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# Filamentary plasma eruptions and their control on the route to fusion energy

## Abstract

The tokamak is the most advanced approach to fusion and is approaching operation under power-plant conditions, promising sustainable, low-emission, baseload power to the grid. As the heating power of a tokamak is increased above a threshold, the plasma suddenly bifurcates to a state of high confinement, creating a region of plasma with a large pressure gradient at its edge. This bifurcation results in a repetitive sequence of explosive filamentary plasma eruptions called edge-localized modes (ELMs). ELMs on next-step tokamaks, such as ITER, will likely cause excessive erosion to plasma-facing components and must be controlled. We present what is understood about how ELMs form, their filamentary nature and the mechanisms that transport heat and particles to the first wall of the tokamak. We also discuss methods to control ELMs, including magnetic perturbations.

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## References

1. Leonard, A. W. Edge-localized-modes in tokamaks. Phys. Plasmas 21, 090501 (2014).

2. JET Team (prepared by Watkins, M. L.). Physics of high performance JET plasmas in DT. Nucl. Fusion 39, 1227–1244 (1999).

3. Dudson, B. D. et al. Experiments and simulation of edge turbulence and filaments in MAST. Plasma Phys. Control. Fusion 50, 124012 (2008).

4. Wagner, F. A quarter-century of H-mode studies. Plasma Phys. Control. Fusion 49, B1–B33 (2007).

5. Connor, J. W. Edge-localized modes — physics and theory. Plasma Phys. Control. Fusion 40, 531–542 (1998).

6. Suttrop, W. The physics of large and small edge localized modes. Plasma Phys. Control. Fusion 42, A1–A14 (2000).

7. Loarte, A. et al. Characteristics of type I ELM energy and particle losses in existing devices and their extrapolation to ITER. Plasma Phys. Control. Fusion 45, 1549–1569 (2003).

8. Cowley, S. C., Wilson, H., Hurricane, O. & Fong, B. Explosive instabilities: from solar flares to edge localized modes in tokamaks. Plasma Phys. Control. Fusion 45, A31–A38 (2003).

9. Kirk, A. et al. Spatial and temporal structure of edge-localized modes. Phys. Rev. Lett. 92, 245002 (2004).

10. Kirk, A. et al. Physics of ELM power fluxes to plasma facing components and implications for ITER. J. Nucl. Mater. 390–391, 727–732 (2009).

11. Yun, G. S. et al. Two-dimensional visualization of growth and burst of the edge-localized filaments in KSTAR H-mode plasmas. Phys. Rev. Lett. 107, 045004 (2011).

12. Freidberg, J. P. Ideal MHD (Cambridge Univ. Press, 2014) ISBN 978-1-107-00625-6.

13. Connor, J. W., Hastie, R. J. & Taylor, J. B. High mode number stability of an axisymmetric toroidal plasma. Proc. R. Soc. Lond. A 365, 1–17 (1979).

14. Wilson, H. R., Cowley, S. C., Kirk, A. & Snyder, P. B. Magneto-hydrodynamic stability of the H-mode transport barrier as a model for edge localized modes: an overview. Plasma Phys. Control. Fusion 48, A71–A84 (2006).

15. Bickerton, R. J., Connor, J. W. & Taylor, J. B. Diffusion driven plasma currents and bootstrap tokamak. Nat. Phys. Sci. 229, 110–112 (1971).

16. Peeters, A. G. The bootstrap current and its consequences. Plasma Phys. Control. Fusion 42, B231–B242 (2000).

17. Hegna, C. C., Connor, J. W., Hastie, R. J. & Wilson, H. R. Toroidal coupling of ideal magnetohydrodynamic instabilities in tokamak plasmas. Phys. Plasmas 3, 584–592 (1996).

18. Connor, J. W., Hastie, R. J. & Wilson, H. R. Magnetohydrodynamic stability of tokamak edge plasmas. Phys. Plasmas 5, 2687–2700 (1998).

19. Snyder, P. B. et al. Edge localized modes and the pedestal: a model based on coupled peeling–ballooning modes. Phys. Plasmas 9, 2037–2043 (2002).

20. Burckhart, A. et al. Inter-ELM behaviour of the electron density and temperature pedestal in ASDEX upgrade. Plasma Phys. Control. Fusion 52, 105010 (2010).

