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Generalized Lawson-Cordey-Mills Accessibility of Fusion Ignition

Luis F. Delgado-Aparicio, Masayuki Ono, and Jonathan E. Menard

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Phys. Rev. Lett. 137, 115102 – Published 10 September, 2026

DOI: https://doi.org/10.1103/mmc9-nzfx

Abstract

A generalized ignition-accessibility framework is developed that unifies Lawson power balance, Cordey accessibility, the marginal ignition ridge, ignition entry points, and Mills thermal-runaway dynamics into a single self-consistent description of reactor-relevant burning plasmas. The 0D analysis recasts fusion ignition as a constrained dynamical pathway rather than a static threshold condition and demonstrates that radiation damping displaces the marginal ignition ridge, Cordey saddle, and ignition entry points toward higher densities and temperatures, thereby increasing the pressure required for ignition. In realistic 3D reactor geometry, this displacement translates into elevated plasma β requirements, establishing a direct connection between power balance, ignition accessibility, and macroscopic magnetohydrodynamic stability limits. A generalized thermal-runaway analysis reveals a previously unrecognized stabilizing feedback arising from transport, impurity and synchrotron damping, and the universally unfavorable power scaling of energy confinement, capable of reducing runaway growth and enabling steady-state burn. Enhanced confinement and spin-polarized fuels partially reopen the ignition window toward near-ideal DT performance.

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References (114)

