Abstract

The two leading concepts for confining high-temperature fusion plasmas are the tokamak and the stellarator. Tokamaks are rotationally symmetric and use a large plasma current to achieve confinement, whereas stellarators are non-axisymmetric and employ three-dimensionally shaped magnetic field coils to twist the field and confine the plasma. As a result, the magnetic field of a stellarator needs to be carefully designed to minimize the collisional transport arising from poorly confined particle orbits, which would otherwise cause excessive power losses at high plasma temperatures. In addition, this type of transport leads to the appearance of a net toroidal plasma current, the so-called bootstrap current. Here, we analyse results from the first experimental campaign of the Wendelstein 7-X stellarator, showing that its magnetic-field design allows good control of bootstrap currents and collisional transport. The energy confinement time is among the best ever achieved in stellarators, both in absolute figures (τE > 100 ms) and relative to the stellarator confinement scaling. The bootstrap current responds as predicted to changes in the magnetic mirror ratio. These initial experiments confirm several theoretically predicted properties of Wendelstein 7-X plasmas, and already indicate consistency with optimization measures.

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Change history

  • 11 September 2018

    In the version of this Article originally published, and in the associated Publisher Correction, the members of the W7-X Team were not included. All versions of the Article, and the Publisher Correction, have now been amended to include these team members.

  • 03 July 2018

    In the version of this Article originally published, A. Mollén’s affiliation was incorrectly denoted as number 10; it should have been 1. Throughout the Article, some technical problems in typesetting meant that the tilde symbol above b and one instance of a superscript 2 were too high to be visible; see the correction notice for details. Finally, the citation to ref. 35 on page one of the Supplementary Information was incorrect; it should have been to ref. 36. These issues have now been corrected.

References

  1. 1.

    Spitzer, L. The stellarator concept. Phys. Fluids 1, 253–264 (1958).

  2. 2.

    Helander, P. et al. Stellarator and tokamak plasmas: a comparison. Plasma Phys. Contr. Fusion 54, 124009 (2012).

  3. 3.

    Galeev, A. A., Sagdeev, R. Z., Furth, H. P. & Rosenbluth, M. N. Plasma diffusion in a toroidal stellarator. Phys. Rev. Lett. 22, 511–514 (1969).

  4. 4.

    Beidler, C. D. & Hitchon, W. N. G. Ripple transport in helical-axis advanced stellarators: a comparison with classical stellarators/torsatrons. Plasma Phys. Contr. Fusion 36, 317–353 (1995).

  5. 5.

    Yokoyama, M. et al. Core electron-root confinement (CERC) in helical plasmas. Nucl. Fusion 47, 1213–1219 (2007).

  6. 6.

    Galeev, A. A. & Sagdeev, R. Z. in Reviews of Plasma Physics Vol. 7 (ed. Leontovich, M. A.) 257–343 (Consultants Bureau, New York, NY, 1979)

  7. 7.

    Palumbo, D. Some considerations on closed configurations of magnetohydrostatic equilibrium. Nuovo Cim. B X53, 507–511 (1968).

  8. 8.

    Nührenberg, J. Development of quasi-isodynamic stellarators. Plasma Phys. Contr. Fusion 52, 124003 (2010).

  9. 9.

    Nührenberg, J. & Zille, R. Stable stellarators with medium β and aspect ratio. Phys. Lett. A 114, 129–132 (1986).

  10. 10.

    Galeev, A. A. Diffusion-electrical phenomena in a plasma confined in a tokamak machine. Sov. Phys. JETP 32, 752–757 (1971).

  11. 11.

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

  12. 12.

    Zarnstorff, M. C. et al. Bootstrap current in TFTR. Phys. Rev. Lett. 60, 1306–1309 (1988).

  13. 13.

    Murakami, M. et al. Bootstrap-current experiments in a toroidal plasma-confinement device. Phys. Rev. Lett. 66, 707–710 (1991).

  14. 14.

    Helander, P. & Nührenberg, J. Bootstrap current and neoclassical transport in quasi-isodynamic stellarators. Plasma Phys. Contr. Fusion 51, 055004 (2009).

  15. 15.

    Landreman, M. & Catto, P. J. Omnigenity as generalized quasisymmetry. Phys. Plasmas 19, 056103 (2012).

  16. 16.

    Hirsch, M. et al. Major results from the stellarator Wendelstein 7-AS. Plasma Phys. Contr. 50, 053001 (2008).

  17. 17.

    Sunn Pedersen, T. et al. Confirmation of the topology of the Wendelstein 7-X magnetic field to better than 1:100,000. Nat. Commun. 7, 13493 (2016).

  18. 18.

    Bozhenkov, S. A. et al. Effect of error field correction coils on W7-X limiter loads. Nucl. Fusion 57, 126030 (2017).

  19. 19.

    Sunn Pedersen, T. et al. Plans for the first plasma operation of Wendelstein 7-X. Nucl. Fusion 55, 126001 (2015).

  20. 20.

    Klinger, T. et al. Performance and properties of the first plasmas of Wendelstein 7-X. Plasma Phys. Contr. Fusion 59, 014018 (2017).

  21. 21.

    Wolf, R. C. et al. Major results from the first plasma campaign of the Wendelstein 7-X stellarator. Nucl. Fusion 57, 102020 (2017).

  22. 22.

    Sunn Pedersen, T. et al. Key results from the first plasma operation phase and outlook for future performance in Wendelstein 7-X. Phys. Plasmas 24, 055503 (2017).

  23. 23.

    Wolf, R. C. et al. Wendelstein 7-X program—Demonstration of a stellarator option for fusion energy. IEEE Trans. Act. Plasma Sci. 44, 1466–1471 (2016).

  24. 24.

    Wurden, G. A. et al. Limiter observations during W7-X first plasmas. Nucl. Fusion 57, 056036 (2017).

  25. 25.

    Yamada, H. et al. Characterization of energy confinement in net-current free plasmas using the extended International Stellarator Database. Nucl. Fusion 45, 1684–1693 (2005).

  26. 26.

    Stroth, U. et al. Energy confinement scaling from the International Stellarator Database. Nucl. Fusion 36, 1063–1077 (1996).

  27. 27.

    Dinklage, A. et al. Physics model assessment of the energy confinement time scaling in stellarators. Nucl. Fusion 47, 1265–1273 (2007).

  28. 28.

    Hirsch, M. et al. Confinement in Wendelstein 7-X limiter plasmas. Nucl. Fusion 57, 086010 (2017).

  29. 29.

    Doyle, E. J. et al. Chapter 2: Plasma confinement and transport. Nucl. Fusion 47, S18–S127 (2007).

  30. 30.

    Turkin, Yu. et al. Neoclassical transport simulations for stellarators. Phys. Plasmas 18, 022505 (2011).

  31. 31.

    Turkin, Yu, Maaßberg, H., Beidler, C. D., Geiger, J. & Marushchenko, N. Current control by ECCD for W7-X. Fusion Sci. Technol. 50, 387–394 (2006).

  32. 32.

    Bosch, H.-S. et al. Final integration, commissioning and start of the Wendelstein 7-X stellarator operation. Nucl. Fusion 57, 116015 (2017).

  33. 33.

    Marsen, S. et al. First results from protective ECRH diagnostics for Wendelstein 7-X. Nucl. Fusion 57, 086014 (2017).

  34. 34.

    Moseev, D. et al. Inference of the microwave absorption coefficient from stray radiation measurements in Wendelstein 7-X. Nucl. Fusion 57, 036013 (2017).

  35. 35.

    Wauters, T. et al. Wall conditioning by ECRH discharges and He-GDC in the limiter phase of Wendelstein 7-X. Nucl. Fusion 58, 066013 (2018).

  36. 36.

    Beidler, C. D. et al. Benchmarking of the mono-energetic transport coefficients—results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS). Nucl. Fusion 51, 076001 (2011).

  37. 37.

    Beidler, C. et al. Physics and engineering design for Wendelstein VII-X. Fusion Technol. 17, 148–168 (1990).

  38. 38.

    Hirshman, S. P., van Rij, W. I. & Merkel, P. Three-dimensional free boundary calculations using a spectral Green's function method. Comp. Phys. Comm. 43, 143–155 (1986).

  39. 39.

    Bozhenkov, S. A. et al. Service oriented architecture for scientific analysis at W7-X. An example of a field line tracer. Fusion Eng. Des. 88, 2997–3006 (2013).

