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Tokamak level performance in the optimized stellarator Wendelstein 7-X with stable peaked density profiles

S. Bannmann1,*, O. Ford1, S. A. Bozhenkov1, T. Stange1, R. Lopez-Cansino2, A. Langenberg1, M. Wappl1, J. Brunner1, G. Fuchert1 et al.

T. Gonda1, D. Hartmann1, J. Knauer1, H. Laqua1, P. McNeely1, N. Pablant3, E. Pasch1, P. Poloskei1, K. Rahbarnia1, N. Rust1, F. Warmer1, R. C. Wolf1, and the W7-X Team

  • *Contact author: sebastian.bannmann@ipp.mpg.de

Phys. Rev. E 114, 015201 – Published 1 July, 2026

DOI: https://doi.org/10.1103/q59k-8m26

Abstract

Progress towards achieving net gain from nuclear fusion is typically characterized by the triple product nTτ. Although stellarators have several benefits for a reactor, such as the inherent steady-state capability and the lack of disruptions, the maximum achieved triple product has historically lagged behind that of tokamaks. In the large optimized stellarator Wendelstein 7-X, a triple product of (1.10±0.15)×1020m−3keVs has recently been achieved and held stable for 1.9 s. This marks an important step in stellarator core plasma performance and puts it in line with H-mode performance in similar sized tokamaks. The progress in Wendelstein 7-X performance is due to the suppression of ion-temperature-gradient turbulence by strong density gradients. In the record case, these are maintained by a fine balance of the core particle transport and central fueling using neutral beam injection. The duration of the scenario was limited in time only by technical restrictions of the neutral beam injectors and control of the divertor heat loads. This paper presents the result in the context of the leading magnetic confinement devices along with details of the scenario.

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Corrections

3 August, 2026

Correction: The name F. Warmer was missing from the author list at publication and has been inserted as the 20th author.

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References (79)

  1. J. D. Lawson, Some criteria for a power producing thermonuclear reactor, Proc. Phys. Soc. B 70, 6 (1957).
  2. S. E. Wurzel and S. C. Hsu, Progress toward fusion energy breakeven and gain as measured against the Lawson criterion, Phys. Plasmas 29, 062103 (2022).
  3. JET Team, Fusion energy production from a deuterium-tritium plasma in the JET tokamak, Nucl. Fusion 32, 187 (1992).
  4. M. Greenwald, Density limits in toroidal plasmas, Plasma Phys. Controlled Fusion 44, R27 (2002).
  5. P. Helander, C. D. Beidler, T. M. Bird, M. Drevlak, Y. Feng, R. Hatzky, F. Jenko, R. Kleiber, J. H. E. Proll, Y. Turkin, and P. Xanthopoulos, Stellarator and tokamak plasmas: A comparison, Plasma Phys. Controlled Fusion 54, 124009 (2012).
  6. F. Wagner, Stellarators and optimised stellarators, Fusion Technol. 33, 67 (1998).
  7. H. Maassberg, R. Brakel, R. Burhenn, U. Gasparino, P. Grigull, M. Kick, G. Kuhner, H. Ringler, F. Sardei, U. Stroth, and A. Weller, Transport in stellarators, Plasma Phys. Controlled Fusion 35, B319 (1993).
  8. G. Grieger and I. Milch, Das Fusionsexperiment WENDELSTEIN 7-X, Phys. Bl. 49, 1001 (1993).
  9. R. Wolf, T. Andreeva, S. Bozhenkov, C. Brandt, R. Burhenn, B. Buttenschön, G. Fuchert, B. Geiger, O. Grulke, H. Laqua, N. Pablant, K. Rahbarnia, T. Stange, A. von Stechow, N. Tamura, H. Thomsen, Y. Turkin, T. Wegner, I. Abramovic, S. Äkäslompolo, et al., Major results from the first plasma campaign of the Wendelstein 7-X stellarator, Nucl. Fusion 57, 102020 (2017).
