Ian G. Stewart

We demonstrate the design of a flexible, university-scale hybrid tokamak-stellarator experiment based on an axisymmetric array of planar high-temperature superconducting (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 estimated engineering limits. We find that the field error sets a minimum coil-plasma distance which bounds the axisymmetric envelope available to the boundary, 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 edge 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 triangularity δ ≈ ± 0.6 —all at peak pointwise coil forces within estimated HTS tolerances. We show the same array can additionally correct 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.

This work presents the compact experimental negative triangularity (NT) reactor (CENTAUR), a low overnight cost, high-field tokamak, breakeven reactor design, achieving a predicted total fusion power of 40 MW and scientific energy gain of 1.3. Ballooning stability calculations confirm that the device’s pedestal is within the first stability regime, which is consistent with the expected ELM-free operation associated with NT plasmas. The geometry of the NT divertor allows for high fraction of radiated power (13.5 % ) between the separatrix and plasma facing components. Heat transport modeling based on simulations of the edge region show heat loads into plasma facing components well below material limits. The magnet system employs rare-earth barium copper oxide high-temperature superconductors in 18 toroidal field coils, an hourglass-shaped central solenoid, and six poloidal field coils to support high-field ( B 0 = 10.9 T) plasma confinement, shaping, and current drive. Neutronics analysis shows that a 12 cm B 4 C shield keeps superconducting magnet heating below the 33 K quench limit during 10 s, 40 MW DT pulses. With this shielding, the modeled fluence indicates HTS components can survive more than ten times the 3000-pulse design lifetime. Iteration of economic analysis in tandem with the technical design process allows CENTAUR to achieve its overnight cost goal of $2 billion US determined using a custom costing model that predicts a total overnight cost of 1.6 B ± 0.2 B US.

Non-axisymmetric magnetic field coils have been designed to provide efficient error field (EF) correction and suppress edge localized modes in SPARC—a compact high-field tokamak that is presently under construction at Commonwealth Fusion Systems. These designs utilize the Generalized Perturbed Equilibrium Code’s (GPEC’s) representation of the multi-modal, non-axisymmetric plasma response to optimize the geometric coupling between EF correction coil arrays and the desired core or edge plasma response. Error field correction coils are designed to couple to the plasma-amplified kink that dominates the drive of core resonances. The maximum allowable EF is projected to SPARC using an empirical scaling that is consistent with linear and nonlinear magnetohydrodynamics (MHD) modeling expectations. Asymmetric construction and assembly tolerances are then balanced against the corresponding kA-turns needed for correction to levels below the allowable limit. These physics-driven coil designs provide confidence in our ability to operate SPARC in new high field tokamak regimes without EF induced locked modes.

Benign termination, in which magnetohydrodynamic (MHD) instabilities deconfine runaway electrons (REs) following hydrogenic injections, is a promising strategy for mitigating dangerous RE loads after disruptions. Recent experiments on the Joint European Torus (JET) have explored this scenario at higher pre-disruptive plasma currents than are achievable on other devices, revealing challenges in obtaining benign terminations at I p ⩾ 2.5 MA. This work analyzes the evolution of these high-current RE beams and their terminating MHD events using fast magnetic sensor measurements and EFIT equilibrium reconstructions for approximately 40 JET and 20 DIII-D tokamak discharges. On JET, unsuccessful non-benign terminations occur at low edge safety factor ( q edge ≈ 2 ), and are preceded by intermittent, non-terminating MHD events at higher rational q _edge . Trends in the internal inductance l i indicate more peaked RE current profiles in the high- I p non-benign population, which may hinder successful recombination through re-ionization of the companion plasma. In contrast, benign terminations on JET typically occur at higher q edge ⩾ 3 and exhibit less peaked RE current profiles. DIII-D displays a broader range of terminating edge safety factors, again correlated with the measured l i values. Across both tokamaks, the RE current peaking is therefore found to determine which MHD instability boundary is encountered, a result confirmed by linear resistive MHD modeling with the CASTOR3D code. Measured growth rates are similar for benign and non-benign cases, indicating that ideal MHD timescales at low density after hydrogenic injection do not alone explain efficient RE deconfinement. Instead, non-benign cases are most readily characterized by their comparably lower overall MHD perturbation amplitudes δ B . These observations suggest that the interplay between ideal and resistive dynamics governs the termination process, with implications for extrapolating benign RE termination to high- I p reactor scenarios.

The SPARC tokamak is a high-field, Bt0 ∼12 T, medium-sized, R0 = 1.85 m, tokamak that is presently under construction in Devens, MA, led by Commonwealth Fusion Systems. It will be used to de-risk the high-field tokamak path to a fusion power plant and demonstrate the commercial viability of fusion energy. SPARC’s first campaign plan is to achieve Qfus > 1 using an ICRF-heated, 15 m from the center of the tokamak, on the other side of a 2.4 m concrete shielding wall. A series of 31 large-scale penetrations have been included in the SPARC Tokamak Hall to facilitate integration of early campaign diagnostics and to provide upgradability.

To achieve its performance goals, SPARC plans to operate in equilibrium configurations with a strong elongation of κ areal ∼ 1.75 , which in turn will destabilize the n = 0 vertical instability. However, SPARC also features a relatively thick conducting wall that is designed to withstand disruption forces, leading to lower vertical instability growth rates than usually encountered. In this work, we use the TokSyS framework to survey families of accessible shapes near the SPARC baseline configuration, finding maximum growth rates in the range of γ ≲ 100 s⁻¹. The addition of steel vertical stability plates has only a modest ( ∼ 25 % ) effect on reducing the vertical growth rate and almost no effect on the plasma controllability when the full vertical stability system is taken into account, providing flexibility in the plate conductivity in the SPARC design. Analysis of the maximum controllable displacement on SPARC is used to inform the power supply voltage and current limit requirements needed to control an initial vertical displacement of 5% of the minor radius. From the expected spectra of plasma disturbances and diagnostic noise, requirements for filter latency and vertical stability coil heating tolerances are also obtained. Small modifications to the outboard limiter location are suggested to allow for an unmitigated vertical disturbance as large as 5% of the minor radius without allowing the plasma to become limited. Further, investigations with the 3D COMSOL code reveal that strategic inclusion of insulating structures within the VSC supports are needed to maintain sufficient magnetic response. The workflows presented here help to establish a model for the integrated predictive design for future devices by coupling engineering decisions with physics needs.

Accurate reconstruction of the plasma equilibrium is imperative for successful operation of the SPARC tokamak. In order to assess the expected reconstruction accuracy throughout the duration of design-point discharges, the EFIT equilibrium reconstruction code was deployed for SPARC. Reconstructions from SPARC baseline scenarios were compared with free-boundary equilibria generated by FreeGS, Toksys, and the Tokamak Simulation Code. The key geometric areas of interest, where design constraints are imposed, included: the inner and outer midplane gaps, the X-point locations, as well as the strike point locations. Successful reconstructions of various reference discharges, using deviations in these key geometric quantities as metrics, were calculated from synthetic signals considering an optimized equilibrium magnetic sensor set. The optimization process for this sensor set combined a scan of randomized sensor placement with a linear perturbation analysis to determine critical sensor locations, while simultaneously conforming to design constraints on the sensor placement. This optimized set was also successful in performing equilibrium reconstructions with the addition of error to synthetic measurements of magnetic flux and magnetic field, as well as contributions from eddy currents in conducting structures. These methods represent a workflow of optimization and validation that balances the engineering constraints of sensor placement with achieving sufficient reconstruction fidelity for science and operations missions for SPARC.