Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Stable Small Plasmas at the Density Limit in the W7-X Stellarator

A. Pandey1,*, T. S. Pedersen2, G. Fuchert1, T. Szepesi3,4, D. Zhang1, T. Stange1, A. Buzas3,4, T. Romba1, F. Reimold1 et al.

V. Perseo1, S. Kwak1, G. Kocsis3,4, G. Cseh3,4, T. Gonda5, G. Schlisio1, M. Hirsch1, N. Chaudhary1, and W7-X team†

  • *Contact author: arun.pandey@ipp.mpg.de
  • †See Supplemental Material [1] for the W7-X Team.

Phys. Rev. Lett. 135, 175101 – Published 21 October, 2025

DOI: https://doi.org/10.1103/cfg9-v8hf

Abstract

Experiments in the Wendelstein 7-X (W7-X) stellarator with plasma density beyond the established density limit in stellarators [Scalings of energy confinement and density limit in stellarator/heliotron devices, Nucl. Fusion 30, 11 (1990).] resulted in unusual, reduced size, fully radiative plasmas lasting stably for many confinement times [Small, stable plasmas, fully decoupled from the plasma-facing components in W7-X, Stellarator News 175, 1 (2021).]. In these experiments, the plasma had shrunk to a significantly smaller minor radius due to intense edge radiation from a radiating mantle and had no contact with material components, yet it remained relatively well confined for many confinement times with electron temperatures on the order of 1 keV. To our knowledge, this is the first definitive experimental long-time stability demonstration of such high-temperature contactless plasmas in the laboratory. It is shown that the onset and extent of this fully radiative small plasma state is predictable. The stability of the plasma size is elucidated with a simple power-balance model. In other helical devices such as the Large Helical Device (LHD) and the Wendelstein 7-AS (W7-AS), plasmas that start shrinking suffered from core impurity accumulation leading to a collapse whereas this was generally not observed for these W7-X plasmas.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (34)

