pith. sign in

arxiv: 2606.13326 · v1 · pith:YQQLK7QJnew · submitted 2026-06-11 · ⚛️ physics.plasm-ph

Feasibility of a Flexible, Hybrid Tokamak-Stellarator Experiment using an Axisymmetric Dipole Coil Array

Jacob Halpern , Mohammed Haque , Elizabeth Paul , Carlos Paz-Soldan , Rithik Banerjee , Talia Angles , Frederick Sheehan , Ian Stewart This is my paper

Pith reviewed 2026-06-27 05:23 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords hybrid tokamak-stellaratordipole coil arrayquasi-axisymmetricrotational transformHTS coilsplasma equilibriaMHD stabilizationcoil ripple correction
0
0 comments X

The pith

A single axisymmetric array of planar dipole coils can generate tokamak, stellarator, and hybrid plasma equilibria within engineering limits.

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

The paper demonstrates that a fixed university-scale array of high-temperature superconductor dipole coils supports many plasma shapes by optimizing coil currents in one stage. It reaches vacuum stellarators with rotational transform up to 0.2, finite-beta hybrids with on-axis iota near 1 that include stabilizing vacuum transform, and tokamaks with elongation 1.7 and triangularity 0.6. All cases keep peak coil forces below HTS limits. A reader would care because the approach offers one hardware set for hybrid confinement studies instead of separate machines.

Core claim

We demonstrate the design of a flexible, university-scale hybrid tokamak-stellarator experiment based on an axisymmetric array of planar HTS dipole coils. Because the coil array has few geometric degrees of freedom, we use single-stage optimization of the coil currents initialized from two-stage solutions to obtain mutually consistent equilibria and coil sets within realistic engineering limits. From this single coil array we obtain a broad range of equilibria—quasi-axisymmetric vacuum stellarators with ι up to 0.2, finite-β hybrids with realistic profiles reaching on-axis ι ≈ 1 and vacuum transform relevant for MHD stabilization, and strongly shaped tokamaks with elongation κ = 1.7 and tria

What carries the argument

Axisymmetric array of planar HTS dipole coils whose currents are optimized in a single stage, which confines the boundary to a roughly fixed axisymmetric envelope while allowing trade-offs among rotational transform, volume, coil current, and quasi-symmetry error.

Load-bearing premise

Single-stage optimization of coil currents initialized from two-stage solutions will produce mutually consistent plasma equilibria and coil sets that remain inside realistic limits on field error and forces.

What would settle it

If an optimized current set for a target hybrid equilibrium produces measured pointwise coil forces above HTS tolerance or field errors that eliminate the intended iota profile, the feasibility result would be falsified.

Figures

Figures reproduced from arXiv: 2606.13326 by Carlos Paz-Soldan, Elizabeth Paul, Frederick Sheehan, Ian Stewart, Jacob Halpern, Mohammed Haque, Rithik Banerjee, Talia Angles.

Figure 1
Figure 1. Figure 1: Illustration of the design over a 180◦ toroidal sector showing the elliptical vacuum vessel and coils in light and dark grey, respectively. We have labeled the free vacuum vessel geometry parameters, R0,V V , aV V , and bV V . The outboard coil array we remove to demonstrate sparsity in section 3.2.4 are shown in green. We do not show any central solenoid or vertical field coils, which are not considered i… view at source ↗
Figure 2
Figure 2. Figure 2: Postprocessing analysis of the equilibrium initial condition obtained from stage-I optimization. (a) Equilibrium cross section at equally spaced toroidal locations, with the magnetic axis points shown as black Xs and the vessel constraint in solid black. (b) Rotational transform profile versus normalized toroidal flux (c) Square root of the normalized sum of quasi-axisymmetry-breaking modes in Boozer coord… view at source ↗
Figure 3
Figure 3. Figure 3: Maximum magnetic field at the dipole coil centers normalized by the toroidal field versus surface average field error for 100 randomly sampled coil sets with optimized currents for Nθ = 9, 10, 11. We plot the Pareto optimal solutions in solid black. The field error threshold required to initialize the single-stage algorithm is plotted as a vertical dashed red line. The minimum current, Pareto optimal solut… view at source ↗
Figure 4
Figure 4. Figure 4: Left: Square root of the normalized sum of quasi-axisymmetry-breaking Fourier harmonics in Boozer coordinates for single-stage optimizations at varying rotational transform ι and p-norm targets I p=20 T , starting from the Nθ = 10 initial condition in fig. 3. Each p-norm threshold is shown as a different marker shape. We only plot optimizations where full nested flux surfaces were observed. Right: The same… view at source ↗
Figure 5
Figure 5. Figure 5: Poincar´e plots at ϕ = 0 for the (a) ιT = 0.15 and (b) ιT = 0.2 configurations, both with I p=20 T = 250 kA and VT = 0.3 m3 . The optimized surface boundary is shown in black. 3.2.3 Geometric Interpretation of the Tradeoffs For a deeper look into the tradeoffs in fig. 4, we now plot the magnetic surface cross sections, axis locations, and toroidally averaged currents for some representative cases. In fig. … view at source ↗
Figure 6
Figure 6. Figure 6: Optimized magnetic surface cross sections at equally spaced toroidal locations in a field period, with the magnetic axis location for each shown as a black X. We scan ιT = 0.05, 0.1, 0.15 from (a)-(c), respectively, with fixed I p=20 T = 250 kA and VT = 0.3 m3 . The vacuum vessel is shown in black, and the dipole coil cross sections are colored based on their toroidally averaged current magnitude. However,… view at source ↗
Figure 7
Figure 7. Figure 7: Optimized magnetic surface cross sections at equally spaced toroidal locations in a field period, with the magnetic axis location for each shown as a black X. We scan I p=20 T = 100, 150, 250 kA from (a)-(c), respectively, with fixed ιT = 0.1 and VT = 0.3 m3 . The vacuum vessel is shown in black, and the dipole coil cross sections are colored based on their toroidally averaged current magnitude [PITH_FULL… view at source ↗
Figure 8
Figure 8. Figure 8: Configurations with a varying volume target of (a) 0.25 m3 (b) 0.3 m3 (c) 0.35 m3 and (d) 0.4 m3 at fixed I p=20 T = 200 kA and ιT = 0.1. We show the cross sections at 4 equally spaced toroidal locations for a field period, along with their magnetic axis location as a black X. The vacuum vessel is shown in black, and the dipole coil cross sections are colored based on their toroidally averaged current magn… view at source ↗
Figure 9
Figure 9. Figure 9: Magnetic surface cross sections at equally spaced toroidal locations for a field period for the outboard sparsity configuration with I p=20 T = 250 kA, VT = 0.3 m3 , and (a) ιT = 0.05 and (b) ιT = 0.1. The magnetic axis locations are shown as black X’s, the vacuum vessel is shown in black, and the dipole coil cross sections are colored based on the toroidally averaged current magnitude. 3.3 Finite-β Optimi… view at source ↗
Figure 10
Figure 10. Figure 10: Left: realistic HBT-EP profiles we incorporated into our vacuum solution from the single-stage optimization routine as a function of the normalized toroidal flux s. The pressure profile p is shown in solid orange and the total enclosed toroidal current Ienc is shown in dashed blue. Right: rotational transform profile ι for both the vacuum equilibrium in solid black and finite-β VMEC equilibria in dashed r… view at source ↗
Figure 11
Figure 11. Figure 11 [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Coil ripple parameter δ (eq. (16)) on the outboard midplane of a sample tokamak configuration as a function of the number of TF coils for several cases: the ripple from the TF coils alone (blue circles), the ripple from the TF coils and a dense dipole coil array (red squares), and the ripple from the TF coils and dipole coils without the outboard midplane coil (green triangles). We fix the number of toroi… view at source ↗
Figure 13
Figure 13. Figure 13: Demonstration of both a negative (left) and positive (right) triangularity tokamak equilibrium created using the axisymmetric dipole array approximated as PF coils with equal and opposite currents. The elongation κ ≈ 1.7 in both equilibria, and δ ≈ ±0.6. The vacuum vessel is shown in grey, the limiter (1 cm offset from the vacuum vessel) is in black, and the PF coils are shown as small grey rectangles. We… view at source ↗
Figure 14
Figure 14. Figure 14: Analytic examples of axis torsion (top) and rotating ellipse (bottom) shaping cases with the amplitude, and therefore the axis rotational transform, increasing left to right. The dashed black curve indicates the enveloping axisymmetric boundary. For each panel, we plot the cross section at a few different toroidal locations in various colors. The panel titles show the corresponding volume ratio of the non… view at source ↗
read the original abstract

We demonstrate the design of a flexible, university-scale hybrid tokamak-stellarator experiment based on an axisymmetric array of planar HTS dipole coils. Because the coil array has few geometric degrees of freedom, we use single-stage optimization of the coil currents initialized from two-stage solutions to obtain mutually consistent equilibria and coil sets within realistic engineering limits. We find that the field error and coil current thresholds set minimum and maximum coil-plasma distances that confine the boundary to a roughly fixed axisymmetric envelope, within which rotational transform, volume, coil current, and quasi-symmetry (QS) error trade off against one another. Tighter current limits delocalize the non-axisymmetric shaping and raise QS error at fixed transform. From this single coil array we obtain a broad range of equilibria-quasi-axisymmetric vacuum stellarators with $\iota$ up to 0.2, finite-$\beta$ hybrids with realistic profiles reaching on-axis $\iota$ $\approx$ 1 and vacuum transform relevant for MHD stabilization, and strongly shaped tokamaks with elongation $\kappa$ = 1.7 and triangularity $\delta$ = $\pm$0.6, all at peak pointwise coil forces well below the HTS tolerance. We show the same array can additionally correct toroidal field (TF) coil ripple, reducing the number of TF coils required compared to the equivalent tokamak. These results establish the design as a promising platform for hybrid tokamak-stellarator research.

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 manuscript claims that a single axisymmetric array of planar HTS dipole coils, with currents optimized in a single-stage procedure initialized from two-stage solutions, can produce a broad family of mutually consistent plasma equilibria inside realistic engineering limits. These include quasi-axisymmetric vacuum stellarators (ι up to 0.2), finite-β hybrids (on-axis ι ≈ 1 with vacuum transform for MHD stabilization), and strongly shaped tokamaks (κ = 1.7, δ = ±0.6), all at peak coil forces below HTS tolerance; the same array can also reduce TF-coil ripple. The field-error and current thresholds are said to confine the plasma boundary to a fixed axisymmetric envelope within which ι, volume, current, and QS error trade off.

Significance. If the numerical results are shown to be robust, the work would establish a compact, university-scale platform capable of exploring hybrid tokamak-stellarator physics in a single device. The use of a geometrically simple HTS coil set with demonstrated flexibility across vacuum, finite-β, and tokamak regimes, together with ripple-correction capability, would be a notable engineering and physics contribution to the design of flexible stellarator-tokamak experiments.

major comments (2)
  1. [Abstract (optimization paragraph)] Abstract, paragraph on optimization approach: the central feasibility claim rests on single-stage current optimization (initialized from two-stage solutions) yielding mutually consistent equilibria and coil sets inside field-error and force limits, yet no quantitative error bars, convergence diagnostics, validation against independent equilibrium codes, or sensitivity analysis on the post-hoc distance constraints are supplied; without these the reported ι ≈ 1 hybrids and κ = 1.7 tokamaks cannot be assessed for robustness.
  2. [Abstract and optimization section] Abstract and optimization description: the reported values of ι, κ, and δ are outputs of the same current-fitting procedure that defines the design; while external HTS force limits are invoked, the manuscript does not demonstrate that the achieved metrics remain inside those limits independently of the fitting targets, creating a circularity burden for the “broad range of equilibria” claim.
minor comments (2)
  1. [Notation and definitions] Notation for quasi-symmetry error and the precise definition of the axisymmetric envelope should be stated explicitly in the main text rather than left to figure captions.
  2. [Results presentation] The manuscript would benefit from a short table summarizing the achieved ι, κ, δ, QS error, and peak force for each class of equilibrium together with the corresponding coil-plasma distance bounds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and for identifying areas where the robustness of the optimization results could be presented more clearly. We address each major comment below and have revised the manuscript to incorporate additional diagnostics and clarifications.

read point-by-point responses

  1. Referee: [Abstract (optimization paragraph)] Abstract, paragraph on optimization approach: the central feasibility claim rests on single-stage current optimization (initialized from two-stage solutions) yielding mutually consistent equilibria and coil sets inside field-error and force limits, yet no quantitative error bars, convergence diagnostics, validation against independent equilibrium codes, or sensitivity analysis on the post-hoc distance constraints are supplied; without these the reported ι ≈ 1 hybrids and κ = 1.7 tokamaks cannot be assessed for robustness.

    Authors: We agree that the original manuscript lacks explicit convergence diagnostics, error bars, and sensitivity analysis. In the revised version we add a dedicated subsection on optimization convergence, including residual norms across multiple initializations, a sensitivity study varying the post-hoc distance constraints by ±10%, and cross-validation of selected equilibria against an independent VMEC run. These additions directly support the robustness of the ι ≈ 1 hybrid and κ = 1.7 tokamak cases. revision: yes

  2. Referee: [Abstract and optimization section] Abstract and optimization description: the reported values of ι, κ, and δ are outputs of the same current-fitting procedure that defines the design; while external HTS force limits are invoked, the manuscript does not demonstrate that the achieved metrics remain inside those limits independently of the fitting targets, creating a circularity burden for the “broad range of equilibria” claim.

    Authors: The HTS force limits are fixed external engineering constraints applied uniformly during every optimization run, independent of the target rotational transform or boundary shape. The single-stage procedure minimizes field error subject to these fixed current and force bounds; the resulting ι, κ, and δ values are therefore outcomes, not inputs. We have revised the optimization section to separate the constraint-enforcement step from the achieved plasma metrics and to tabulate the peak forces for each equilibrium class, confirming they remain below the HTS threshold irrespective of the target values. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are direct outputs of stated optimization method

full rationale

The paper is an engineering design study that optimizes coil currents (free parameters) to achieve target equilibria and then reports the achieved ι, κ, δ, and force values. This is the explicit method, not a first-principles derivation that reduces to its inputs by construction. No self-citations, uniqueness theorems, or ansatzes are invoked in the provided text. External HTS force limits serve as independent benchmarks. The central feasibility claim rests on the optimization outputs satisfying those limits, which does not constitute circularity under the defined patterns.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The design rests on standard MHD equilibrium solvers and HTS material limits drawn from prior literature; coil currents and distance thresholds are the primary fitted elements.

free parameters (2)
  • coil currents
    Optimized in single-stage procedure to achieve target rotational transform, shape, and quasi-symmetry while respecting force and field-error limits.
  • coil-plasma distance bounds
    Derived from field-error and current thresholds; used to confine the plasma boundary.
axioms (2)
  • standard math MHD force balance and Grad-Shafranov or 3D equilibrium equations hold for the target plasmas
    Invoked to generate the reported equilibria from the optimized coil currents.
  • domain assumption HTS coil force tolerance is known and fixed from material data
    Used as hard constraint on acceptable designs.

pith-pipeline@v0.9.1-grok · 5823 in / 1468 out tokens · 31445 ms · 2026-06-27T05:23:33.984735+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

85 extracted references · 82 canonical work pages · 2 internal anchors

  1. [1]

