Columbia Stellarator eXperiment (CSX)
- CSX is a compact stellarator that reuses CNT infrastructure while adopting optimized non-planar NI-HTS coils to study quasi-axisymmetric (QA) neoclassical plasma physics.
- It integrates innovative single-stage optimization that co-designs plasma geometry, coil structures, and HTS tape orientation, ensuring robust manufacturability and operational flexibility.
- The design effectively mitigates finite-build effects and HTS strain while enabling comprehensive diagnostics for neoclassical transport, flow damping, and island physics.
The Columbia Stellarator eXperiment (CSX) is a compact, university-scale stellarator at Columbia University conceived as an upgrade of the Columbia Non-neutral Torus (CNT). Its central aims are to study neoclassical physics in configurations close to quasi-axisymmetry (QA), to demonstrate non-insulated high-temperature superconducting (NI-HTS) coils in a stellarator geometry, and to provide hands-on education in stellarator design, construction, and operation. The device reuses CNT’s cylindrical vacuum vessel and two circular planar poloidal-field (PF) coils, while replacing CNT’s in-vessel interlinked coils with two optimized non-planar interlinked (IL) coils wound from ReBCO tape. Across the design literature, CSX is characterized by single-stage plasma–coil optimization, explicit HTS strain control, and a progression from preliminary filament-level designs to a finalized finite-build configuration selected for construction (Baillod et al., 2024, Baillod et al., 2 Jan 2026).
1. Origins, institutional setting, and design lineage
CSX is defined by hardware reuse and by a shift in mission relative to CNT. CNT was built for non-neutral plasmas, whereas CSX is designed for neutral-plasma stellarator physics with an emphasis on QA, neoclassical transport, and flow damping. The cylindrical CNT vessel and the two circular planar PF coils are retained, and the original in-vessel interlinked copper coils are replaced by two custom 3D NI-HTS IL coils. Early CSX design studies also described the possibility of adding windowpane coils wrapped around the cylindrical vessel to enhance shaping and trim, but these were treated as an optional upgrade rather than the base configuration (Baillod et al., 2024).
The project objectives are stated consistently across the design and engineering papers, though with increasing specificity over time. The 2024 design study emphasized a tight-aspect-ratio QA plasma that fits within the existing CNT vessel, provides sufficient rotational transform to confine ion banana orbits, and respects coil-to-vessel, coil-to-plasma, and coil-to-coil constraints while remaining manufacturable with NI-HTS tape (Baillod et al., 2024). The 2026 final-design update articulated three principal goals: studying neoclassical physics in configurations close to QA, demonstrating NI-HTS coils in a stellarator geometry, and training students through the full lifecycle of stellarator realization (Baillod et al., 2 Jan 2026).
The literature also shows a progression in operating assumptions. Early CSX optimization studies were framed around reuse of CNT’s 2.45 GHz, 10 kW ECH system and CNT-like plasma parameters, including , , , and volume-averaged (Baillod et al., 2024). Later final-configuration and prototype studies were scaled to an on-axis magnetic field target of , with magnet-development work explicitly organized around that field level (Baillod et al., 2 Jan 2026, Schmeling et al., 8 Oct 2025). This suggests a design evolution from an initial low-, CNT-infrastructure-constrained physics concept to a more fully engineered QA stellarator with dedicated HTS magnet capability.
A recurrent misconception is that CSX is merely a continuation of CNT with modest geometric changes. The published design work instead describes a different machine class: the vacuum vessel and PF coils are inherited, but the magnetic configuration is rebuilt around two non-planar NI-HTS IL coils and single-stage QA optimization. Related compact-stellarator studies with CNT-like planar coils or tilted circular toroidal-field coils are discussed in the literature as relevant comparators or precursors, but they are not the CSX build configuration (Yu et al., 2021, Nath et al., 8 Apr 2026).
2. Magnetic configuration and QA targets
The final CSX magnetic configuration has field periods and is stellarator symmetric. The coil set consists of two interlinked NI-HTS coils inside the cylindrical vessel and two planar, water-cooled copper PF coils outside the vessel. In the final selected configuration, the major radius is , the minor radius is , the aspect ratio is , and the plasma volume is 0. The minimum coil-to-plasma separation is 1, the coil-to-coil distance is 2, and the coil-to-vessel distance is 3 (Baillod et al., 2 Jan 2026).
The magnetic field is analyzed in Boozer coordinates, with
4
QA quality is measured through the spectral content of 5. The final-design paper defines
6
where 7 are Fourier amplitudes of 8 on the boundary. The target was QA error below 9, and the final re-optimized finite-build model achieved 0, with maximum normal field error on the boundary 1 (Baillod et al., 2 Jan 2026).
Rotational transform was a central design constraint from the outset. Early optimization papers derived a minimum transform 2 from a banana-width argument and targeted 3, away from low-order rationals (Baillod et al., 2024). The final configuration was designed to have a vacuum rotational transform near 4, with sensitivity studies imposing 5 so as to avoid the 6 and 7 rationals in standard operation (Baillod et al., 2 Jan 2026). Earlier strain-focused preliminary work adopted a looser physics target, requiring 8 and plasma volume 9, reflecting its status as a preliminary coil-plasma-tape optimization rather than the final machine definition (Huslage et al., 2024).
CSX also incorporates controlled configurational flexibility. Rigid rotation of the IL coil pair by an angle 0 modifies the transform profile and resonant content. The reference QA configuration corresponds to 1, with 2 and 3. At 4, 5 crosses the 6 resonance and produces large core islands, while 7 raises 8 to 9 and the edge QA error to 0, enabling controlled QA degradation (Baillod et al., 2 Jan 2026). This makes island physics and symmetry-breaking transport part of the intended experimental envelope rather than mere error scenarios.
A significant design trade-off concerned magnetic well. A magnetic-well or Mercier-stability proxy was tested during the design process but was found to compete with QA quality, and the final build configuration prioritized QA for the initial experimental program (Baillod et al., 2 Jan 2026). This does not imply that stability considerations were ignored; rather, the published rationale is that the first CSX campaign is a low-1, vacuum-QA experiment focused on neoclassical metrics.
3. Single-stage optimization and design evolution
CSX is notable for adopting single-stage optimization rather than the more traditional two-stage separation between plasma optimization and coil design. The explicit rationale is that the machine has few coils, a tight aspect ratio, and stringent engineering constraints, so many idealized plasma shapes would be unrealizable with the available coil set and inherited vessel geometry. Single-stage methods co-optimize plasma geometry, coil shapes, coil currents, and HTS winding angles from the outset (Baillod et al., 2024).
Two distinct single-stage formalisms were deployed in the 2024 design study. The first couples fixed-boundary VMEC equilibria to coil optimization in SIMSOPT, minimizing
2
where the plasma term includes QA error, rotational transform, and volume, and the coil-coupling term includes regularization and a quadratic-flux penalty on the normal field at the VMEC boundary. The second, which proved especially important for CSX, is the Boozer-surface approach, in which an approximate magnetic surface 3 is constructed directly for the vacuum field and the objective
4
is minimized over coil variables. In this framework, the QA residual on 5 is
6
The Boozer-surface approach was reported to be faster, less noisy, and more robust to island formation for the CSX vacuum-field problem (Baillod et al., 2024).
The optimization variables included the plasma boundary, IL coil centerlines parameterized by Fourier series, IL and PF currents, and winding-angle Fourier coefficients. Engineering constraints were embedded through penalties enforcing minimum IL–IL separation 7, minimum IL–plasma separation 8, minimum IL–vessel separation 9, and prescribed coil-length bounds 0 in the 2024 studies. When windowpane coils were considered, their currents were limited by 1 (Baillod et al., 2024).
Those early studies produced several candidate configurations. Among the Boozer-surface solutions, 2 decreased from 3 at 4 to 5 for one 6 case, while a windowpane-assisted case reached 7 (Baillod et al., 2024). The 2026 final-design update retained the Boozer-surface strategy but extended it in four directions: a finite-build multi-filament coil model, a new concavity–torsion penalty for windability, refined engineering thresholds, and systematic sensitivity analyses. Algorithmically, the final study used SIMSOPT with BFGS from scipy.optimize, random sampling of weights and thresholds, about 8 optimizations per stage, staged spectral resolutions 9, coil resolutions 0, and winding-angle resolution 1 (Baillod et al., 2 Jan 2026).
4. ReBCO tapes, strain metrics, and windability
A defining engineering constraint for CSX is the use of ReBCO HTS tape in non-planar stellarator coils. ReBCO enables higher field strengths and higher-temperature operation than NbTi or Nb2Sn, but its brittle ceramic functional layer is sensitive to strain, especially under hard-way bending and torsion. For CSX, this made tape-orientation optimization an intrinsic part of equilibrium and coil design rather than a post-processing detail (Huslage et al., 2024).
The strain model is formulated on the coil centerline using either a Frenet frame or a centroid frame. For a filament 3, the centroid-frame normal is defined by projection of the vector to the coil centroid, which avoids Frenet-normal flips near straight segments. The local tape orientation is then represented by a rotation angle 4 in the 5–6 plane:
7
Using this rotated frame, the curvature components and torsion relevant for tape strain are
8
For a tape of width 9 and thickness 0, the hard-way bending and torsional strains are
1
Because 2 for thin tapes, normal easy-way bending is much less restrictive than hard-way bending and can be neglected in practice (Huslage et al., 2024).