  1. J. D. Lawson, Some Criteria for a Power producing thermonuclear reactor, Technical report. Atomic Energy Research Establishment, Harwell Bershire, U. K. A. E. R. E. GP/R 1807 (1955).
  2. J. D. Lawson, Proc. Phys. Soc. London Sect. B 70, 6 (1957).
  3. J. Wesson, Tokamaks (Oxford University Press, New York, 2004), 3rd ed.
  4. R. G. Mills, Four Lectures on Fusion Power, MATT-145 (1962).
  5. R. G. Mills, Nucl. Fusion 7, 223 (1967).
  6. R. G. Mills, Proceedings of Symposium on Engineering Problems of Fusion Research: held at the Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico: April 8-11, B1-1 (United States Atomic Energy Commission, Germantown, MD, 1969).
  7. D. A. Uzdensky, Astrophysics and Space Science Library 427, 473 (2016).
  8. J. D. Hare et al., Phys. Plasmas 14, 102703 (2017).
  9. R. Datta et al., Phys. Rev. Lett. 132, 155102 (2024).
  10. R. Datta et al., Phys. Plasmas 31, 052110 (2024).
  11. L. F. Delgado-Aparicio et al., Phys. Rev. Lett. 110, 065006 (2013).
  12. L. F. Delgado-Aparicio et al., Rev. Sci. Instrum. 83, 10E517 (2012).
  13. L. F. Delgado-Aparicio et al., Nucl. Fusion 53, 043019 (2013).
  14. L. E. Sugiyama, Phys. Plasmas 20, 032504 (2013).
  15. A. Wingen, R. S. Wilcox, S. K. Seal, E. A. Unterberg, M. R. Cianciosa, L. F. Delgado-Aparicio, S. P. Hirshman, and L. L. Lao, Nucl. Fusion 58, 036004 (2018).
  16. A. Wingen, R. S. Wilcox, L. F. Delgado-Aparicio, R. Granetz, S. Houshmandyar, S. Shiraiwa, M. R. Cianciosa, and S. K. Seal, Phys. Plasmas 26, 022501 (2019).
  17. D. A. Gates and L. F. Delgado-Aparicio, Phys. Rev. Lett. 108, 165004 (2012).
  18. D. A. Gates, L. F. Delgado-Aparicio, and R. B. White, Nucl. Fusion 53, 063008 (2013).
  19. D. A. Gates, D. Brennan, L. F. Delgado-Aparicio, and R. White, Phys. Plasmas 22, 060701 (2015).
  20. Q. Teng, D. P. Brennan, L. F. Delgado-Aparicio, D. A. Gates, and R. B. White, Nucl. Fusion 56, 106001 (2016).
  21. R. Neu et al., Nucl. Fusion 45, 209 (2005).
  22. F. Romanelli et al., Nucl. Fusion 53, 104002 (2013).
  23. G. Verdoolaege et al., Proceedings of the 27th IAEA Fusion Energy Conference (International Atomic Energy Agency, Vienna, Austria, 2018).
  24. G. Verdoolaege et al., Nucl. Fusion 61, 076006 (2021).
  25. A. Saltzman, P. Rodriguez-Fernandez, T. Body, A. Ho, and N. T. Howard, Nucl. Fusion 66, 026005 (2026).
  26. A. Gallo et al., Nucl. Mater. Energy 41, 101741 (2024).
  27. A. Gallo et al., Nucl. Mater. Energy 46, 102042 (2026).
  28. J. Hobirk et al., Nucl. Fusion (to be published).
  29. J. Butt et al., Phys. Plasmas (to be published).
  30. M. Greewald et al., The High-Field Path to Practical Fusion Energy, PSFC/RR-18-2 report (2018).
  31. M. Greewald et al., J. Plasma Phys. 86, 861860501 (2020).
  32. A. J. Creely et al., J. Plasma Phys. 86, 865860502 (2020).
  33. P. Rodriguez-Fernandez, N. T. Howard, M. J. Greenwald, A. J. Creely, J. W. Hughes, J. C. Wright, C. Holland, Y. Lin, and F. Sciortino, J. Plasma Phys. 86, 865860503 (2020).
  34. H. Meyer et al., Phil. Trans. R. Soc. A, 382, 20230406 (2024).
  35. C. L. Wilson et al., Nucl. Fusion 66, 086002 (2025).
  36. J. Willis et al., Nucl. Fusion 66, 086001 (2025).
  37. M. Scarpari et al., arXiv:2512.16604.
  38. https://euro-fusion.org/wp-content/uploads/2025/11/BEST-Research-Plan-v1.1.pdf.
  39. IAEA World Fusion Outlook 2025, 3rd ed. (International Atomic Energy Agency, Vienna, Austria, 2025), https://www.iaea.org/publications/15935/iaea-world-fusion-outlook-2025.
  40. K. Ikeda et al., Nucl. Fusion 47, E01 (2007).
  41. A. Loarte et al., ITR-25-005 (2025).
  42. T. M. Collaboration, G. Rutherford et al., Plasma Phys. Controlled Fusion 66, 105006 (2024).
  43. M. A. Miller, D. Arnold, M. Wigram, A. O. Nelson, J. Witham, G. Rutherford, H. Choudhury, C. Cummings, C. Paz-Soldan, and D. G. Whyte, Plasma Phys. Controlled Fusion 66, 125004 (2024).
  44. H. S. Wilson et al., Plasma Phys. Control Fusion 67, 015026 (2024).
  45. A. Balestri, J. Ball, and S. Coda, Nucl. Fusion 65, 106023 (2025).
  46. J. Lion et al., Fusion Eng. Des. 214, 114868 (2025).
  47. S. Lazerson et al., 51th EPS Conference on Contr. Fusion and Plasma Phys, p. 4.221 (European Physical Society, Mulhouse, France, 2025).
  48. Gauss Fusion, GIGA, CDR Executive Summary (Gauss Fusion, Garching bei München, Germany, 2026), https://gauss-fusion.com/cdr-executivesummary.
  49. J. E. Menard et al., Next-step low-aspect-ratio tokamak design studies, in Proceedings of the 29th IAEA Fusion Energy Conf. (International Atomic Energy Agency, Vienna, Austria, 2023).
  50. T. Brown and J. E. Menard, Fusion Eng. Des. 192, 113583 (2023).
  51. J. W. Bae, K. Borowiec, V. Badalassi, J. Parisi, A. Diallo, J. Menard, A. Khodak, and T. Brown, Nucl. Fusion 65, 086051 (2025).
  52. K. Shah, J. W. Berkery, J. E. Menard, L. F. Delgado-Aparicio, M. Ono, and E. Emdee, Plasma Phys. Controlled Fusion 67, 115018 (2025).
  53. M. Ono et al., Nucl. Fusion 64, 086021 (2024).
  54. F. Romanelli et al., Nucl. Fusion 64, 112015 (2024).
  55. F. Crisanti et al., Nucl. Fusion 64, 106040 (2024).
  56. V. Prost and F. A. Volpe, Nucl. Fusion 64, 026007 (2024).
  57. C. C. Hegna et al., J. Plasma Phys. 91, E76 (2025).
  58. W. Gutenfelder et al., J. Plasma Phys. 91, E83 (2025).
  59. C. P. S. Swanson, D. A. Gates, S. T. A. Kumar, M. F. Martin, T. G. Kruger, D. W. Dudt, and P. J. Bonofiglo, Nucl. Fusion 65, 026053 (2025).
  60. C. P. S. Swanson et al., J. Fusion Eng. Design 232, 115999 (2026).
  61. S. T. A. Kumar et al., J. Fusion Eng. Design 232, 115998 (2026).
  62. H. S. Bosch and G. M. Hale, Nucl. Fusion 32, 611 (1992).
  63. H. S. Bosch and G. M. Hale, Nucl. Fusion 33, 1919 (1993).
  64. D. Post, R. V. Jensen, C. B. Tarter, W. H. Grasberger, and W. A. Lokke, At. Data Nucl. Data Tables 20, 397 (1977).
  65. R. V. Jensen et al., Nucl. Fusion 17, 6 (1977).
  66. D. Reiter et al., Nucl. Fusion 30, 214 (1990).
  67. T. Putterich, R. Neu, R. Dux, A. D. Whiteford, M. G. O’Mullane, and H. P. Summers, Nucl. Fusion 50, 025012 (2010).
  68. T. Putterich, E. Fable, R. Dux, M. O’Mullane, R. Neu, and M. Siccinio, Nucl. Fusion 59, 056013 (2019).
  69. F. Albajar et al., Nucl. Fusion 49, 116017 (2009).
  70. D. M Meade, Nucl. Fusion 14, 289 (1974).
  71. W. A. Houlberg, Nucl. Fusion 22, 935 (1982).
  72. J. P. Freidberg, F. J. Mangiarotti, and J. Minervini, Phys. Plasmas 22, 070901 (2015).