  10. T. Klinger, A. Alonso, S. Bozhenkov, R. Burhenn, A. Dinklage, G. Fuchert, J. Geiger, O. Grulke, A. Langenberg, M. Hirsch, G. Kocsis, J. Knauer, A. Krämer-Flecken, H. Laqua, S. Lazerson, M. Landreman, H. Maaßberg, S. Marsen, M. Otte, N. Pablant, et al., Performance and properties of the first plasmas of Wendelstein 7-X, Plasma Phys. Controlled Fusion 59, 014018 (2017).
  11. C. Beidler, G. Grieger, F. Herrnegger, E. Harmeyer, J. Kisslinger, W. Lotz, H. Maassberg, P. Merkel, J. Nuehrenberg, F. Rau, J. Sapper, F. Sardei, R. Scardovelli, A. Schlueter, and H. Wobig, Physics and engineering design for Wendelstein VII-X, Fusion Technol. 17, 148 (1990).
  12. C. D. Beidler, H. M. Smith, A. Alonso, T. Andreeva, J. Baldzuhn, M. N. A. Beurskens, M. Borchardt, S. A. Bozhenkov, K. J. Brunner, H. Damm, M. Drevlak, O. P. Ford, G. Fuchert, J. Geiger, P. Helander, U. Hergenhahn, M. Hirsch, U. Höfel, Y. O. Kazakov, R. Kleiber, et al., Demonstration of reduced neoclassical energy transport in Wendelstein 7-X, Nature (London) 596, 221 (2021).
  13. M. Beurskens, S. Bozhenkov, O. Ford, P. Xanthopoulos, A. Zocco, Y. Turkin, A. Alonso, C. Beidler, I. Calvo, D. Carralero, T. Estrada, G. Fuchert, O. Grulke, M. Hirsch, K. Ida, M. Jakubowski, C. Killer, M. Krychowiak, S. Kwak, S. Lazerson, et al., Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas, Nucl. Fusion 61, 116072 (2021).
  14. M. Beurskens, C. Angioni, S. A. Bozhenkov, O. Ford, C. Kiefer, P. Xanthopoulos, Y. Turkin, J. Alcusón, J. Baehner, C. Beidler, G. Birkenmeier, E. Fable, G. Fuchert, B. Geiger, O. Grulke, M. Hirsch, M. Jakubowski, H. Laqua, A. Langenberg, S. Lazerson, et al., Confinement in electron heated plasmas in Wendelstein 7-X and ASDEX upgrade; the necessity to control turbulent transport, Nucl. Fusion 62, 016015 (2022).
  15. W. Horton, Turbulent Transport in Magnetized Plasmas (World Scientific, Singapore, 2012).
  16. P. Xanthopoulos et al., Turbulence mechanisms of enhanced performance stellarator plasmas, Phys. Rev. Lett. 125, 075001 (2020).
  17. J. H. E. Proll, P. Helander, J. W. Connor, and G. G. Plunk, Resilience of quasi-isodynamic stellarators against trapped-particle instabilities, Phys. Rev. Lett. 108, 245002 (2012).
  18. G. G. Plunk, P. Xanthopoulos, G. M. Weir, S. A. Bozhenkov, A. Dinklage, G. Fuchert, J. Geiger, M. Hirsch, U. Hoefel, M. Jakubowski, A. Langenberg, N. Pablant, E. Pasch, T. Stange, D. Zhang, and the W7-X Team, Stellarators resist turbulent transport on the electron Larmor scale, Phys. Rev. Lett. 122, 035002 (2019).
  19. J. A. Alcusón, P. Xanthopoulos, G. G. Plunk, P. Helander, F. Wilms, Y. Turkin, A. von Stechow, and O. Grulke, Suppression of electrostatic micro-instabilities in maximum-J stellarators, Plasma Phys. Controlled Fusion 62, 035005 (2020).
  20. S. Bozhenkov, Y. Kazakov, O. Ford, M. Beurskens, J. Alcusón, J. Alonso, J. Baldzuhn, C. Brandt, K. Brunner, H. Damm, G. Fuchert, J. Geiger, O. Grulke, M. Hirsch, U. Höfel, Z. Huang, J. Knauer, M. Krychowiak, A. Langenberg, H. Laqua, et al., High-performance plasmas after pellet injections in Wendelstein 7-X, Nucl. Fusion 60, 066011 (2020).