The CSX implementation penalizes exceedance of strain limits through
3
with 4 by default. The same formalism also penalizes net tape rotation relative to a reference frame through
5
For CSX, this was evaluated against the centroid frame and also against the Frenet frame. No integral constraint of the form 6 was imposed; instead, the magnitude of 7 itself was minimized along the coil (Huslage et al., 2024).
The dedicated strain-optimization study adopted a conservative HTS strain threshold of 8 for CSX, used 9, and imposed 0 per IL coil together with vessel-clearance constraints. After single-stage optimization of the plasma surface, coil geometry, and tape orientation, the filament geometry was fixed and a second pass optimized 1 alone. The resulting torsional and binormal-curvature strain profiles lay below the imposed 2 threshold, and the optimized tape frame closely tracked the centroid frame so as to avoid large cumulative twists during winding (Huslage et al., 2024).
The final 2026 machine definition refined these preliminary windability objectives. Engineering constraints were stated as HTS strain below 3, total coil length below 4, adequate clearances, and forces within support capability. The final study added a concavity–torsion penalty,
5
specifically to improve windability of NI-HTS tape in concave regions (Baillod et al., 2 Jan 2026). Taken together, these formulations make the winding path an optimized geometric degree of freedom, not a mere manufacturing afterthought.
5. Final finite-build configuration and robustness
The 2026 update reports the final configuration chosen to be built. The coil system comprises two interlinked NI-HTS coils inside the vessel and two planar copper PF coils outside it. Coil lengths are 6. The IL coil current is 7, the PF coil current is 8, and each HTS IL coil contains 9 parallel tape stacks or channels, each with 0 turns, for a total of 1 HTS winds per coil. The maximum force on the coils is 2 (Baillod et al., 2 Jan 2026).
A major advance in the final design was explicit treatment of finite-build effects. The characteristic half-size of the coil pack is 3, and thick-coil field errors were estimated to scale approximately as 4. For CSX, 5, implying that thick-coil effects are not negligible. The finite-build field model uses a centroid frame 6 and an HTS frame rotated by 7, with individual filaments placed at
8
Field convergence was checked by filament-number scans; typical refinements used 9 normal plus 00 binormal filament, and an 01-normal-filament test confirmed convergence of boundary metrics (Baillod et al., 2 Jan 2026).
The finite-build analysis altered both magnetic and mechanical conclusions. Relative to the single-filament model, an unreoptimized finite-build realization increased 02 from 03 to 04 and increased the maximum HTS strain from 05 to 06. Direct re-optimization of the finite-build model then restored performance to 07, 08, and maximum HTS strain 09 (Baillod et al., 2 Jan 2026). This is a central result of the final CSX paper: thick-coil effects are appreciable, but they can be mitigated within the same optimization framework.
Sensitivity analysis was used to convert this nominal design into an experimentally actionable tolerance budget. Manufacturing errors were represented by two Gaussian processes: local 3D-printing error with 10 and correlation length 11–12, and smooth winding-pack deviations with 13 and 14. Installation errors were modeled as rigid shifts and tilts. A Monte Carlo study defined success as 15 and 16, obtaining at least 17 success for 18 and 19. Shape-gradient-derived uniformly distributed tolerances were 20 for QA error and 21 for 22, indicating that rotational transform is roughly three times more sensitive than QA error (Baillod et al., 2 Jan 2026).
The published mitigation strategy is correspondingly explicit. If assembly tolerances are not met, error-field correction coils can be designed to trim 23 and QA error. The omission of a magnetic-well objective is acknowledged as a residual risk at higher pressure, but the initial program is intentionally low-24 and centered on neoclassical measurements rather than finite-25 MHD performance (Baillod et al., 2 Jan 2026).
6. Prototype magnet program and enabling technologies
A staged prototype campaign was undertaken to de-risk the CSX magnet system before full-scale coil manufacture. The program comprises three non-planar NI-HTS magnet prototypes, designated P1, P2, and P3, and focuses on additive-manufactured coil frames, winding mechanics, cooling, joints, passive quench mitigation, and diagnostics (Schmeling et al., 8 Oct 2025).
P1 was a planar elliptical double-pancake baseline. Its frame was printed in two sections with dovetail joints and then welded. The coil had 26 total turns, used ChipQuik Sn42/Bi57.6/Ag0.4 solder potting baked at 27, operated at 28, and measured a total resistance of 29. At 30, it produced an on-axis field of 31, consistent with predictions for the planar geometry. The stated implication was validation of additive manufacture, sectional joining, baseline winding, and field prediction in a simple geometry (Schmeling et al., 8 Oct 2025).
