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The interaction of Alfvén eigenmodes (AEs) and energetic particles is one of many important factors determining the success of future tokamaks. In JET, eight in-vessel antennas were installed to actively probe stable AEs with frequencies ranging 25–250 kHz and toroidal mode numbers |n| < 20. During the 2019–2020 deuterium campaign, almost 7500 resonances and their frequencies f 0, net damping rates γ < 0, and toroidal mode numbers were measured in almost 800 plasma discharges. From a statistical analysis of this database, continuum and radiative damping are inferred to increase with edge safety factor, edge magnetic shear, and when including non-ideal effects. Both stable AE observations and their associated damping rates are found to decrease with |n|. Active antenna excitation is also found to be ineffective in H-mode as opposed to L-mode; this is likely due to the increased edge density gradient’s effect on accessibility and ELM-related noise’s impact on mode identification. A novel measurement is reported of a marginally stable, edge-localized ellipticity-induced AE probed by the antennas during high-power auxiliary heating (ion cyclotron resonance heating and neutral beam injection) up to 25 MW. NOVA-K kinetic-MHD simulations show good agreement with experimental measurements of f 0, γ, and n, indicating the dominance of continuum and electron Landau damping in this case. Similar experimental and computational studies are planned for the recent hydrogen and ongoing tritium campaigns, in preparation for the upcoming DT campaign.

The kinetic-MHD hybrid simulation approach for macroscopic instabilities in plasmas can be extended to include the kinetic effects of both thermal ions and energetic ions. The new coupling scheme includes synchronization of density and parallel velocity between thermal ions and MHD, in addition to pressure coupling, to ensure the quasineutrality condition and avoid numerical errors. The new approach has been implemented in the kinetic-MHD code M3D-C1-K, and was used to study the thermal ion kinetic effects and Landau damping in fishbone modes in both DIII-D and NSTX. It is found that the thermal ion kinetic effects can cause an increase of the frequencies of the non-resonant $n=1$ fishbone modes driven by energetic particles for $q_\mathrm{min}>1$, and Landau damping can provide additional stabilization effects. A nonlinear simulation for $n=1$ fishbone mode in NSTX is also performed, and the perturbation on magnetic flux surfaces and the transport of energetic particles are calculated., 18 pages, 16 figures

Beam modulation effects on Alfvén eigenmode stability have been investigated in a recent DIII-D experiment and show that variations in neutral beam modulation period can have an impact on the beam driven Alfvén eigenmode spectrum and resultant fast ion transport despite similar time-averaged input power. The experiment was carried out during the current ramp phase of L-mode discharges heated with sub-Alfvénic 50–80 kV deuterium neutral beams that drive a variety of Alfvén eigenmodes unstable. The modulation period of two interleaved beams with different tangency radii was varied from shot to shot in order to modify the relative time dependent mix of the beam pitch angle distribution as well as the persistence of a bump-on-tail feature near the injection energy (a feature confirmed by imaging neutral particle analyzer measurements). As the beam modulation period is varied from 7 ms to 30 ms on/off (typical full energy slowing down time of τ slow ≈ 50 ms at mid-radius), toroidicity-induced Alfvén eigenmodes (TAEs) located in the outer periphery of the plasma become intermittent and coincident with the more tangential beam. Core mode activity changes from reversed shear Alfvén eigenmodes (RSAEs) to a mix of RSAE and beta-induced Alfvén eigenmodes. Discharges with 30 ms on/off period do not have a persistent bump-on-tail feature, have the lowest average mode amplitude and least fast ion transport. Detailed analysis of an individual TAE using TRANSP kick modeling (Monte Carlo evolution of the distribution function with probabilistic ‘kicks’ by the AEs) and the resistive MHD code with kinetic fast ions, MEGA, find no strong role of energy gradient drive due to bump-on-tail features. Instead, the observed TAE modulation with interleaved beams is likely a pitch angle dependent result combined with slowing down of the tangential beam between pulses. For the conditions investigated, bump-on-tail contributions to TAE drive were found to be 5% or less of the total drive at any given time.

JET experiments have shown that the three-ion scenarios using waves in the ion cyclotron range of frequencies (ICRF) is an efficient way to build fast ion population through beam ion acceleration by radio frequency (RF) waves. Such a heating scheme is applied to plasmas with at least two thermal ion species. Analysis of mixed discharges with complex heating schemes requires a workflow that allows to model thermal and fast ion transport consistently. This paper is dedicated to modelling of a mixed plasma discharge with significant fraction of fast ions and contributes to development of fast ion transport models. For interpretive analysis with the TRANSP code a JET hydrogen-deuterium plasma discharge with neutral beam injection (NBI) and ICRF heating has been chosen. The task is complicated by NBI-ICRF synergy and plasma magnetohydrodynamic activity, like sawtooth crashes. D beam ions accelerated by RF waves form a high energy tail in fast ion distribution. Significant difference between the neutron rate computed by TRANSP and measured one is observed if the same diffusivity for electrons and ions is assumed. Sensitivity studies show that uncertainties in input plasma parameters and thermal ion transport models are crucial for modelling mixed plasma discharges and increased D transport is required to reach the plasma composition consistent with diagnostic measurements at the plasma edge. Fast ion redistribution by a sawtooth instability is characterised by non-resonant transport due to reconnection of magnetic field lines and resonant transport caused by resonance interaction between the instability and fast ions. With ORBIT simulations it has been shown that resonant interaction strongly affects fast ions of high energies, like beam ions accelerated by RF waves and fusion products. For the considered case, fast ion profiles simulated by ORBIT remain peaked after the sawtooth crashes.

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 seconds, and has available up to 15 MW of Neutral Beam Injection (NBI) power at different tangency radii and 6 MW of High Harmonic Fast Wave (HHFW) 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 parameter space that is relevant for both -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 (PFC) solutions. This paper summarizes recent analysis, theory and modelling progress to advance the tokamak physics basis in the areas of macrostability and 3D fields, energetic particle stability and fast ion transport, thermal transport and pedestal structure, boundary and plasma material interaction, RF heating, scenario optimization and real-time control.

Advanced operation scenarios such as high poloidal beta (β P) or high q min are promising concepts to achieve the steady-state high-performance fusion plasmas. However, those scenarios are prone to substantial Alfvénic activity, causing fast-ion transport and losses. Recent experiments with the advanced operation scenario on KSTAR tokamak have shown that the electron cyclotron current drive (ECCD) is able to mitigate and suppress the beam-ion driven toroidal Alfvén eigenmodes (TAEs) for over several tens of global energy confinement time. Co-current directional intermediate off-axis ECCD lowers the central safety factor slightly and tilts the central q-profile shape so that the continuum damping in the core region increases. Besides, the rise of central plasma pressure and increased thermal-ion Landau damping contribute to TAE stabilization. While the TAEs are suppressed, neutron emission rate and total stored energy increase by approximately 45% and 25%, respectively. Fast-ion transport estimated by TRANSP calculations approaches the classical level during the TAE suppression period. Substantial reduction in fast-ion loss and neutron deficit is also observed. Enhancement of fast-ion confinement by suppressing the TAEs leads to an increase of non-inductive current fraction and will benefit the sustainment of the long-pulse high-performance discharges.

Large burst activity, identified as toroidal Alfvén eigenmode (TAE) avalanche, occurs frequently in neutral-beam heated plasmas in National Spherical Torus Experiment (NSTX). Based on the typical experimental observation of TAE avalanche on NSTX, a self-consistent nonlinear multiple wave-number (k ∥ ≃ n/R, where n toroidal mode-number and R major radius) simulation associated with TAE avalanches is performed using the experimental parameters and profiles before the occurrence of TAE avalanche as the M3D-K input. The wave–wave nonlinear coupling among different modes and the resonant interaction between different modes and energetic-ions during TAE avalanches are identified in the nonlinear multiple wave-number simulations. The resonance overlap during the TAE avalanche is clearly observed in the simulation. It is found that the effective wave–wave coupling and a sufficiently strong drive are two important ingredients for the onset of TAE avalanches. TAE avalanche is considered to be a strongly nonlinear process and it is always accompanied by the simultaneous rapid frequency-chirping and large amplitude bursting of multiple modes and significant energetic-ion losses. The experimental phenomenon is observed on NSTX and is qualitatively reproduced by the simulation results in this work. These findings indicate that the onset of avalanche is triggered by nonlinearity of the system, and are also conducive to understanding the underlying mechanism of avalanche transport of energetic particles in the future burning plasmas, such as International Thermonuclear Experiment Reactor.

Abrupt large events in the Alfvenic and sub-Alfvenic 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 ( $v_{\textrm {inj.}}/v_{A}$ ), the $q$ -profile, and the ratio of the neutral beam beta and the total plasma beta ( $\beta _{\textrm {beam},i}/\beta $ ). In agreement with the previous work by Fredrickson et al. , we find a correlation between $\beta _{\textrm {beam},i}$ 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 $v_{\varphi } \lessapprox ({1}/{4})(v_{\textrm {inj.}} - 3v_{A})$ , where $v_{\varphi }$ is the rotation velocity.

Understanding the effect of Alfvén eigenmodes (AEs) and neoclassical tearing modes (NTMs) on fast ions is highly important for fusion reactors due to potentially strong resonant interactions between the fast ions and the modes. Here, we use the four-view fast-ion D-alpha (FIDA) diagnostic installed in the DIII-D tokamak to reconstruct the fast-ion velocity distribution at two radial positions during two sequential discharges with strong and weak mode activity, respectively. The velocity-space coverage of the diagnostics, however, only allows reliable reconstructions of fast ions with positive pitches. Therefore, we suggest new tomographic inversion methods relying on prior information outside the well-diagnosed region. We find that within the population of fast ions with positive pitches, ions, at all energies, are transported away from the measurement volumes. Comparisons between the reconstructions and kick model simulations, where the mode activity is considered, reveal that low-frequency modes such as the NTMs and low-frequency AEs contribute significantly to the positive-pitch fast-ion transport in the central measurement volume, whereas TAEs and EAEs become important farther out and are responsible for decreased fast-ion confinement.

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.

Experimental results from the National Spherical Torus Experiment (NSTX), a medium-size spherical tokamak with a compact divertor, and DIII-D, a large conventional aspect ratio tokamak, demonstrate that the snowflake (SF) divertor configuration may provide a promising solution for mitigating divertor heat loads and target plate erosion compatible with core H-mode confinement in the future fusion devices, where the standard radiative divertor solution may be inadequate. In NSTX, where the initial high-power SF experiment was performed, the SF divertor was compatible with H-mode confinement, and led to the destabilization of large Edge Localized Modes (ELMs). However, a stable partial detachment of the outer strike point was also achieved where inter-ELM peak heat flux was reduced by factors 3–5, and peak ELM heat flux was reduced by up to 80% (see standard divertor). The DIII-D studies show the SF divertor enables significant power spreading in attached and radiative divertor conditions. Results include: compatibility with the core and pedestal, peak inter-ELM divertor heat flux reduction due to geometry at lower $n_{e}$ , and ELM energy and divertor peak heat flux reduction, especially prominent in radiative $D_{2}$ -seeded SF divertor, and nearly complete power detachment and broader radiated power distribution in the radiative $D_{2}$ -seeded SF divertor at $P_{\text {SOL}}=3-4$ MW. A variety of SF configurations can be supported by the divertor coil set in NSTX Upgrade. Edge transport modeling with the multifluid edge transport code UEDGE shows that the radiative SF divertor can successfully reduce peak divertor heat flux for the projected $P_{\text {SOL}} \simeq 9$ MW case. The radiative SF divertor with carbon impurity provides a wider $n_{e}$ operating window, 50% less argon is needed in the impurity-seeded SF configuration to achieve similar $q_{\text {peak}}$ reduction factors (see standard divertor).

Significant variations in MHD activity and fast-ion transport are observed in the DIIID 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 qmin. The lower ratio of fast-ion injection speed vinj to Alfven speed valfven and slight drop of safety factor qmin during ECCD may also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction Pf/Ptotal is less than 0.53 and vinj/valfven is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. Here, Pf and Ptotal are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The correlation with qmin is weaker and qmin is around unity in all the cases. The reason why the instability transition correlates with Pf/Ptotal and vinj/valfven 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)TM], 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.

This paper describes a study of the cross-correlations between edge fluctuations as seen in the gas puff imaging (GPI) diagnostic and low frequency coherent magnetic fluctuations (MHD) in H-mode plasmas in NSTX. The main new result was that large blobs in the scrape-off-layer were significantly correlated with MHD activity in the 3–6 kHz range in 21 of the 223 shots examined. There were also many other shots in which fluctuations in the GPI signal level and its peak radius Rpeak were correlated with MHD activity but without any significant correlation of the MHD with large blobs. The structure and motion of the MHD are compared with those of the correlated blobs, and some possible theoretical mechanisms for the MHD-blob correlation are discussed.