  21. T. Klinger, T. Andreeva, S. Bozhenkov, C. Brandt, R. Burhenn, B. Buttenschön, G. Fuchert, B. Geiger, O. Grulke, H. Laqua, N. Pablant, K. Rahbarnia, T. Stange, A. von Stechow, N. Tamura, H. Thomsen, Y. Turkin, T. Wegner, I. Abramovic, S. Äkäslompolo, et al., Overview of first Wendelstein 7-X high-performance operation, Nucl. Fusion 59, 112004 (2019).
  22. J. Baldzuhn et al., Enhanced energy confinement after series of pellets in Wendelstein 7-X, Plasma Phys. Controlled Fusion 62, 055012 (2020).
  23. O. Ford, M. Beurskens, S. Bozhenkov, S. Lazerson, L. Vanó, A. Alonso, J. Baldzuhn, C. Beidler, C. Biedermann, R. Burhenn, G. Fuchert, D. Hartmann, M. Hirsch, A. Langenberg, H. Laqua, P. McNeely, N. Pablant, E. Pasch, F. Reimold, T. Romba, et al., Turbulence-reduced high-performance scenarios in Wendelstein 7-X, Nucl. Fusion 64, 086067 (2024).
  24. P. McNeely, M. Barlak, J. Baldzuhn, S. Bozhenkov, M. Drevlak, G. Gawlik, B. Heinemann, D. Holtum, J. Jagielski, R. Kairys, R. Nocentini, R. Riedl, P. Rong, N. Rust, R. Schroeder, E. Speth, A. Stäbler, A. Turos, and R. Wolf, Current status of the neutral beam heating system of W7-X, Fusion Eng. Des. 88, 1034 (2013).
  25. S. A. Lazerson, O. Ford, S. Äkaslompolö, S. Bozhenkov, C. Slaby, L. Vanó, A. Spanier, P. McNeely, N. Rust, D. Hartmann, P. Poloskei, B. Buttenschön, R. Burhenn, N. Tamura, R. Bussiahn, T. Wegner, M. Drevlak, Y. Turkin, K. Ogawa, J. Knauer, et al., First neutral beam experiments on Wendelstein 7-X, Nucl. Fusion 61, 096008 (2021).
  26. S. A. Lazerson, O. P. Ford, C. Nuehrenberg, S. Äkäslompolo, P. Z. Poloskei, M. Machielsen, P. McNeely, L. Vanó, N. Rust, S. Bozhenkov, T. W. Neelis, J. P. Graves, D. Pfefferlé, A. Spanier, D. Hartmann, N. Marushchenko, Y. Turkin, M. Hirsch, N. Chaudhary, U. Hoefel, et al., Validation of the BEAMS3D neutral beam deposition model on Wendelstein 7-X, Nucl. Fusion 60, 076020 (2020).
  27. H. Thienpondt, J. M. García-Regaña, I. Calvo, J. A. Alonso, J. L. Velasco, A. González-Jerez, M. Barnes, K. Brunner, O. Ford, G. Fuchert, J. Knauer, E. Pasch, L. Vanó, and The Wendelstein 7-X Team, Prevention of core particle depletion in stellarators by turbulence, Phys. Rev. Res. 5, L022053 (2023).
  28. S. Bannmann, O. Ford, U. Hoefel, P. Poloskei, A. Pavone, S. Kwak, J. Svensson, S. Lazerson, P. McNeely, N. Rust, D. Hartmann, E. Pasch, G. Fuchert, R. Wolf, and the W7-X-Team, Fast forward modeling of neutral beam injection and halo formation including full Balmer-α emission prediction at W7-X, J. Instrum. 18, P10029 (2023).