    Physics of Plasmas , volume =

    Suppression of Vertical Instability in Elongated Current-Carrying Plasmas by Applying Stellarator Rotational Transform , author =. Physics of Plasmas , volume =. doi:10.1063/1.4878615 , urldate =

    work page doi:10.1063/1.4878615

  2. [2]

    Nuclear Fusion , volume =

    Enhancing Stellarator Accessibility through Port Size Optimization , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/adf11e , urldate =

    work page doi:10.1088/1741-4326/adf11e

  3. [3]

    and Paul, E.J

    Baillod, A. and Paul, E.J. and Rawlinson, G. and Haque, M. and Freiberger, S.W. and Thapa, S. , year = 2025, month = jan, journal =. Integrating Novel Stellarator Single-Stage Optimization Algorithms to Design the. doi:10.1088/1741-4326/ada6dd , urldate =

    work page doi:10.1088/1741-4326/ada6dd 2025

  4. [4]

    Update on the Design of the

    Baillod, Antoine and Veksler, Avigdor and Lopez, Rohan and Schmeling, Dylan and Campagna, Michael and Paul, Elizabeth and Knyazev, Alexey , year = 2026, month = jan, number =. Update on the Design of the. doi:10.48550/arXiv.2601.00673 , urldate =. arXiv , keywords =:2601.00673 , primaryclass =

    work page doi:10.48550/arxiv.2601.00673 2026

  5. [5]

    and Igochine, V

    Bandyopadhyay, I. and Igochine, V. and Sauter, O. and Sabbagh, S.A. and Park, J.-K. and Nardon, E. and Villone, F. and Maraschek, M. and Pautasso, G. and Eidietis, N. and Jardin, S.C. and Humphreys, D.A. and Dubrov, M. and Artola, F.J. and. Nuclear Fusion , volume =. doi:10.1088/1741-4326/ade7a0 , urldate =

    work page doi:10.1088/1741-4326/ade7a0

  6. [6]

    Journal of Plasma Physics , volume =

    Understanding Trade-Offs in Stellarator Design with Multi-Objective Optimization , author =. Journal of Plasma Physics , volume =. doi:10.1017/S0022377823000788 , urldate =

    work page doi:10.1017/s0022377823000788

  7. [7]

    Physics of Plasmas , volume =

    Needed Computations and Computational Capabilities for Stellarators , author =. Physics of Plasmas , volume =. doi:10.1063/5.0211063 , urldate =

    work page doi:10.1063/5.0211063

  8. [8]

    Stellarators and the Path from

    Boozer, Allen H , year = 2008, month = nov, journal =. Stellarators and the Path from. doi:10.1088/0741-3335/50/12/124005 , urldate =

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

  9. [9]

    Physics of Plasmas , volume =

    Use of Nonaxisymmetric Shaping in Magnetic Fusiona) , author =. Physics of Plasmas , volume =. doi:10.1063/1.3099330 , urldate =

    work page doi:10.1063/1.3099330

  10. [10]

    and Andreeva, T

    Bosch, H.-S. and Andreeva, T. and Brakel, R. and Br. Engineering. IEEE Transactions on Plasma Science , volume =. doi:10.1109/TPS.2018.2818934 , urldate =

    work page doi:10.1109/tps.2018.2818934 2018

  11. [11]

    arXiv , keywords =:2401.09021 , primaryclass =

    A Family of Quasi-Axisymmetric Stellarators with Varied Rotational Transform , author =. arXiv , keywords =:2401.09021 , primaryclass =

    work page arXiv

  12. [12]

    Clark, A. W. and Doumet, M. and Hammond, K. C. and Kornbluth, Y. and Spong, D. A. and Sweeney, R. and Volpe, F. A. , year = 2014, month = nov, journal =. Proto-. doi:10.1016/j.fusengdes.2014.07.012 , urldate =

    work page doi:10.1016/j.fusengdes.2014.07.012 2014

  13. [13]

    Nuclear Fusion , volume =

    Effect of Toroidal Field Ripple on Plasma Rotation in. Nuclear Fusion , volume =. doi:10.1088/0029-5515/48/3/035007 , urldate =

    work page doi:10.1088/0029-5515/48/3/035007

  14. [14]

    Physics of Plasmas , volume =

    Current Potential Patches , author =. Physics of Plasmas , volume =. doi:10.1063/5.0218972 , urldate =

    work page doi:10.1063/5.0218972

  15. [15]

    Nuclear Fusion , volume =

    Global Stellarator Coil Optimization with Quadratic Constraints and Objectives , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/ada810 , urldate =

    work page doi:10.1088/1741-4326/ada810

  16. [16]

    Physics of Plasmas , volume =

    Vertical Stability in a Current-Carrying Stellarator , author =. Physics of Plasmas , volume =. doi:10.1063/1.873916 , urldate =

    work page doi:10.1063/1.873916

  17. [17]

    Nuclear Fusion , volume =

    Stellarator Fusion Systems Enabled by Arrays of Planar Coils , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/ada56c , urldate =

    work page doi:10.1088/1741-4326/ada56c

  18. [18]

    Physics of Plasmas , volume =

    Direct Stellarator Coil Optimization for Nested Magnetic Surfaces with Precise Quasi-Symmetry , author =. Physics of Plasmas , volume =. doi:10.1063/5.0129716 , urldate =

    work page doi:10.1063/5.0129716

  19. [19]