  40. 40.

    Hirshman, S. P., Shaing, K. C., van Rij, W. I. & Crume, E. C. Jr. Plasma transport coefficients for nonsymmetric toroidal confinement systems. Phys. Fluids 29, 2951–2959 (1986).

  41. 41.

    van Rij, W. I. & Hirshman, S. P. Variational bounds for transport coefficients in three‐dimensional toroidal plasmas. Phys. Fluids B 1, 563–569 (1989).

  42. 42.

    Landreman, M., Smith, H. M., Mollén, A. & Helander, P. Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas. Phys. Plasmas 21, 042503–042503 (2014).

  43. 43.

    Marushchenko, N., Turkin, Yu & Maaßberg, H. Ray-tracing code TRAVIS for ECR heating, EC current drive and ECE diagnostic. Comp. Phys. Comm. 185, 165–176 (2014).

  44. 44.

    Feng, Y., Sardei, F., Kisslinger, J., Grigull, P., Mc Cormick, K. & Reiter, D. 3D edge modeling and island divertor physics. Contrib. Plasma Phys. 44, 57–69 (2004).

  45. 45.

    Effenberg, F. et al. Numerical investigation of plasma edge transport and limiter heat fluxes in Wendelstein 7-X startup plasmas with EMC3-EIRENE. Nucl. Fusion 57, 036021 (2017).

  46. 46.

    Krychowiak, M. et al. Overview of diagnostic performance and results for the first operation phase in Wendelstein 7-X. Rev. Sci. Instrum. 87, 11D304 (2016).

  47. 47.

    Endler, M. et al. Engineering design for the magnetic diagnostics of Wendelstein 7-X. Fusion Eng. Des. 100, 468–494 (2015).

  48. 48.

    Pablant, N. A. et al. Core radial electric field and transport in Wendelstein 7-X plasmas. Phys. Plasmas 25, 022508 (2018).

  49. 49.

    Krämer-Flecken, A. et al. Investigation of turbulence rotation in limiter plasmas at W7-X with a new installed poloidal correlation reflectometry. Nucl. Fusion 57, 066023 (2017).

  50. 50.

    Romé, M., Erckmann, V., Gasparino, U. & Karulin, N. Electron cyclotron resonance heating and current drive in the W7-X stellarator. Plasma Phys. Contr. Fusion 40, 511–530 (1998).

Download references

Acknowledgements

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 under grant agreement 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This work is partially supported by the US Department of Energy under a project agreement with the Max Planck Institute for Plasma Physics.

