török, O. Panasenco, V.S. Titov, Z. Mikić, K.K. Reeves, M. Velli, J.A. Linker, G. De Toma, A model for magnetically coupled sympathetic eruptions. ApJ Lett. 739, L63 (2011). https://doi.org/10.1088/2041-8205/739/2/L63

  80. D. Wang, R. Liu, Y. Wang, K. Liu, J. Chen, J. Liu, Z. Zhou, M. Zhang, Critical height of the torus instability in two-ribbon solar flares. ApJL 843, L9 (2017). https://doi.org/10.3847/2041-8213/aa79f0

  81. W. Wang, R. Liu, Y. Wang, Q. Hu, C. Shen, C. Jiang, C. Zhu, Buildup of a highly twisted magnetic flux rope during a solar eruption. Nat. Commun. 8, 1330 (2017). https://doi.org/10.1038/s41467-017-01207-x

  82. D. Wang, R. Liu, Y. Wang, T. Gou, Q. Zhang, Z. Zhou, M. Zhang, Unraveling the links among sympathetic eruptions. ApJ 869, 177 (2018). https://doi.org/10.3847/1538-4357/aaef35

  83. C. Xia, J. Teunissen, I. El Mellah, E. Chané, R. Keppens, MPI-AMRVAC 2.0 for solar and astrophysical applications. ApJ Supplement Series 234(30), (2018). https://doi.org/10.3847/1538-4365/aaa6c8

  84. C. Xia, R. Keppens, Formation and plasma circulation of solar prominences. ApJ 823, 22 (2016). https://doi.org/10.3847/0004-637X/823/1/22

  85. C. Xia, R. Keppens, P. Antolin, O. Porth, Simulating the in situ condensation process of solar prominences. ApJ Lett. 792, L38 (2014). https://doi.org/10.1088/2041-8205/792/2/L38

  86. C. Xia, R. Keppens, Y. Guo, Three-dimensional prominence-hosting magnetic configurations: creating a helical magnetic flux rope. ApJ 780, 130 (2014). https://doi.org/10.1088/0004-637X/780/2/130

  87. Q. Zhang, R. Liu, Y. Wang, C. Shen, K. Liu, J. Liu, S. Wang, A prominence eruption driven by flux feeding from chromospheric fibrils. ApJ 789(2), 133 (2014). https://doi.org/10.1088/0004-637X/789/2/133

  88. X. Zhao, C. Xia, R. Keppens, W. Gan, Formation and initiation of erupting flux rope and embedded filament driven by photospheric converging motion. ApJ 841, 106 (2017). https://doi.org/10.3847/1538-4357/aa7142

  89. X. Zhao, C. Xia, T. Van Doorsselaere, R. Keppens, W. Gan, Forward modeling of SDO/AIA and X-ray emission from a simulated flux rope ejection. ApJ 872, 190 (2019). https://doi.org/10.3847/1538-4357/ab0284

  90. X. Zhou, J. Büchner, M. Bárta, W. Gan, S. Liu, Electron acceleration by cascading reconnection in the solar corona. II. Resistive electric field effects. ApJ 827, 94 (2016). https://doi.org/10.3847/0004-637X/827/2/94

  91. Z. Zhou, X. Cheng, J. Zhang, Y. Wang, D. Wang, L. Liu, B. Zhuang, J. Cui, Why do torus-unstable solar filaments experience failed eruptions? ApJ Lett. 877(2), L28 (2019). https://doi.org/10.3847/2041-8213/ab21cb

  92. C. Zhu, D. Alexander, Eruption of a bifurcated solar filament. Sol. Phys. 289(1), 279–288 (2014). https://doi.org/10.1007/s11207-013-0349-x

  93. C. Zhu, R. Liu, D. Alexander, X. Sun, R.T.J. McAteer, Complex flare dynamics initiated by a filament-filament interaction. ApJ 813(1), 60 (2015). https://doi.org/10.1088/0004-637X/813/1/60

  94. P. Zou, C. Jiang, X. Feng, P. Zuo, Y. Wang, F. Wei, A two-step magnetic reconnection in a confined X-class flare in solar active region 12673. ApJ 870, 97 (2019). https://doi.org/10.3847/1538-4357/aaf3b7

  95. F.P. Zuccarello, G. Aulanier, S.A. Gilchrist, Critical decay index at the onset of solar eruptions. ApJ 814, 126 (2015). https://doi.org/10.1088/0004-637X/814/2/126

Download references


RK thanks Chun Xia at Yunnan University, Kunming; Weiqun Gan at Purple Mountain Observatory, Nanjing; as well as Chen Peng-Fei at Nanjing University, Nanjing, for kind hospitality during his sabbatical stay. RK was supported by a joint FWO-NSFC Grant G0E9619N and by his ERC Advanced Grant PROMINENT. BR was supported by an Alexander von Humboldt Fellowship. YG was supported by NSFC (11773016, 11733003, 11533005 and 11961131002). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 833251 PROMINENT ERC-ADG 2018).

Author information

Correspondence to Rony Keppens.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Keppens, R., Guo, Y., Makwana, K. et al. Ideal MHD instabilities for coronal mass ejections: interacting current channels and particle acceleration. Rev. Mod. Plasma Phys. 3, 14 (2019). https://doi.org/10.1007/s41614-019-0035-z

Download citation


  • MHD instabilities
  • Coronal mass ejections
  • Solar corona