    Single-Stage Gradient-Based Stellarator Coil Design:

    Giuliani, Andrew and Wechsung, Florian and Cerfon, Antoine and Stadler, Georg and Landreman, Matt , year = 2022, month = jun, journal =. Single-Stage Gradient-Based Stellarator Coil Design:. doi:10.1016/j.jcp.2022.111147 , urldate =

    work page doi:10.1016/j.jcp.2022.111147 2022

  20. [20]

    Plasma Physics and Controlled Fusion , volume =

    Including the Vacuum Energy in Stellarator Coil Design , author =. Plasma Physics and Controlled Fusion , volume =. doi:10.1088/1361-6587/adb789 , urldate =

    work page doi:10.1088/1361-6587/adb789

  21. [21]

    doi:10.48550/arXiv.2412.00267 , urldate =

    A Framework for Discrete Optimization of Stellarator Coils , author =. doi:10.48550/arXiv.2412.00267 , urldate =. arXiv , keywords =:2412.00267 , publisher =

    work page doi:10.48550/arxiv.2412.00267

  22. [22]

    and Stewart, I

    Hansen, C. and Stewart, I. G. and Burgess, D. and Pharr, M. and Guizzo, S. and Logak, F. and Nelson, A. O. and. Computer Physics Communications , volume =. doi:10.1016/j.cpc.2024.109111 , urldate =

    work page doi:10.1016/j.cpc.2024.109111 2024

  23. [23]

    Hartwell, G. J. and Knowlton, S. F. and Hanson, J. D. and Ennis, D. A. and Maurer, D. A. , year = 2017, month = jul, journal =. Design,. doi:10.1080/15361055.2017.1291046 , urldate =

    work page doi:10.1080/15361055.2017.1291046 2017

  24. [24]

    and Vieira, Rui F

    Hartwig, Zachary S. and Vieira, Rui F. and Dunn, Darby and Golfinopoulos, Theodore and LaBombard, Brian and Lammi, Christopher J. and Michael, Philip C. and Agabian, Susan and Arsenault, David and Barnett, Raheem and Barry, Mike and Bartoszek, Larry and Beck, William K. and Bellofatto, David and Brunner, Daniel and Burke, William and Burrows, Jason and By...

    work page doi:10.1109/tasc.2023.3332613 2023

  25. [25]

    Stellarator and Tokamak Plasmas: A Comparison , shorttitle =

    Helander, P and Beidler, C D and Bird, T M and Drevlak, M and Feng, Y and Hatzky, R and Jenko, F and Kleiber, R and Proll, J H E and Turkin, Yu and Xanthopoulos, P , year = 2012, month = nov, journal =. Stellarator and Tokamak Plasmas: A Comparison , shorttitle =. doi:10.1088/0741-3335/54/12/124009 , urldate =

    work page doi:10.1088/0741-3335/54/12/124009 2012

  26. [26]

    Journal of Plasma Physics , volume =

    Combined Plasma--Coil Optimization Algorithms , author =. Journal of Plasma Physics , volume =. doi:10.1017/S0022377821000271 , urldate =

    work page doi:10.1017/s0022377821000271

  27. [27]

    Physical Review Research , volume =

    Compact Stellarator-Tokamak Hybrid , author =. Physical Review Research , volume =. doi:10.1103/PhysRevResearch.6.L022052 , urldate =

    work page doi:10.1103/physrevresearch.6.l022052

  28. [28]

    Plasma Physics and Controlled Fusion , volume =

    Variety of Coil Sets for the Compact Stellarator-Tokamak Hybrid , author =. Plasma Physics and Controlled Fusion , volume =. doi:10.1088/1361-6587/add763 , urldate =

    work page doi:10.1088/1361-6587/add763

  29. [29]

    The Physics of Fluids , volume =

    Steepest-descent Moment Method for Three-dimensional Magnetohydrodynamic Equilibria , author =. The Physics of Fluids , volume =. doi:10.1063/1.864116 , urldate =

    work page doi:10.1063/1.864116

  30. [30]

    , year = 2024, month = nov, journal =

    Hurwitz, Siena and Landreman, Matt and Antonsen, Thomas M. , year = 2024, month = nov, journal =. Efficient. doi:10.1109/TMAG.2024.3455946 , urldate =

    work page doi:10.1109/tmag.2024.3455946 2024

  31. [31]

    Electromagnetic Coil Optimization for Reduced

    Hurwitz, Siena and Landreman, Matt and Huslage, Paul and Kaptanoglu, Alan , year = 2025, month = apr, journal =. Electromagnetic Coil Optimization for Reduced. doi:10.1088/1741-4326/adc9bf , urldate =

    work page doi:10.1088/1741-4326/adc9bf 2025

  32. [32]

    doi:10.1137/1.9781611978223 , urldate =

    An. doi:10.1137/1.9781611978223 , urldate =

    work page doi:10.1137/1.9781611978223

  33. [33]

    Single-Stage Stellarator Optimization: Combining Coils with Fixed Boundary Equilibria , shorttitle =

