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
  • Editors' Suggestion
  • Open Access

Runaway electrons during a coil quench in stellarators

Pavel Aleynikov*, Per Helander, and Håkan M. Smith

  • *Contact author: pavel.aleynikov@ipp.mpg.de

Phys. Rev. Applied 25, 024065 – Published 20 February, 2026

DOI: https://doi.org/10.1103/v4s5-p4fr

Abstract

It is shown that avalanches of runaway electrons can arise in stellarators, even if there is no net toroidal current in the plasma or the magnetic-field coils, if the current in the latter varies rapidly enough, e.g., due to a superconductor quench. In present-day devices such as W7-X, significant runaway generation is theoretically possible only at very low gas or plasma density in the vacuum vessel, e.g., between discharges, if a seed population of free electrons is present. In reactor-scale stellarators, more dangerous runaway generation may occur both between discharges and during low-density plasma operation. Since a radiation-induced seed population is necessarily present in an activated device, an accidental coil ramp-down could convert substantial magnetic energy into wall-damaging runaway currents. There is, however, much more time to mitigate such events than in tokamak disruptions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (28)

  1. B. N. Breizman, P. Aleynikov, E. M. Hollmann, and M. Lehnen, Physics of runaway electrons in tokamaks, Nucl. Fusion 59, 083001 (2019).
  2. P. Helander, L.-G. Eriksson, and F. Andersson, Runaway acceleration during magnetic reconnection in tokamaks, Plasma Phys. Controlled Fusion 44, B247 (2002).
  3. M. Salewski, et al., Energetic particle physics: Chapter 7 of the special issue: On the path to tokamak burning plasma operation, Nucl. Fusion 65, 043002 (2025).
  4. W. Bernstein, F. Chen, M. Heald, and A. Kranz, Runaway electrons and co-operative phenomena in B-1 stellarator discharges, J. Nucl. Energy (1954) 7, 276 (1958).
  5. A. C. England, G. L. Bell, R. H. Fowler, J. C. Glowienka, J. H. Harris, D. K. Lee, M. Murakami, G. H. Neilson, D. A. Rasmussen, J. A. Rome, M. J. Saltmarsh, and J. B. Wilgen, Runaway electron studies in the ATF torsatron, Phys. Fluids B: Plasma Phys. 3, 1671 (1991).
  6. L. Rodríguez-Rodrigo, A. López-Fraguas, and A. Gabriel, Runaway electrons control during ramp-up and ramp-down of the magnetic fields in the coils of the TJ-II flexible heliac (abstract), Rev. Sci. Instrum. 70, 645 (1999).
  7. V. Moiseenko, V. Korovin, I. Tarasov, M. Tarasov, D. Sitnikov, I. Garkusha, N. Zamanov, M. Lytova, R. Pavlichenko, A. Kulaga, et al., The effect of an electrostatic field on runaway electrons in the Uragan-3M stellarator, Tech. Phys. Lett. 40, 669 (2014).
  8. D. A. Rasmussen, A. C. England, C. C. Eberle, W. R. Devan, J. H. Harris, T. C. Jernigan, R. R. Kindsfather, R. N. Morris, M. Murakami, G. H. Neilson, J. A. Rome, M. J. Saltmarsh, R. B. Wysor, O. Motojima, H. Okada, and K. Uo, Suppression of x-rays generated by runaway electrons in ATF, in Proceedings of the U.S.–Japan Heliotron-Stellarator Workshop (Oak Ridge National Lab., TN, USA; Kyoto Univ., Japan, 1987).
  9. A. C. England, W. R. DeVan, C. C. Eberle, R. H. Fowler, W. A. Gabbard, J. C. Glowienka, J. H. Harris, G. R. Haste, R. R. Kindsfather, and R. N. Morris, Runaway studies in the ATF (Advanced Toroidal Facility) torsatron, Tech. Rep. (Oak Ridge National Lab., TN, USA, 1988).
