pith. sign in

arxiv: 2604.07367 · v1 · submitted 2026-04-06 · ⚛️ physics.plasm-ph · econ.GN· physics.soc-ph· q-fin.EC

Criteria for the economic viability of fusion power plants

D.G. Whyte , A. Lo , R. Bielajew , M. Hancock , R. Moeykens , G. Shaw This is my paper

Pith reviewed 2026-05-10 19:18 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph econ.GNphysics.soc-phq-fin.EC
keywords fusion power plantseconomic viabilityQ_econfusion energy gaindesign parameterspower densitycomponent lifetime
0
0 comments X

The pith

A single economic gain factor Q_econ sets viability criteria for fusion power plants independent of scale or technology type

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a framework to assess the economic viability of fusion power plants across different concepts. Drawing from the Lawson criterion for scientific gain, it normalizes parameters to the energy capture surface and assumes temporal equilibrium to derive an economic gain factor Q_econ. This results in nonlinear equations controlled by ten parameters such as fusion power density, component lifetime, energy fluence, energy price, and efficiencies. The approach allows high-level insights into design, finance, and operational tradeoffs without depending on absolute plant power or specific fusion methods.

Core claim

The derivation of the economic gain factor, Q_econ, results in nonlinear equations with ten controlling normalized design parameters ranging from fusion power density and surface component lifetime to energy fluence, price of energy, and component efficiency and cost. These criteria are independent of the power plant's absolute power and impartial to the particulars of its fusion technology.

What carries the argument

The economic gain factor Q_econ derived from normalized parameters on the energy capture surface under temporal equilibrium conditions.

If this is right

  • The criteria apply universally to any fusion confinement concept.
  • Varying the ten parameters reveals tradeoffs that can improve economic prospects.
  • Viability assessments become possible at any power scale without adjustment.
  • Insights guide design choices in power density, lifetimes, and costs independently of technology details.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This framework could help prioritize research by showing which parameters most strongly affect overall economics.
  • Small modular fusion approaches might prove viable if they achieve favorable values in the normalized metrics.
  • Linking Q_econ to plasma performance models would enable simultaneous optimization of scientific and economic performance.

Load-bearing premise

The exploitation of temporal equilibrium and normalization of parameters to the energy capture surface.

What would settle it

Measurement of the actual economic performance of a fusion power plant and comparison to the Q_econ predicted from its measured values of the ten controlling parameters.

read the original abstract

Commercial fusion energy requires frameworks to assess both the scientific and economic viability of a wide variety of fusion concepts. Inspired by the Lawson criterion's ability to universally describe fusion energy gain, a generalized framework is developed to determine the economic gain of fusion power plants. The model exploits temporal equilibrium, and engineering and cost parameters normalized to the energy capture surface. The derived criteria for economic gain are therefore independent of the power plant's absolute power, impartial to the particulars of its fusion technology, and can be applied to any fusion confinement concept. The derivation of the economic gain factor, $Q_{econ}$, results in nonlinear equations with ten controlling normalized design parameters ranging from fusion power density and surface component lifetime to energy fluence, price of energy, and component efficiency and cost. These ten controlling parameters are varied over a wide range to provide high-level insights in design, finance and operational tradeoffs that improve the prospects for economically viable fusion energy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims to derive a universal economic gain factor Q_econ for fusion power plants, analogous to the Lawson criterion. Using assumptions of temporal equilibrium and normalization of engineering and cost parameters to the energy capture surface, the framework results in nonlinear equations governed by ten normalized design parameters. These parameters include fusion power density, surface component lifetime, energy fluence, price of energy, and component efficiency and cost. The criteria are asserted to be independent of the plant's absolute power and impartial to the specific fusion technology, applicable to any confinement concept. The ten parameters are varied over wide ranges to provide insights into design, finance, and operational tradeoffs.