In tokamak discharges, toroidal Alfven eigenmodes often experience complex semi-periodic frequency modulation known as chirping. These events modify the local high energy particle distribution and are expected to occur in many future fusion devices, which include energetic beams or fusion products. This paper presents a study of simulations of mode chirping made in order to better understand its phase-space properties in a realistic tokamak configuration. We find a mechanism that permits rapid repeated chirping with strong amplitude variation in each chirp. Each chirp is associated with an amplitude crash to low magnitude and local manipulation of the density gradients through a shift of mode phase through π. The chirping produces high density clumps, which propagate down the fast ion density gradient and low density holes that propagate up the density gradient away from the resonance. This flow of particles across the resonance provides an energy source and local gradients for repeated chirping.

In some tokamak discharges, a number of Alfven eigenmodes (AEs) have been observed to cause a large-scale collapse of the high energy particle distribution, a phenomenon referred to as an avalanche. We examine the necessary conditions for an avalanche using the available experimental information from NSTX on the equilibrium and mode properties for two cases, one with a measurable but benign AE activity and one with an AE activity leading up to an avalanche. To produce an avalanche, the modes present in the discharge must possess resonances that can overlap with a modest increase in instability magnitude, providing a path to global particle stochastic motion. We find that the modes present in the avalanche-free discharge do not provide such a path even at a very large amplitude. During the discharge which subsequently produces an avalanche, the high energy population is growing and the Alfven frequency is dropping due to increasing density, and we find that both these changes, producing a small increased drive or an increased resonance width for the Alfven modes, can lead in this case to uncontrolled mode growth and large-scale beam particle loss.

Rare Alfv\'enic wave transitions between fixed-frequency and chirping phases are identified in NSTX, where Alfv\'enic waves are normally observed to exhibit either chirping or avalanching responses. For those transitions, we apply a criterion [Duarte et al, Nucl. Fusion 57, 054001 (2017)] to predict the nature of fast ion redistribution in tokamaks to be in the convective or diffusive nonlinear regimes. For NSTX discharges in which the transition is not accompanied by changes in the beam deposited power or modifications in the injected radiofrequency power, it has been found that the anomalous fast ion transport is a likely mediator of the bifurcation between the fixed-frequency mode behavior and rapid chirping. For a quantitative assessment, global gyrokinetic simulations of the effects of electrostatic ion temperature gradient turbulence and trapped electron mode turbulence on chirping were pursued using the GTS code. The investigation is extended by means of predictive studies of the probable spectral behavior of Alfv\'enic eigenmodes for baseline ITER cases consisting of elmy, advanced and hybrid scenarios. It has been observed that most modes are found to be borderline between the steady and the chirping phases.

Lithium sputtering yields and gross impurity influxes from lithium-coated graphite and molybdenum plasma facing components (PFCs) have been analyzed for the first time in the National Spherical Torus Experiment (NSTX) divertor during H-mode NBI-heated discharges. Motivated by the beneficial effects of lithium conditioning on discharge performance and reproducibility, evaporative lithium coatings were the routine wall conditioning technique in NSTX. Neutral lithium sputtering yields from solid lithium coatings in NSTX were found to be consistent with values reported from test stand experiments from deuterium-saturated lithium (with sputtering yields Y Li ∼0.03–0.07 Y Li ∼ 0.03 – 0.07 ). Temperature-enhanced lithium sputtering was observed on lithium-coated graphite and molybdenum as a result of PFC heating by both embedded heaters and incident plasma heat flux, leading to Y Li ∼0.1–0.2 Y Li ∼ 0.1 – 0.2 for surface temperatures above the lithium melting point.

The snowflake divertor is a proposed technique for coping with the tokamak power exhaust problem in next-step experiments and eventually reactors, where extreme power fluxes to material surfaces represent a leading technological and physics challenge. In lithium-conditioned National Spherical Torus Experiment (NSTX) discharges, application of the snowflake divertor typically induced partial outer divertor detachment and severalfold heat flux reduction. UEDGE is used to analyze and compare conventional and snowflake divertor configurations in NSTX. Matching experimental upstream profiles and divertor measurements in the snowflake requires target recycling of 0.97 vs. 0.91 in the conventional case, implying partial saturation of the lithium-based pumping mechanism. Density scans are performed to analyze the mechanisms that facilitate detachment in the snowflake, revealing that increased divertor volume provides most of the parallel heat flux reduction. Also, neutral gas power loss is magnified by the increased wetted area in the snowflake, and plays a key role in generating volumetric recombination.

