Nikolas C. Logan

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.

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 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.

Resonant drive in tokamaks is routinely quantified using a variety of different metrics that target different aspects of a resonant response to an external perturbation. Two of the most direct metrics, Δ _mn and b _pen , are widely used but their relative behavior was previously uncharacterized. This work examines how these metrics representing the shielding current and penetrated field relate in resistive perturbed tokamak equilibria using asymptotically matched solutions with a resistive MHD inner layer model in GPEC. b _pen scales with Lundquist number as S ^-2/3 until saturation at low S , and Δ _mn remains consistent with its ideal definition but is affected by global kink structure. Both metrics are shown to yield closely similar dominant coupling modes within the same resistive model. However, the resistive physics shifts this dominant mode spectrum to lower poloidal mode numbers m in a low-rotation ITER equilibrium. This alteration is predicted to be observable in experiment in the form of optimal relative phasings of resonant magnetic perturbation coils.

A new classical tearing mode (TM) stability simulation workflow has been developed that solves the resistive inner-layer equations in a plasma slab to yield a linear, quasi-toroidal TM growth rate γ and mode rotation frequency ω . This workflow combines two-fluid and drift MHD effects in a slab approximation of the resistive inner layer (SLAYER) with an effective tearing stability index as Δ ( γ , ω ) = Δ ′ − Δ crit . SLAYER is used to calculate the inner-layer Δ ( γ , ω ) , the STRIDE code is used to calculate a toroidal Δ ′ that includes shaping effects, and the toroidal Δ crit incorporates effects of thermal conduction on Glasser stabilization. This workflow is rapid and numerically robust across reactor-relevant plasma conditions, and yields growth rates that closely align with analytic predictions in well-documented linear growth rate regimes. Using synthetic equilibria, TM stability was calculated across scans of plasma β , inverse aspect-ratio, and toroidal current profile gradient. These scans effectively benchmarked this STRIDE+SLAYER workflow against existing models and showed reliable stability predictions in shaped H-mode-like plasmas. This capability to quickly and robustly predict classical tearing stability in tokamaks will facilitate the mapping of TM stable operational regimes and design of safe discharge trajectories in future devices.

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.

The neoclassical tearing mode (NTM) stability metric—minimum marginally stable island width w m ∗ —was compared across 14651 inductive high-field tokamak pilot plant equilibria. Larger devices with reduced elongation and/or increased minor radius demonstrated an order-of-magnitude increase in w m ∗ , primarily due to a reduction in bootstrap drive. This work is part of an ongoing effort to ensure passive NTM-stability in the ARC tokamak, in which the technology to achieve active tearing-suppression with localised electron cyclotron current drive does not yet exist. The equilibrium scenarios in the database were Monte Carlo generated and normalised to the same > 400MW fusion power, minimum pressure scenario at a range of plasma currents, before tearing analysis using the modified Rutherford equation was applied for all resonant poloidal and toroidal m , n modes up to n = 4. Single-helicity toroidal Δ ′ calculations in resistive DCON set the minimum marginally stable island width, and a simple modal scaling proportional to − m 2 n − 1 was identified for high- m Δ ′ values. The dominant correlates of w m ∗ and Δ ′ across the database were analysed using interpretable machine learning techniques.

Non-axisymmetric magnetic field coils have been designed to provide efficient error field 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 3D 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 error field is projected to SPARC using an empirical scaling that is consistent with linear and nonlinear 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 error field induced locked modes.

The National Spherical Torus Experiment Upgrade (NSTX-U) is preparing to resume operation, representing a crucial step toward realizing compact, cost-effective fusion pilot plants (FPPs). In advance of this, extensive modeling and data analysis have been conducted to advance the physics basis for low-aspect-ratio, high-performance plasma regimes, focusing on three core objectives: confinement and stability, power and particle handling, and steady-state operation. Significant progress has been made in understanding the electron temperature flattening in high-β plasmas, which is shown to be driven by a complex interplay of MHD instabilities (e.g., non-resonant infernal modes), fast-ion-driven Alfvén eigenmodes, and electron and ion-scale micro-instabilities, particularly Kinetic Ballooning Modes (KBMs), whose destabilization is strongly dependent on parallel magnetic field fluctuations (δB _‖ ). Furthermore, a new Gyrokinetic Critical Pedestal model was developed, accurately predicting pedestal structure by identifying KBMs as the primary stability limit, offering a critical constraint for future high-confinement scenarios. To address the challenge of high heat flux, novel liquid lithium plasma-facing components were modeled. The analysis confirmed that lithium vapor shielding is a self-regulating mechanism for heat mitigation, while also emphasizing that strong main ion parallel flow is essential to minimize core lithium contamination. Finally, progress toward steady-state operation was anchored by developing the required physics basis and control tools. This includes predictive modeling for Reversed Magnetic Shear sustainment, demonstrating that magnetic island-induced bootstrap current reduction is negligible in STs, and advancing real-time control and disruption avoidance capabilities. The development of high-speed surrogate models (e.g., MMMNet) provides computationally efficient tools vital for non-inductive scenario optimization and integrated, low-disruptivity operations planned for NSTX-U.

We report the experimental results of controlling the pedestal-top electron density by applying resonant magnetic perturbation (RMP) with in-vessel control coils and the main gas puff in the 2024-2025 KSTAR experimental campaign. The density is reconstructed using a parameterized ψ N grid and five channels of line-averaged density measured by the two-colored interferometer (TCI). The reconstruction procedure is accelerated by deploying a multi-layer perceptron to run in approximately 120 µ s and is sufficiently fast for real-time control. A proportional-integral controller was adopted, with the controller gains estimated from the system identification procedure. The experimental results demonstrate that the developed controller can follow a dynamic target while exclusively using both actuators. The absolute percentage errors between the electron density at ψ N = 0.89 and the target were approximately 1.5% median and a 2.5% average, respectively. The developed controller can even lower the density by using the pump-out mechanism under RMP, and it can follow a more dynamic range of density targets than a single actuator controller. The developed controller will enable experimental scenario exploration within a shot by dynamically setting the density target or maintaining a constant electron density within a discharge.