Significance. If the derivation holds and the assumptions are valid, this would be a significant contribution by providing a technology-independent framework for economic assessment in fusion, similar to scientific criteria. It could help in evaluating and optimizing various fusion concepts on equal footing, offering high-level insights into tradeoffs. The normalization to energy capture surface is a key strength if it successfully eliminates dependencies. This has potential to influence R&D strategies in the field.

major comments (2)
  1. The central claim of independence from absolute power and impartiality to fusion technology rests on the temporal equilibrium assumption and surface normalization. However, this assumption does not hold for pulsed fusion concepts, where low duty cycle, time-varying power, and thermal cycling introduce additional parameters such as pulse frequency, charging overhead, and intermittent revenue. These are not among the ten listed normalized variables and cannot be eliminated by surface normalization, risking hidden technology-specific dependencies. This directly challenges the applicability to 'any fusion confinement concept'.
  2. The abstract describes the derivation leading to nonlinear equations but does not supply the actual equations or the explicit definitions of the ten parameters. Without these, the claim that the criteria are independent of absolute power and impartial to fusion technology specifics cannot be verified, and the potential for circularity in parameter selection (if any are chosen post-hoc to demonstrate positive Q_econ) remains unaddressed.
minor comments (2)
  1. The abstract is dense and could be improved by including at least one key equation or a clearer list of the ten parameters for better readability.
  2. Consider adding references to existing economic models for fusion power plants to contextualize the novelty of this framework.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments, which have helped us improve the clarity and scope of our manuscript. We address each major comment in detail below. Where appropriate, we have revised the manuscript to incorporate the feedback.

read point-by-point responses

  1. Referee: The central claim of independence from absolute power and impartiality to fusion technology rests on the temporal equilibrium assumption and surface normalization. However, this assumption does not hold for pulsed fusion concepts, where low duty cycle, time-varying power, and thermal cycling introduce additional parameters such as pulse frequency, charging overhead, and intermittent revenue. These are not among the ten listed normalized variables and cannot be eliminated by surface normalization, risking hidden technology-specific dependencies. This directly challenges the applicability to 'any fusion confinement concept'.

    Authors: We agree that the temporal equilibrium assumption is key and that pulsed concepts introduce time-dependent effects not explicitly listed. However, our framework is designed around time-averaged quantities normalized to the energy capture surface. Parameters such as fusion power density can represent average values over the pulse cycle, while surface component lifetime can incorporate degradation from thermal cycling and fatigue. Charging overhead and intermittent revenue can be folded into the efficiency and cost parameters or the price of energy term. This preserves the independence from absolute power and allows application across concepts, including pulsed ones, at the level of effective parameters. We acknowledge that for highly intermittent systems, additional modeling may be needed, but the ten parameters provide a flexible basis. In the revised manuscript, we will add a subsection discussing the extension to pulsed fusion concepts and how duty cycle effects are incorporated via averaging. revision: partial

  2. Referee: The abstract describes the derivation leading to nonlinear equations but does not supply the actual equations or the explicit definitions of the ten parameters. Without these, the claim that the criteria are independent of absolute power and impartial to fusion technology specifics cannot be verified, and the potential for circularity in parameter selection (if any are chosen post-hoc to demonstrate positive Q_econ) remains unaddressed.

    Authors: The abstract is intended as a concise summary, while the full derivation of the nonlinear equations for Q_econ and the explicit definitions of the ten normalized parameters (including fusion power density, surface component lifetime, energy fluence, price of energy, component efficiency, and costs) are provided in detail in the body of the manuscript, particularly in the sections deriving the economic gain factor. To enhance verifiability, we will revise the abstract to briefly enumerate the ten parameters and cite the key equations. Regarding circularity, the parameters are selected a priori based on fundamental physical, engineering, and economic considerations relevant to fusion plants; they are then varied over wide ranges in sensitivity analyses to explore tradeoffs, rather than being adjusted post-hoc to achieve positive Q_econ. This approach demonstrates robustness across plausible ranges. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation of Q_econ criteria

full rationale

The paper explicitly builds the Q_econ framework by assuming temporal equilibrium and normalizing engineering/cost parameters to the energy capture surface, then states that the resulting nonlinear equations with ten parameters are therefore independent of absolute power and impartial to fusion technology. This independence follows directly from the stated modeling choices rather than emerging as an independent prediction or first-principles result that reduces to the inputs by construction. Parameters are described as varied over ranges for design insights, with no evidence of post-hoc fitting, self-citation load-bearing for uniqueness, or smuggling of ansatzes. The derivation is self-contained under its assumptions and does not exhibit any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework rests on the ability to normalize parameters to the energy capture surface and exploit temporal equilibrium; the ten controlling parameters function as free variables whose specific values are not derived but varied to explore tradeoffs. No invented physical entities are introduced.

