Evan Maxwell Bursch

This work provides evidence that established error field penetration threshold scalings remain applicable during plasma current ramp-up. In dedicated DIII-D experiments with imposed n=1 perturbations during extended Ip ramps, an apparent empirical threshold is found between 2 and 3 kA of applied 3D coil current, above which MHD modes are seeded. The imposed perturbation couples to the rational surfaces present during the ramp, seeding near the q=4 surface and penetrating as an m/n=3/1 mode by the end of the perturbation phase. To interpret these observations, multi-machine penetration threshold scalings are combined with equilibrium-based overlap metrics from the GPEC code, including the in-situ error fields of the device. This modeling reproduces the observed onset in the amplitude scan and classifies mode seeding across a database of 12 ramp-up discharges spanning a range of plasma currents and densities. Across this database, the seeding seems to be controlled by the applied 3D coil current rather than by the plasma current or its ramp rate. Accounting for the in-situ error fields is found to be important for reliable prediction. These results are consistent with the robustness of scaling-based penetration metrics when coupled to detailed 3D field modeling under transient ramp-up conditions, and suggest the importance of accounting for in-situ error fields when assessing additional externally induced perturbations. This work is motivated by future tokamaks in which transient, non-axisymmetric error fields can arise during startup, for example from closed-loop, passive runaway electron mitigation coils energized by loop voltage ramping up plasma current.

This paper presents an updated n = 1 error field penetration threshold scaling, which increases fit quality compared to previous error field scaling laws, is produced from an expanded database, and exhibits reduced uncertainty in projections to future conventional tokamaks. It improves confidence in tokamak engineering tolerances, which are a significant driver of cost and time constraints on device construction. We add J-TEXT data, new JET data, and create the scaling using only conventional tokamak Ohmic and L-mode experiments. Since H-mode plasmas are more resilient to error field penetration, this scaling predicts what is likely the most dangerous regime of error field penetration for new tokamak designs. These decisions improve confidence in the error field penetration threshold scaling and its application in the construction and design decisions of any future conventional tokamak or fusion pilot plant.

The Fourier decomposition of a magnetic field perturbation on a tokamak flux surface is not unique; different choices of magnetic coordinates and of the weighting applied to the Fourier integrand yield different spectra, and hence different apparent coupling between an applied 3D field and the plasma. An area weighting of the Fourier integrand preserves the resonant coefficients on rational surfaces [Park et al., Phys. Plasmas 15, 064501 (2008)]. That result constrains only the resonant field components at rational surfaces in the plasma interior; the coordinate dependence of the external Fourier spectrum, or of quantities on arbitrary flux surfaces, which determines the coupling to resonant magnetic perturbation coils and error-field penetration, was left untreated. This paper shows that pairing a square-root-area-weighted vacuum field perturbation with a full-area-weighted resonant field yields a coupling matrix C whose singular values are invariant under coordinate transformations and whose right singular vectors reconstruct to a consistent real-space field pattern across coordinate systems, completing the coordinate-invariance picture for the plasma-3D-field coupling paradigm. Calculations with the Generalized Perturbed Equilibrium Code confirm the analytic result and show that improperly weighted coupling matrices can produce dominant modes whose overlap with the vacuum field perturbation differs by a factor of 2–3 between coordinate systems for strongly shaped, low aspect ratio equilibria, with the discrepancy growing with inverse aspect ratio. The same coordinate dependence afflicts alternative formulations such as the three-mode metric or zeroing the q=2 resonant field without proper weighting. The result applies to any tool computing Fourier spectra of resonant or external quantities on flux surfaces.

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.

This work reports on DIII-D experiments aimed at extending resonant magnetic perturbation (RMP) suppression of edge localized modes (ELMs) to n = 1 fields, where n is the toroidal mode number. Modeling of the 3D ideal MHD plasma response to the RMPs using the GPEC code is used to quantify edge and core resonant fluxes, guiding experimental strategies to increase plasma resilience against core error field penetration, optimize multi-coil phasing, and explore higher q 95 operation. In DIII-D, ELM mitigation is regularly observed across a wide range of n = 1 RMP scenarios. A ∼ 100 ms phase of complete ELM suppression was achieved at q 95 ∼ 3.9 using an odd-parity coil configuration. The suppressed phase exhibited clear signatures of RMP ELM suppression, including the elimination of D α spikes, increased pedestal rotation, enhanced magnetic response, and elevated broadband density turbulence. An optimized coil configuration for edge-to-core resonant flux did show increased edge resonance indicated by increased density pumpout, but did not yield RMP ELM suppression. At q 95 ∼ 5.1 , a bifurcation to a grassy-like ELM regime occurred, while large type-I ELMs persisted. These results demonstrate progress in experimental access to n = 1 RMP ELM suppression in DIII-D, motivating further study for robust access. This work also highlights the potential role of 3D edge stability as well as rational surface alignment in RMP ELM suppression access, which has important implications for the use of low- n RMPs in future reactor-scale devices.

Magnetic islands strongly influence cross-field electron transport in magnetized plasmas. In particular, bifurcations of the island topology modify the number and location of O-points, X-points, and separatrix boundaries, thereby altering diffusion pathways. In recent DIII-D experiments, external magnetic perturbations were used to rotate and periodically bifurcate the island on the q = 2 surface, causing a switchback between a q = 2 / 1 -dominated structure and a narrower q = 4 / 2 -dominated structure. To investigate how this topological change affects electron transport, we employ the field line tracing code TRIP3D with an implemented collisional operator. Thermal, tracer electrons launched from O-points, X-points, and outside separatrix boundaries reveal distinct diffusion regimes, including classical, subdiffusive, and superdiffusive behavior, depending on both the dominant island mode and launch location. These results suggest that island bifurcation can alter electron diffusion across rational surfaces, with direct implications for particle confinement. While the present work emphasizes diffusion as a general framework, the findings provide insight into the conditions under which electron trapping into an island or stochastization of the island’s separatrix can enable additional mechanisms, such as the generation of energetic electrons.

The optimal configuration choice between positive triangularity (PT) and negative triangularity (NT) tokamaks for fusion power plants hinges on navigating different operational constraints rather than achieving specific plasma performance metrics. This study presents a systematic comparison using constrained multi-objective optimization with the integrated FUsion Synthesis Engine (FUSE) framework. Over 200 000 integrated design evaluations were performed exploring the trade-offs between capital cost minimization and operational reliability (maximizing q ₉₅ ) while satisfying engineering constraints including 250 ± 50 MW net electric power, tritium breeding ratio > 1.1, power exhaust limits and an hour flattop time. Both configurations achieve similar cost-performance Pareto fronts through contrasting design philosophies. PT, while demonstrating resilience to pedestal degradation (compensating for up to 40% reduction), are constrained to larger machines ( R ₀ > 6.5 m) by the narrow operational window between L–H threshold requirements and the research-established power exhaust limit ( P sol / R < 15 MW m ⁻¹ ). This forces optimization through comparatively reduced magnetic field (∼8 T). NT configurations exploit their freedom from these constraints to access compact, high-field designs ( R 0 ∼ 5.5 m, B ₀ > 12 T), creating natural synergy with advancing HTS technology. Sensitivity analyses reveal that PT’s economic viability depends critically on uncertainties in L–H threshold scaling and power handling limits. Notably, a 50% variation in either could eliminate viable designs or enable access to the compact design space. These results suggest configuration selection should be risk-informed: PT offers the lowest-cost path when operational constraints can be confidently predicted, while NT is robust to large variations in constraints and physics uncertainties.

We have extended the radiation diffusion model of Hammer and Rosen [Phys. Plasmas 10, 1829 (2003)] to diverging spherical and cylindrical geometries. The effect of curvilinear geometry on the supersonic, expanding wavefront increases as the internal radius of a spherical or cylindrical shell approaches zero. Small spherical geometries are important for modeling systems at the size scale of inertial confinement fusion capsules, at these scales existing quasi-analytic models for planar geometry significantly disagree with the results of simulation. With this method, the benefits of rapid iteration can be applied to common spherical systems at much smaller length scales. We present comparisons between numerical diffusion solutions and the analytic model to give ranges of applicability for the model.