21. Dickinson, D. et al. Kinetic instabilities that limit β in the edge of a tokamak plasma: a picture of an H-mode pedestal. Phys. Rev. Lett. 108, 135002 (2012).

22. Hatch, D. R. et al. Gyrokinetic study of ASDEX upgrade inter-ELM pedestal profile evolution. Nucl. Fusion 55, 063028 (2015).

23. Snyder, P. B. et al. A first-principles predictive model of the pedestal height and width: development, testing and ITER optimization with the EPED model. Nucl. Fusion 51, 103016 (2011).

24. Saarelma, S. et al. Integrated modelling of H-mode pedestal and confinement in JET-ILW. Plasma Phys. Control. Fusion 60, 014042 (2018).

25. Maggi, C. F. et al. Pedestal confinement and stability in JET-ILW ELMy H-modes. Nucl. Fusion 55, 113031 (2015).

26. Bowman, C. et al. Pedestal evolution physics in low triangularity JET tokamak discharges with ITER-like wall. Nucl. Fusion 58, 016021 (2018).

27. Snyder, P. B. et al. Super H-mode: theoretical prediction and initial observations of a new high performance regime for tokamak operation. Nucl. Fusion 55, 083026 (2015).

28. Zohm, H. Edge localized modes (ELMs). Plasma Phys. Control. Fusion 38, 105–128 (1996).

29. Oyama, N. et al. Energy loss for grassy ELMs and effects of plasma rotation on the ELM characteristics in JT-60U. Nucl. Fusion 45, 871–881 (2005).

30. Wilson, H. R. & Cowley, S. C. Theory for explosive ideal magnetohydrodynamic instabilities in plasmas. Phys. Rev. Lett. 92, 175006 (2004).

31. Ham, C. J., Cowley, S. C., Brochard, G. & Wilson, H. R. Nonlinear stability and saturation of ballooning modes in tokamaks. Phys. Rev. Lett. 116, 235001 (2016).

32. Ham, C. J., Cowley, S. C., Brochard, G. & Wilson, H. R. Nonlinear ballooning modes in tokamaks: stability and saturation. Plasma Phys. Control. Fusion. 60, 075017 (2018).

33. Hutchinson, I. H. Principles of Plasma Diagnostics (Cambridge Univ. Press, 2002)

34. Kirk, A. et al. Evolution of the pedestal on MAST and the implications for ELM power loadings. Plasma Phys. Control. Fusion 49, 1259–1275 (2007).

35. Vianello, N. et al. Direct observation of current in Type-I edge-localized-Mode filaments on the ASDEX upgrade tokamak. Phys. Rev. Lett. 106, 125002 (2011).

36. Beurskens, M. N. A. et al. Pedestal and scrape-off layer dynamics in ELMy H-mode plasmas in JET. Nucl. Fusion 49, 125006 (2009).

37. Eich, T. et al. ELM divertor peak energy fluence scaling to ITER with data from JET, MAST and ASDEX upgrade. Nucl. Mater. Energy 12, 84–90 (2017).

38. Becoulet, M. et al. Edge localized mode physics and operational aspects in tokamaks. Plasma Phys. Control. Fusion 45, A93–A113 (2003).

39. Alladio, F., Mancuso, A. & Micozzi, P. Rotating twisted filaments buoyancy: comparison between the convective region of the sun and the edge of a tokamak plasma. Plasma Phys. Control. Fusion 50, 124019 (2008).

40. Evans, T. E. et al. A conceptual model of the magnetic topology and nonlinear dynamics of ELMs. J. Nucl. Mater. 390, 789–792 (2009).

41. Rack, M. et al. Thermoelectric currents and their role during ELM formation in JET. Nucl. Fusion 52, 074012 (2012).

42. Freethy, S. J. et al. Electron kinetics inferred from observations of microwave bursts during edge localized modes in the mega-amp spherical tokamak. Phys. Rev. Lett. 114, 125004 (2015).

43. Galdon-Quiroga, J. et al. Beam-ion acceleration during edge localized modes in the ASDEX upgrade tokamak. Phys. Rev. Lett. 121, 025002 (2018).

44. Galdon-Quiroga, J. et al. Velocity space resolved absolute measurement of fast ion losses induced by a tearing mode in the ASDEX Upgrade tokamak. Nucl. Fusion 58, 036005 (2018).