P2 was the first explicitly non-planar, higher-strain prototype. Its frame was printed in four sections and joined by dovetail joints and spring pins. The coil was wound to 32 turns, rather than the initially expected 33, because a high-torsion segment impeded further winding in that prototype. It used Sn63Pb37 solder potting baked at 34 for 35 minutes and was tested in a conduction-cooled bell-jar cryostat with a Sumitomo 408S cold head. Under load, measured temperatures were 36 at the top sensor, 37 at the bottom sensor, and 38 at the HTS–copper interface. The prototype operated up to 39, corresponding to 40, produced about 41 at a Hall probe about 42 from the axis, and showed agreement with Biot–Savart modeling within about 43. Its effective resistance was 44, and non-insulated dynamics were characterized by 45 decay times of 46 minutes from Hall data and 47 minutes from voltage decay. Inductance inferred from back-emf during current ramps was 48, versus a Grover thin-ring estimate of 49. Quench onset above about 50 was traced to local heating in an HTS–copper clamp region, identifying a concrete scale-up risk (Schmeling et al., 8 Oct 2025).
P3 extends the concept to the concave, high-field regime most relevant to CSX. It introduces non-planar geometry with concave winding sections, dual double-pancakes, 51 turns, 52-deep and 53-wide channels with 54 separators, and bolted sectional interfaces to improve thermal contact. It is designed for 55 operation, to approach the 56 target and to move toward the CSX requirement of 57 on axis and about 58 peak on-coil field. Co-winding of HTS tapes is planned to enhance current sharing (Schmeling et al., 8 Oct 2025).
Several enabling technologies recur throughout the prototype program. The coil frames are printed in AlSi10Mg and segmented to accommodate printer-bed limits while preserving geometric fidelity. Winding is performed with a gimballed constant-tension system based on a central ball joint, intended to keep the tape perpendicular to channel walls as winding angles vary. Solder potting is used deliberately to create radial current redistribution paths and passive quench mitigation in NI operation. Lap-joint development has achieved sub-microohm performance: a 59 ReBCO lap joint measured about 60 at 61 in LN62 (Schmeling et al., 8 Oct 2025). These results do not by themselves validate the full CSX coil, but they substantially reduce uncertainty in manufacture, cooling, and protection.
7. Physics program, diagnostics, and remaining trade-offs
The final CSX design is not only a magnet-construction exercise; it is structured around a specific neoclassical physics program. Post-processing with the SFINCS code solves the drift-kinetic equation in Boozer coordinates,
63
with deuterium plasma assumptions, 64, 65, impurities neglected, and 66. The ambipolar 67 is obtained by scanning 68 and minimizing the net radial current (Baillod et al., 2 Jan 2026).
These calculations indicate a substantial improvement over CNT. The effective ripple 69 is reported to be substantially reduced compared to CNT and comparable to CSSC and HSX devices of similar scale. Using the same ambipolar-adjusted profiles, the neoclassical heat flux through the LCFS satisfies
70
while a gyro-Bohm estimate suggests
71
This places CSX in a regime in which neoclassical and microturbulent heat fluxes may be comparable, rather than one in which ripple-dominated neoclassical loss overwhelms all other transport channels (Baillod et al., 2 Jan 2026).
Flow-damping measurements are an explicit experimental target. The total flow is written as
72
and the flux-surface-averaged torque density relevant for toroidal rotation is
73
Using a biased “spin-up” state near 74, the final paper considers 75 and an ambipolar state 76, obtaining a flow-damping time of about 77. The authors state that this lies within standard diagnostic sampling capabilities from kHz to MHz. Planned diagnostics for this program include a Mach probe or equivalent to measure flows and a biasing probe to impose 78 perturbations (Baillod et al., 2 Jan 2026).
Operational flexibility is built into the coil-support system through rotatable flanges and an indexing pin joint, allowing controlled rigid rotation of the IL coil pair. In the baseline setting 79, the machine operates in its reference QA state; at 80, it is intended to access the 81 resonance and generate large core islands; and at 82, it deliberately degrades QA while increasing 83 (Baillod et al., 2 Jan 2026). CSX is therefore designed not only to verify optimization predictions in a nominal state but also to probe symmetry breaking and island physics in a controlled way.
The remaining trade-offs are stated candidly in the final design literature. Magnetic-well optimization was sacrificed because it degraded QA. Bootstrap current density and full transport-coefficient sets were not reported in the final physics paper, which instead focused on flows, torque, 84, and heat flux. Shafranov shift and finite-85 equilibrium changes were not part of the present configuration selection. The initial CSX campaign is thus best understood as a vacuum-QA, low-86, NI-HTS stellarator experiment in which the principal scientific tests concern neoclassical confinement, flow damping, symmetry control, and the agreement between single-stage optimization and as-built performance (Baillod et al., 2 Jan 2026, Baillod et al., 2024).