  29. D. Carralero, T. Estrada, E. Maragkoudakis, T. Windisch, J. Alonso, M. Beurskens, S. Bozhenkov, I. Calvo, H. Damm, O. Ford, G. Fuchert, J. García-Regaña, N. Pablant, E. Sánchez, E. Pasch, J. Velasco, and the Wendelstein 7-X team, An experimental characterization of core turbulence regimes in Wendelstein 7-X, Nucl. Fusion 61, 096015 (2021).
  30. A. v. Stechow, O. Grulke, T. Wegner, J. H. E. Proll, J. A. Alcusón, H. M. Smith, J. Baldzuhn, C. D. Beidler, M. N. A. Beurskens, S. A. Bozhenkov, E. Edlund, B. Geiger, Z. Huang, O. P. Ford, G. Fuchert, A. Langenberg, N. Pablant, E. Pasch, M. Porkolab, K. Rahbarnia, et al., Suppression of core turbulence by profile shaping in Wendelstein 7-X, arXiv:2010.02160.
  31. T. Romba, F. Reimold, R. Jaspers, O. Ford, L. Vanó, T. Klinger, and the W7-X Team, Suppression of anomalous impurity transport in NBI-heated W7-X plasmas, Nucl. Fusion 63, 076023 (2023).
  32. T. Romba, F. Reimold, S. Bannmann, T. Bleher, O. Ford, P. Z. Poloskei, and M. Wappl, The suppression of anomalous impurity transport above a critical normalized density gradient scale length in Wendelstein 7-X, Plasma Phys. Controlled Fusion 67, 065016 (2025).
  33. S. A. Bozhenkov, O. P. Ford, M. Wappl, S. Bannmann, T. Romba, V. Perseo, K. Aleynikova, D. Zhang, I. Amri, J.-P. Bäehner, J. Baldzuhn, L. R. Baylor, Y. Boumendjel, C. Brandt, K. J. Brunner, C. Büschel, D. Carralero, A. Dinklage, T. Estrada, G. Fuchert, et al., Routes to high-performance operation in Wendelstein 7-X: turbulence suppression with shaping of the density profile, Plasma Phys. Controlled Fusion 68, 055015 (2026).
  34. J. Lion, J.-C. Anglès, L. Bonauer, A. Bañón Navarro, S. Cadena Ceron, R. Davies, M. Drevlak, N. Foppiani, J. Geiger, A. Goodman, W. Guo, E. Guiraud, F. Hernández, S. Henneberg, R. Herrero, C. Hintze, H. Höchter, J. Jelonnek, F. Jenko, R. Jorge, et al., Stellaris: A high-field quasi-isodynamic stellarator for a prototypical fusion power plant, Fusion Eng. Des. 214, 114868 (2025).
  35. G. G. Plunk, A. G. Goodman, P. Xanthopoulos, P. Costello, H. M. Smith, K. Aleynikova, C. D. Beidler, M. Drevlak, and P. Helander, Enhanced performance in quasi-isodynamic max-J stellarators with a turbulent particle pinch, Phys. Rev. E 113, 045215 (2026).
  36. D. L. C. Agapito Fernando, A. Bañón Navarro, D. Carralero, A. Alonso, A. Di Siena, J. L. Velasco, F. Wilms, G. Merlo, F. Jenko, S. A. Bozhenkov, E. Pasch, G. Fuchert, K. J. Brunner, J. Knauer, A. Langenberg, N. A. Pablant, T. Gonda, O. P. Ford, L. Vanó, T. Windisch, et al., Validation of a comprehensive first-principles-based framework for predicting the performance of future stellarators, Phys. Plasmas 32, 073904 (2025).
  37. H. Cu-Castillo, A. B. Navarro, G. Merlo, F. Reimold, T. Romba, O. Ford, S. Bannmann, L. Vanó, M. Wappl, J. Geiger, A. Zocco, F. Jenko, and W7X-Team, Microtearing turbulence and its role in high-density-gradient plasmas in Wendelstein 7-X, Phys. Rev. Lett. (2026).