free parameters (1)
  • Ten normalized design parameters (fusion power density, surface component lifetime, energy fluence, price of energy, and
    These are varied over wide ranges to generate insights; abstract does not state whether any are fitted to historical data or chosen ad hoc.
axioms (2)
  • domain assumption Temporal equilibrium can be used to model economic gain
    Invoked as the basis for the derivation in the abstract.
  • domain assumption Engineering and cost parameters can be normalized to the energy capture surface without loss of generality
    This normalization is stated to make the criteria independent of absolute power and technology specifics.

pith-pipeline@v0.9.0 · 5482 in / 1491 out tokens · 59677 ms · 2026-05-10T19:18:07.339952+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

73 extracted references · 73 canonical work pages

  1. [1]

    https://www.fusionindustryassociation.org/wp-content/uploads/2024/07/2024- global-fusion-industry-report-FIA.pdf (2024)

    Fusion Industry Association: 2024 Global Fusion Industry Report. https://www.fusionindustryassociation.org/wp-content/uploads/2024/07/2024- global-fusion-industry-report-FIA.pdf (2024)

    work page 2024

  2. [2]

    Physical Review Letters 132(6), 065102 (2024)

    Abu-Shawareb, H., Acree, R., Adams, P., Adams, J., Addis, B., Aden, R., Adrian, P., Afeyan, B., Aggleton, M., Aghaian, L., et al.: Achievement of target gain larger than unity in an inertial fusion experiment. Physical Review Letters 132(6), 065102 (2024)

    work page 2024

  3. [3]

    : The SPARC toroidal field model coil program

    Hartwig, Z.S., Vieira, R.F., Dunn, D., Golfinopoulos, T., LaBombard, B., Lammi, C.J., Michael, P.C., Agabian, S., Arsenault, D., Barnett, R., et al. : The SPARC toroidal field model coil program. IEEE Transactions on Applied Superconductivity 34(2), 1–16 (2023)

    work page 2023

  4. [4]

    Pro- ceedings of the Physical Society

    Lawson, J.D.: Some criteria for a power producing thermonuclear reactor. Pro- ceedings of the Physical Society. Section B 70(1), 6 (1957) https://doi.org/10. 1088/0370-1301/70/1/303

    work page 1957

  5. [5]

    Physics of Plasmas 29(6), 062103 (2022)

    Wurzel, S.E., Hsu, S.C.: Progress toward fusion energy breakeven and gain as measured against the Lawson criterion. Physics of Plasmas 29(6), 062103 (2022)

    work page 2022

  6. [6]

    Rutkowski, J

    Rutkowski, A., Harter, J., Parisi, J.: Scalable Chrysopoeia via (n, 2n) Reactions Driven by Deuterium-Tritium Fusion Neutrons (2025). https://arxiv.org/abs/ 2507.13461

    work page arXiv 2025

  7. [7]

    Technical report, Idaho National Laboratory (INL), Idaho Falls, ID (United States); Argonne … (2023)

    Larsen, L.M., Abou-Jaoude, A., Guaita, N., Stauff, N.: Nuclear energy cost esti- mates for net zero world initiative. Technical report, Idaho National Laboratory (INL), Idaho Falls, ID (United States); Argonne … (2023)

    work page 2023

  8. [8]

    : HYLIFE − II: A molten-salt inertial fusion energy power plant design

    Moir, R., Bieri, R., Chen, X., Dolan, T., Hoffman, M., House, P., Leber, R., Lee, J., Lee, Y., Liu, J., et al. : HYLIFE − II: A molten-salt inertial fusion energy power plant design. Fusion technology 25(1), 5–25 (1994)

    work page 1994

  9. [9]

    Journal of Fusion Energy 38(1), 199–203 (2019)

    Laberge, M.: Magnetized target fusion with a spherical tokamak. Journal of Fusion Energy 38(1), 199–203 (2019)

    work page 2019

  10. [10]

    : The aries-at advanced tokamak, advanced technology fusion power plant

    Najmabadi, F., Abdou, A., Bromberg, L., Brown, T., Chan, V., Chu, M., Dahlgren, F., El-Guebaly, L., Heitzenroeder, P., Henderson, D., et al. : The aries-at advanced tokamak, advanced technology fusion power plant. Fusion Engineering and Design 80(1-4), 3–23 (2006)

    work page 2006

  11. [11]

    : Overview of the ARIES − RS reversed-shear tokamak power plant study

    Najmabadi, F., Team, T.A., Bathke, C.G., Billone, M.C., Blanchard, J.P., Bromberg, L., Chin, E., Cole, F.R., Crowell, J.A., Ehst, D.A., et al. : Overview of the ARIES − RS reversed-shear tokamak power plant study. Fusion Engineering and Design 38(1-2), 3–25 (1997)

    work page 1997

  12. [12]

    National Academies of Sciences, Engineering, and Medicine: Bringing Fusion to the US Grid, (2021) 61

    work page 2021

  13. [13]

    Physics of Plasmas 30(9) (2023)

    Levitt, B., Meier, E., Umstattd, R., Barhydt, J., Datta, I., Liekhus-Schmaltz, C., Sutherland, D., Nelson, B.: The zap energy approach to commercial fusion. Physics of Plasmas 30(9) (2023)

    work page 2023

  14. [14]

    Fusion Science and Technology 80(1), 1–16 (2024)

    Shumlak, U., Meier, E., Levitt, B.: Fusion gain and triple product for the sheared- flow-stabilized z pinch. Fusion Science and Technology 80(1), 1–16 (2024)

    work page 2024

  15. [15]

    Fusion Engineering and Design 100, 378–405 (2015)

    Sorbom, B., Ball, J., Palmer, T., Mangiarotti, F., Sierchio, J., Bonoli, P., Kasten, C., Sutherland, D., Barnard, H., Haakonsen, C., et al.: Arc: A compact, high-field, fusion nuclear science facility and demonstration power plant with demountable magnets. Fusion Engineering and Design 100, 378–405 (2015)

    work page 2015

  16. [16]

    conference presentation, June 2025, Symposium on Fusion Engineering, Cambridge, MA, USA (2025)

    Creely, A.: Progress toward the ARC fusion power plant. conference presentation, June 2025, Symposium on Fusion Engineering, Cambridge, MA, USA (2025)

    work page 2025

  17. [17]

    : MANTA: a negative-triangularity nasem-compliant fusion pilot plant

    Rutherford, G., Wilson, H.S., Saltzman, A., Arnold, D., Ball, J.L., Benjamin, S., Bielajew, R., Boucaud, N., Calvo-Carrera, M., Chandra, R., et al. : MANTA: a negative-triangularity nasem-compliant fusion pilot plant. Plasma Physics and Controlled Fusion 66(10), 105006 (2024)

    work page 2024

  18. [18]

    Physics of Plasmas 31(11) (2024)

    Thomas, C., Tabak, M., Alexander, N., Galloway, C., Campbell, E., Farrell, M., Kline, J., Montgomery, D., Schmitt, M., Christopherson, A., et al.: Hybrid direct drive with a two-sided ultraviolet laser. Physics of Plasmas 31(11) (2024)

    work page 2024

  19. [19]

    Fusion Engineering and Design 202, 114333 (2024)

    Ogando, F., Tobin, M.T., Meier, W.R., Farga-Ninoles, G., Marian, J., Reyes, S., Sanz, J., Galloway, C.: Preliminary nuclear analysis of hylife-iii: A thick- liquid-wall chamber for inertial fusion energy. Fusion Engineering and Design 202, 114333 (2024)

    work page 2024

  20. [20]

    Science 278(5342), 1419–1422 (1997)

    Rostoker, N., Binderbauer, M.W., Monkhorst, H.J.: Colliding beam fusion reactor. Science 278(5342), 1419–1422 (1997)

    work page 1997

  21. [21]

    Fusion Technology 21(4), 2307–2323 (1992)

    Momota, H., Ishida, A., Kohzaki, Y., Miley, G.H., Ohi, S., Ohnishi, M., Sato, K., Steinhauer, L.C., Tomita, Y., Tuszewski, M.: Conceptual design of the d-3he reactor artemis. Fusion Technology 21(4), 2307–2323 (1992)

    work page 1992

  22. [22]

    Journal of Fusion Energy 42(2), 30 (2023)

    Kirtley, D., Milroy, R.: Fundamental scaling of adiabatic compression of field reversed configuration thermonuclear fusion plasmas. Journal of Fusion Energy 42(2), 30 (2023)

    work page 2023

  23. [23]

    In: APS Division of Plasma Physics Meeting Abstracts, vol

    Kirtley, D., Lewis, S., Pancotti, A.: Fundamental theory of the direct magnetic energy recovery in a thermonuclear field reversed configuration system. In: APS Division of Plasma Physics Meeting Abstracts, vol. 2024, pp. 05–008 (2024)

    work page 2024

  24. [24]

    Nuclear Fusion 65(10), 106019 (2025)

    Slough, J.: A compact fusion reactor based on the staged compression of a field reversed configuration. Nuclear Fusion 65(10), 106019 (2025)

    work page 2025

  25. [25]

    : Confinement performance predictions for a high field axisymmetric tandem mirror

    Frank, S., Viola, J., Petrov, Y., Anderson, J., Bindl, D., Biswas, B., Caneses- Marin, J.F., Endrizzi, D.A., Furlong, K., Harvey, R., et al. : Confinement performance predictions for a high field axisymmetric tandem mirror. Journal of 62 Plasma Physics 91(4), 110 (2025)

    work page 2025

  26. [26]

    : Prospects for a high-field, com- pact break-even axisymmetric mirror (beam) and applications

    Forest, C., Anderson, J., Endrizzi, D., Egedal, J., Frank, S., Furlong, K., Ialovega, M., Kirch, J., Harvey, R., Lindley, B., et al. : Prospects for a high-field, com- pact break-even axisymmetric mirror (beam) and applications. Journal of Plasma Physics 90(1), 975900101 (2024)

    work page 2024

  27. [27]

    In: 2013 IEEE 25th Symposium on Fusion Engineering (SOFE), pp

    Laberge, M., Howard, S., Richardson, D., Froese, A., Suponitsky, V., Reynolds, M., Plant, D.: Acoustically driven magnetized target fusion. In: 2013 IEEE 25th Symposium on Fusion Engineering (SOFE), pp. 1–7 (2013). IEEE

    work page 2013

  28. [28]

    In: 30th International Symposium on Shock Waves 2: ISSW30-Volume 2, pp

    Suponitsky, V., Plant, D., A vital, E., Munjiza, A.: Propagation of pressure waves in compression system prototype for magnetized target fusion reactor in general fusion inc. In: 30th International Symposium on Shock Waves 2: ISSW30-Volume 2, pp. 955–960 (2017). Springer

    work page 2017

  29. [29]

    : Stellaris: A high- field quasi-isodynamic stellarator for a prototypical fusion power plant

    Lion, J., Anglès, J.-C., Bonauer, L., Navarro, A.B., Ceron, S.C., Davies, R., Drevlak, M., Foppiani, N., Geiger, J., Goodman, A., et al. : Stellaris: A high- field quasi-isodynamic stellarator for a prototypical fusion power plant. Fusion Engineering and Design 214, 114868 (2025)

    work page 2025

  30. [30]

    : The ARIES − AT advanced tokamak, advanced technology fusion power plant

    Najmabadi, F., Abdou, A., Bromberg, L., Brown, T., Chan, V., Chu, M., Dahlgren, F., El-Guebaly, L., Heitzenroeder, P., Henderson, D., et al. : The ARIES − AT advanced tokamak, advanced technology fusion power plant. Fusion Engineering and Design 80(1-4), 3–23 (2006)

    work page 2006

  31. [31]

    Physics of Plasmas 32(9) (2025)

    Alexander, A., Benedetti, L.R., Bhattacharyya, I., Bowen, J., Cabatu, J., Cacdac, V., Chhavi, C., Chen, C., Chen, K., Clark, D., et al.: Affordable, manageable, practical, and scalable (amps) high-yield and high-gain inertial fusion. Physics of Plasmas 32(9) (2025)

    work page 2025

  32. [32]

    : Prospects for pilot plants based on the tokamak, spherical tokamak and stellarator

    Menard, J., Bromberg, L., Brown, T., Burgess, T., Dix, D., El-Guebaly, L., Ger- rity, T., Goldston, R.J., Hawryluk, R., Kastner, R., et al. : Prospects for pilot plants based on the tokamak, spherical tokamak and stellarator. Nuclear Fusion 51(10), 103014 (2011)

    work page 2011

  33. [33]

    Report No

    Hubert, M.: DOE Hydrogen Program Record. Report No. 24005 (2024)

    work page 2024

  34. [34]

    Criteria for the economic viability of fusion power plants

    Lo, A.: Properties of Qecon: Concavity, Log-Log-Concavity, and Implications for Closest-Viable-Design Optimization. Supplement to D. Whyte et al., “Criteria for the economic viability of fusion power plants” (2025)

    work page 2025

  35. [35]

    Oxford University Press, Oxford (2014)

    Pareto, V.: Manual of Political Economy: a Critical and Variorum Edition. Oxford University Press, Oxford (2014)

    work page 2014

  36. [36]

    Nuclear Fusion 22(7), 935 (1982)

    Houlberg, W., Attenberger, S., Hively, L.: Contour analysis of fusion reactor plasma performance. Nuclear Fusion 22(7), 935 (1982)

    work page 1982

  37. [37]

    : Overview of the SPARC 63 tokamak

    Creely, A., Greenwald, M.J., Ballinger, S.B., Brunner, D., Canik, J., Doody, J., Fülöp, T., Garnier, D., Granetz, R., Gray, T., et al. : Overview of the SPARC 63 tokamak. Journal of Plasma Physics 86(5), 865860502 (2020)

    work page 2020

  38. [38]

    Journal of Portfolio Management 21, 49–58 (1994)

    Sharpe, W.F.: The sharpe ratio. Journal of Portfolio Management 21, 49–58 (1994)

    work page 1994

  39. [39]

    https://en.wikipedia.org/wiki/Joint_European_Torus (2025)

    Joint European Torus. https://en.wikipedia.org/wiki/Joint_European_Torus (2025)

    work page 2025

  40. [40]

    In: 17th IEEE/NPSS Symposium Fusion Engineering (Cat

    Meade, D.M., Woolley, R.D.: Affordable near-term burning-plasma experiments. In: 17th IEEE/NPSS Symposium Fusion Engineering (Cat. No. 97CH36131), vol. 1, pp. 237–240 (1997). IEEE

    work page 1997

  41. [41]

    Nuclear Fusion 55(10), 104001 (2015)

    Romanelli, F., et al.: Overview of the JET results. Nuclear Fusion 55(10), 104001 (2015)

    work page 2015

  42. [42]

    : Fusion plasma experiments on TFTR: A 20 year retrospective

    Hawryluk, R., Batha, S., Blanchard, W., Beer, M., Bell, M., Bell, R., Berk, H., Bernabei, S., Bitter, M., Breizman, B., et al. : Fusion plasma experiments on TFTR: A 20 year retrospective. Physics of Plasmas 5(5), 1577–1589 (1998)

    work page 1998

  43. [43]

    IEEE Transactions on plasma science 44(9), 1466–1471 (2016)

    Wolf, R., Beidler, C., Dinklage, A., Helander, P., Laqua, H., Schauer, F., Pedersen, T.S., Warmer, F.: Wendelstein 7 − X program—demonstration of a stellarator option for fusion energy. IEEE Transactions on plasma science 44(9), 1466–1471 (2016)

    work page 2016

  44. [44]

    : Progress summary of LHD engineering design and construction

    Motojima, O., Akaishi, K., Chikaraishi, H., Funaba, H., Hamaguchi, S., Imagawa, S., Inagaki, S., Inoue, N., Iwamoto, A., Kitagawa, S., et al. : Progress summary of LHD engineering design and construction. Nuclear Fusion 40(3Y), 599 (2000)

    work page 2000

  45. [45]

    https://en.wikipedia.org/wiki/Wendelstein_7-X (2025)

    Wendelstein 7-X. https://en.wikipedia.org/wiki/Wendelstein_7-X (2025)

    work page 2025

  46. [46]

    https://www.japantimes.co.jp/life/2010/09/29/digital/japanese-facility-aimed- at-creating-a-sun-on-earth/ (2010)

    Carr, S.: Japanese facility aimed at creating a sun on Earth. https://www.japantimes.co.jp/life/2010/09/29/digital/japanese-facility-aimed- at-creating-a-sun-on-earth/ (2010)

    work page 2010

  47. [47]

    Physics Today (2018)

    Kramer, D.: ITER disputes DOE’s cost estimate of fusion project. Physics Today (2018). https://doi.org/10.1063/PT.6.2.20180416a

    work page doi:10.1063/pt.6.2.20180416a 2018

  48. [48]

    Nuclear Fusion 47(6), 01 (2007)

    Ikeda, K.: Progress in the ITER physics basis. Nuclear Fusion 47(6), 01 (2007)

    work page 2007

  49. [49]

    : Spherical torus concept as power plants—the ARIES − ST study

    Najmabadi, F., et al. : Spherical torus concept as power plants—the ARIES − ST study. Fusion Engineering and Design 65(2), 143–164 (2003)

    work page 2003

  50. [50]

    : The ARIES − CS compact stellarator fusion power plant

    Najmabadi, F., Raffray, A., Abdel-Khalik, S., Bromberg, L., Crosatti, L., El- Guebaly, L., Garabedian, P., Grossman, A., Henderson, D., Ibrahim, A., et al. : The ARIES − CS compact stellarator fusion power plant. Fusion Science and Technology 54(3), 655–672 (2008)

    work page 2008

  51. [51]

    Fusion Science and Technology 60(1), 66–71 (2011) 64

    Anklam, T.M., Dunne, M., Meier, W.R., Powers, S., Simon, A.J.: LIFE: the case for early commercialization of fusion energy. Fusion Science and Technology 60(1), 66–71 (2011) 64

    work page 2011

  52. [52]

    Physics Today 75(5), 20–22 (2022)

    Kramer, D.: Further delays at ITER are certain, but their duration isn’t clear. Physics Today 75(5), 20–22 (2022)

    work page 2022

  53. [53]

    https://sciencebusiness.net/news/iter-fusion-project-confirms-more-delays- and-eu5b-cost-overrun (2024)

    Matthews, D.: ITER fusion project confirms more delays and €5B cost over- run. https://sciencebusiness.net/news/iter-fusion-project-confirms-more-delays- and-eu5b-cost-overrun (2024)

    work page 2024

  54. [54]

    Physics Today (2021)

    Kramer, D.: Investors flock to MIT fusion spinoff. Physics Today (2021). https://doi.org/10.1063/PT.6.2.20211209a

    work page doi:10.1063/pt.6.2.20211209a 2021

  55. [55]

    : Remote handling maintenance of ITER

    Haange, R., et al. : Remote handling maintenance of ITER. Nuclear Fusion 39(11Y), 2043 (1999)

    work page 2043

  56. [56]

    : Long term project in ASDEXUpgrade: Implementation of ferritic steel as in vessel wall

    Zammuto, I., Giannone, L., Houben, A., Herrmann, A., Kallenbach, A., et al. : Long term project in ASDEXUpgrade: Implementation of ferritic steel as in vessel wall. Fusion Engineering and Design 98, 1419–1422 (2015)

    work page 2015

  57. [57]

    https://en.wikipedia.org/wiki/Rolls-Royce_Trent_900 (2025)

    Rolls-Royce Trent 900. https://en.wikipedia.org/wiki/Rolls-Royce_Trent_900 (2025)

    work page 2025

  58. [58]

    https://www.coxautoinc.com/market-insights/june-2025-atp- report (2025)

    COX Automotive. https://www.coxautoinc.com/market-insights/june-2025-atp- report (2025)

    work page 2025

  59. [59]

    https://www.autoinsurance.com/guide/average-car-weight/ (2025)

    Auto Insurance. https://www.autoinsurance.com/guide/average-car-weight/ (2025)

    work page 2025

  60. [60]