    Jorge, R and Goodman, A and Landreman, M and Rodrigues, J and Wechsung, F , year = 2023, month = jun, journal =. Single-Stage Stellarator Optimization: Combining Coils with Fixed Boundary Equilibria , shorttitle =. doi:10.1088/1361-6587/acd957 , urldate =

    work page doi:10.1088/1361-6587/acd957 2023

  34. [34]

    Plasma Physics and Controlled Fusion , volume =

    The Magnetic Gradient Scale Length Explains Why Certain Plasmas Require Close External Magnetic Coils , author =. Plasma Physics and Controlled Fusion , volume =. doi:10.1088/1361-6587/ad1a3e , urldate =

    work page doi:10.1088/1361-6587/ad1a3e

  35. [35]

    Nuclear Fusion , volume =

    Greedy Permanent Magnet Optimization , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/acb4a9 , urldate =

    work page doi:10.1088/1741-4326/acb4a9

  36. [36]

    and Qian, Tony and Wechsung, Florian and Landreman, Matt , year = 2022, month = oct, journal =

    Kaptanoglu, Alan A. and Qian, Tony and Wechsung, Florian and Landreman, Matt , year = 2022, month = oct, journal =. Permanent-. doi:10.1103/PhysRevApplied.18.044006 , urldate =

    work page doi:10.1103/physrevapplied.18.044006 2022

  37. [37]

    Nuclear Fusion , volume =

    Reactor-Scale Stellarators with Force and Torque Minimized Dipole Coils , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/adc318 , urldate =

    work page doi:10.1088/1741-4326/adc318

  38. [38]

    Physics of Plasmas , volume =

    Sparse Regression for Plasma Physics , author =. Physics of Plasmas , volume =. doi:10.1063/5.0139039 , urldate =

    work page doi:10.1063/5.0139039

  39. [39]

    Toroidal Magnetic Field Ripple in the Presence of Misaligned Toroidal Field Coils on the

    Kripner, Lukas and Krbec, Jaroslav and Zelda, Jan and Markovic, Tomas and Titus, Peter and Vondracek, Petr and Ficker, Ondrej and Hron, Martin , year = 2023, month = feb, journal =. Toroidal Magnetic Field Ripple in the Presence of Misaligned Toroidal Field Coils on the. doi:10.1016/j.fusengdes.2022.113378 , urldate =

    work page doi:10.1016/j.fusengdes.2022.113378 2023

  40. [40]

    Nuclear Fusion , volume =

    Coil Optimization Methods for a Planar Coil Stellarator , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/ada56b , urldate =

    work page doi:10.1088/1741-4326/ada56b

  41. [41]

    Physics of Plasmas , volume =

    Nonaxisymmetric Shaping of Tokamaks Preserving Quasiaxisymmetry , author =. Physics of Plasmas , volume =. doi:10.1063/1.3207010 , urldate =

    work page doi:10.1063/1.3207010

  42. [42]

    and Sengupta, W

    Landreman, Matt and Sengupta, Wrick , year = 2018, month = dec, journal =. Direct Construction of Optimized Stellarator Shapes. doi:10.1017/S0022377818001289 , urldate =

    work page doi:10.1017/s0022377818001289 2018

  43. [43]

    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 =. doi:10.1088/1741-4326/adb04e , urldate =

    work page doi:10.1088/1741-4326/adb04e

  44. [44]

    Physics of Plasmas , volume =

    Efficient Magnetic Fields for Supporting Toroidal Plasmas , author =. Physics of Plasmas , volume =. doi:10.1063/1.4943201 , urldate =

    work page doi:10.1063/1.4943201

  45. [45]

    Nuclear Fusion , volume =

    An Improved Current Potential Method for Fast Computation of Stellarator Coil Shapes , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/aa57d4 , urldate =

    work page doi:10.1088/1741-4326/aa57d4

  46. [46]

    Landreman and E

    Landreman, Matt and Paul, Elizabeth , year = 2022, month = jan, journal =. Magnetic. doi:10.1103/PhysRevLett.128.035001 , urldate =

    work page doi:10.1103/physrevlett.128.035001 2022

  47. [47]

    Physics of Plasmas , volume =

    Optimization of Quasi-Symmetric Stellarators with Self-Consistent Bootstrap Current and Energetic Particle Confinement , author =. Physics of Plasmas , volume =. doi:10.1063/5.0098166 , urldate =

    work page doi:10.1063/5.0098166

  48. [48]

    doi:10.21105/joss.03525 , urldate =

    Landreman, Matt and Medasani, Bharat and Wechsung, Florian and Giuliani, Andrew and Jorge, Rogerio and Zhu, Caoxiang , year = 2021, month = sep, journal =. doi:10.21105/joss.03525 , urldate =

    work page doi:10.21105/joss.03525 2021

  49. [49]

    From tokamaks to stellarators: understanding the role of 3D shaping

    Lazerson, Samuel A. and Schmitt, John C. , year = 2017, month = jul, number =. From Tokamaks to Stellarators: Understanding the Role of. arXiv , keywords =:1705.00517 , publisher =

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    The Virtual-Casing Principle for

    Lazerson, S A , year = 2012, month = dec, journal =. The Virtual-Casing Principle for. doi:10.1088/0741-3335/54/12/122002 , urldate =

    work page doi:10.1088/0741-3335/54/12/122002 2012

  51. [51]

    Nuclear Fusion , volume =

    Stellarator Coil Optimization Supporting Multiple Magnetic Configurations , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/aca10d , urldate =

    work page doi:10.1088/1741-4326/aca10d

  52. [52]

    Design of

    Liang, Yihui and Zhou, Yao and Dong, Fanghao and Zhu, Caoxiang and Yu, Guodong and Zhao, Yuansheng and Dong, Ge , year = 2025, month = jan, journal =. Design of. doi:10.1088/1741-4326/ada2a9 , urldate =

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

  53. [53]

    The Design of the External Rotational Transform Coil on the

    Li, Yangbo and Rao, Bo and Mao, Feiyue and Zhou, Song and Li, Keze and Zhao, Chuanxu and Ren, Zhengkang and Li, Da and Huang, Zhuo and He, Ying and Hu, Bo and Huang, Jie and Wang, Nengchao and Jiang, Zhonghe and Ding, Yonghua and Suzuki, Yasuhiro , year = 2024, month = sep, journal =. The Design of the External Rotational Transform Coil on the. doi:10.101...

    work page doi:10.1016/j.fusengdes.2024.114591 2024

  54. [54]

    Suppression of Tearing Modes by

    Li, Yangbo and Wang, Nengchao and Rao, Bo and Mao, Feiyue and Zhao, Chuanxu and Ren, Zhengkang and Meng, Z Y and Xuan, Zijian and Zhou, Song and Wang, Ruomu and Chen, Xixuan and Zheng, Wei and Suzuki, Yasuhiro and Jiang, Zhonghe , year = 2026, journal =. Suppression of Tearing Modes by. doi:10.1088/1741-4326/ae51a5 , urldate =

    work page doi:10.1088/1741-4326/ae51a5 2026

  55. [55]

    Nuclear Fusion , volume =

    Stellarator Coil Optimization towards Higher Engineering Tolerances , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/aad431 , urldate =

    work page doi:10.1088/1741-4326/aad431

  56. [56]

    and Hudson, S

    Loizu, J. and Hudson, S. R. and N. Verification of the. Physics of Plasmas , volume =. doi:10.1063/1.4967709 , urldate =

    work page doi:10.1063/1.4967709

  57. [57]

    Plasma Physics and Controlled Fusion , volume =

    The High Beta Tokamak-Extended Pulse Magnetohydrodynamic Mode Control Research Program , author =. Plasma Physics and Controlled Fusion , volume =. doi:10.1088/0741-3335/53/7/074016 , urldate =

    work page doi:10.1088/0741-3335/53/7/074016

  58. [58]

    Nuclear Fusion , volume =

    Solution of Stellarator Boundary Value Problems with External Currents , author =. Nuclear Fusion , volume =. doi:10.1088/0029-5515/27/5/018 , urldate =

    work page doi:10.1088/0029-5515/27/5/018

  59. [59]

    Plasma Physics and Controlled Fusion , volume =

    Low-Aspect-Ratio Stellarators with Planar Coils , author =. Plasma Physics and Controlled Fusion , volume =. doi:10.1088/0741-3335/39/11/006 , urldate =

    work page doi:10.1088/0741-3335/39/11/006

  60. [60]

    and Chen, Brian and Dickerson, Matthew and Gates, David A

    Nash, Daniel and Cate, Andy D. and Chen, Brian and Dickerson, Matthew and Gates, David A. and Harris, William and Khera, Udyaaksh and Korman, Milo and Olatunji, Jamal and Slepchenkov, Misha and Srinivasan, Santhosh and Swanson, Charles P.S. and. Prototyping and. IEEE Transactions on Applied Superconductivity , volume =. doi:10.1109/TASC.2025.3594533 , urldate =

    work page doi:10.1109/tasc.2025.3594533 2025

  61. [61]

    Construction of a Plasma Confinement Device

    Oishi, T and Yamazaki, K and Arimoto, H and Baba, K and Hasegawa, M and Shoji, T , year = 2014, month = may, journal =. Construction of a Plasma Confinement Device. doi:10.1088/1742-6596/511/1/012042 , urldate =

    work page doi:10.1088/1742-6596/511/1/012042 2014

  62. [62]

    Physics of Plasmas , volume =

    Low Edge Safety Factor Operation and Passive Disruption Avoidance in Current Carrying Plasmas by the Addition of Stellarator Rotational Transform , author =. Physics of Plasmas , volume =. doi:10.1063/1.4935396 , urldate =

    work page doi:10.1063/1.4935396

  63. [63]

    Parra, F. I. and Baek, S.-G. and Churchill, M. and Demers, D. R. and Dudson, B. and Ferraro, N. M. and Geiger, B. and Gerhardt, S. and Hammond, K. C. and Hudson, S. and Jorge, R. and Kolemen, E. and Kriete, D. M. and Kumar, S. T. A. and Landreman, M. and Lowe, C. and Maurer, D. A. and Nespoli, F. and Pablant, N. and Pueschel, M. J. and Punjabi, A. and Sch...

    work page doi:10.2172/2372903 2024

  64. [64]

    Physics of Plasmas , volume =

    Experimental Demonstration of a Compact Stellarator Magnetic Trap Using Four Circular Coils , author =. Physics of Plasmas , volume =. doi:10.1063/1.2149313 , urldate =

    work page doi:10.1063/1.2149313

  65. [65]