Author information

Author notes

  1. A full list of authors and affiliations appear at the end of the paper.

Affiliations

  1. Max-Planck-Institut für Plasmaphysik, Greifswald, Germany

    • A. Dinklage
    • , C. D. Beidler
    • , P. Helander
    • , G. Fuchert
    • , H. Maaßberg
    • , K. Rahbarnia
    • , T. Sunn Pedersen
    • , Y. Turkin
    • , R. C. Wolf
    • , T. Andreeva
    • , S. Bozhenkov
    • , B. Buttenschön
    • , Y. Feng
    • , J. Geiger
    • , M. Hirsch
    • , U. Höfel
    • , M. Jakubowski
    • , T. Klinger
    • , J. Knauer
    • , A. Langenberg
    • , H. P. Laqua
    • , N. Marushchenko
    • , A. Mollén
    • , U. Neuner
    • , H. Niemann
    • , E. Pasch
    • , L. Rudischhauser
    • , H. M. Smith
    • , T. Stange
    • , G. Weir
    • , T. Windisch
    • , D. Zhang
    • , S. Äkäslompolo
    • , A. Ali
    • , J.Alcuson Belloso
    • , P. Aleynikov
    • , K. Aleynikova
    • , T. Andreeva
    • , J. Baldzuhn
    • , M. Banduch
    • , C. Beidler
    • , A. Benndorf
    • , M. Beurskens
    • , C. Biedermann
    • , D. Birus
    • , M. Blatzheim
    • , T. Bluhm
    • , D. Böckenhoff
    • , M. Borchardt
    • , H.-S. Bosch
    • , L.-G. Böttger
    • , S. Bozhenkov
    • , R. Brakel
    • , Ch. Brandt
    • , T. Bräuer
    • , H. Braune
    • , K.-J. Brunner
    • , B. Brünner
    • , R. Burhenn
    • , R. Bussiahn
    • , B. Buttenschön
    • , V. Bykov
    • , A. Card
    • , A. Carls
    • , S. Degenkolbe
    • , A. Dinklage
    • , C.P. Dhard
    • , M. Drevlak
    • , P. Drewelow
    • , A. Dudek
    • , P. van Eeten
    • , G. Ehrke
    • , M. Endler
    • , E. Erckmann
    • , N. Fahrenkamp
    • , J.-H. Feist
    • , J. Fellinger
    • , Y. Feng
    • , O. Ford
    • , G. Fuchert
    • , B. Geiger
    • , J. Geiger
    • , D. Gradic
    • , M. Grahl
    • , H. Grote
    • , O. Grulke
    • , P. Hacker
    • , K. Hammond
    • , H.-J. Hartfuß
    • , D. Hartmann
    • , D. Hathiramani
    • , B. Hein
    • , S. Henneberg
    • , P. Helander
    • , C. Hennig
    • , M. Hirsch
    • , U. Höfel
    • , H. Hölbe
    • , A. Hölting
    • , M. Jakubowski
    • , H. Jenzsch
    • , J.-P. Kallmeyer
    • , U. Kamionka
    • , C. Killer
    • , R. Kleiber
    • , T. Klinger
    • , J. Knauer
    • , A. Könies
    • , M. Köppen
    • , R. König
    • , P. Kornejew
    • , R. Krampitz
    • , J. Krom
    • , M. Krychowiak
    • , G. Kühner
    • , S. Kwak
    • , A. Langenberg
    • , H. Laqua
    • , H.P. Laqua
    • , R. Laube
    • , S. Lazerson
    • , L. Lewerentz
    • , J.-F. Lobsien
    • , J.Loizu Cisquella
    • , A. Lorenz
    • , H. Maaßberg
    • , S. Marsen
    • , M. Marushchenko
    • , P. McNeely
    • , O. Mishchenko
    • , B. Missal
    • , A. Mollen
    • , T. Mönnich
    • , D. Moseev
    • , M. Nagel
    • , D. Naujoks
    • , U. Neuner
    • , H. Niemann
    • , C. Nührenberg
    • , J. Nührenberg
    • , J.W. Oosterbeek
    • , M. Otte
    • , N. Panadero
    • , E. Pasch
    • , A. Pavone
    • , V. Perseo
    • , D. Pilopp
    • , S. Pingel
    • , G. Plunk
    • , A.Puig Sitjes
    • , F. Purps
    • , K. Rahbarnia
    • , J. Riemann
    • , K. Riße
    • , A. Rodatos
    • , P. Rong
    • , L. Rudischhauser
    • , K. Rummel
    • , T. Rummel
    • , A. Runov
    • , N. Rust
    • , J. Schacht
    • , F. Schauer
    • , G. Schlisio
    • , M. Schneider
    • , W. Schneider
    • , M. Schröder
    • , T. Schröder
    • , R. Schroeder
    • , B. Shanahan
    • , P. Sinha
    • , C. Slaby
    • , H. Smith
    • , A. Spring
    • , T. Stange
    • , U. Stridde
    • , T.Sunn Pedersen
    • , J. Svensson
    • , H. Thomsen
    • , H.Trimino Mora
    • , Y. Turkin
    • , I. Vakulchyk
    • , S. Valet
    • , H. Viebke
    • , R. Vilbrandt
    • , F. Warmer
    • , L. Wegener
    • , T. Wegner
    • , G. Weir
    • , J. Wendorf
    • , U. Wenzel
    • , F. Wilde
    • , T. Windisch
    • , E. Winkler
    • , R. Wolf
    • , P. Xanthopoulos
    • , D. Zhang
    • , J. Zhu
    •  & A. Zocco
  2. E.-M.-Arndt Universität Greifswald, Greifswald, Germany

    • A. Dinklage
    • , P. Helander
    • , T. Sunn Pedersen
    •  & T. Klinger
  3. Technische Universität Berlin, Berlin, Germany

