Andreas Kleiner

The EPED model (Snyder et al 2011 Nucl. Fusion 51 103016) has had success in describing the pedestal structure of Type-I ELM and QH-mode plasmas in tokamaks, by combining kinetic ballooning mode (KBM) and peeling–ballooning (PB) constraints. Within EPED, the KBM constraint is often approximated by a technique using calculated ideal ballooning mode (IBM) thresholds, fit to a functional form designed to capture non-local effects. It has been noted that quantitative differences between local ideal MHD and gyro-kinetic (GK) ballooning stability can be larger at low aspect ratio. KBM critical pedestals are consistent with observations in initial studies on conventional and spherical tokamaks. In this work, the application of a reduced model for the calculation of the kinetic ballooning stability boundary is presented based on a novel and newly developed gyro-fluid system (GFS) code (Staebler et al 2023 Phys. Plasmas 30 102501). GFS is observed to capture KBMs in DIII-D as well as the NSTX pedestals, opening a route to integrating this model into EPED. Finally, high but finite n global ballooning modes are observed to limit the access to the local 2nd stability and thus provide a transport mechanism that constrains the pedestal evolution with β p , ped . The high n global ballooning stability is approximated by its ideal MHD analog using ELITE. It is shown that nearly-local high n modes with k y ρ s ∼ 0.25 − 0.5 can provide a proxy for the critical β p , ped when a 2nd stable access exists on DIII-D plasmas. The use of GFS and ELITE scaling in EPED provides improved agreement to EPED1 in an initial comparison with DIII-D pedestal data.

Thermal response simulations of plasma-facing components (PFCs) in the SPARC tokamak, performed with the HEAT code, show that three-dimensional (3D) heat loads resulting from stationary n=1 perturbations require highly radiative scenarios, with up to 95% of the power crossing the separatrix (PSOL) being radiated, to maintain PFC temperatures within acceptable operational limits, whereas the application of slowly rotating 3D fields substantially reduces the thermal loads. The HEAT module, developed to predict heat loads from non-axisymmetric plasmas, is extended to model time-dependent heat flux patterns generated by rotating 3D fields, and a comprehensive thermal analysis is performed on PFCs subjected to both the maximum and minimum power loads, as well as to rotating heat flux distributions, to evaluate the temperature evolution for varying perturbation amplitudes and rotation frequencies. The extension of this analysis to 3D fields with toroidal mode number n=2 shows that this configuration leads to weaker localized heat flux peaks relative to the n=1 case, enabling safe operation with less than 80% of the power radiated when static 3D fields of low amplitude are applied, while using slowly rotating fields at higher amplitudes. These results indicate that n=2 perturbations are generally less detrimental to divertor power exhaust, emphasizing the strong dependence of divertor power exhaust on the characteristics of the applied 3D fields.

The research programme performed on the Mega Amp Spherical Tokamak (MAST) Upgrade experiment has made significant advances in developing the physics understanding of low aspect ratio tokamaks in support of the operation of ITER and design of fusion powerplants. High performance plasma scenarios have been developed to facilitate a broad programme of experiments, in which confinement is constrained by the presence of m / n = 2/1 modes that cause substantial losses of fast ions. The onset of these modes coincides with the q = 2 surface residing in a local minimum in the toroidal current density profile. The maximum electron temperature at the pedestal top, T _e,ped is limited with gas fuelling to ∼350 eV to maintain regular ELMs; higher T _e,ped results in a transition to a non-stationary ELM-free regime. The operational space of spherical tokamaks has been expanded into small and ELM-free regimes. Strong shaping of the last closed flux surface can induce a transition from large to small ELMs, and ELM suppression with resonant magnetic perturbations has been observed for the first time in a low aspect ratio tokamak. Negative triangularity shaping has induced a transition from ELMy H-mode to a high-performance L-mode regime for the first time in a low aspect ratio tokamak. In studies of fast ion confinement, losses of fast particles due to Global Alfvén Eigenmodes have been identified. Interactions between fast ions generated by off-axis neutral beam injection and thermal neutrals can result in significant losses of fast ions. Experiments with on- and off-axis neutral beam injection exhibit a flux pumping mechanism, where the central safety factor is held to ∼1 in the absence of sawteeth. In studies of pedestal physics, it has been found that elevated main chamber neutral pressures result in an increase in the electron density and reduction in the temperature at the pedestal top. Advances in understanding plasma exhaust include the integration of a high-performance plasma core with detached outer divertors in the X -point target configuration. A newly commissioned lower divertor cryopump reduces the lower divertor neutral pressure by up to 50%, with minimal effect on the main chamber or upper divertor. New measurements and SOLPS-ITER simulations emphasise the importance of plasma–neutral interactions on divertor detachment in the conditions accessible in experiments. Real-time control of the ionisation front location in both divertor chambers independently has been demonstrated in double null experiments, enabled by the tightly baffled divertor chambers.

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.

Stability of edge-localized modes (ELMs) in spherical tokamaks is explored using the extended MHD model. Linear NIMROD simulations have been performed for three NSTX discharges 132543, 132588, and 141133, to investigate the role of resistivity, diffusivity, and shear flows on the onset of ELMs. The first discharge represents the wide pedestal regime and the later two discharges represent ELM-free enhanced pedestal H-mode. We first present the effect of toroidal rotation shear and find a flow shear destabilizing effect in these NSTX discharges. Simulations are also extended to include the two-fluid and ion gyroviscosity effects. Simulations show that the flow shear can shift the mode spectrum and alter the critical condition of ELM onset. We also uncover that ELM onset prediction in spherical tokamaks requires effects beyond MHD, in particular gyroviscosity and diamagnetic terms could stabilize Peeling-Ballooning modes consistent with the experimental observation of ELM-free regimes in NSTX. The findings give new insight into the nature of the interplay between resistivity, flows, and diamagnetic stabilization in ELM suppression and have potential applications to ELM control schemes in NSTX-U and next-generation spherical tokamaks. This study identifies the essential physical effects that must be included in future predictive and validation simulations.

3D heat flux calculations at the lower outer divertor plate of SPARC using the HEAT code show that 3D fields generated from error field correction coils can lead to enhanced peak heat fluxes up to 15 times larger compared to the axisymmetric case. Previously employed to simulate axisymmetric heat flux on 3D plasma facing components, the HEAT code can now predict 3D heat flux generated by non-axisymmetric plasmas. This is achieved via a new HEAT module which leverages the 3D field line tracing capabilities of MAFOT starting from an M3D-C1 (MHD resistive code) perturbed equilibria. The resulting heat flux is assigned using the magnetic footprint and the heat flux layer model, an extension of the 2D heat flux model also known as the Eich, to 3D non-axisymmetric plasmas. For SPARC, the new capabilities of HEAT are used to calculate the 3D heat loads resulting from n = 1 perturbation fields (with n indicating the toroidal periodicity) applied through a toroidal array of six picture frame coils with different amplitude. The comparison with the unperturbed case shows significant changes in shape and intensity of the heat flux profile. The results show that the application of n = 1 3D field leads to a localized enhancement of the heat flux peak, influenced by the wetted area impacted by the magnetic footprint, and the appearance of a secondary heat flux peak, whose intensity depends on amplitude of the applied 3D field and toroidal location.

We investigate how non-ideal-MHD effects, in particular plasma resistivity, impact the peeling-ballooning stability thresholds in spherical tokamaks. This analysis follows the discovery of resistive kink-peeling modes in ELMing NSTX discharges. In the present study we extend this modeling to ELMing pulses in MAST and MAST-U, where we find a clear resistive scaling for peeling-ballooning modes. While in NSTX ideal-MHD predicts stability for ELMing discharges, in MAST-U we find that the plasma is slightly unstable to peeling-ballooning modes, but is fully stabilized once diamagnetic effects are considered in terms of a growth rate normalization. A resistive power law scaling is calculated for these modes on MAST-U, which lies in between that of tearing modes and resistive interchange modes. A comparison between M3D-C1 and NIMROD shows reasonable agreement for this scaling. Resistivity destabilizes the modes and the peeling-ballooning unstable domain is considerably expanded in both, MAST and MAST-U. In addition to the MAST/-U pulses we also analyze resistive PB stability in a NSTX-similarity discharge on DIII-D. While having a different aspect ratio from NSTX, this discharge uses NSTX-like shaping parameters, toroidal field and plasma current. By considering these discharges alongside NSTX cases, we identify conditions influencing the onset of resistive peeling-ballooning modes. Our findings indicate that magnetic shear in the pedestal region is closely linked to the emergence of resistive edge modes.

The application of resonant magnetic perturbations (RMPs) induces striated heat fluxes on the divertor plate in tokamaks. These striated heat fluxes were previously considered strike point splitting by the intersection between the divertor and predicted magnetic lobe structures. Recently, the existence of stationary 3D filaments has been observed for the first time in National Spherical Torus Experiment (NSTX) plasmas with toroidal mode number n = 3 RMPs. Magnetic field line tracing of these filaments from the midplane to the divertor is consistent with the quantity and the radial and toroidal location of striated heat fluxes observed on the divertor. This study suggests that divertor striated heat flux patterns are linked to these stationary filaments rather than to strike point splitting or magnetic lobe structures for NSTX. This finding will help guide future efforts to understand the heat flux striations in NSTX with RMPs in order to control and reduce the divertor peak heat flux.

A new comprehensive module to simulate heat fluxes from three-dimensional (3D) magnetic fields has been implemented in the HEAT code. Especially compact tokamaks like SPARC require tools to predict and manage large heat fluxes. Existing release versions of HEAT can only simulate axisymmetric heat flux on 3D plasma facing components. The new module uses an M3D-C1 perturbed equilibrium and the MAFOT code to trace field lines of the perturbed 3D magnetic field. Heat flux is then assigned to the resulting footprints via a 3D layer model. The model distinguishes between the scrape-off layer, the magnetic lobes and the private flux region, and employs only 0D parameters like the layer width, diffusive spread and the last closed flux surface position in the perturbed edge to generate a heat flux profile. The magnitude is normalized to the total input power. Resulting heat flux simulations are compared and validated against infrared measurements in the DIII-D tokamak with applied 3D fields; good agreement is found for several cases. The new module can now be applied to the SPARC tokamak; a preliminary result for applied rotating 3D fields is shown.

Using a single toroidal array of coils to reduce the m , n = 2 , 1 resonant error field (EF) produced by the misalignment of the axisymmetric coils in SPARC can result in the enhancement of the local divertor heat fluxes. Managing high divertor heat fluxes ( q ∥ ≃ 10 GW m⁻²) poses a challenge for compact tokamak devices such as SPARC. The presence of non-axisymmetric magnetic field perturbations adds complexity to the problem by generating intricate 3D edge magnetic topologies that alter the heat flux distributions on the target plates. The aim of this work is to investigate the impact of the EF correction (EFC) on the heat fluxes at the divertor plates in SPARC. The MHD code M3DC1 has been used to simulate the 3D magnetic perturbations generated by the shift and tilt of several axisymmetric coils within specified tolerances, as well as from the array of EFC coils located at the midplane. Using a heuristic model that extends the concept of an axisymmetric heat flux layer to 3D plasmas, the resultant heat flux distributions is derived from magnetic footprints calculated with the MAFOT code. The results show that the EFC could either decrease or further enhance the local heat flux when used to correct the m , n = 2 , 1 resonant EF to enhance the core plasma performance.