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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.

Abnormal (deviating from the target) variations in the plasma vertical position Z and current $I_\textrm{p}$ (such as vertical displacements, transient $I_\textrm{p}$ ‘spikes’ and quenches) constitute common elements of a disruption, a phenomenon that is to be mitigated, or ultimately avoided in future reactor-relevant tokamaks. While these abnormalities are generally recognized cross-shot and cross-device, details in terms of appearance (or not) and order of these abnormalities in disruption event chains (DEC) are bound to the plasma state at the time of the chain initiation. Detection of these abnormalities is thus indicative not only of the onset of the plasma collapse itself but also of the disruption driving cause that is promoted at a particular plasma state. Here, the occurrence of disruptions, explored via the detection of an $I_\textrm{p}$ quench, and the analysis of DEC constituted by $I_\textrm{p}$ and Z abnormalities is reported for in total seven full device-year pairs of operation of three machines (4, 2 and 1 years of KSTAR, MAST-U and NSTX-U operation, respectively) using the DECAF code expanded tools and capabilities. It is shown that the disruption occurrence depends not only on the details of the plasma state but also on (device-dependent) technical elements of the shot exit scenario. Year-to-year changes in the main disruption causes and a reduction in the disruptivity rate, bound by device and operation upgrades, are reported. Particular trigger instances of DEC (and the full chains when applicable) are shown to occupy different parts of the operation space diagrams, in accordance with prior expectations. Plasma elongation is identified as an important factor influencing details of the chains and its role will be further explored.

A more complete non-perturbative magnetohydrodynamic (MHD)-kinetic hybrid formulation is developed by including the perturbed electrostatic potential δφ in the particle Lagrangian. The fluid-like counter-parts of the hybrid equations, in the Chew-Goldberger-Low high-frequency limit, are also derived and utilized to test the new toroidal implementation in the MARS-K code. Application of the updated non-perturbative hybrid model for a high- β spherical tokamak plasma in MAST finds that the perturbed electrostatic potential generally plays a minor role in the n = 1 ( n is the toroidal mode number) resistive wall mode instability. The effect of δφ is largely destabilizing, with the growth rate of the instability increased by several (up to 20) percent as compared to the case without including δφ . A similar relative change is also obtained for the kinetic-induced resonant field amplification effect at high- β in the MAST plasma considered. The updated capability of the MARS-K code allows quantitative exploration of drift kinetic effects on various MHD instabilities and the antenna-driven plasma response where the electrostatic perturbation, coupled to magnetic perturbations, may play important roles.

A gyrokinetic threshold model for pedestal width–height scaling prediction is applied to multiple devices. A shaping and aspect ratio scan is performed on National Spherical Torus Experiment (NSTX) equilibria, finding $\Delta_{\mathrm{ped}} = 0.92 A^{1.04} \kappa^{-1.24} 0.38^{\delta} \beta_{\theta,\mathrm{ped}}^{1.05}$ for the wide-pedestal branch with pedestal width $\Delta_{\mathrm{ped}}$ , aspect ratio A , elongation κ , triangularity δ , and normalized pedestal height $\beta_{\theta,\mathrm{ped}}$ . The width–transport scaling is found to vary significantly if the pedestal height is varied either with a fixed density or fixed temperature, showing how fueling and heating sources affect the pedestal density and temperature profiles for the kinetic-ballooning-mode (KBM) limited profiles. For an NSTX equilibrium, at fixed density, the wide branch is $\Delta_{\mathrm{ped} } = 0.028 \left(q_\textrm e/\Gamma_\textrm e - 1.7 \right)^{1.5} \sim \eta_\textrm e ^{1.5}$ and at fixed temperature $\Delta_{\mathrm{ped} } = 0.31 \left(q_\textrm e/\Gamma_\textrm e - 4.7 \right)^{0.85}$ $ \sim \eta_\textrm e ^{0.85}$ , where $q_\textrm e$ and $\Gamma_\textrm e$ are turbulent electron heat and particle fluxes and $\eta_\textrm e = \nabla \ln T_\textrm e / \nabla \ln n_\textrm e$ for an electron temperature $T_\textrm e$ and density $n_\textrm e$ . Pedestals close to the KBM limit are shown to have modified turbulent transport coefficients compared to the strongly driven KBMs. The role of flow shear is studied as a width–height scaling constraint and pedestal saturation mechanism for a standard and lithiated wide pedestal discharge. Finally, the stability, transport, and flow shear constraints are combined and examined for an NSTX experiment.

The elimination of the need for an Ohmic heating solenoid may be the most impactful design driver for the realization of economical compact fusion tokamak reactor systems. However, this would require fully non-inductive start-up and current ramp-up from zero plasma current and low electron temperature of sub-keV to the full plasma current of ∼10–15 MA at 20–30 keV electron temperature. To address this challenge, an efficient solenoid-free start-up and ramp-up scenario utilizing a low-field-side-launched extraordinary mode at the fundamental electron cyclotron harmonic frequency (X–I) is proposed, which has more than two orders of magnitude higher electron cyclotron current drive (ECCD) efficiency than the conventional ECCD for the sub-keV start-up regime. A time dependent model was developed to simulate the start-up scenarios. For the Spherical Tokamak Advanced Reactor (STAR) (Menard et al 2023 Next-Step Low-Aspect-Ratio Tokamak Design Studies (IAEA)), it was found that to fully non-inductively ramp-up to 15 MA, it would take about 25 MW of EC power at 170 GHz. Because of the relatively large plasma volume of STAR, radiation losses must be considered. It is important to make sure that high Z impurities are kept sufficiently low during the early current start-up phase where the temperature is sub-keV range. Since the initial current ramp up takes place at a factor of ten lower density compared to the sustained regimes, it is important to transition into a higher bootstrap fraction discharge at lower density to minimize the ECCD power requirement during the densification. For the sustainment phase an array of eight gyrotron launchers with a total of about 60 MW of fundamental O-mode was found to be sufficient to provide the required axis-peaked external current drive. High efficiencies between 19–57 kA MW ^−1 were found with optimal aiming, and these were resilient to small changes in aiming angles and density and temperature profiles.

Linear magnetohydrodynamic (MHD) simulations for the SMall Aspect Ratio Tokamak (SMART) have been carried out for the first time, for both positive (PT) and negative triangularity (NT) shaped plasmas using the MARS-F code. The MHD stability of projected SMART plasmas against internal kinks, infernal modes and edge peeling-ballooning modes have been analyzed for a wide range of realistic equilibria. A stabilization of internal kinks and infernal modes is observed when increasing the safety factor profile and reducing plasma beta. PT shaped plasmas are more stable against both internal kinks and infernal modes than their counterpart NT shaped plasmas. Toroidal flows have little impact on the MHD stability of the internal kinks, but they have a strong stabilizing effect on infernal modes, which can be further mitigated in NT shaped plasmas. The MHD stability of peeling-ballooning modes is reduced in NT shaped plasmas, as observed in conventional tokamaks.

The SMall Aspect Ratio Tokamak (SMART) is currently being commissioned at the University of Seville and will be able to compare the performance of positive and negative triangularity plasmas at low aspect ratio. Predictive simulations have been performed for different machine scenarios and heating schemes using the TRANSP code. The objectives of these simulations are to predict the parameters expected in positive triangularity plasmas, to guide diagnostic development, and to validate transport models. Several reduced turbulence models have been used to predict electron and ion temperatures for the operational phase 2. All models provide similar results from approximately mid-radius to the separatrix but important discrepancies are found in the core region. These positive triangularity results are compared with experiments from a similar size machine like GLOBUS-M2. The multi-mode model (MMM) shows the best agreement. Simulations with different boundary conditions have been performed and no strong differences have been observed between them. The impact of neutral beam injection (NBI) on the predicted profiles has also been addressed. Rotation reduces turbulence levels so higher temperatures are achieved when included in the simulations. Studying the different contributions to the thermal diffusivities, it is observed that electron temperature gradient (ETG) turbulence dominates at the plasma core while micro-tearing modes (MTM) dominate at the edge in the electron channel. In the ion channel, the neoclassical contribution is dominant at the core and at the very edge while the Weiland component, which includes ion temperature gradient mode (ITG), trapped electron mode (TEM), kinetic ballooning mode (KBM), peeling mode (PM) and collisionless and collision dominated magnetohydrodynamic (MHD) modes governs the mid-radius region. For phase 3, two plasmas with different electron densities have been studied. The case with lower density matches well a specific discharge of GLOBUS-M2. The higher density plasma shows high performance with $\beta_N \approx 3.8$ .

Long-pulse plasma operation at high normalized beta, βN, above the n = 1 ideal MHD no-wall stability limit in KSTAR is presently limited by tearing instabilities rather than resistive wall modes. H-mode plasma operation during the recent KSTAR device campaign produced discharges having strong m/n = 2/1 tearing instabilities at βN lower than the ideal MHD no-wall beta limit. The unstable tearing mode consequently reduced plasma confinement and toroidal plasma rotation significantly. The experiment confirmed that an extended duration of electron cyclotron heating (ECH) at the initial phase of the discharge plays a critical role in mode destabilization. To study destabilizing mechanisms that affect the mode growth, the stability of the observed tearing modes from plasmas with significantly different βN is computed by using the resistive DCON code and the M3D-C1 code employing different physics. The computed tearing stability index, Δ′, differs between the mode that is destabilized by the early ECH at lower βN, and the mode that is destabilized at higher βN with observed mode triggering activity. Equilibrium reconstructions that include constraints from internal profile diagnostics are used as input for reliable computation of stability. The modified Rutherford equation (MRE) describing the evolution of the neoclassical tearing mode (NTM) island width has been constructed for KSTAR plasmas by using plasma parameters computed by the TRANSP code. In preparation for long-pulse plasma operation at higher beta utilizing increased plasma heating power, a resistive wall mode (RWM) active feedback control algorithm that includes magnetic sensor compensation of the prompt applied field and the field from the induced current on the passive conductors has been completed and enabled on KSTAR. Use of multiple toroidal sensor arrays is enabled for increased control performance by including the effect of varied mode helicities in the outboard region where the mode measurement is made. This analysis on beta-limiting instabilities and active mode control provides the required foundation for high confinement plasma operation on KSTAR without disruption. [ABSTRACT FROM AUTHOR]

One of the biggest challenges to achieve the goal of producing fusion energy in tokamak devices is the necessity of avoiding disruptions of the plasma current due to instabilities. The disruption event characterization and forecasting (DECAF) framework has been developed in this purpose, integrating physics models of many causal events that can lead to a disruption. Two different machine learning approaches are proposed to improve the ideal magnetohydrodynamic (MHD) no-wall limit component of the kinetic stability model included in DECAF. First, a random forest regressor (RFR), was adopted to reproduce the DCON computed change in plasma potential energy without wall effects, , for a large database of equilibria from the national spherical torus experiment (NSTX). This tree-based method provides an analysis of the importance of each input feature, giving an insight into the underlying physics phenomena. Secondly, a fully-connected neural network has been trained on sets of calculations with the DCON code, to get an improved closed form equation of the no-wall limit as a function of the relevant plasma parameters indicated by the RFR. The neural network has been guided by physics theory of ideal MHD in its extension outside the domain of the NSTX experimental data. The estimated value of has been incorporated into the DECAF kinetic stability model and tested against a set of experimentally stable and unstable discharges. Moreover, the neural network results were used to simulate a real-time stability assessment using only quantities available in real-time. Finally, the portability of the model was investigated, showing encouraging results by testing the NSTX-trained algorithm on the mega ampere spherical tokamak (MAST). [ABSTRACT FROM AUTHOR]

Key plasma physics and real-time control elements needed for robustly stable operation of high fusion power discharges in ITER have been demonstrated in recent research worldwide. Recent analysis has identified the current density profile as the main drive for disruptive instabilities in discharges simulating ITER’s baseline scenario with high and low external torque. Ongoing development of model-based profile control and active control of magnetohydrodynamic instabilities is improving the stability of multiple scenarios. Significant advances have been made toward real-time physics-based prediction of instabilities, including path-oriented analysis, active sensing, and machine learning techniques for prediction that are beginning to go beyond simple disruption mitigation trigger applications. Active intervention contributes to prevention of disruptions, including forced rotation of magnetic islands to prevent wall locking, and localized heating/current drive to shrink the islands. Stable discharge rampdowns have been achieved with the fastest ITER-like scaled current ramp rates, while maintaining an X-point configuration. These elements are being integrated into stable operating scenarios and new event-handling systems for off-normal events in order to develop the physics basis and techniques for robust control in ITER. [ABSTRACT FROM AUTHOR]

The mission of the spherical tokamak NSTX-U is to explore the physics that drives core and pedestal transport and stability at high- and low collisionality, as part of the development of the spherical tokamak (ST) concept towards a compact, low-cost ST-based pilot plant. NSTX-U will ultimately operate at up to 2 MA and 1 T with up to 12 MW of neutral beam injection power for 5 s. NSTX-U will operate in a regime where electromagnetic instabilities are expected to dominate transport, and beam-heated NSTX-U plasmas will explore a portion of energetic particle parameter space that is relevant for both -heated conventional and low aspect ratio burning plasmas. NSTX-U will also develop the physics understanding and control tools to ramp-up and sustain high performance plasmas in a fully-noninductive fashion. NSTX-U began research operations in 2016, but a failure of a divertor magnetic field coil after ten weeks of operation resulted in the suspension of operations and initiation of recovery activities. During this period, there has been considerable work in the area of analysis, theory and modeling of data from both NSTX and NSTX-U, with a goal of understanding the underlying physics to develop predictive models that can be used for high-confidence projections for both ST and higher aspect ratio regimes. These studies have addressed issues in thermal plasma transport, macrostability, energetic particlet-driven instabilities at ion-cyclotron frequencies and below, and edge and divertor physics. [ABSTRACT FROM AUTHOR]

The National Spherical Torus Experiment Upgrade (NSTX-U) will advance the physics basis required for achieving steady-state, high-beta, and high-confinement conditions in a tokamak by accessing high toroidal fields (1 T) and plasma currents (1.0–2.0 MA) in a low aspect ratio geometry (A  =  1.6–1.8) with flexible auxiliary heating systems (12 MW NBI, 6 MW HHFW). This paper describes the progress in the development of L- and H-mode discharge scenarios and the commissioning of operational tools in the first ten weeks of operation that enable the scientific mission of NSTX-U. Vacuum field calculations completed prior to operations supported the rapid development and optimization of inductive breakdown at different values of ohmic solenoid current. The toroidal magnetic field (BT0  =  0.65 T) exceeded the maximum values achieved on NSTX and novel long-pulse L-mode discharges with regular sawtooth activity exceeded the longest pulses produced on NSTX (tpulse  >  1.8 s). The increased flux of the central solenoid facilitated the development of stationary L-mode discharges over a range of density and plasma current (Ip). H-mode discharges achieved similar levels of stored energy, confinement (H98y,2  >  1) and stability (βN/βN-nowall  >  1) compared to NSTX discharges for Ip  ⩽  1 MA. High-performance H-mode scenarios require an L–H transition early in the Ip ramp-up phase in order to obtain low internal inductance (li) throughout the discharge, which is conducive to maintaining vertical stability at high elongation (κ  >  2.2) and achieving long periods of MHD quiescent operations. The rapid progress in developing L- and H-mode scenarios in support of the scientific program was enabled by advances in real-time plasma control, efficient error field identification and correction, effective conditioning of the graphite wall and excellent diagnostic availability. [ABSTRACT FROM AUTHOR]

The National Spherical Torus Experiment (NSTX) has undergone a major upgrade, and the NSTX Upgrade (NSTX-U) Project was completed in the summer of 2015. NSTX-U first plasma was subsequently achieved, diagnostic and control systems have been commissioned, the H-mode accessed, magnetic error fields identified and mitigated, and the first physics research campaign carried out. During ten run weeks of operation, NSTX-U surpassed NSTX record pulse-durations and toroidal fields (TF), and high-performance ~1 MA H-mode plasmas comparable to the best of NSTX have been sustained near and slightly above the n  =  1 no-wall stability limit and with H-mode confinement multiplier H98y,2 above 1. Transport and turbulence studies in L-mode plasmas have identified the coexistence of at least two ion-gyro-scale turbulent micro-instabilities near the same radial location but propagating in opposite (i.e. ion and electron diamagnetic) directions. These modes have the characteristics of ion-temperature gradient and micro-tearing modes, respectively, and the role of these modes in contributing to thermal transport is under active investigation. The new second more tangential neutral beam injection was observed to significantly modify the stability of two types of Alfven eigenmodes. Improvements in offline disruption forecasting were made in the areas of identification of rotating MHD modes and other macroscopic instabilities using the disruption event characterization and forecasting code. Lastly, the materials analysis and particle probe was utilized on NSTX-U for the first time and enabled assessments of the correlation between boronized wall conditions and plasma performance. These and other highlights from the first run campaign of NSTX-U are described. [ABSTRACT FROM AUTHOR]

Tokamak plasma experiments on the DIII-D device (Luxon et al 2005 Fusion Sci. Tech. 48 807) demonstrate high-performance, negative central shear (NCS) equilibria with enhanced stability when the minimum safety factor exceeds 2, qualitatively confirming theoretical predictions of favorable stability in the NCS regime. The discharges exhibit good confinement with an L-mode enhancement factor H89  =  2.5, and are ultimately limited by the ideal-wall external kink stability boundary as predicted by ideal MHD theory, as long as tearing mode (TM) locking events, resistive wall modes (RWMs), and internal kink modes are properly avoided or controlled. Although the discharges exhibit rotating TMs, locking events are avoided as long as a threshold minimum safety factor value is maintained. Fast timescale magnetic feedback control ameliorates RWM activity, expanding the stable operating space and allowing access to values approaching the ideal-wall limit. Quickly growing and rotating instabilities consistent with internal kink mode dynamics are encountered when the ideal-wall limit is reached. The RWM events largely occur between the no- and ideal-wall pressure limits predicted by ideal MHD. However, evaluating kinetic contributions to the RWM dispersion relation results in a prediction of passive stability in this regime due to high plasma rotation. In addition, the ideal MHD stability analysis predicts that the ideal-wall limit can be further increased to by broadening the current profile. This path toward improved stability has the potential advantage of being compatible with the bootstrap-dominated equilibria envisioned for advanced tokamak (AT) fusion reactors. [ABSTRACT FROM AUTHOR]

Marginal stability points of global modes during high plasma pressure operation in the National Spherical Torus Experiment (NSTX) device can be found by computing kinetic modifications to ideal magnetohydrodynamic limits on stability. Calculations with the DCON code for nearly five thousand experimental equilibria show that previous estimates of the no-wall limit (below which the ideal kink/ballooning mode would be stable even without conducting structure surrounding the plasma) on the plasma beta (a ratio of plasma pressure to magnetic pressure) and internal inductance (a measure of the current profile peakedness) were relatively accurate, though about 10% low. The no-wall beta limit also decreased with increasing aspect ratio and increasing broadness of the pressure profile, and these dependencies have implications for the upgrade to NSTX which has a larger aspect ratio and new neutral beams that may increase the broadness of pressure and current profiles. Kinetic modifications to ideal limits calculated with the Modifications to Ideal Stability by Kinetic effects (MISK) code are further validated by detailed comparison with experimental results from NSTX. In several discharges the code predicts a transition from damping of the mode to growth as the time approaches the experimental time of marginal stability to the resistive wall mode (RWM). The main stabilization mechanism is through rotational resonances with the motions of thermal particles in the plasma, though energetic particles also contribute to stability, and it is often when the plasma rotation falls in between these resonances that the RWM was destabilized in NSTX. The calculations are found to be slightly affected by changing the assumed magnetic structure of the mode as well. These validations are important for real-time assessment of stability limits for disruption avoidance, and reliable projections of the stability of future devices. [ABSTRACT FROM AUTHOR]