We show that the degradation of fast-ion confinement in steady-state DIII-D discharges is quantitatively consistent with predictions based on the effects of multiple unstable Alfven eigenmodes on beam-ion transport. Simulation and experiment show that increasing the radius where the magnetic safety factor has its minimum is effective in minimizing beam-ion transport. This is favorable for achieving high performance steady-state operation in DIII-D and future reactors. A comparison between the experiments and a critical gradient model, in which only equilibrium profiles were used to predict the most unstable modes, show that in a number of cases this model reproduces the measured neutron rate well.

Modulation of mode amplitude and frequency of TAE modes, observed experimentally and referred to as chirping, is investigated using a guiding center code and a δf formalism. Chirping is observed as the development in time of Fourier sidebands that move above and below the nominal mode frequency. Subsequent doubling of the sidebands is also sometimes observed. Equilibria with conventional positive magnetic shear are used, as well as NSTX reversed shear cases. The onset of chirping can be triggered by a sudden increase in mode damping, as can occur by the mode contacting the continuum.

An analytical theory based on the MHD model is presented for understanding the coupling between the shear Alfven wave and the slow magnetosonic wave (or the so called slow mode) in the frequency range below the Toroidal Alfven Eigenmode (TAE) continuum spectrum gap. In tokamak plasmas, coupling of the Alfven m poloidal harmonic and the slow mode m ± 1 harmonics causes the Alfven m harmonic continuous spectrum to be uplifted from the uncoupled Alfven spectrum by an amount related to the plasma pressure and the geodesic magnetic field curvature. However, the frequency of one of the slow mode m ± 1 harmonics is reduced by the same pressure-curvature coupling effect. But the frequency of the other slow mode harmonic is relatively unaffected. As a result, the Alfven-slow (AS) mode continuous spectrum is broken up into two Alfven-Slow (AS) gaps below the TAE continuum gap. Coupling of the Alfven m harmonic with the slow mode m ± 2 harmonics also creates additional AS gaps if their frequencies cross each other. The AS gap widths increase with the plasma pressure. The creation of AS gaps allows the existence of several new types of Alfven-Slow Eigenmodes (ASEs). The radial structure of these new ASEs does not intersect with the continuous spectrum and thus does not suffer from continuum damping. The Beta-induced Alfven-Acoustic Eigenmode (BAAE) is one type of ASEs with frequency in the lowest AS frequency gap. However, the BAAE usually interacts with the Alfven-Slow continuum and suffers from continuum damping. The existence of ASEs is ubiquitous for normal and reserve safety factor profiles, broad range of plasma β values, different plasma shapes, and many different toroidal mode numbers. The newly discovered ASEs provide explanation for the experimentally observed Beta-induced Alfven Eigenmodes destabilized by fast ions with frequencies below the TAE frequency gap.

The resonance broadened quasilinear (RBQ) model for the problem of relaxing the hot ion distribution function in constant-of-motion 3D space [Gorelenkov et al., Nucl. Fusion 58, 082016 (2018)] is presented with the self-consistent evolution of multiple Alfven eigenmode amplitudes. The RBQ model represents the generalization of the earlier published model [Berk et al., Nucl. Fusion 35, 1661 (1995)] by carefully examining the wave particle interaction in the presence of realistic Alfven eigenmode (AE) structures and pitch angle scattering with the help of the guiding center code ORBIT. One aspect of the generalization is that the RBQ model goes beyond the local perturbative-pendulumlike approximation for the wave particle dynamics near the resonance. An iterative procedure is introduced to account for eigenstructures varying within the resonances. It is found that a radially localized mode structure implies a saturation level 2–3 times smaller than that predicted by an earlier bump-on-tail quasilinear model that employed uniform mode structures. We apply the RBQ code to a DIII-D plasma with an elevated q-profile where the beam ion profiles exhibit stiff transport properties [Collins et al., Phys. Rev. Lett. 116, 095001 (2016)]. The properties of AE driven fast ion distribution relaxation are studied for validations of the applied RBQ model in DIII-D discharges. Initial results show that the model is robust, is numerically efficient, and can predict fast ion relaxation in present and future burning plasma experiments.The resonance broadened quasilinear (RBQ) model for the problem of relaxing the hot ion distribution function in constant-of-motion 3D space [Gorelenkov et al., Nucl. Fusion 58, 082016 (2018)] is presented with the self-consistent evolution of multiple Alfven eigenmode amplitudes. The RBQ model represents the generalization of the earlier published model [Berk et al., Nucl. Fusion 35, 1661 (1995)] by carefully examining the wave particle interaction in the presence of realistic Alfven eigenmode (AE) structures and pitch angle scattering with the help of the guiding center code ORBIT. One aspect of the generalization is that the RBQ model goes beyond the local perturbative-pendulumlike approximation for the wave particle dynamics near the resonance. An iterative procedure is introduced to account for eigenstructures varying within the resonances. It is found that a radially localized mode structure implies a saturation level 2–3 times smaller than that predicted by an earlier bump-on-tail quasilinear model...