45. Pamela, S. J. P. et al. Nonlinear MHD simulations of edge-localized-modes in JET. Plasma Phys. Control. Fusion 53, 054014 (2011).

46. Pamela, S. J. P. et al. Recent progress in the quantitative validation of JOREK simulations of ELMs in JET. Nucl. Fusion 57, 076006 (2017).

47. Snyder, P. B. et al. Pedestal stability comparison and ITER pedestal prediction. Nucl. Fusion 49, 085035 (2009).

48. Bécoulet, M. et al. Non-linear MHD modelling of edge localized modes dynamics in KSTAR. Nucl. Fusion 57, 116059 (2017).

49. Huysmans, G. T. A. & Czarny, O. MHD stability in X-point geometry: simulation of ELMs. Nucl. Fusion 47, 659–666 (2007).

50. Ebrahimi, F. Nonlinear reconnecting edge localized modes in current-carrying plasmas. Phys. Plasmas 24, 056119 (2017).

51. Kirk, A. et al. Evolution of filament structures during edge-localized modes in the MAST tokamak. Phys. Rev. Lett. 96, 185001 (2006).

52. Mink, A. F. et al. Nonlinear coupling induced toroidal structure of edge localized modes. Nucl. Fusion 58, 026011 (2018).

53. Pamela, S. J. P. et al. Non-linear MHD simulations of ELMs in JET and quantitative comparisons to experiments. Plasma Phys. Control. Fusion 58, 014026 (2016).

54. Kirk, A. et al. Recent progress in understanding the processes underlying the triggering of and energy loss associated with type I ELMs. Nucl. Fusion 54, 114012 (2014).

55. Huysmans, G. T. A., Pamela, S. J. P., van der Plas, E. & Ramet, P. Non-linear MHD simulations of edge localized modes (ELMs). Plasma Phys. Control. Fusion 51, 124012 (2009).

56. Henneberg, S. A., Cowley, S. C. & Wilson, H. R. Explosive ballooning mode instability in tokamaks: modelling the ELM cycle. 41st EPS Conference, Berlin, Germany P1.066 (2014).

57. Henneberg, S. A., Cowley, S. C. & Wilson, H. R. Interacting filamentary eruptions in magnetised plasmas. Plasma Phys. Control. Fusion 57, 125010 (2015).

58. Brodrick, J. P. et al. Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications. Phys. Plasmas 24, 092309 (2017).

59. Snyder, P. B. et al. ELMs and constraints on the H-mode pedestal: peeling–ballooning stability calculation and comparison with experiment. Nucl. Fusion 44, 320–328 (2004).

60. Herrmann, A. Overview on stationary and transient divertor heat loads. Plasma Phys. Control. Fusion 44, 883–903 (2002).

61. Lang, P. et al. ELM pace making and mitigation by pellet injection in ASDEX Upgrade. Nucl. Fusion 44, 665–677 (2004).

62. Baylor, L. R. et al. Reduction of edge-localized mode intensity using high-repetition-rate pellet injection in tokamak H-mode plasmas. Phys. Rev. Lett. 110, 245001 (2013).

63. Futatani, S. et al. Non-linear MHD modelling of ELM triggering by pellet injection in DIII-D and implications for ITER. Nucl. Fusion 54, 073008 (2014).

64. Lang, P. T. et al. ELM control strategies and tools: status and potential for ITER. Nucl. Fusion 53, 043004 (2013).

65. Degeling, A. W. et al. Magnetic triggering of ELMs in TCV. Plasma Phys. Control. Fusion 45, 1637 (2003).

66. Lang, P. T. et al. Frequency control of type-I ELMs by magnetic triggering in ASDEX Upgrade. Plasma Phys. Control. Fusion 46, L31–L39 (2004).

67. de La Luna, E. et al. Understanding the physics of ELM pacing via vertical kicks in JET in view of ITER. Nucl. Fusion 56, 026001 (2015).

68. Gerhardt, S. P. et al. First observation of ELM pacing with vertical jogs in a spherical torus. Nucl. Fusion 50, 064015 (2010).

69. Jayhyun Kim et al. ELM control experiments in the KSTAR device. Nucl. Fusion 52, 114011 (2012).

70. Garzotti, L. et al. Investigating pellet ELM triggering physics using the new small size pellet launcher at JET. 37th EPS Conference, Dublin, Ireland P2.131 (2010).

