Galina Avdeeva

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.

In studying a particular non-stationary NSTX L-mode plasma, we observed unexpectedly high levels of flux—first with quasilinear (TGLF) modeling and subsequently with nonlinear gyrokinetic simulations. Upon more detailed analysis, a novel confinement regime was discovered in which a modest increase in E×B shear (beyond baseline experimental estimates) rapidly reduced turbulent transport to levels consistent with power balance. This modest increase is plausible given the errors inherent to the estimation of shearing rates, and the added complexity of the non-stationary (time-dependent) power balance. Remarkably, an additional small increase in shear yields the familiar ion-neoclassical transport level with what appears to be the onset of high-k electron transport only. Although analyses using the TGLF-SAT2 model successfully capture numerous parametric dependencies of this plasma, TGLF does not reproduce the rapid E×B stabilization seen in CGYRO. We believe the results presented should help to better characterize the nonlinear physics of spherical tokamak confinement regimes, provide useful ST datasets for reduced model development, and motivate more accurate experimental diagnosis of E×B shearing rates.

Time-dependent, predictive simulations were performed with the 1.5D tokamak integrated modeling code TRANSP on a large set of well-analyzed, high performing discharges from the National Spherical Torus Experiment (NSTX) in order to evaluate how well modern reduced transport models can reproduce experimentally observed temperature profiles in spherical tokamaks. Overall, it is found that simulations using the Multi-Mode Model (MMM) more consistently agree with the NSTX observations than those using the Trapped Gyro-Landau Fluid (TGLF) model, despite TGLF requiring orders of magnitude greater computational cost. When considering all examined discharges, MMM has median overpredictions of electron temperature ( T e ) and ion temperature ( T i ) profiles of 28% and 27%, respectively, relative to the experiment. TGLF overpredicts T e by 46%, with much larger variance than MMM, and underpredicts T i by 25%. As the ratio of kinetic to magnetic field pressure ( β ) is increased across NSTX discharges, TGLF predicts lower T e and significant flattening of the T i profile, conflicting with NSTX observations. When using an electrostatic version of TGLF, both T e and T i are substantially overpredicted, underscoring the importance of electromagnetic turbulence in the high β spherical tokamak regime. Additionally, calculations with neural net surrogate models for TGLF were performed outside of TRANSP with a time slice flux matching transport solver, finding better agreement with experiment than the TRANSP simulations, highlighting the impact of different transport solvers and simulation techniques. Altogether, the reasonable agreement with experiment of temperature profiles predicted by MMM motivates a more detailed examination of the sensitivities of the TRANSP simulations with MMM to different NSTX plasma regimes in a companion paper (Lestz et al Plasma Phys. Control. Fusion 67 105030), in preparation for self-consistent, time-dependent predictive modeling of NSTX-U scenarios.

The Multi-Mode Model (MMM) for turbulent transport was applied to a large set of well-analyzed discharges from the National Spherical Torus Experiment (NSTX) in order to evaluate its sensitivities to a wide range of plasma conditions. MMM calculations were performed for hundreds of milliseconds in each discharge by performing time-dependent predictive simulations with the 1.5D tokamak integrated modeling code TRANSP. A closely related study (Lestz et al 2025 Plasma Phys. Control. Fusion 67 105029) concluded that MMM predicted electron and ion temperature profiles that were in reasonable agreement with NSTX observations, generally outperforming a different reduced transport model, TGLF. This finding motivates the more thorough investigation of the characteristics of the MMM predictions conducted in this work. The simulations with MMM have electron energy transport dominated by electron temperature gradient modes in the examined discharges with relatively low plasma β (ratio of kinetic plasma pressure to magnetic field pressure) and high collisionality, transitioning to a mixture of different modes for higher β and lower collisionality. The thermal ion diffusivity predicted by MMM is much smaller than the neoclassical contribution, in line with previous experimental analysis of NSTX. Nonetheless, the electron and ion temperature profiles are coupled via collisional energy exchange and thus sensitive to which transport channels are predicted. The time-dependent simulations with MMM are robust to the simulation start time, converging to remarkably similar temperature profiles later during the discharge. MMM typically overpredicts confinement relative to NSTX observations, leading to the prediction of overly steep temperature profiles. Plasmas with spatially broader temperature profiles, higher plasma β , and longer energy confinement times tend to be predicted by MMM with better agreement with the experiment. These findings provide useful context for understanding the regime-dependent tendencies of MMM in anticipation of self-consistent, time-dependent predictive simulations of NSTX-U discharges with these same modeling tools.