We report here on observations of magnetic fluctuations in the ion-cyclotron frequency range on NSTX and NSTX-U. In many respects, the fluctuations appear similar to the ion cyclotron emission (ICE) seen in conventional tokamaks. However, a significant difference between previous observations of ICE and the ICE on NSTX is that the frequency of ICE in conventional tokamaks is typically near the ion cyclotron frequency of the energetic fast ions at the plasma edge. In NSTX and NSTX-U, the magnetic fluctuation frequency corresponds to the ion cyclotron frequency deeper in the plasma, near the location of an internal transport barrier. As on conventional tokamaks, higher harmonics of the deuterium cyclotron frequency, as high as the seventh, are seen with the strongest signal sometimes from higher harmonics. The emission usually appears as an irregular sequence of short bursts typically ≤100 μs in duration although nearly continuous emission for several ms has also been seen under some conditions. Measurements of the emission with a toroidal array of fast probes show that the emission is a long wavelength, spatially coherent mode. The emission frequency does not follow an Alfvenic scaling with density, as seen for compressional Alfven eigenmodes, but does show a linear scaling with local magnetic field strength. The measured emission shows a compressional polarization consistent with a compressional Alfven wave. No correlation between the neutron rate and the ICE amplitude is seen. Three-wave coupling between the instability responsible for the ICE and lower frequency modes has also been observed.

Deuterium fueling experiments were conducted with the NSTX Liquid Lithium Divertor (LLD). Lithium evaporation recoated the LLD surface to approximate flowing liquid Li to sustain D retention. In the first experiment with the diverted outer strike point on the LLD, the difference between the applied D gas input and the plasma D content reached very high values without disrupting the plasma, as would normally occur in the absence of Li pumping, and there was also little change in plasma D content. In the second experiment, constant fueling was applied, as the LLD temperature was varied to change the surface from solid to liquid. The D retention was relatively constant, and about the same as that for solid Li coatings on graphite, or twice that achieved without Li PFC coatings. Contamination of the LLD surface was also possible due to compound formation and erosion and redeposition from carbon PFCs.

Experimental studies of the novel snowflake divertor concept (D. Ryutov, Phys. Plasmas 14 (2007) 064502) performed in the NSTX and TCV tokamaks are reviewed in this paper. The snowflake divertor enables power sharing between divertor strike points, as well as the divertor plasma-wetted area, effective connection length and divertor volumetric power loss to increase beyond those in the standard divertor, potentially reducing heat flux and plasma temperature at the target. It also enables higher magnetic shear inside the separatrix, potentially affecting pedestal MHD stability. Experimental results from NSTX and TCV confirm the predicted properties of the snowflake divertor. In the NSTX, a large spherical tokamak with a compact divertor and lithium-coated graphite plasma-facing components (PFCs), the snowflake divertor operation led to reduced core and pedestal impurity concentration, as well as reappearance of Type I ELMs that were suppressed in standard divertor H-mode discharges. In the divertor, an otherwise inaccessible partial detachment of the outer strike point with an up to 50% increase in divertor radiation and a peak divertor heat flux reduction from 3-7 MW/m(2) to 0.5-1 MW/m(2) was achieved. Impulsive heat fluxes due to Type-I ELMs were significantly dissipated in the high magnetic flux expansion region. In the TCV, a medium-size tokamak with graphite PFCs, several advantageous snowflake divertor features (cf. the standard divertor) have been demonstrated: an unchanged L-H power threshold, enhanced stability of the peeling-ballooning modes in the pedestal region (and generally an extended second stability region), as well as an H-mode pedestal regime with reduced (x2-3) Type I ELM frequency and slightly increased (20-30%) normalized ELM energy, resulting in a favorable average energy loss comparison to the standard divertor. In the divertor, ELM power partitioning between snowflake divertor strike points was demonstrated. The NSTX and TCV experiments are providing support for the snowflake divertor as a viable solution for the outstanding tokamak plasma-material interface issues. (C) 2013 Elsevier B.V. All rights reserved.