  73. The energy gain, Q=PFusion/PHeat, quantifies the ratio of fusion power produced to external heating required to sustain the plasma.

  74. E. A. Chaniotakis, Ph. D thesis, Massachusetts Institute of Technology (1990).
  75. E. A. Chaniotakis, J. P. Freidberg, and D. R. Cohn, PFC/JA-90-39 report (1990).
  76. H. P. Furth et al., PPPL report 2722 (1990).
  77. O. Mitarai, A. Hirose, and H. M. Skarsgard, Fusion Technol. 20, 208 (1991).
  78. T. C. Luce, Phys. Plasmas 18, 030501 (2011).
  79. X. Litaduon et al., Nucl. Fusion 66, 095001 (2026).
  80. T. Fonghuetti et al., Nucl. Fusion 65, 056018 (2025).
  81. R. Dumont et al., Nucl. Fusion 66, 106006 (2026).
  82. X. Gong et al., Nucl. Fusion 64, 112013 (2024).
  83. Y. Song et al., Sci. Adv. 9, eabq5273 (2023).
  84. H. S. Kim et al., Nucl. Fusion 64, 016033 (2024).
  85. Y. S. Na et al., Nucl. Fusion 66, 026049 (2026).
  86. Y. Yang, Z. Song, H. Tan, M. Zhang, and B. Rao, IEEE Trans. Plasma Sci. 44, 93 (2016).
  87. Y. Murakami, T. Amano, K. Shimizu, and M. Shimada, J. Nucl. Mater. 313–316, 1161 (2003).
  88. R. M. Kulsrud, H. P. Furth, E. J. Valeo, and M. Goldhaber, Phys. Rev. Lett. 49, 1248 (1982).
  89. R. M. Kulsrud, E. J. Valeo, and S. C. Cowley, Nucl. Fusion 26, 1443 (1986).
  90. S. Cowley, R.  M. Kulsrud, and E. Valeo, Phys. Fluids 29, 430 (1986).
  91. B. Heidbrink et al., Front. Phys. 12, 1 (2024).
  92. A. V. Garcia, W. W. Heidbrink, and A. M. Sandorfi, Nucl. Fusion 63, 026030 (2023).
  93. J. Parisi et al., arXiv:2406.05970.
  94. J. W. S. Cook, Nucl. Fusion 66, 056044 (2026).
  95. M. Okamoto and M. Ohnishi, J. Nucl. Sci. Technol. 20, 366 (1983).
  96. K. Borras, Phys. Scr. 16, 107 (1987).
  97. E. Schuster, M. Krstić, and G. Tynan, Fusion Sci. Technol. 43, 18 (2003).
  98. L. F. Delgado-Aparicio et al., Plasma Phys. Controlled Fusion 68, 045041 (2026).
  99. M. Ono, L. F. Delgado-Aparicio, and J. Menard, Nucl. Fusion (to be published).
  100. L. F. Delgado-Aparicio and M. Ono, Nucl. Fusion (to be published).
  101. S. Kaye et al., Nucl. Fusion 37, 1303 (1997).
  102. M. R. Wade and J. A. Leuer, Fusion Sci. Technol. 77, 119–143 (2021).
  103. H. Zohm, Philos. Trans. A Math. Phys. Eng. Sci. 377, 20170437 (2019).
  104. F. Troyon, A. Roy, W. A. Cooper, F. Yasseen, and A. Turnbull, Plasma Phys. Controlled Fusion 30, 1597 (1988).
  105. M. Greenwald, Plasma Phys. Controlled Fusion 44, R27 (2002).
  106. S. Sudo, Y. Takeiri, H. Zushi, F. Sano, K. Itoh, K. Kondo, and A. Iiyoshi, Nucl. Fusion 30, 11 (1990).
  107. G. Fuchert et al., Nucl. Fusion 60, 036020 (2020).
  108. R. Maingi et al., Phys. Rev. Lett. 107, 145004 (2011).
  109. S. P. Gerhardt, J. M. Canik, R. Maingi, D. Battaglia, R. E. Bell, W. Guttenfelder, B. P. LeBlanc, D. R. Smith, H. Yuh, and S. Sabbagh, Nucl. Fusion 54, 083021 (2014).
  110. D. Boyle, R. Majeski, J. C. Schmitt, C. Hansen, R. Kaita, S. Kubota, M. Lucia, and T. D. Rognlien, Phys. Rev. Lett. 119, 015001 (2017).
  111. D. Boyle et al., Nucl. Fusion 63, 056020 (2023).
  112. A. Maan et al., Nucl. Mater. Energy 35, 101408 (2023).
  113. A. Maan et al., Phys. Plasmas 31, 022505 (2024).
  114. D. P. Boyle et al., Nucl. Mater. Energy 43, 101949 (2025).

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Phys. Rev. Lett. 137, 115102– Published 10 September, 2026
  • Received 28 April 2026
  • Accepted 17 August 2026
Article part of CHORUS
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