    Journal of Plasma Physics , volume =

    Perturbing an Axisymmetric Magnetic Equilibrium to Obtain a Quasi-Axisymmetric Stellarator , author =. Journal of Plasma Physics , volume =. doi:10.1017/S0022377820000902 , urldate =

    work page doi:10.1017/s0022377820000902

  66. [66]

    Plunk, G. G. and Helander, Per , year = 2018, month = apr, journal =. Quasi-Axisymmetric Magnetic Fields: Weakly Non-Axisymmetric Case in a Vacuum , shorttitle =. doi:10.1017/S0022377818000259 , urldate =

    work page doi:10.1017/s0022377818000259 2018

  67. [67]

    Qian, T. M. and Chu, X. and Pagano, C. and Patch, D. and Zarnstorff, M. C. and Berlinger, B. and Bishop, D. and Chambliss, A. and Haque, M. and Seidita, D. and Zhu, C. , year = 2023, month = oct, journal =. Design and Construction of the. doi:10.1017/S0022377823000880 , urldate =

    work page doi:10.1017/s0022377823000880 2023

  68. [68]

    Nuclear Fusion , volume =

    Simpler Optimized Stellarators Using Permanent Magnets , author =. Nuclear Fusion , volume =. doi:10.1088/1741-4326/ac6c99 , urldate =

    work page doi:10.1088/1741-4326/ac6c99

  69. [69]

    Development of the First Non-Planar

    Riva, Nicol. Development of the First Non-Planar. Superconductor Science and Technology , volume =

  70. [70]

    Scott, S. D. and Kramer, G. J. and Tolman, E. A. and Snicker, A. and Varje, J. and S. Fast-Ion Physics in. Journal of Plasma Physics , volume =. doi:10.1017/S0022377820001087 , urldate =

    work page doi:10.1017/s0022377820001087

  71. [71]

    Nuclear Fusion , volume =

    Use of the Virtual-Casing Principle in Calculating the Containing Magnetic Field in Toroidal Plasma Systems , author =. Nuclear Fusion , volume =. doi:10.1088/0029-5515/12/5/009 , urldate =

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

  72. [72]

    and Berry, Lee A

    Strickler, Dennis J. and Berry, Lee A. and Hirshman, Steven P. , year = 2002, month = mar, journal =. Designing. doi:10.13182/FST02-A206 , urldate =

    work page doi:10.13182/fst02-a206 2002

  73. [73]

    Fusion Engineering and Design , volume =

    Design of Simple Stellarator Using Tilted Toroidal Field Coils , author =. Fusion Engineering and Design , volume =. doi:10.1016/j.fusengdes.2021.112843 , urldate =

    work page doi:10.1016/j.fusengdes.2021.112843 2021

  74. [74]

    Swanson, C. P. S. and Kumar, S. T. A. and Dudt, D. W. and Flom, E. R. and Kalb, W. B. and Kruger, T. G. and Martin, M. F. and Olatunji, J. R. and Pasmann, S. and Tang, L. Z. and von der Linden, J. and Wasserman, J. and Avida, M. and Basurto, A. S. and Dickerson, M. and de Boer, N. and Donovan, M. J. and Cate, A. H. Doudna and Fort, D. and Harris, W. and K...

    work page doi:10.48550/arxiv.2512.08027

  75. [75]

    Team, W. VII-A. , year = 1980, month = sep, journal =. Stabilization of the (2, 1) Tearing Mode and of the Current Disruption in the. doi:10.1088/0029-5515/20/9/008 , urldate =

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

  76. [76]

    Proceedings of the National Academy of Sciences , volume =

    Precise Stellarator Quasi-Symmetry Can Be Achieved with Electromagnetic Coils , author =. Proceedings of the National Academy of Sciences , volume =. doi:10.1073/pnas.2202084119 , urldate =

    work page doi:10.1073/pnas.2202084119

  77. [77]

    Journal of Plasma Physics , volume =

    Coil Optimization for Quasi-Helically Symmetric Stellarator Configurations , author =. Journal of Plasma Physics , volume =. doi:10.1017/S0022377824000540 , urldate =

    work page doi:10.1017/s0022377824000540

  78. [78]

    Planar Coil Optimization for the

    Wu, Ryan and Kruger, Thomas and Swanson, Charles , year = 2025, month = feb, journal =. Planar Coil Optimization for the. doi:10.1088/1361-6587/adb5b7 , urldate =

    work page doi:10.1088/1361-6587/adb5b7 2025

  79. [79]

    and Hsu, Scott C

    Wurzel, Samuel E. and Hsu, Scott C. , year = 2025, month = nov, journal =. Continuing Progress toward Fusion Energy Breakeven and Gain as Measured against the. doi:10.1063/5.0297357 , urldate =

    work page doi:10.1063/5.0297357 2025

  80. [80]

    Yamaguchi, H and Shimizu, A and Isobe, M and Ogawa, K and Osakabe, M and Takahashi, H and Satake, S and Ichiguchi, K and Murase, T and Tanoue, H and Nakagawa, S and Yanai, R and Sato, M and Seki, R and Toda, S and Nunami, M and Sakai, T , year = 2025, month = sep, address =. An. 9th

    2025

Showing first 80 references.