71. Jakubowski, M. et al. Overview of the results on divertor heat loads in RMP controlled H-mode plasmas on DIII-D. Nucl. Fusion 49, 095013 (2009).

72. Viezzer, E. Access and sustainment of naturally ELM-free and small-ELM regimes. Nucl. Fusion 58, 115002 (2018).

73. Evans, T. E. et al. Suppression of large edge-localized modes in high-confinement DIII-D plasmas with a stochastic magnetic boundary. Phys. Rev. Lett. 92, 235003 (2004).

74. Suttrop, W. et al. Experimental conditions to suppress edge localised modes by magnetic perturbations in the ASDEX Upgrade tokamak. Nucl. Fusion 58, 096031 (2018).

75. Jeon, Y. M. et al. Suppression of edge localized modes in high-confinement KSTAR plasmas by nonaxisymmetric magnetic perturbations. Phys. Rev. Lett. 109, 035004 (2012).

76. Sun, Y. et al. Nonlinear transition from mitigation to suppression of the edge localized mode with resonant magnetic perturbations in the EAST tokamak. Phys. Rev. Lett. 117, 115001 (2016).

77. Liu, Y. et al. Modelling of plasma response to resonant magnetic perturbation fields in MAST and ITER. Nucl. Fusion 51, 083002 (2011).

78. Wade, M. R. et al. Advances in the physics understanding of ELM suppression using resonant magnetic perturbations in DIII-D. Nucl. Fusion 55, 023002 (2015).

79. Paz-Soldan, C. et al. The effect of plasma shape and neutral beam mix on the rotation threshold for RMP-ELM suppression. Nucl. Fusion 59, 056012 (2019).

80. Willensdorfer, M. et al. Field-line localized destabilization of ballooning modes in three-dimensional tokamaks. Phys. Rev. Lett. 119, 085002 (2017).

81. Federici, G., Loarte, A. & Strohmayer, G. Assessment of erosion of the ITER divertor targets during type I ELMs. Plasma Phys. Control. Fusion. 45, 1523 (2003).

82. Pankin, A. Y. et al. Modelling of ELM dynamics for DIII-D and ITER. Plasma Phys. Control. Fusion 49, S63–S75 (2007).

83. Dudson, B. D. et al. Simulation of edge localized modes using BOUT++. Plasma Phys. Control. Fusion 53, 054005 (2011).

84. Whyte, D. G. et al. I-mode: an H-mode energy confinement regime with L-mode particle transport in Alcator C-Mod. Nucl. Fusion 50, 105005 (2010).

85. Burrell, K. H. et al. Discovery of stationary operation of quiescent H-mode plasmas with net-zero neutral beam injection torque and high energy confinement on DIII-D. Phys. Plasmas 23, 056103 (2016).

86. Kamada, K. et al. Pedestal characteristics and extended high-βp ELMy H-mode regime in JT-60U. Plasma Phys. Control. Fusion 44, A279–A286 (2002).

87. Kirk, A. Nuclear fusion: bringing a star down to Earth. Contemp. Phys. 57, 1–18 (2016).

88. Pamela, S. et al. Resistive MHD simulation of edge-localized modes for double-null discharges in the MAST device. Plasma Phys. Control. Fusion 55, 095001 (2013).

## Acknowledgements

The authors gratefully acknowledge the comments on this manuscript given by Samuli Saarelma, William Morris and Jack Connor. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement no. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This work has been part-funded by the RCUK Energy Programme (grant number EP/P012450/1). To obtain further information on the data and models underlying this paper, please contact PublicationsManager@ukaea.uk. Simulations published in this review have benefited from the support of EUROfusion on the Marconi HPC cluster (CINECA, Italy), as well as the support of PRACE on the MareNostrum HPC cluster (BSC, Spain).

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Correspondence to Christopher Ham.

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Nature Reviews Physics thanks F. Jenko and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Ham, C., Kirk, A., Pamela, S. et al. Filamentary plasma eruptions and their control on the route to fusion energy. Nat Rev Phys 2, 159–167 (2020). https://doi.org/10.1038/s42254-019-0144-1

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• DOI: https://doi.org/10.1038/s42254-019-0144-1