Major developments on the Mega Amp Spherical Tokamak (MAST) have enabled important advances in support of ITER and the physics basis of a spherical tokamak (ST) based component test facility (CTF), as well as providing new insight into underlying tokamak physics. For example, L–H transition studies benefit from high spatial and temporal resolution measurements of pedestal profile evolution (temperature, density and radial electric field) and in support of pedestal stability studies the edge current density profile has been inferred from motional Stark effect measurements. The influence of the q-profile and E × B flow shear on transport has been studied in MAST and equilibrium flow shear has been included in gyro-kinetic codes, improving comparisons with the experimental data. H-modes exhibit a weaker q and stronger collisionality dependence of heat diffusivity than implied by IPB98(y,2) scaling, which may have important implications for the design of an ST-based CTF. ELM mitigation, an important issue for ITER, has been demonstrated by applying resonant magnetic perturbations (RMPs) using both internal and external coils, but full stabilization of type-I ELMs has not been observed. Modelling shows the importance of including the plasma response to the RMP fields. MAST plasmas with q > 1 and weak central magnetic shear regularly exhibit a long-lived saturated ideal internal mode. Measured plasma braking in the presence of this mode compares well with neo-classical toroidal viscosity theory. In support of basic physics understanding, high resolution Thomson scattering measurements are providing new insight into sawtooth crash dynamics and neo-classical tearing mode critical island widths. Retarding field analyser measurements show elevated ion temperatures in the scrape-off layer of L-mode plasmas and, in the presence of type-I ELMs, ions with energy greater than 500 eV are detected 20 cm outside the separatrix. Disruption mitigation by massive gas injection has reduced divertor heat loads by up to 70%.

Modulation of various neutral beam sources probes the interaction of fast ions with tearing modes (TM) in the DIII-D tokamak. As measured by electron cyclotron emission, the tearing modes have an island width of ~8 cm and change phase at the q = 2 surface. (Here, m is the poloidal mode number and n is the toroidal mode number.) Deuterium neutral beam injection by six sources with differing injection geometries produces the fast ions. To study the interaction in different parts of phase space, on successive discharges, one of the six sources is modulated at 20 Hz to populate different fast-ion orbits. The modulation only changes the island width by a few millimeters, implying that any fast-ion effect on mode stability is below detection limits. When compared to the expected signals in the absence of TM-induced transport, both the average and modulated neutron signals deviate, implying that fast-ion transport occurs in much of phase space. Fast-ion D α (FIDA) measurements detect reductions in signal at wavelengths that are sensitive to counter-passing ions. Neutral particle analyzer data imply poor confinement of trapped fast ions. Calculations of the expected fast-ion transport that use measured TM properties successfully reproduce the data.

Analysis of fast-ion D-alpha (FIDA) data on National Spherical Torus Experiment-Upgrade (NSTX-U) shows that the cold Dα line contaminates the FIDA baseline. The scattered light is comparable to the FIDA emission. A scattering correction is required to extract the FIDA signal. Two methods that relate the scattered light contamination to the intensity of the cold Dα line are employed. One method uses laboratory measurements with a calibration lamp; the other method uses data acquired during plasma operation and singular value decomposition analysis. After correction, both the FIDA spectra and spatial profile are in better agreement with theoretical predictions.