    • R. C. Wolf
    •  & F. Köster
  4. CIEMAT, Madrid, Spain

    • A. Alonso
    • , A. Alonso
    • , E. Ascasibar
    • , E. Blanco
    • , I. Calvo
    • , A. Cappa
    • , F. Castejon
    • , A. de la Pena
    • , H. Esteban
    • , T. Estrada
    • , J. Fontdecaba
    • , J.García Regaña
    • , M. Garcia-Munoz
    • , C. Guerard
    • , J.Hernandez Sanchez
    • , C. Hidalgo
    • , K. McCarthy
    • , L.Pacios Rodriguez
    • , N.Panadero Alvarez
    • , M. Sanchez
    • , B. van Milligen
    •  & J.-L. Velasco
  5. Australian National University, Canberra, Australia

    • B. Blackwell
    • , B. Blackwell
    • , J. Howard
    •  & A. Wright
  6. IPPLM, Warsaw, Poland

    • A. Czarnecka
    • , M. Kubkowska
    • , A. Czarnecka
    • , W. Figacz
    • , T. Fornal
    • , A. Galkowski
    • , M. Gruca
    • , S. Jablonski
    • , J. Kacmarczyk
    • , N. Krawczyk
    • , M. Kubkowska
    • , G. Pelka
    • , L. Ryc
    • , M. Scholz
    •  & J. Wolowski
  7. University of Wisconsin-Madison, Madison, WI, USA

    • F. Effenberg
    • , O. Schmitz
    • , T. Barbui
    • , F. Effenberg
    • , H. Frerichs
    • , J. Green
    • , T. Kremeyer
    • , O. Schmitz
    • , L. Stephey
    •  & V. Winters
  8. Wigner RCP, Budapest, Hungary

    • G. Kocsis
    • , T. Szepesi
    • , G. Anda
    • , G. Cseh
    • , T. Ilkei
    • , G. Kocsis
    • , G. Náfrádi
    • , S. Récsei
    • , V. Szabó
    • , T. Szabolics
    • , T. Szepesi
    • , Z. Szökefalvi-Nagy
    • , S. Tulipán
    •  & S. Zoletnik
  9. FZ-Jülich, Jülich, Germany

    • A. Krämer-Flecken
    • , J. Assmann
    • , W. Behr
    • , O. Bertuch
    • , W. Biel
    • , V. Borsuk
    • , S. Brezinsek
    • , Y. Cai
    • , A. Charl
    • , G. Czymek
    • , P. Denner
    • , T. Dittmar
    • , M. Dostal
    • , Ph. Drews
    • , A. Freund
    • , Y. Gao
    • , N. Gierse
    • , X. Han
    • , F. Harberts
    • , K.P. Hollfeld
    • , D. Höschen
    • , M. Knaup
    • , A. Knieps
    • , R. Koslowski
    • , A. Krämer-Flecken
    • , Th. Krings
    • , M. Lennartz
    • , Y. Liang
    • , Ch. Linsmeier
    • , S. Liu
    • , O. Marchuk
    • , Ph. Mertens
    • , O. Neubauer
    • , G. Offermanns
    • , A. Panin
    • , M. Rack
    • , D. Reiter
    • , G. Satheeswaran
    • , H. Schmitz
    • , B. Schweer
    • , A. Terra
    • , J. Thomas
    • , B. Unterberg
    • , M. Vervier
    • , E. Wang
    • , N. Wang
    •  & Y. Wei
  10. Princeton Plasma Physics Laboratory, Princeton, NJ, USA

    • N. Pablant
    • , P. Bolgert
    • , D. Gates
    • , P. Heitzenroeder
    • , B. Israeli
    • , S. Langish
    • , D. Loesser
    • , M. Mardenfeld
    • , D. Mikkelsen
    • , J. Mittelstaedt
    • , H. Neilson
    • , N. Pablant
    • , A. Reiman
    • , M. Sibilia
    • , P. Titus
    • , M. Zarnstorff
    •  & H. Zhang
  11. LANL, Los Alamos, NM, USA

    • G. A. Wurden
    •  & G. Wurden
  12. University of Maryland, College Park, MA, USA

    • M. Landreman
  13. Laboratory for Plasma Physics of the Ecole Royale Militaire/Koninklijke Militaire School (LPP-ERM/KMS), Bruxelles, Belgium