  1. See Supplemental Material at http://link.aps.org/supplemental/10.1103/cfg9-v8hf for the members of the W7-X team.
  2. J. D. Lawson, Some criteria for a power producing thermonuclear reactor, Proc. Phys. Soc. London Sect. B 70, 6 (1957).
  3. 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).
  4. Y. Feng et al., Understanding detachment of the W7-X island divertor, Nucl. Fusion 61, 086012 (2021).
  5. D. A. Gates and L. Delgado-Aparicio, Origin of tokamak density limit scalings, Phys. Rev. Lett. 108, 165004 (2012).
  6. W. Suttrop, K. Buchl, J. Fuchs, M. Kaufmann, K. Lackner, M. Maraschek, V. Mertens, R. Neu, M. Schittenhelm, M. Sokoll, and H. Zohm, Tearing mode formation and radiative edge cooling prior to density limit disruptions in ASDEX upgrade, Nucl. Fusion 37, 119 (1997).
  7. R. B. White, D. A. Gates, and D. P. Brennan, Thermal island destabilization and the greenwald limit, Phys. Plasmas 22, 022514 (2015).
  8. B. J. Peterson, Y. Xu, S. Sudo, T. Tokuzawa, K. Tanaka, M. Osakabe, S. Morita, M. Goto, S. Sakakibara, J. Miyazawa, K. Kawahata, N. Ohyabu, H. Yamada, O. Kaneko, and A. Komori, Multifaceted asymmetric radiation from the edge-like asymmetric radiative collapse of density limited plasmas in the large helical device, Phys. Plasmas 8, 3861 (2001).
  9. L. Giannone, J. Baldzuhn, R. Burhenn, P. Grigull, U. Stroth, F. Wagner, R. Brakel, C. Fuchs, H. J. Hartfuss, K. McCormick, A. Weller, C. Wendland, K. Itoh, and S.-I. Itoh (NBI Team, ECRH Team, and W7-AS Team), Physics of the density limit in the W7-AS stellarator, Plasma Phys. Controlled Fusion 42, 603 (2000).
  10. K. Itoh and S.-I. Itoh, Detached and attached plasma in stellarators, J. Phys. Soc. Jpn. 57, 1269 (1988).
  11. B. J. Peterson et al., Characteristics of radiating collapse at the density limit in the large helical device, Plasma Fusion Res. 1, 045 (2006).
  12. K. Ida, M. Yoshinuma, M. Yokoyama, S. Inagaki, N. Tamura, B. Peterson, T. Morisaki, S. Masuzaki, A. Komori, Y. Nagayama, K. Tanaka, K. Narihara, K. Watanabe, and C. Beidler (LHD Experimental Group), Control of the radial electric field shear by modification of the magnetic field configuration in LHD, Nucl. Fusion 45, 391 (2005).
  13. L. Giannone, R. Burhenn, K. McCormick, R. Brakel, Y. Feng, P. Grigull, and Y. Igitkhanov (NBI Team, ECRH Team, and the W7-AS Team), Radiation power profiles and density limit with a divertor in the W7-AS stellarator, Plasma Phys. Controlled Fusion 44, 2149 (2002).
  14. G. Fuchert et al., Increasing the density in Wendelstein 7-X: Benefits and limitations, Nucl. Fusion 60, 036020 (2020).
  15. T. S. Pedersen (the W7-X Team), Small, stable plasmas, fully decoupled from the plasma-facing components in W7-X, Stellarator News 175, 1 (2021), https://stelnews.info/pdf/issue_175.
  16. A. Langenberg et al., Impurity transport studies at Wendelstein 7-X by means of x-ray imaging spectrometer measurements, Plasma Phys. Controlled Fusion 61, 014030 (2018).
  17. A. Langenberg et al., Charge-state independent anomalous transport for a wide range of different impurity species observed at Wendelstein 7-X, Phys. Plasmas 27, 052510 (2020).
  18. T. Wegner, J.-P. Bähner, B. Buttenschön, A. Langenberg, and A. von Stechow, Overview of core impurity transport in the first divertor operation of Wendelstein 7-X, J. Plasma Phys. 89, 955890302 (2023).
  19. M. Hölzl and S. Günter (ASDEX Upgrade Team), Heat diffusion across magnetic islands and ergodized plasma regions in realistic tokamak geometry, Phys. Plasmas 15, 072514 (2008).
  20. M. Hölzl, S. Günter, I. Classen, Q. Yu, the TEXTOR Team, and E. Delabie, Determination of the heat diffusion anisotropy by comparing measured and simulated electron temperature profiles across magnetic islands, Nucl. Fusion 49, 115009 (2009).
  21. L. Giannone et al. (W7-AS Team), Bolometer tomography at the density limit of the HDH mode in the W7-AS stellarator, Plasma Phys. Controlled Fusion 45, 1713 (2003).
  22. U. Stroth, M. Bernert, D. Brida, M. Cavedon, R. Dux, E. Huett, T. Lunt, O. Pan, and M. Wischmeier (the ASDEX Upgrade Team), Model for access and stability of the x-point radiator and the threshold for marfes in tokamak plasmas, Nucl. Fusion 62, 076008 (2022).
  23. C. Breton, C. Michelis, and M. Mattioli, Ionization equilibrium and radiative cooling of a high temperature plasma, J. Quant. Spectrosc. Radiat. Transfer 19, 367 (1976).
  24. S. Kwak, U. Hergenhahn, U. Höfel, M. Krychowiak, A. Pavone, J. Svensson, O. Ford, R. König, S. Bozhenkov, G. Fuchert, E. Pasch, K. J. Brunner, J. Knauer, P. Kornejew, H. Trimiño Mora, T. S. Pedersen (The W7-X Team), Bayesian inference of spatially resolved Zeff profiles from line integrated bremsstrahlung spectra, Rev. Sci. Instrum. 92, 043505 (2021).
  25. ADAS—Atomic data and analaysis structure, http://www.adas.ac.uk./.
  26. M. Beurskens et al. (The W7-X Team), Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas, Nucl. Fusion 61, 116072 (2021).
  27. A. Buzás, C. Biedermann, G. Cseh, G. Kocsis, M. Krause, T. Szepesi, and M. Szűcs, Estimating plasma size by visible emission patterns in the Wendelstein 7-X stellarator, Fusion Eng. Des. 220, 115304 (2025).
  28. S. Sudo, Y. Takeiri, H. Zushi, F. Sano, K. Itoh, K. Kondo, and A. Iiyoshi, Scalings of energy confinement and density limit in stellarator/heliotron devices, Nucl. Fusion 30, 11 (1990).
  29. C. D. Beidler et al., Demonstration of reduced neoclassical energy transport in Wendelstein 7-X, Nature (London) 596, 221 (2021).
  30. T. Horie, S. Tsujimura, A. Minato, and T. Tone, Lifetime analysis for fusion reactor first walls and divertor plates, Fusion Eng. Des. 5, 221 (1987).
  31. R. Mitteau, M. Sugihara, R. Raffray, S. Carpentier-Chouchana, H. Labidi, M. Merola, R. A. Pitts, and P. Stangeby, Lifetime analysis of the iter first wall under steady-state and off-normal loads, Phys. Scr. 2011, 014081 (2011).
  32. J. Miyazawa et al. (The LHD Experimental Group), Density limit study focusing on the edge plasma parameters in LHD, Nucl. Fusion 48, 015003 (2008).
  33. S. Bozhenkov et al. (W7-X Team), High-performance plasmas after pellet injections in Wendelstein 7-X, Nucl. Fusion 60, 066011 (2020).
  34. A. Pandey, Replication Data for Paper Stable small plasmas at the density limit in W7-X, V1, Demo Dataverse, https://doi.org/10.70122/FK2/WQXRZV (2025).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation