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arxiv: 2606.18029 · v1 · pith:NA2W4ABUnew · submitted 2026-06-16 · ⚛️ physics.plasm-ph

Understanding and Quantifying Banana Coil Magnetic Fields and Forces for Enhanced Optimisation

Annika Zettl , Tobias Schuett , Sophia Henneberg This is my paper

Pith reviewed 2026-06-26 22:20 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords banana coilstokamak-stellarator hybridcoil optimizationforce reductionmagnetic fieldsfusion confinementengineering constraints
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The pith

Optimizing banana coils with force constraints produces shapes that reduce forces while reproducing hybrid magnetic configurations.

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

This paper shows that banana coils for tokamak-stellarator hybrids can be optimized not only for geometry but also for engineering constraints such as forces. The resulting coil shapes have characteristic features that generate magnetic fields allowing analysis of how forces are reduced. This builds on earlier findings that such coils can reproduce desired hybrid configurations when combined with standard tokamak coils. Readers interested in fusion device design would care because addressing coil forces is key to practical engineering of compact, high-performance reactors.

Core claim

The paper claims that when banana coils are optimized including force and other engineering metrics, they develop characteristic non-planar geometries. These geometries generate fields that reproduce the optimized tokamak-stellarator hybrid configurations from prior work, and the fields permit analysis of the mechanisms by which the optimization reduces forces.

What carries the argument

The optimization of banana coils under expanded engineering objectives including forces, which produces reproducible magnetic configurations and allows quantification of force reduction.

If this is right

  • Characteristic shapes emerge in force-optimized banana coils.
  • The generated magnetic fields support analysis of force-reduction mechanisms.
  • Prior hybrid configurations remain reproducible under the expanded optimization.
  • Force reduction occurs through specific modifications to coil geometry.

Where Pith is reading between the lines

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

  • Similar optimization strategies could apply to other non-planar coil designs in stellarators.
  • Quantified force mechanisms might inform material choices or support structures in fusion devices.
  • Extending this to include additional constraints like stress or heat could further improve coil practicality.

Load-bearing premise

The previously demonstrated reproducibility of hybrid magnetic configurations by banana coils holds when the optimization objective is broadened to include force minimization and other engineering metrics.

What would settle it

Demonstrating that no set of force-optimized banana coils can generate the magnetic field needed to match the target hybrid configuration from earlier studies.

Figures

Figures reproduced from arXiv: 2606.18029 by Annika Zettl, Sophia Henneberg, Tobias Schuett.

Figure 1
Figure 1. Figure 1: The three different Hybrid equilibria for which we found coils in this work, labelled as [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A schematic plot of the self and TF force on a banana coil as a function of its distance [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: An example of “escaping coils”. In this case, very long banana coils arrange themselves [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A sketch of the two options to place non-linked coils respecting stellarator symmetry. In [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: A diagram illustrating a banana coil beside a plasma boundary, with red dots showing the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The maximum local curvature and minimum coil-plasma separation of the optimised [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Relationship between the coil width and the net twist angle. The colour scale represents [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Examples coils from the automated optimisation for the H1 Hybrid equilibrium. Panel [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Central curve–plasma distance as a function of the banana coil current. The colour scale [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Magnetic field strength per unit current near the plasma centre from a single banana coil, [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Trade-off between the integrated force magnitude, [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Integrated force on the banana coil as a function of the maximum force for optimisations [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Maximum force on the banana coil per unit current versus the radius at which the [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Maximum toroidal field force on the banana coil per unit current versus the radius at [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Various plots for optimised coils with a force threshold of 1 [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Various plots for optimised coils with zero force threshold for the H2 boundary(with [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Various plots for optimised coils with zero force threshold for the H3 boundary (with [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
read the original abstract

The optimised tokamak-stellarator hybrid concept (Henneberg and Plunk 2024) has the potential to combine tokamak and stellarator advantages to achieve magnetically confined fusion. These compact quasi-axisymmetric designs can have a low aspect ratio and large plasma volume, good particle confinement, and relatively simple coils. Previous work showed that such magnetic configurations can in principle be reproduced by a single type of non-planar "banana coil" alongside the conventional tokamak coilset (Henneberg and Plunk 2025). In this work, we optimise banana coils while also considering engineering constraints beyond simple geometric measures. We quantify the characteristic geometries of force-optimised banana coils and the magnetic fields they generate, and analyse the mechanisms by which forces may be reduced through optimisation.

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

1 major / 1 minor

Summary. The manuscript extends prior work on tokamak-stellarator hybrid concepts by optimizing non-planar banana coils under expanded engineering constraints (including forces) beyond pure geometry, quantifies the resulting coil shapes and generated fields, and analyzes force-reduction mechanisms while claiming to reproduce the quasi-axisymmetric hybrid configurations of Henneberg and Plunk 2025.

Significance. If substantiated, the results would provide a concrete route to engineering-constrained coil sets for compact QA hybrids, directly addressing the gap between idealized magnetic configurations and practical force/engineering limits.

major comments (1)
  1. [Abstract] Abstract: the central claim that force-optimized banana coils 'reproduce prior hybrid configurations' is unsupported by any reported quantitative metrics (field-error norms, iota profiles, quasi-axisymmetry measures, or residual error comparisons to the 2025 reference); this directly undermines the premise that the subsequent force-reduction analysis applies to the same magnetic configurations.
minor comments (1)
  1. The optimization objective function (weighting of force terms versus field-reproduction terms) is not explicitly defined; adding this would clarify how the expanded constraints affect the solution space.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and the recommendation for major revision. We address the single major comment point-by-point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that force-optimized banana coils 'reproduce prior hybrid configurations' is unsupported by any reported quantitative metrics (field-error norms, iota profiles, quasi-axisymmetry measures, or residual error comparisons to the 2025 reference); this directly undermines the premise that the subsequent force-reduction analysis applies to the same magnetic configurations.

    Authors: We agree that the abstract does not provide quantitative metrics demonstrating that the force-optimized banana coils reproduce the target quasi-axisymmetric hybrid configurations from Henneberg and Plunk 2025. While the optimization procedure is initialized from and constrained toward those configurations, the absence of explicit comparisons (e.g., field-error norms, iota profiles, or QA measures) leaves the claim unsubstantiated in the current text. In the revised manuscript we will add a dedicated subsection or figure with these metrics, including direct residual-error comparisons to the 2025 reference, to confirm that the force-optimized coils retain the essential magnetic properties before presenting the force-reduction analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; optimization and analysis are independent of cited baseline.

full rationale

The paper conducts a new optimization of banana coils that incorporates force and engineering metrics beyond the geometric measures of the 2025 reference, then quantifies the resulting coil shapes and generated fields. The citation to Henneberg and Plunk 2025 supplies only the starting hybrid configuration that the prior geometry-only coils could reproduce; the present work does not treat reproduction under the expanded objective as given by that citation or by any fitted parameter. No equation or claim reduces a derived field property or force-reduction mechanism to a quantity defined from the same data or prior result by construction. The self-citation is background and does not carry the central claims.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no explicit free parameters, axioms, or invented entities can be extracted. The work assumes the prior magnetic configurations remain valid targets under expanded optimization.

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discussion (0)

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Reference graph

Works this paper leans on

63 extracted references · 42 canonical work pages

  1. [1]

    Physica D: Nonlinear Phenomena , author =

    Stellarator symmetry , volume =. Physica D: Nonlinear Phenomena , author =. 1998 , keywords =. doi:10.1016/S0167-2789(97)00216-9 , abstract =

    work page doi:10.1016/s0167-2789(97)00216-9 1998

  2. [2]

    Henneberg, S. A. and Plunk, G. G. , month = jun, year =. Compact stellarator-tokamak hybrid , volume =. Physical Review Research , publisher =. doi:10.1103/PhysRevResearch.6.L022052 , abstract =

    work page doi:10.1103/physrevresearch.6.l022052

  3. [3]

    Physical Review Research , author =

    Exploring novel compact quasi-axisymmetric stellarators , volume =. Physical Review Research , author =. 2024 , keywords =. doi:10.1103/PhysRevResearch.6.L042052 , language =

    work page doi:10.1103/physrevresearch.6.l042052 2024

  4. [4]

    Journal of Plasma Physics , volume =

    Perturbing an axisymmetric magnetic equilibrium to obtain a quasi-axisymmetric stellarator , volume =. Journal of Plasma Physics , author =. 2020 , keywords =. doi:10.1017/S0022377820000902 , abstract =

    work page doi:10.1017/s0022377820000902 2020

  5. [5]

    Journal of Plasma Physics , author =

    Representing the boundary of stellarator plasmas , volume =. Journal of Plasma Physics , author =. 2021 , keywords =. doi:10.1017/S0022377821000891 , abstract =

    work page doi:10.1017/s0022377821000891 2021

  6. [6]

    Theory of plasma confinement in non-axisymmetric magnetic fields , volume =

    Helander, Per , month = jul, year =. Theory of plasma confinement in non-axisymmetric magnetic fields , volume =. Reports on Progress in Physics , publisher =. doi:10.1088/0034-4885/77/8/087001 , abstract =

    work page doi:10.1088/0034-4885/77/8/087001

  7. [7]

    Plasma Physics and Controlled Fusion , author =

    The virtual-casing principle and. Plasma Physics and Controlled Fusion , author =. 2015 , keywords =. doi:10.1088/0741-3335/57/11/115006 , abstract =

    work page doi:10.1088/0741-3335/57/11/115006 2015

  8. [8]

    Nuclear Fusion , volume =

    Use of the virtual-casing principle in calculating the containing magnetic field in toroidal plasma systems , volume =. Nuclear Fusion , author =. 1972 , keywords =. doi:10.1088/0029-5515/12/5/009 , language =

    work page doi:10.1088/0029-5515/12/5/009 1972

  9. [9]

    Wiedman, A and Buller, Stefan and Landreman, Matt , doi =. Coil. Journal of Plasma Physics , volume=. 2024 , publisher=

    2024

  10. [10]

    Nuclear Fusion , volume =

    An improved current potential method for fast computation of stellarator coil shapes , volume =. Nuclear Fusion , author =. 2017 , note =. doi:10.1088/1741-4326/aa57d4 , abstract =

    work page doi:10.1088/1741-4326/aa57d4 2017

  11. [11]

    Design of

    Design of. Nuclear Fusion , author =. 2025 , keywords =. doi:10.1088/1741-4326/ada2a9 , abstract =

    work page doi:10.1088/1741-4326/ada2a9 2025

  12. [12]

    Journal of Plasma Physics , author =

    Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum , volume =. Journal of Plasma Physics , author =. 2018 , keywords =. doi:10.1017/S0022377818000259 , abstract =

    work page doi:10.1017/s0022377818000259 2018

  13. [13]

    Physics of Plasmas , volume =

    Optimization of quasi-symmetric stellarators with self-consistent bootstrap current and energetic particle confinement , volume =. Physics of Plasmas , author =. 2022 , keywords =. doi:10.1063/5.0098166 , abstract =

    work page doi:10.1063/5.0098166 2022

  14. [14]

    Journal of Plasma Physics , author =

    Optimization of finite-build stellarator coils , volume =. Journal of Plasma Physics , author =. 2020 , keywords =. doi:10.1017/S0022377820000756 , abstract =

    work page doi:10.1017/s0022377820000756 2020

  15. [15]

    Journal of Mathematical Physics , author =

    Some mathematics for quasi-symmetry , volume =. Journal of Mathematical Physics , author =. 2020 , keywords =. doi:10.1063/1.5142487 , abstract =

    work page doi:10.1063/1.5142487 2020

  16. [16]

    Plasma Physics and Controlled Fusion , volume =

    The magnetic gradient scale length explains why certain plasmas require close external magnetic coils , volume =. Plasma Physics and Controlled Fusion , author =. 2024 , keywords =. doi:10.1088/1361-6587/ad1a3e , abstract =

    work page doi:10.1088/1361-6587/ad1a3e 2024

  17. [17]

    Nuclear Fusion , volume =

    Kaptanoglu, Alan A. and Wiedman, Alexander and Halpern, Jacob and Hurwitz, Siena and Paul, Elizabeth J. and Landreman, Matt , month = apr, year =. Reactor-scale stellarators with force and torque minimized dipole coils , volume =. Nuclear Fusion , publisher =. doi:10.1088/1741-4326/adc318 , abstract =

    work page doi:10.1088/1741-4326/adc318

  18. [18]

    Journal of Plasma Physics , volume =

    Combined plasma–coil optimization algorithms , volume =. Journal of Plasma Physics , author =. 2021 , keywords =. doi:10.1017/S0022377821000271 , abstract =

    work page doi:10.1017/s0022377821000271 2021

  19. [19]

    Plasma Physics and Controlled Fusion , author =

    Optimization of compact quasi-axisymmetric stellarators , volume =. Plasma Physics and Controlled Fusion , author =. 2025 , pages =. doi:10.1088/1361-6587/add598 , abstract =

    work page doi:10.1088/1361-6587/add598 2025

  20. [20]

    The Physics of Fluids , volume =

    Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria , volume =. The Physics of Fluids , author =. 1983 , pages =. doi:10.1063/1.864116 , abstract =

    work page doi:10.1063/1.864116 1983

  21. [21]

    Plasma Physics and Controlled Fusion , author =

    Physics in the magnetic configuration space of. Plasma Physics and Controlled Fusion , author =. 2015 , pages =. doi:10.1088/0741-3335/57/1/014004 , abstract =

    work page doi:10.1088/0741-3335/57/1/014004 2015

  22. [22]

    Physics of Plasmas , volume =

    Low edge safety factor operation and passive disruption avoidance in current carrying plasmas by the addition of stellarator rotational transform , volume =. Physics of Plasmas , author =. 2015 , pages =. doi:10.1063/1.4935396 , abstract =

    work page doi:10.1063/1.4935396 2015

  23. [23]

    Plasma Physics and Controlled Fusion , volume =

    Variety of coil sets for the compact stellarator-tokamak hybrid , volume =. Plasma Physics and Controlled Fusion , author =. 2025 , pages =. doi:10.1088/1361-6587/add763 , abstract =

    work page doi:10.1088/1361-6587/add763 2025

  24. [24]

    Plasma Physics and Controlled Fusion , author =

    Back to the figure-8 stellarator , volume =. Plasma Physics and Controlled Fusion , author =. 2025 , pages =. doi:10.1088/1361-6587/adb64b , abstract =

    work page doi:10.1088/1361-6587/adb64b 2025

  25. [25]

    Landreman and E

    Magnetic. Physical Review Letters , author =. 2022 , pages =. doi:10.1103/PhysRevLett.128.035001 , language =

    work page doi:10.1103/physrevlett.128.035001 2022

  26. [26]

    Physics of Plasmas , volume =

    Nonaxisymmetric shaping of tokamaks preserving quasiaxisymmetry , volume =. Physics of Plasmas , author =. 2009 , pages =. doi:10.1063/1.3207010 , abstract =

    work page doi:10.1063/1.3207010 2009

  27. [27]

    The Physics of Fluids , author =

    Transport and isomorphic equilibria , volume =. The Physics of Fluids , author =. 1983 , pages =. doi:10.1063/1.864166 , abstract =

    work page doi:10.1063/1.864166 1983

  28. [28]

    Byrd, R. H. and Peihuang, L. and Nocedal, J. , month = mar, year =. A limited-memory algorithm for bound-constrained optimization , doi =. UNT Digital Library , publisher =

  29. [29]

    Mathematical Programming , author =

    On the limited memory. Mathematical Programming , author =. 1989 , keywords =. doi:10.1007/BF01589116 , abstract =

    work page doi:10.1007/bf01589116 1989

  30. [30]

    and Wolf, R.C

    Bosch, H.-S. and Wolf, R.C. and Andreeva, T. and Baldzuhn, J. and Birus, D. and Bluhm, T. and Bräuer, T. and Braune, H. and Bykov, V. and Cardella, A. and Durodié, F. and Endler, M. and Erckmann, V. and Gantenbein, G. and Hartmann, D. and Hathiramani, D. and Heimann, P. and Heinemann, B. and Hennig, C. and Hirsch, M. and Holtum, D. and Jagielski, J. and J...

    work page doi:10.1088/0029-5515/53/12/126001

  31. [31]

    , year = 2024, month = nov, journal =

    Efficient. IEEE Transactions on Magnetics , author =. 2024 , keywords =. doi:10.1109/TMAG.2024.3455946 , number =

    work page doi:10.1109/tmag.2024.3455946 2024

  32. [32]

    Electromagnetic Coil Optimization for Reduced

    Hurwitz, Siena and Landreman, Matt and Huslage, Paul and Kaptanoglu, Alan , month = apr, year =. Electromagnetic coil optimization for reduced. Nuclear Fusion , publisher =. doi:10.1088/1741-4326/adc9bf , language =

    work page doi:10.1088/1741-4326/adc9bf

  33. [33]

    Physics Letters A , author =

    Extreme low aspect ratio stellarators , volume =. Physics Letters A , author =. 1998 , pages =. doi:10.1016/S0375-9601(98)00215-1 , abstract =

    work page doi:10.1016/s0375-9601(98)00215-1 1998

  34. [34]

    , month = jul, year =

    Moroz, Paul E. , month = jul, year =. Spherical. Physical Review Letters , publisher =. doi:10.1103/PhysRevLett.77.651 , abstract =

    work page doi:10.1103/physrevlett.77.651

  35. [35]

    Nuclear Fusion , author =

    Stabilization of the (2, 1) tearing mode and of the current disruption in the. Nuclear Fusion , author =. 1980 , pages =. doi:10.1088/0029-5515/20/9/008 , abstract =

    work page doi:10.1088/0029-5515/20/9/008 1980

  36. [36]

    Stellarators and the Path from

    Stellarators and the path from. Plasma Physics and Controlled Fusion , author =. 2008 , pages =. doi:10.1088/0741-3335/50/12/124005 , abstract =

    work page doi:10.1088/0741-3335/50/12/124005 2008

  37. [37]

    Journal of Open Source Software , volume =

    Landreman, Matt and Giuliani, Andrew and Dudt, Daniel and others , title =. Journal of Open Source Software , volume =. 2022 , doi =

    2022

  38. [38]

    Nuclear Fusion , volume=

    Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section , author=. Nuclear Fusion , volume=. 2025 , publisher=

    2025

  39. [39]

    doi:10.21105/joss.03525 , urldate =

    Landreman, Matt and Medasani, Bharat and Wechsung, Florian and Giuliani, Andrew and Jorge, Rogerio and Zhu, Caoxiang , title =. doi:10.21105/joss.03525 , year =

    work page doi:10.21105/joss.03525

  40. [40]

    and Kaufmann, M

    Gruber, O. and Kaufmann, M. and Köppendörfer, W. and Lackner, K. and Neuhauser, J. , month = may, year =. Physics background of the. doi:10.1016/0022-3115(84)90153-3 , journal =

    work page doi:10.1016/0022-3115(84)90153-3

  41. [41]

    Plasma Physics and Controlled Fusion , author =

    Major results from the stellarator. Plasma Physics and Controlled Fusion , author =. 2008 , pages =. doi:10.1088/0741-3335/50/5/053001 , language =

    work page doi:10.1088/0741-3335/50/5/053001 2008

  42. [42]

    doi:10.1137/1.9781611978223 , urldate =

    Imbert-Gérard, Lise-Marie and Paul, Elizabeth J. and Wright, Adelle M. , year =. An. doi:10.1137/1.9781611978223 , publisher =

    work page doi:10.1137/1.9781611978223

  43. [43]

    Physics of Plasmas , author =

    W7-. Physics of Plasmas , author =. 2005 , pages =. doi:10.1063/1.1927100 , number =

    work page doi:10.1063/1.1927100 2005

  44. [44]

    G. J. Hartwell and S. F. Knowlton and J. D. Hanson and D. A. Ennis and D. A. Maurer , title =. Fusion Science and Technology , volume =. 2017 , publisher =. doi:10.1080/15361055.2017.1291046 , eprint =

    work page doi:10.1080/15361055.2017.1291046 2017

  45. [45]

    Plasma Physics and Controlled Fusion , author =

    Overview of the. Plasma Physics and Controlled Fusion , author =. 2000 , pages =. doi:10.1088/0741-3335/42/11/303 , number =

    work page doi:10.1088/0741-3335/42/11/303 2000

  46. [46]

    1999 , publisher=

    Numerical Optimization , author=. 1999 , publisher=

    1999

  47. [47]

    Nuclear Fusion , author =

    Effect of the magnetic field ripple on diffusion in. Nuclear Fusion , author =. 1972 , pages =. doi:10.1088/0029-5515/12/6/010 , abstract =

    work page doi:10.1088/0029-5515/12/6/010 1972

  48. [48]

    1962 , publisher=

    Classical Electrodynamics , author=. 1962 , publisher=

    1962

  49. [49]

    1972 , publisher=

    Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , author=. 1972 , publisher=

    1972

  50. [50]

    1987 , month =

    Wesson, J , title =. 1987 , month =

    1987

  51. [51]

    and Abe, Y

    Yamazaki, K. and Abe, Y. and Physics, Nagoya Univ (Japan) Inst of Plasma , month = feb, year =

  52. [52]

    Fusion Engineering and design , volume=

    Design of the national compact stellarator experiment (NCSX) , author=. Fusion Engineering and design , volume=. 2003 , publisher=

    2003

  53. [53]

    Theory of Fusion Plasmas: Proceedings of the Joint Varenna-Lausanne International Workshop , pages=

    Quasi-axisymmetric tokamaks , author=. Theory of Fusion Plasmas: Proceedings of the Joint Varenna-Lausanne International Workshop , pages=. 1994 , organization=

    1994

  54. [54]

    Plasma Physics and Controlled Fusion , volume=

    Physics of the compact advanced stellarator NCSX , author=. Plasma Physics and Controlled Fusion , volume=

  55. [55]

    Physical Review Letters , volume=

    Magnetic fields with precise quasisymmetry for plasma confinement , author=. Physical Review Letters , volume=. 2022 , publisher=

    2022

  56. [56]

    Nuclear Fusion , volume=

    Properties of a new quasi-axisymmetric configuration , author=. Nuclear Fusion , volume=. 2019 , publisher=

    2019

  57. [57]

    Plasma physics and controlled fusion , volume=

    The ITER design , author=. Plasma physics and controlled fusion , volume=

  58. [58]

    arXiv preprint arXiv:2606.04122 , year=

    Compact quasiaxisymmetric stellarators, a near axisymmetric theory , author=. arXiv preprint arXiv:2606.04122 , year=

    Pith/arXiv arXiv

  59. [59]

    arXiv preprint arXiv:2605.21814 , year=

    Optical analogy for stellarators: Ridges as caustics and coils as singularities , author=. arXiv preprint arXiv:2605.21814 , year=

    Pith/arXiv arXiv

  60. [60]

    arXiv preprint arXiv:2604.12339 , year=

    Estimating coil features from an equilibrium , author=. arXiv preprint arXiv:2604.12339 , year=

    Pith/arXiv arXiv

  61. [61]

    Journal of Plasma Physics , volume=

    A comprehensive exploration of quasisymmetric stellarators and their coil sets , author=. Journal of Plasma Physics , volume=. 2025 , publisher=

    2025

  62. [62]

    Journal of Plasma Physics , volume=

    Constructing precisely quasi-isodynamic magnetic fields , author=. Journal of Plasma Physics , volume=. 2023 , publisher=

    2023

  63. [63]

    Journal of Plasma Physics , volume=

    Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation , author=. Journal of Plasma Physics , volume=. 2024 , publisher=

    2024