  38. X. Litaudon, H.-S. Bosch, T. Morisaki, M. Barbarino, A. Bock, E. Belonohy, S. Brezinsek, J. Bucalossi, S. Coda, R. Daniel, A. Ekedahl, K. Hanada, C. Holcomb, J. Huang, S. Ide, M. Jakubowski, B. V. Kuteev, E. Lerche, T. Luce, P. Maget, et al., Long plasma duration operation analyses with an international multi-machine (tokamaks and stellarators) database, Nucl. Fusion 64, 015001 (2024).
  39. F. Wagner, J. Baldzuhn, R. Brakel, R. Burhenn, V. Erckmann, T. Estrada, P. Grigull, H. J. Hartfuss, G. Herre, M. Hirsch, J. V. Hofmann, R. Jaenicke, A. Rudyj, U. Stroth, and A. Weller, H-mode of W7-AS stellarator, Plasma Phys. Controlled Fusion 36, A61 (1994).
  40. ITER Physics Expert Group on Confinement and Transport, ITER Physics Expert Group on Confinement Modelling and Database, and ITER Physics Basis Editors, Chapter 2: Plasma confinement and transport, Nucl. Fusion 39, 2175 (1999).
  41. A. Bock, E. Fable, R. Fischer, M. Reich, D. Rittich, J. Stober, M. Bernert, A. Burckhart, H. Doerk, M. Dunne, B. Geiger, L. Giannone, V. Igochine, A. Kappatou, R. McDermott, A. Mlynek, T. Odstrčil, G. Tardini, H. Zohm, and The ASDEX upgrade Team, Non-inductive improved H-mode operation at ASDEX upgrade, Nucl. Fusion 57, 126041 (2017).
  42. X. Litaudon, A. Bécoulet, F. Crisanti, R. Wolf, Y. Baranov, E. Barbato, M. Bécoulet, R. Budny, C. Castaldo, R. Cesario, C. Challis, G. Conway, M. D. Baar, P. D. Vries, R. Dux, L. Eriksson, B. Esposito, R. Felton, C. Fourment, D. Frigione, et al., Progress towards steady-state operation and real-time control of internal transport barriers in JET, Nucl. Fusion 43, 565 (2003).
  43. A. M. Garofalo, E. J. Doyle, J. R. Ferron, C. M. Greenfield, R. J. Groebner, A. W. Hyatt, G. L. Jackson, R. J. Jayakumar, J. E. Kinsey, R. J. La Haye, G. R. McKee, M. Murakami, M. Okabayashi, T. H. Osborne, C. C. Petty, P. A. Politzer, H. Reimerdes, J. T. Scoville, W. M. Solomon, H. E. St. John, et al., Access to sustained high-beta with internal transport barrier and negative central magnetic shear in DIII-D, Phys. Plasmas 13, 056110 (2006).
  44. B. Wan, Y. Liang, X. Gong, N. Xiang, G. Xu, Y. Sun, L. Wang, J. Qian, H. Liu, L. Zeng, L. Zhang, X. Zhang, B. Ding, Q. Zang, B. Lyu, A. Garofalo, A. Ekedahl, M. Li, F. Ding, S. Ding, et al., Recent advances in EAST physics experiments in support of steady-state operation for ITER and CFETR, Nucl. Fusion 59, 112003 (2019).
  45. O. Grulke, C. Albert, J. Alcuson Belloso, P. Aleynikov, K. Aleynikova, A. Alonso, G. Anda, T. Andreeva, M. Arvanitou, E. Ascasibar, E. Aymerich, K. Avramidis, J.-P. Bähner, S.-G. Baek, M. Balden, J. Baldzuhn, S. Ballinger, M. Banduch, S. Bannmann, A. Bañón Navarro, et al., Overview of the first Wendelstein 7-X long pulse campaign with fully water-cooled plasma facing components, Nucl. Fusion 64, 112002 (2024).
  46. K. Rahbarnia, H. Thomsen, U. Neuner, J. Schilling, J. Geiger, G. Fuchert, T. Andreeva, M. Endler, D. Hathiramani, T. Bluhm, M. Zilker, B. Carvalho, A. Werner, and Wendelstein 7-X Team, Diamagnetic energy measurement during the first operational phase at the Wendelstein 7-X stellarator, Nucl. Fusion 58, 096010 (2018).
  47. A. Pavone, U. Hergenhahn, M. Krychowiak, U. Hoefel, S. Kwak, J. Svensson, P. Kornejew, V. Winters, R. Koenig, M. Hirsch, K.-J. Brunner, E. Pasch, J. Knauer, G. Fuchert, E. Scott, M. Beurskens, F. Effenberg, D. Zhang, O. Ford, L. Vanó, et al., Measurements of visible bremsstrahlung and automatic Bayesian inference of the effective plasma charge Zeff at W7-X, J. Instrum. 14 (10), C10003.
  48. T. Romba, Validation of the W7-X CXRS for impurity density profiles, Master's thesis, Eindhoven University of Technology, 2021, https://research.tue.nl/en/studentTheses/validation-of-the-w7-x-cxrs-for-impurity-density-profiles.
  49. H. Yamada, J. Harris, A. Dinklage, E. Ascasibar, F. Sano, S. Okamura, J. Talmadge, U. Stroth, A. Kus, S. Murakami, M. Yokoyama, C. Beidler, V. Tribaldos, K. Watanabe, and Y. Suzuki, Characterization of energy confinement in net-current free plasmas using the extended International Stellarator Database, Nucl. Fusion 45, 1684 (2005).
  50. J. Cordey, K. Thomsen, A. Chudnovskiy, O. Kardaun, T. Takizuka, J. Snipes, M. Greenwald, L. Sugiyama, F. Ryter, A. Kus, J. Stober, J. DeBoo, C. Petty, G. Bracco, M. Romanelli, Z. Cui, Y. Liu, D. McDonald, A. Meakins, Y. Miura, et al., Scaling of the energy confinement time with β and collisionality approaching ITER conditions, Nucl. Fusion 45, 1078 (2005).
  51. A. Dinklage, E. Ascasíbar, C. D. Beidler, R. Brakel, J. Geiger, J. H. Harris, A. Kus, S. Murakami, S. Okamura, R. Preuss, F. Sano, U. Stroth, Y. Suzuki, J. Talmadge, V. Tribaldos, K. Y. Watanabe, A. Weller, H. Yamada, and M. Yokoyama, Assessment of global stellarator confinement: Status of the International stellarator confinement database, Fusion Sci. Technol. 51, 1 (2007).
  52. J. Miyazawa, H. Yamada, R. Sakamoto, H. Funaba, K. Y. Watanabe, S. Sakakibara, K. Ida, M. Goto, T. Morisaki, S. Murakami, S. Inagaki, and LHD Experiment Group, Characteristics of the global energy confinement and central pressure in LHD, Fusion Sci. Technol. 58, 29 (2010).
  53. G. Manfredi and M. Ottaviani, Gyro-Bohm scaling of ion thermal transport from global numerical simulations of ion-temperature-gradient-driven turbulence, Phys. Rev. Lett. 79, 4190 (1997).
  54. U. Stroth, G. Fuchert, M. Beurskens, G. Birkenmeier, P. Schneider, E. Scott, K. Brunner, F. Günzkofer, P. Hacker, O. Kardaun, J. Knauer, K. Rahbarnia, D. Zhang, and MST1 team, Stellarator-tokamak energy confinement comparison based on ASDEX upgrade and Wendelstein 7-X hydrogen plasmas, Nucl. Fusion 61, 016003 (2021).
  55. U. Stroth, M. Murakami, R. Dory, H. Yamada, S. Okamura, F. Sano, and T. Obiki, Energy confinement scaling from the International stellarator database, Nucl. Fusion 36, 1063 (1996).
  56. F. Warmer, C. D. Beidler, A. Dinklage, R. Wolf, and The W7-X Team, From W7-X to a HELIAS fusion power plant: Motivation and options for an intermediate-step burning-plasma stellarator, Plasma Phys. Controlled Fusion 58, 074006 (2016).