  10. D. Birus, M. Schneider, T. Rummel, and M. Fricke, The quench detection system of Wendelstein 7-X, Fusion Eng. Des. 86, 1566 (2011). Proceedings of the 26th Symposium of Fusion Technology (SOFT-26).
  11. K. Risse, T. Rummel, T. Mönnich, F. Füllenbach, and H.-S. Bosch, Updates on protection system for Wendelstein 7-X superconducting magnets, Fusion Eng. Des. 146, 910 (2019). sI:SOFT-30.
  12. P. Helander, Theory of plasma confinement in non-axisymmetric magnetic fields, Rep. Progr. Phys. 77, 087001 (2014).
  13. The radial orbit excursion is of the order of Δr∼γmec/(eB), which is about 1 cm for a 10-MeV electron in W7-X. Here, γ denotes the Lorentz factor, me is the electron rest mass, and c is the speed of light.
  14. H. Bethe, Bremsformel für elektronen relativistischer geschwindigkeit, Z. Phys. 76, 293 (1932).
  15. Y. A. Sokolov, Multiplication of accelerated electrons in a tokamak, JETP Lett. 29, 218 (1979).
  16. A. Gurevich, G. Milikh, and R. Roussel-Dupre, Runaway electron mechanism of air breakdown and preconditioning during a thunderstorm, Phys. Lett. A 165, 463 (1992).
  17. R. Jayakumar, H. Fleischmann, and S. Zweben, Collisional avalanche exponentiation of runaway electrons in electrified plasmas, Phys. Lett. A 172, 447 (1993).
  18. Y.-K. Kim, J. P. Santos, and F. Parente, Extension of the binary-encounter-dipole model to relativistic incident electrons, Phys. Rev. A 62, 052710 (2000).
  19. J. Connor and R. Hastie, Relativistic limitations on runaway electrons, Nucl. Fusion 15, 415 (1975).
  20. M. N. Rosenbluth and S. V. Putvinski, Theory for avalanche of runaway electrons in tokamaks, Nucl. Fusion 37, 1355 (1997).
  21. J. R. Martín-Solís, A. Loarte, and M. Lehnen, Runaway electron dynamics in tokamak plasmas with high impurity content, Phys. Plasmas 22, 092512 (2015).
  22. L. Hesslow, O. Embréus, O. Vallhagen, and T. Fülöp, Influence of massive material injection on avalanche runaway generation during tokamak disruptions, Nucl. Fusion 59, 084004 (2019).
  23. Note that the trapped particle fraction can be significant in stellarators, even on the magnetic axis. In W7-X, the trapped fraction on axis typically ranges from 0.15 to 0.3.
  24. F. Schauer, K. Egorov, and V. Bykov, HELIAS 5-B magnet system structure and maintenance concept, Fusion Eng. Des. 88, 1619 (2013). Proceedings of the 27th Symposium On Fusion Technology (SOFT-27); Liège, Belgium, September 24-28, 2012.
  25. C. Hegna, D. Anderson, E. Andrew, A. Ayilaran, A. Bader, T. Bohm, K. C. Mata, J. Canik, L. Carbajal, A. Cerfon, et al., The infinity two fusion pilot plant baseline plasma physics design, J. Plasma Phys. 91, E76 (2025).
  26. C. Killer, P. Aleynikov, C. Biedermann, C. Dhard, P. Drews, Y. Gao, O. Grulke, M. Jakubowski, A. Knieps, G. Kocsis, D. Naujoks, A. Puig Sitjes, M. Spolaore, T. Stange, T. Szepesi, A. Tancetti, and H. Thomsen, Observation of non-thermal electrons outside the sol in the Wendelstein 7-X stellarator, Nucl. Mater. Energy 33, 101274 (2022).
  27. P. Aleynikov, Data to support Figures 1 and 2 in “Runaway electrons during a coil quench in stellarators”, https://doi.org/10.5281/zenodo.18196420 (2026).
  28. J. R. Cary and A. J. Brizard, Hamiltonian theory of guiding-center motion, Rev. Mod. Phys. 81, 693 (2009).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation