Abstract Among the burning plasma controllers for research fusion reactors, the dud detector will be of primary importance as it determines whether the plasma is performing well or if it is a dud. In the latter case, the discharge needs to be terminated to remain within tritium and neutron activation limits. To this scope, monitors which track the plasma performance will be integrated in the plasma control system. In this work, we present a novel dud detector that has been empirically identified based on deuterium–tritium (DT) campaigns carried out at JET and TFTR. This controller estimates a proxy of the neutron rate using a combination of the diamagnetic energy and the density peakedness. If the predicted neutron rate deviates from the real-time measurement, then the dud detector will trigger an alarm leading to a safe plasma termination if plasma recovery is not expected or, to actuator requests when adjustment is possible. This monitoring function can also be coupled with equilibrium solver and control-oriented models, such as RAPDENS, as proposed in the 15 MA plasma current, 5.3 T toroidal magnetic field baseline DT ITER scenario.

The measurements using the high resolution electron cyclotron emission radiometry and the charge exchange and recombination spectroscopy are processed using analytic formulas to allow for the detection of islands as small as 1.9 cm. In contrast to large, saturated magnetic islands which are relatively well understood to be governed by the loss of bootstrap current inside the island, small islands are less well understood due to the difficulty of their accurate measurement in tokamaks. Here, 'small' islands are islands comparable in size to the ion banana width, which can be as small as 0.8 cm at DIII-D. The new measurement methods allow for the detection of small island widths when the predicted increase of mode frequency to match the Doppler shifted ion diamagnetic frequency is observed. Therefore, for the first time, the mode frequency increase can be unambiguously associated to the acceleration of the magnetic island propagation. Such association allows for a further development and validation of the much-debated theory of ion polarization currents, which is thought to govern the small island growth.

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 set of nonlinear simulations has been performed in order to study the nonlinear evolution of unstable global Alfv & eacute;n eigenmodes in the National Spherical Torus Experiment-Upgrade (NSTX-U). Results of the single toroidal mode number, n, simulations are compared with a full nonlinear simulation (all toroidal harmonics included). In single-n simulations, the conservation of two integrals of motion of a particle in a cyclotron resonance with a monochromatic wave is demonstrated, resulting in a one-dimensional evolution of the particle distribution in ( E,mu,p(phi)) phase-space. Nonlinear simulations (both single-n and full nonlinear) show a significant redistribution of the resonant fast ions, especially in the pitch parameter. Thus, the changes in the resonant particle's parallel and perpendicular energies can be several times larger than the total particle energy change, with only a small fraction transferring into the excitation of the mode itself. This implies that even a relatively small amplitude mode can significantly modify the beam distribution in the resonant region. For the NSTX-U case considered, the single-n simulation results are close to full nonlinear simulation only for the most unstable mode, in which case the saturation amplitudes and changes in the fast ion distribution are comparable. In contrast, peak amplitudes of subdominant modes in all-n simulations are smaller by a factor of 3-10 compared to single-n runs due to the flattening of the beam ion distribution by the fastest growing mode.

This article presents a survey of NSTX cases to study the microtearing mode (MTM) stabilities using the newly developed global reduced model for Slab-Like Microtearing modes (SLiM). A trained neutral network version of SLiM enables rapid assessment (0.05s/mode) of MTM with $98\%$ accuracy providing an opportunity for systemic equilibrium reconstructions based on the matching of experimentally observed frequency bands and SLiM prediction across a wide range of parameters. Such a method finds some success in the NSTX discharges, the frequency observed in the experiment matches with what SLiM predicted. Based on the experience with SLiM analysis, a workflow to estimate the potential MTM frequency for a quick assessment based on experimental observation has been established.

The spherical tokamak NSTX and the upgraded, higher toroidal field, NSTX-U, routinely create plasmas with large un-thermalized populations of super-Alfvénic fast ions. This population of non-thermal energetic ions excites a broad spectrum of Alfvénic waves, from the lower frequency (≈30 kHz–≈200 kHz) toroidal Alfvén eigenmodes (Cheng and Chance 1986 Phys. Fluids 29 3695), to the higher frequency (400 kHz–3 MHz) global Alfvén eigenmodes (GAEs) and compressional Alfvén eigenmodes (Goedbloed 1975 Phys. Fluids 18 1258). In this paper we present evidence that the GAE non-linearly excite modes, presumably GAE, at frequencies consistent with non-linear or 3-wave coupling. The observation of the excitation of 2 nd harmonic GAE through the intrinsic non-linearity of Global Alfvén modes demonstrates that the non-linear terms can act as an exciter-antenna inside the plasma, broadcasting at harmonics of the mode frequency and with concomitantly shorter wavelengths. As with experiments using external antenna to excite otherwise weakly stable Alfvénic modes, this data can provide information about the stability of modes at harmonics of the GAE. It may also provide information on the nature of the non-linearities in the wave dispersion equation or a direct measure of the mode amplitude (Smith et al 2006 Phys. Plasmas 13 042504). We also report that the short wavelength 2 nd harmonic GAE can be strongly toroidally localized. The observation that the shorter wavelength ( n ≈ 20) 2 nd harmonic modes can be toroidally localized potentially has implications for the impact of fast-ion driven instabilities on fast-ion confinement in ITER and future fusion reactors (Gorelenkov et al 2014 Nucl. Fusion 54 125001).

The observed bifurcations of the low frequency (<50 kHz) and low toroidal periodicity (n < 5) magnetohydrodynamic (MHD) activity often present in the initial part of the National Spherical Tokamak Experiment (NSTX) discharges can be explained by the evolution of the radial profile of the safety factor (q=rBϕ/RBθ) crossing multiple rational surfaces in the core. Important performance limiting instability mechanisms in the NSTX spherical tokamak are often linked to low frequency and low-n MHD activity. They are quite common in long-pulse NSTX plasmas. They can be present at the beginning of the plasma current flat-top, at the end of the discharge or during the whole duration, and they have been observed to deleteriously impact performance over a wide range of q95. An interesting feature observed in some NSTX discharges is the presence of a bifurcation in the frequency of the low n modes, as low as n = 1, that have frequencies comparable to the plasma core rotation divided by n. Equilibrium reconstructions constrained by magnetic diagnostics data and motional stark effect pitch angle radial profiles suggest that the observed bifurcations are linked to a fast evolving minimum value of q. 3D non-linear resistive MHD simulations show that these modes are ideal and exist as non-resonant before the correspondent rational surface enters the plasma.

Spontaneous neoclassical tearing modes (spontaneous NTMs) have been observed in the National Spherical Torus Experiment (NSTX). Recently, a TRANSP based model for the modified Rutherford equation analysis was developed to accurately predict the effect of fast ions on the growth of magnetic islands. The goal of this paper is to utilize the TRANSP NTM model to understand the role of fast ions in NSTX spontaneous NTMs. Our analysis shows that when the passing fast ion driven kinetic neoclassical polarization current term is larger than 1% of the bootstrap current term in the modified Rutherford equation, fast ions play a decisive role in the early growth phase of spontaneous NTM. This result is applicable to any tokamak plasmas with a fast ion drift orbit width, or the fast ion poloidal Larmor radius, comparable to the magnetic island width.

Energetic-particle-induced geodesic acoustic modes, EGAMs (Fu, Phys. Rev. Let. , vol. 101, 2008, pp. 185002), driven by neutral beam injection (NBI), have been observed in many DIII-D tokamak experiments (Nazikian et al. , Phys. Rev. Lett. , vol. 101, 2008, pp. 185001). This mechanism has been theoretically investigated in (Qiu et al. , Plasma Phys. Control. Fusion , vol. 52, 2010, pp. 095003), using a sharp energetic particle distribution function, and in (Qu et al. , Plasma Phys. Control. Fusion , vol. 59, 2017, pp. 055018), where the dispersion relation and eigenmode behaviour were obtained for the situation of early beam scenario, that is, for times smaller than the beam slowing down time. In this work, we extend these studies determining the eigenmode for beyond the slowing down time, in a scenario with reverse safety factor $q$ profile, where a small concentration of energetic ions can produce an off-axis maximum in the GAM dispersion relation. The characteristics of EGAM are analytically studied with the drift kinetic equation together with the MHD code NOVA. The toroidal energetic ion transit frequency, coupled with the GAM frequency, produces the maximum in the dispersion relation where the eigenmode can be found. The quantitative correspondence of experimental results with the predictions of the proposed model is analysed.

Previously, edge-localized mode (ELM)-free and inter-ELM divertor peak heat flux reduction induced by an edge harmonic oscillation (EHO) was observed in NSTX [Gan et al., Nucl. Fusion 57, 126053 (2017)]. This paper introduces new analysis of the EHO impact on the divertor heat flux. It was found that enhanced edge turbulence significantly altered the divertor heat flux footprint in NSTX H-modes, relative to ELM-free discharges. When the background edge fluctuation level was low, the EHO significantly increased the heat flux width and decreased the divertor peak heat flux. When the background edge fluctuation level was high, the EHO actually increased the divertor peak heat flux. Furthermore, it was also found that the heat flux width increased with the increasing frequency of the EHO.

The growth of magnetic islands in NSTX is modeled successfully, with the consideration of passing fast ions. It is shown that a good quantitative agreement between simulation and experimental measurement can be achieved when the uncompensated cross-field current induced by passing fast ions is included in the island growth model. The fast ion parameters, along with other equilibrium parameters, are obtained self-consistently using the TRANSP code with the assumptions of the ‘kick’ model (Podestà et al 2017 Plasma Phys. Control. Fusion 59 095008). The results show that fast ions can contribute to overcoming the stabilizing effect of polarization current for magnetic island growth.

The mission of the low aspect ratio spherical tokamak NSTX-U is to advance the physics basis and technical solutions required for optimizing the configuration of next-step steady-state tokamak fusion devices. NSTX-U will ultimately operate at up to 2 MA of plasma current and 1 T toroidal field on axis for 5 s, and has available up to 15 MW of neutral beam injection power at different tangency radii and 6 MW of high harmonic fast wave heating. With these capabilities NSTX-U will develop the physics understanding and control tools to ramp-up and sustain high performance fully non-inductive plasmas with large bootstrap fraction and enhanced confinement enabled via the low aspect ratio, high beta configuration. With its unique capabilities, NSTX-U research also supports ITER and other critical fusion development needs. Super-Alfvénic ions in beam-heated NSTX-U plasmas access energetic particle (EP) parameter space that is relevant for both α-heated conventional and low aspect ratio burning plasmas. NSTX-U can also generate very large target heat fluxes to test conventional and innovative plasma exhaust and plasma facing component solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, EP stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control.

Theoretical and numerical study of Alfvén eigenmodes (AEs) in the sub-cyclotron frequency range explains the observed frequency scaling with beam parameters in experiments across different devices. Global Alfvén (GAEs) and compressional Alfvén eigenmodes (CAEs) are frequently excited during neutral beam injection (NBI) in the National Spherical Torus Experiment (NSTX/NSTX-U), as well as other beam-heated devices such as MAST and DIII-D. These modes are driven unstable through the Doppler shifted cyclotron resonance with the NBI ions and can be excited in ITER due to super-Alfvénic velocities and anisotropy of the fast ion distribution. Numerical models and theory for sub-cyclotron frequency modes, previously developed and used to study the excitation of GAEs/CAEs in the NSTX(-U), have been successfully applied to explain the DIII-D observations. Simulations for DIII-D demonstrate that the modes with ω / ω ci ∼ 0.6, previously mis-identified as CAEs, have shear polarization and should be identified as the GAEs. Simulation results match the observed frequencies and estimated toroidal mode numbers in DIII-D experiments. Good agreement is found between scaling of the experimentally observed GAE frequencies with NBI parameters for NSTX, NSTX-U and DIII-D and scaling predicted by the theory and simulations. The DIII-D simulation results also demonstrate that GAEs can be excited for larger aspect-ratio devices and smaller (sub-Alfvénic) beam injection velocities, therefore they can be unstable in ITER.

We report here on the discovery on NSTX-U of a qualitatively new type of non-thermal emission from plasmas in the ion-cyclotron frequency range (ICE). This new type of ICE is weakly damped, γdamp/ωICE ≈ 0.14%, low order eigenmodes, excited by a fast ion population radially located near an internal transport barrier. The ICE appears as repetitive bursts with durations of ≈1 ms, and the bursts exhibit frequency chirps upwards and/or downwards with maximum δf/f ≈ 1%. We refer to this chirping ICE as ch-ICE. The bursts are longer than the typical ICE bursts of ≈100 μs reported previously for NSTX and NSTX-U, for simplicity, NSTX(-U). The chirping resembles that seen in modeling of weakly unstable fast particle driven instabilities (cf, Berk et al 1997 Phys. Lett. A 234 213). These data also provide some preliminary indications of non-linear coupling between the ch-ICE harmonics. Despite extensive experimental and theoretical studies of ICE, theoretical understanding of ICE remains qualitative at best. The detailed experimental observations of ICE from NSTX(-U) find a wide variation in the ICE characteristics. The new observations of ch-ICE presented here, combined with the characteristics of ICE on NSTX(-U) previously reported (Fredrickson et al 2019 Phys. Plasmas 26 032111), could guide the development of more complete theoretical models of ICE.

Alfv\'enic modes in the current quench (CQ) stage of the tokamak disruption have been observed in experiments. In DIII-D the excitation of these modes is associated with the presence of high-energy runaway electrons, and a strong mode excitation is often associated with the failure of RE plateau formation. In this work we present results of self-consistent kinetic-MHD simulations of RE-driven compressional Alfv\'en eigenmodes (CAEs) in DIII-D disruption scenarios, providing an explanation of the CQ modes. Simulation results reveal that high energy trapped REs can have resonance with the Alfv\'en mode through their precession motion, and the resonance frequency is proportional to the energy of REs. The mode frequencies and their relationship with the RE energy are consistent with experimental observation. The perturbed magnetic fields from the modes can lead to spatial diffusion of runaway electrons including the nonresonant passing ones, thus providing the theoretical basis for a potential approach for runaway electron mitigation.

One aspect of the interaction between fast ions and magnetohydrodynamic (MHD) instabilities is the fast ion transport. Coupled kink and tearing MHD instabilities have also been reported to cause fast ion transport. Recently, the ‘kick’ model has been developed to compute the evolution of the fast ion distribution from neutral beam injection using instabilities as phase-space resonance sources. The goal of this paper is to utilize the kick model to understand the physics of fast ion transport caused by the coupled kink and tearing modes. Soft x-ray diagnostics are used to identify the mode parameters in the National Spherical Torus Experiment. The comparison of neutron rates measured and computed from time-dependent TRANSP simulation with the kick model shows that the coupling of kink and tearing mode is important in determination of the fast ion transport. The numerical scan of the mode parameters shows that the relative phase of the kink and tearing modes and the overlapping of kink and tearing mode resonances in the phase space can affect the fast ion transport, suggesting that the synergy of the coupled modes may be causing the fast ion transport.

Abrupt large events in the Alfvenic and subAlfvenic frequency bands in tokamaks are typically correlated with increased fast-ion loss. Here, machine learning is used to speed up the laborious process of characterizing the behavior of magnetic perturbations from corresponding frequency spectrograms that are typically identified by humans. The analysis allows for comparison between different mode character (such as quiescent, fixed frequency, chirping, and avalanching) and plasma parameters obtained from the TRANSP code, such as the ratio of the neutral beam injection (NBI) velocity and the Alfven velocity (v(inj.)/v(A)), the q-profile, and the ratio of the neutral beam beta and the total plasma beta (beta(beam),i/beta). In agreement with the previous work by Fredrickson et al., we find a correlation between beta(beam, i) and mode character. In addition, previously unknown correlations are found between moments of the spectrograms and mode character. Character transition from quiescent to nonquiescent behavior for magnetic fluctuations in the 50-200 kHz frequency band is observed along the boundary v phi less than or similar to (1/4)(v(inj.) - 3(vA)), where v. is the rotation velocity.

The Enhanced Pedestal (EP) H-mode regime is an attractive wide-pedestal high-βp scenario for the National Spherical Torus Experiment Upgrade (NSTX-U) and next-step devices as it achieves enhanced energy confinement (H98y,2 > 1.5), large normalized pressure (βN > 5), and significant bootstrap fraction (fBS > 0.6) at Ip/BT = 2 MA/T. This regime is realized when the edge ion collisionality becomes sufficiently small that a positive feedback interaction occurs between a reduction in the ion neoclassical energy transport and an increase in the particle transport from pressure-driven edge instabilities. The EP H-mode was most often observed as a transition following a large edge-localized mode in conditions with low edge neutral recycling. It is hypothesized that the onset of pressure-driven instabilities prior to the full recovery of the neutral density leads to a temporary period with an elevated ion temperature gradient that triggers the transition to EP H-mode. Linear CGYRO and M3D-C1 calculations are compared to beam emission spectroscopy and magnetic spectroscopy in order to describe the evolution of the edge particle transport mechanisms during the ELM recovery and the saturated EP H-mode state. The observations are consistent with the hypothesis that the onset of pressure-driven edge instabilities, such as the kinetic ballooning mode and kink-peeling mode, can be responsible for the increased particle transport in EP H-mode.

Significant variations in MHD activity and fast-ion transport are observed in the DIII-D high-beta, steady-state hybrid discharges with a mixture of electron cyclotron (EC) waves and neutral beam injection (NBI). When electron cyclotron heating (ECH) or current drive (ECCD) is applied, Alfven eigenmodes (AEs) are usually suppressed and replaced by low-frequency bursting modes. The analysis of a recently compiled database of hybrid discharges suggests that the change of the fast-ion pressure especially the perpendicular pressure is the main factor responsible for the instability transition although the transition in some discharges can also be explained by a slight drop of the safety factor q(min). The lower ratio of fast-ion injection speed v(inj) to Alfven speed v(alfven) and slight drop of q(min) during ECCD also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction P-f/P-total is less than 0.53 and v(inj)/v(alfven) is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. Here, P-f and P-total are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The correlation with q(min) is weaker, and qmin is around unity in all the cases. The reason why the instability transition correlates with P-f/P-total and v(inj)/v(alfven) is that they can significantly modify the drive of low-frequency bursting modes and AEs. The explanation is supported by the observation that low-frequency bursting modes are rarely seen in the hybrids with NBI only, with EC waves and counter-NBI, or with high plasma density. A careful check of the low-frequency bursting modes suggests that they are mainly chirping (neoclassical) tearing modes (referred to as chirping (N)TMs), i.e. the mode frequency firstly jumps up from the steady (N)TM frequency, then chirps down, and finally returns to the steady (N)TM frequency. Occasionally, the (N)TMs are fully stabilized and replaced with pure fishbones. The resonance condition calculation and 'Kick' model simulations suggest that (N)TMs and fishbones can interact through modification of the fast ion distribution in phase space, which influences the drive.