  57. F. Wagner, S. Bäumel, J. Baldzuhn, N. Basse, R. Brakel, R. Burhenn, A. Dinklage, D. Dorst, H. Ehmler, M. Endler, V. Erckmann, Y. Feng, F. Gadelmeier, J. Geiger, L. Giannone, P. Grigull, H.-J. Hartfuss, D. Hartmann, D. Hildebrandt, M. Hirsch, et al., W7-AS: One step of the Wendelstein stellarator line, Phys. Plasmas 12, 072509 (2005).
  58. U. Stroth, J. Baldzuhn, J. Geiger, T. Geist, L. Giannone, H.-J. Hartfuß, M. Hirsch, R. Jaenicke, M. Kick, J. P. Koponen, G. Kühner, F.-P. Penningsfeld, F. Wagner, and the W7-AS Team, High-confinement NBI discharges in the W7-AS stellarator, Plasma Phys. Controlled Fusion 40, 1551 (1998).
  59. M. Kick, H. Maaßberg, M. Anton, J. Baldzuhn, M. Endler, C. Görner, M. Hirsch, A. Weller, S. Zoletnik, and the W7-AS Team, Electric field and transport in W7-AS, Plasma Phys. Controlled Fusion 41, A549 (1999).
  60. M. Hirsch, J. Baldzuhn, C. Beidler, R. Brakel, R. Burhenn, A. Dinklage, H. Ehmler, M. Endler, V. Erckmann, Y. Feng, J. Geiger, L. Giannone, G. Grieger, P. Grigull, H.-J. Hartfuß, D. Hartmann, R. Jaenicke, R. König, H. P. Laqua, H. Maaßberg, et al., Major results from the stellarator Wendelstein 7-AS, Plasma Phys. Controlled Fusion 50, 053001 (2008).
  61. J. S. Hu, Z. Sun, H. Y. Guo, J. G. Li, B. N. Wan, H. Q. Wang, S. Y. Ding, G. S. Xu, Y. F. Liang, D. K. Mansfield, R. Maingi, X. L. Zou, L. Wang, J. Ren, G. Z. Zuo, L. Zhang, Y. M. Duan, T. H. Shi, L. Q. Hu, and East team, New steady-state quiescent high-confinement plasma in an experimental advanced superconducting tokamak, Phys. Rev. Lett. 114, 055001 (2015).
  62. F. Warmer, C. D. Beidler, A. Dinklage, Y. Turkin, and R. Wolf, Limits of confinement enhancement for stellarators, Fusion Sci. Technol. 68, 727 (2015).
  63. C. Angioni, A. G. Peeters, G. V. Pereverzev, F. Ryter, G. Tardini (ASDEX Upgrade Team), Density peaking, anomalous pinch, and collisionality in tokamak plasmas, Phys. Rev. Lett. 90, 205003 (2003).
  64. C. Angioni, A. Peeters, X. Garbet, A. Manini, F. Ryter, and ASDEX upgrade team, Density response to central electron heating: Theoretical investigations and experimental observations in ASDEX upgrade, Nucl. Fusion 44, 827 (2004).
  65. C. Angioni, E. Fable, M. Greenwald, M. Maslov, A. G. Peeters, H. Takenaga, and H. Weisen, Particle transport in tokamak plasmas, theory and experiment, Plasma Phys. Controlled Fusion 51, 124017 (2009).
  66. X. Wang, S. Mordijck, E. Doyle, T. Rhodes, L. Zeng, G. McKee, M. Austin, O. Meneghini, G. Staebler, and S. Smith, Understanding ECH density pump-out in DIII-D H-mode plasmas, Nucl. Fusion 57, 116046 (2017).
  67. A. Zabolotsky, H. Weisen, and TCV Team, Density profile peaking in the presence of ECRH heating in TCV, Plasma Phys. Controlled Fusion 48, 369 (2006).
  68. F. Effenberg, S. Brezinsek, Y. Feng, R. König, M. Krychowiak, M. Jakubowski, H. Niemann, V. Perseo, O. Schmitz, D. Zhang, T. Barbui, C. Biedermann, R. Burhenn, B. Buttenschön, G. Kocsis, A. Pavone, F. Reimold, T. Szepesi, H. Frerichs, Y. Gao, et al., First demonstration of radiative power exhaust with impurity seeding in the island divertor at Wendelstein 7-X, Nucl. Fusion 59, 106020 (2019).