    Princeton University Press, Princeton, NJ (2017)

    Lo, A.W.: Adaptive Markets: Financial Evolution at the Speed of Thought. Princeton University Press, Princeton, NJ (2017)

    work page 2017

  61. [61]

    Oxford University Press, Oxford, UK (2024)

    Lo, A.W., Zhang, R.: The Adaptive Markets Hypothesis: An Evolutionary Approach to Understanding Financial System Dynamics. Oxford University Press, Oxford, UK (2024)

    work page 2024

  62. [62]

    Springer, Berlin Heidelberg (2007)

    Was, G.S.: Fundamentals of Radiation Materials Science: Metals and Alloys. Springer, Berlin Heidelberg (2007)

    work page 2007

  63. [63]

    Reports on progress in physics 18(1), 1 (1955)

    Kinchin, G., Pease, R.: The displacement of atoms in solids by radiation. Reports on progress in physics 18(1), 1 (1955)

    work page 1955

  64. [64]

    Fusion Science and Technology 64(2), 65–75 (2013)

    Zinkle, S.J.: Challenges in developing materials for fusion technology-past, present and future. Fusion Science and Technology 64(2), 65–75 (2013)

    work page 2013

  65. [65]

    : Determination of radiation dam- age limits to high-temperature superconductors in reactor-relevant conditions to inform compact fusion reactor design

    Sorbom, B., Hartwig, Z., Kesler, L., Whyte, D., Minervini, J., Short, M., Wright, G., Takayasu, M., Ames, M., Kohse, G., et al. : Determination of radiation dam- age limits to high-temperature superconductors in reactor-relevant conditions to inform compact fusion reactor design. In: 26th IAEA Fusion Energy Conf. Kyoto, Japan, 17–22 October (2016)

    work page 2016

  66. [66]

    American Institute of Physics, New York (1985) 65

    Stacey Jr, W., Steiner, D.: Fusion: An Introduction to the Physics and Technology of Magnetic Confinement Fusion. American Institute of Physics, New York (1985) 65

    work page 1985

  67. [67]

    personal communication, 2024-04-13

    Hartwig, Z.S. personal communication, 2024-04-13

    work page 2024

  68. [68]

    Nuclear Fusion 17(1), 13 (1977) 66 S1 Properties of Qecon: Concavity, Log-Log-Concavity, and Implications for Closest-Viable-Design Optimization A

    Moreau, D.C.: Potentiality of the proton-boron fuel for controlled thermonuclear fusion. Nuclear Fusion 17(1), 13 (1977) 66 S1 Properties of Qecon: Concavity, Log-Log-Concavity, and Implications for Closest-Viable-Design Optimization A. Lo Laboratory for Financial Engineering, Massachusetts Institute of Technology, Cambridge MA 02139 USA Supplement to Cri...

    work page 1977

  69. [69]

    ss′′ − s′2 = r[log(1 + r) − r]/(1 + r)2 < 0, since log(1 + r) < r for r > 0

    work page

  70. [70]

    g′ = −1/(ew − 1) < 0

    work page

  71. [71]

    Therefore det H = (+)()()(+) > 0

    g′′w + g′ = [ ew(w − 1) + 1] /(ew − 1)2 > 0, since h(w) = ew(w − 1) + 1 satisfies h(0) = 0 and h′(w) = wew > 0. Therefore det H = (+)()()(+) > 0. Together, H11 0, H22 0, det H 0 establish positive semidefiniteness. □ S1.5.3 The full 10-parameter result Theorem 6 (Log-log-concavity of Qecon) Qecon is log-log-concave as a function of all 10 parameters on R1...

    work page

  72. [72]

    βcY pX and mSp: monomials, hence log-log-affine

    work page

  73. [73]

    closest

    mF φX and mF φpτ : products of monomials with φ, which is log-log-convex by Lemma 5. In log-coordinates, log(mF φX) = ℓmF + ℓX + log φ; since log φ is convex in (ℓi, ℓτL) and the remaining terms are linear, the sum is convex. Hence log D is convex in ℓ, and log Qecon = log N log D is concave. 69 Note: With Lemma 5 now fully proved analytically (all three ...

    work page