    • F. Durodie
    • , A. Goriaev
    • , Y. Kazakov
    • , J. Ongena
    • , M. Vergote
    •  & T. Wauters
  14. Lithuanian Energy Institute, Kaunas, Lithuania

    • R. Alzbutas
    • , G. Dundulis
    • , T. Kaliatka
    • , R. Karalevicius
    • , M. Povilaitis
    • , S. Rimkevicius
    •  & E. Urbonavicius
  15. Massachusetts Institute of Technology, Cambridge, MA, USA

    • S.-G. Baek
    • , J. Maisano-Brown
    •  & J. Terry
  16. National Centre for Nuclear Reserach Świerk, Narodowe Centrum Badań Jądrowych, Świerk, Poland

    • M. Barlak
    • , G. Gawlik
    • , J. Jagielski
    • , R. Koziol
    •  & P. Kraszewsk
  17. Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany

    • K. Baumann
    • , G. Dammertz
    • , W.H. Fietz
    • , G. Gantenbein
    • , M. Huber
    • , H. Hunger
    • , S. Illy
    • , J. Jelonnek
    • , Th. Kobarg
    • , R. Lang
    • , W. Leonhardt
    • , M. Losert
    • , A. Meier
    • , D. Mellein
    • , D. Papenfuß
    • , A. Samartsev
    • , T. Scherer
    • , A. Schlaich
    • , W. Spiess
    • , M. Thumm
    • , S. Wadle
    •  & J. Weggen
  18. Max-Planck-Institut für Plasmaphysik, Garching bei München, Germany

    • J. Boscary
    • , M. Czerwinski
    • , B. Heinemann
    • , P. Junghans
    • , B. Mendelevitch
    • , R. Nocentini
    • , S. Obermayer
    • , G. Orozco
    • , R. Riedl
    • , P. Scholz
    • , R. Stadler
    • , B. Standley
    • , J. Tretter
    • , A. Vorkörper
    •  & M. Zilker
  19. Eindhoven University of Technology, Eindhoven, Netherlands

    • I. Abramovic
    • , H. Brand
    • , S. Paqay
    •  & J. Proll
  20. University of Cagliary, Cagliari, Italy

    • B. Cannas
    •  & F. Pisano
  21. Consorzio RFX, Padova, Italy

    • L. Carraro
    •  & M. Zuin
  22. Instituto de Plasmas e Fusao Nuclear, Lisboa, Portugal

    • B. Carvalho
    • , A. da Silva
    • , H. Fernandes
    •  & B. Goncalves
  23. Ioffe Physical-Technical Institute of the Russian Academy of Sciences, St Petersburg, Russia

    • F. Chernyshev
  24. Oak Ridge National Laboratory, Oak Ridge, TN, USA

    • M. Cianciosa
    • , M.J. Cole
    • , J.H. Harris
    • , J. Lore
    • , A. Lumsdaine
    •  & D.A. Spong
  25. University of Salerno, Fisciano, Italy

    • R. Citarella
    •  & V. Giannella
  26. Warsaw University of Technology, Warszawa, Poland

    • Ł. Ciupiński
    • , G. Krzesinski
    •  & P. Marek
  27. ENEA—Centro Ricerche Frascati, Frascati, Italy

    • G. Claps
    •  & F. Cordella
  28. Institute of Nuclear Physics PAN, Kraków, Poland

    • A. Czermak
    • , L. Haiduk
    •  & Z. Sulek
  29. University of Szczecin, Szczecin, Poland

    • K. Czerski
  30. University of Milano-Bicocca, Milano, Italy

    • A. da Molin
  31. Auburn University, Auburn, AL, USA

    • D. Ennis
    • , D. Maurer
    • , J. Schmitt
    •  & P. Traverso
  32. Brandenburg University of Technology Cottbus-Senftenberg, Senftenberg, Germany

    • M. Führer
  33. National Institute for Fusion Science, Toki, Japan

    • T. Funaba
    • , X. Huang
    • , K. Ida
    • , H. Kasahara
    • , N. Kenmochi
    • , S. Masuzaki
    • , T. Morisaki
    • , K. Ogawa
    • , B. Peterson
    • , S. Ryosuke
    • , R. Sakamoto
    • , S. Satake
    • , Y. Suzuki
    • , N. Tamura
    • , K. Toi
    • , H. Tsuchiya
    • , T. Tsujimura
    • , H. Yamada
    • , I. Yamada
    • , R. Yasuhara
    •  & M. Yokoyama
  34. Universidad Carlos III de Madrid, Madrid, Spain