  69. Y. Gao, J. Geiger, M. W. Jakubowski, A. Pandey, S. Bozhenkov, Y. Feng, M. Endler, J. Baldzuhn, V. Perseo, T. Kremeyer, G. Schlisio, A. Puig Sitjes, M. Otte, D. Naujoks, M. Krychowiak, R. König, D. Zhang, T. Szepesi, G. Kocsis, G. Cseh, et al., Heat and particle exhaust in high-performance plasmas in Wendelstein 7-X, Nucl. Fusion 64, 076060 (2024).
  70. See Supplemental Material http://link.aps.org/supplemental/10.1103/q59k-8m26 for the members of the W7-X Team.
  71. S. Bozhenkov, M. Beurskens, A. D. Molin, G. Fuchert, E. Pasch, M. Stoneking, M. Hirsch, U. Höfel, J. Knauer, J. Svensson, H. T. Mora, and R. Wolf, The Thomson scattering diagnostic at Wendelstein 7-X and its performance in the first operation phase, J. Instrum. 12 (10), P10004.
  72. K. Brunner, T. Akiyama, M. Hirsch, J. Knauer, P. Kornejew, B. Kursinski, H. Laqua, J. Meineke, H. T. Mora, and R. C. Wolf, Real-time dispersion interferometry for density feedback in fusion devices, J. Instrum. 13 (09), P09002.
  73. O. P. Ford, L. Vanó, J. A. Alonso, J. Baldzuhn, M. N. A. Beurskens, C. Biedermann, S. A. Bozhenkov, G. Fuchert, B. Geiger, D. Hartmann, R. J. E. Jaspers, A. Kappatou, A. Langenberg, S. A. Lazerson, R. M. McDermott, P. McNeely, T. W. C. Neelis, N. A. Pablant, E. Pasch, N. Rust, et al., Charge exchange recombination spectroscopy at Wendelstein 7-X, Rev. Sci. Instrum. 91, 023507 (2020).
  74. A. Langenberg et al., Prospects of X-ray imaging spectrometers for impurity transport: Recent results from the stellarator Wendelstein 7-X (invited), Rev. Sci. Instrum. 89, 10G101 (2018).
  75. O. P. Ford, A. Langenberg, T. Romba, P. Poloskei, M. Zanini, S. Bannmann, T. Gonda, K. Ida, R. L. Cansino, N. Pablant, J. de la Riva Villen, C. Swee, M. Yoshinuma, A. Alonso, B. Geiger, V. Perseo, E. Viezzer, and W7-X Team, Visible core spectroscopy at Wendelstein 7-X, Rev. Sci. Instrum. 95, 083526 (2024).
  76. M. Grahl, J. Svensson, A. Werner, T. Andreeva, S. Bozhenkov, M. Drevlak, J. Geiger, M. Krychowiak, and Y. Turkin, Web services for 3D MHD equilibrium data at Wendelstein 7-X, IEEE Trans. Plasma Sci. 46, 1114 (2018).
  77. S. Hirshman, W. van RIJ, and P. Merkel, Three-dimensional free boundary calculations using a spectral Green's function method, Comput. Phys. Commun. 43, 143 (1986).
  78. M. Wappl, S. A. Bozhenkov, T. Andreeva, S. Bannmann, H. M. Smith, R. C. Wolf, and the W7-X Team, Experimental power balance study on turbulent heat transport at Wendelstein 7-X, Plasma Phys. Controlled Fusion 67, 075025 (2025).
  79. T. Andreeva, J. Geiger, A. Dinklage, G. Wurden, H. Thomsen, K. Rahbarnia, J. Schmitt, M. Hirsch, G. Fuchert, C. Nührenberg, A. Alonso, C. Beidler, M. Beurskens, S. Bozhenkov, R. Brakel, C. Brandt, V. Bykov, M. Grahl, O. Grulke, C. Killer, et al., Magnetic configuration scans during divertor operation of Wendelstein 7-X, Nucl. Fusion 62, 026032 (2022).

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