This paper presents a first detailed gyrokinetic analysis with the goal of understanding the dominant turbulent transport mechanisms and identifying the micro-instabilities present in small-aspect-ratio plasmas in the PI3 device, developed as magnetized target fusion targets. These plasmas are characterized by low temperatures and high collisionality compared to standard tokamaks. Linear and ion-scale nonlinear gyrokinetic flux tube simulations are performed at radial positions r / a = 0.60 , 0.65, 0.70, and 0.75 using the gyrokinetic code CGYRO (Candy et al 2016 J. Comput. Phys. 324 73). Linear stability analysis finds that ion temperature gradient (ITG) modes dominate at ion scales, while electron-temperature gradient modes dominate at electron scales. Trapped electron modes (TEMs) remain stable due to high collisionality. At very low k y ρ s , microtearing modes (MTMs) are linearly unstable at all radial locations. In the nonlinear regime, turbulence is driven primarily by ITG modes, which dominate both ion and electron energy fluxes. Interestingly, although MTMs are linearly unstable, they are suppressed in the nonlinear phase, except for a small, negative magnetic flutter contribution at the outer radius ( r / a = 0.75 ) that slightly reduces the total electron energy flux. The sensitivity of these instabilities to key plasma parameters is investigated. High collisionality significantly reduces nonlinear turbulent fluxes, and lowering collisionality results in a stronger flux increase than an equivalent increase in plasma beta does. Increasing the T i / T e ratio in the linear analysis stabilizes ITG modes, while simultaneously destabilizing long-wavelength MTMs. Finally, turbulent energy fluxes are compared to neoclassical transport values simulated using NEO (Belli et al 2008 Plasma Phys. Control. Fusion 50 095010), showing transport is anomalous at all radii.

This study presents analysis of gyrokinetic simulations on the National Spherical Torus Experiment (NSTX) to investigate the effects of electromagnetic fields on plasma turbulence and transport. The simulations, performed with varying levels of fidelity using the gyrokinetic CGYRO code, include electrostatic (ES), single-field electromagnetic (EM1), and two-field electromagnetic (EM2) models. A detailed comparison across the simulation database reveals that electromagnetic effects increase both predicted growth rates and quasilinear fluxes, with EM2 simulations producing stronger turbulence than ES and EM1 cases. Quasilinear modeling using QLGYRO demonstrates that while the perturbed parallel magnetic field ( δ B ∥ ) does not drastically affect the total flux at experimental gradients, it leads to a shift in the dominant instability, altering mode structures from microtearing to kinetic ballooning modes (KBMs). The proximity of the plasma profiles to the KBM threshold is explored, with the experimental conditions being near the onset of KBM-driven transport. The KBM, with its large growth rates, is identified as a potential driver of electron temperature flattening, as it can rapidly transport heat across flux surfaces. Performing stability analysis shows core-localized unstable a low- n tor mode that could contribute to the flattening at the early times of the discharge. TGYRO predictive modeling, incorporating both TGLF and QLGYRO, indicates that the inclusion of δ B ∥ significantly improves the accuracy of temperature profile predictions in NSTX high-beta plasmas, although challenges remain in modeling the sharp flux discontinuities caused by KBM-driven instabilities.

Extensive linear and nonlinear simulations to study electron temperature gradient (ETG) stability and thermal transport in National Spherical Torus Experiment (NSTX) and NSTX-U plasmas were performed using the fully electromagnetic gyrokinetic code CGYRO. Linear simulations were performed to determine ETG thresholds in different discharges, showing that ETG modes in spherical tokamaks can present different scalings compared to conventional aspect-ratio tokamaks. Nonlinear gyrokinetic simulations were conducted for selected cases to calculate electron thermal transport and compare to experimental values. Results are also compared with those of ETG modes in the multi-mode model and the Trapped-Gyro-Landau-Fluid reduced model codes, to better understand their applicability in spherical tokamaks.

An accurate magnetohydrodynamic (MHD) equilibrium reconstruction is an essential starting point for stability and transport plasma analysis. This work describes an approach for obtaining kinetic equilibrium reconstructions using the OMFIT framework, which has been applied for the first time to spherical tokamak data from NSTX and NSTX-U. The EFIT equilibrium solver is integrated with experimental data analysis procedures and subsequent TRANSP transport simulations to enhance the accuracy of the reconstruction, in particular, at the edge region, by adding constraints on the total pressure and current density profiles, based on the transport code solution. The accuracy of the equilibrium reconstruction depends on the uncertainty and number of constraints, as well as the choice of basis functions to represent the pressure and current density profiles. Improved fidelity of the equilibrium reconstruction is demonstrated by reducing the variability of the magnetic axis and boundary locations from several centimeters, for reconstructions based on magnetic and experimental pressure constraints, to only several millimeters, for kinetic reconstructions based on transport code constraints, when different representations of basis functions were tested. The variability of the safety factor on axis was reduced ten times in the same sensitivity study. The accuracy of the equilibrium reconstruction and subsequent mapping of the experimental kinetic profile data have a significant impact on the trapped gyro Landau fluid and linear CGYRO turbulence simulations, which predict different spectra of unstable modes and turbulent fluxes for cases with different numbers of constraints in the equilibrium reconstruction. Conversely, the stability analysis performed using the GATO code shows plasmas that are stable to n = 1 MHD modes in both equilibria using magnetic and experimental pressure constraints as well as the transport code constrained equilibrium. However, a scan of parameters away from these conditions shows considerable deviation in the threshold of unstable modes between these reconstructions. Therefore, for reliable plasma analysis and use in turbulence and stability calculations, a high-fidelity equilibrium reconstruction with accurate kinetic constraints based on transport code solutions is necessary.

The objectives of NSTX-U research are to reinforce the advantages of STs while addressing the challenges. To extend confinement physics of low-A, high beta plasmas to lower collisionality levels, understanding of the transport mechanisms that set confinement performance and pedestal profiles is being advanced through gyrokinetic simulations, reduced model development, and comparison to NSTX experiment, as well as improved simulation of RF heating. To develop stable non-inductive scenarios needed for steady-state operation, various performance-limiting modes of instability were studied, including MHD, tearing modes, and energetic particle instabilities. Predictive tools were developed, covering disruptions, runaway electrons, equilibrium reconstruction, and control tools. To develop power and particle handling techniques to optimize plasma exhaust in high performance scenarios, innovative lithium-based solutions are being developed to handle the very high heat flux levels that the increased heating power and compact geometry of NSTX-U will produce, and will be seen in future STs. Predictive capabilities accounting for plasma phenomena, like edge harmonic oscillations, ELMs, and blobs, are being tested and improved. In these ways, NSTX-U researchers are advancing the physics understanding of ST plasmas to maximize the benefit that will be gained from further NSTX-U experiments and to increase confidence in projections to future devices.

A theoretical model is presented that for the first time matches experimental measurements of the pedestal width-height Diallo scaling in the low-aspect-ratio high-β tokamak NSTX. Combining linear gyrokinetics with self-consistent pedestal equilibrium variation, kinetic-ballooning, rather than ideal-ballooning plasma instability, is shown to limit achievable confinement in spherical tokamak pedestals. Simulations are used to find the novel Gyrokinetic Critical Pedestal constraint, which determines the steepest pressure profile a pedestal can sustain subject to gyrokinetic instability. Gyrokinetic width-height scaling expressions for NSTX pedestals with varying density and temperature profiles are obtained. These scalings for STs depart significantly from that of conventional aspect ratio tokamaks.