    • A. Gogoleva
    •  & L. Vela
  35. CEA Cadarache, Saint-Paul-lez-Durance, France

    • A. Grosman
    • , M. Houry
    • , V. Moncada
    • , T. Ngo
    • , S. Renard
    •  & J.M. Travere
  36. Culham Centre for Fusion Energy, Abingdon, United Kingdom

    • V. Huber
    • , D. Kinna
    • , S. Schmuck
    • , C.P. von Thun
    •  & M. Turnyanskiy
  37. Budker Institute of Nuclear Physics, Novosibirsk, Russia

    • A. Ivanov
    • , A. Khilchenko
    •  & I.V. Shikhovtsev
  38. University Stuttgart, Institut für Grenzflächenverfahrenstechnik und Plasmatechnologie, Stuttgart, Germany

    • W. Kasparek
    • , M. Krämer
    • , C. Lechte
    • , R. Munk
    • , B. Plaum
    • , F. Remppel
    • , H. Röhlinger
    • , B. Roth
    • , K.-H. Schlüter
    • , S. Wolf
    •  & A. Zeitler
  39. Fraunhofer-Institut für Schicht- und Oberflächentechnik IST, Braunschweig, Germany

    • M. Keunecke
  40. Austrian Academy of Science, Wien, Austria

    • F. Köchl
  41. Institute for Nuclear Research, Kiev, Ukraine

    • Y. Kolesnichenko
    •  & V. Lutsenko
  42. Institute of Applied Physics of the Russian Academy of Science, Nizhny Novgorod, Russia

    • J. Koshurinov
    •  & L. Lubyako
  43. University of Opole, Opole, Poland

    • I. Ksiazek
    • , F. Musielok
    •  & E. Pawelec
  44. Aalto University, Espoo, Finland

    • T. Kurki-Suonio
    •  & S. Sipliä
  45. Physikalisch-Technische Bundesanstalt, Braunschweig, Germany

    • A. Lücke
    • , A. Pieper
    • , H. Schumacher
    • , B. Wiegel
    •  & A. Zimbal
  46. Kyoto University, Kyoto, Japan

    • T. Mizuuchi
    • , S. Murakami
    •  & F. Sano
  47. Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, People’s Republic of China

    • W. Pan
    •  & X. Peng
  48. Institute of Plasma Physics of the Czech Academy of Science, Prague, Czech Republic

    • J. Preinhaelter
    • , J. Urban
    •  & J. Zajac
  49. Instituto di Fisica del Plasma ‘Piero Caldirola’, Milano, Italy

    • M.-E. Puiatti
    •  & M. Romé
  50. Fraunhofer-Institut für Werkzeugmaschinen und Umformtechnik IWU, Chemnitz, Germany

    • H.-J. Roscher
  51. Universität in Rostock, Rostock, Germany

    • J. Skodzik
    •  & D. Timmermann
  52. Lawrence University, Appleton, WI, USA

    • M. Stoneking
  53. Consiglio Nazionale delle Ricerche, Roma, Italy

    • N. Vianello
  54. Univeristät Innsbruck, Innsbruck, Austria

    • R. Schrittwieser

Authors

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Consortia

  1. and the W7-X Team

Contributions

A.D., C.D.B., P.H., T.S.P., R.C.W. and T.K. wrote the paper. A.D., T.S.P., S.B., F.E. and J.G. prepared the configuration changes and the discharge program. A.D., H.M., Y.T., T.A., A.A., C.D.B., F.E., Y.F., J.G., A.M., N.M., H.M.S. and O.S. did modelling and data validation. K.R., B.B., B.B., A.C., G.F., M.H., U.H., M.J., J.K., G.K., A.K.F., M.K., A.L., H.L., U.N., H.N., E.P., N.P., L.R., T.S., T.S., G.W., T.W., G.W. and D.Z. did measurements and data analysis.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to A. Dinklage.

Supplementary information

  1. Supplementary Information

    Supplementary notes, supplementary figures 1–2, supplementary tables 12

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/s41567-018-0141-9

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