An engineering upgrade to the neutral beam system at the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] enables time-dependent programming of the beam voltage and current. Initial application of this capability involves pre-programmed beam voltage and current injected into plasmas that are known to be susceptible to instabilities that are driven by energetic ( E ≥ 40 keV) beam ions. These instabilities, here all Alfven eigenmodes (AEs), increase the transport of the beam ions beyond a classical expectation based on particle drifts and collisions. Injecting neutral beam power, P beam ≥ 2 MW, at reduced voltage with increased current reduces the drive for Alfvenic instabilities and results in improved ion confinement. In lower-confinement plasmas, this technique is applied to eliminate the presence of AEs across the mid-radius of the plasmas. Simulations of those plasmas indicate that the mode drive is decreased and the radial extent of the remaining modes is reduced compared to a higher beam voltage case. In higher-confinement plasmas, this technique reduces AE activity in the far edge and results in an interesting scenario of beam current drive improving as the beam voltage reduces from 80 kV to 65 kV.An engineering upgrade to the neutral beam system at the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] enables time-dependent programming of the beam voltage and current. Initial application of this capability involves pre-programmed beam voltage and current injected into plasmas that are known to be susceptible to instabilities that are driven by energetic ( E ≥ 40 keV) beam ions. These instabilities, here all Alfven eigenmodes (AEs), increase the transport of the beam ions beyond a classical expectation based on particle drifts and collisions. Injecting neutral beam power, P beam ≥ 2 MW, at reduced voltage with increased current reduces the drive for Alfvenic instabilities and results in improved ion confinement. In lower-confinement plasmas, this technique is applied to eliminate the presence of AEs across the mid-radius of the plasmas. Simulations of those plasmas indicate that the mode drive is decreased and the radial extent of the remaining modes is reduced compared to a higher b...

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfv\'enic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

The local properties of the electron energy distribution function are investigated in the electron-cyclotron wave driven toroidal device TORPEX (Fasoli et al 2006 Phys. Plasmas 13 055902). The electron energy distribution function is measured by means of a time-resolved electrostatic energy analyser. The measurements indicate that electrons are accelerated to different energies at the electron-cyclotron and upper-hybrid resonances. Electrons from the upper-hybrid resonance have higher energies and can be described by a secondary maxwellian energy distribution function. The electron energy distribution function is found to be invariant with respect to experimental parameters such as the neutral gas pressure, the magnetic field configuration and the injected microwave power. The implications for a correct modelling of the particle source term for TORPEX plasmas are discussed.

Experimental results from the National Spherical Torus Experiment (NSTX), a medium-size spherical tokamak with a compact divertor, and DIII-D, a large conventional aspect ratio tokamak, demonstrate that the snowflake (SF) divertor configuration (D.D. Ryutov, Phys. Plasmas, 14, 064502, 2007) may provide a promising solution for mitigating divertor heat loads and target plate erosion compatible with core H-mode confinement in future fusion devices, where the standard radiative divertor solution may be inadequate. In NSTX, where the initial high-power SF experiment were performed, the SF divertor was compatible with H-mode confinement, and led to the destabilization of large ELMs. However, a stable partial detachment of the outer strike point was also achieved where inter-ELM peak heat flux was reduced by factors 3–5, and peak ELM heat flux was reduced by up to 80% (cf. standard divertor). The DIII-D studies show the SF divertor enables significant power spreading in attached and radiative divertor conditions. Results include: compatibility with the core and pedestal, peak inter-ELM divertor heat flux reduction due to geometry at lower ne, and ELM energy and divertor peak heat flux reduction, especially prominent in radiative D2-seeded SF divertor, and nearly complete power detachment and broader radiated power distribution in the radiative D2-seeded SF divertor at PSOL = 3 – 4 MW. A variety of SF configurations can be supported by the divertor coil set in NSTX Upgrade. Edge transport modeling with the multi-fluid edge transport code UEDGE shows that the radiative SF divertor can successfully reduce peak divertor heat flux for the projected PSOL ≃ 9 MW case. The radiative SF divertor with carbon impurity provides a wider ne operating window, 50% less argon is needed in the impurity-seeded SF configuration to achieve similar qpeak reduction factors (cf. standard divertor).

The plasma particle source resulting from ionization by microwaves in the electron-cyclotron range of frequencies is investigated in the simple magnetized torus TORPEX ( Fasoli A et al 2006 Phys. Plasmas 13 055902), together with its dependence upon experimental parameters, such as the absorbed microwave power, the magnetic field configuration and the neutral gas pressure. The relative contributions to the ionization rate from thermal electrons and from suprathermal electrons accelerated at the plasma resonances are quantified through a global particle balance. An expression for the spatial profile of the particle source is derived from the experimental results and a simple numerical code.

© 2015 IOP Publishing Ltd. We carry out a quantitative comparison between gas puff imaging (GPI) turbulence measurements in Alcator C Mod inner wall limited discharges (Zweben et al 2009 Phys. Plasmas 18 082505) and 3D flux driven drift reduced Braginskii turbulence simulations of scrape off layer dynamics. The comparison is carried out for a series of inner wall limited discharges where the magnetic field and the density are varied. The comparison between GPI data and non linear simulations yields overall good agreement for several observables such as the Da emission levels and intermittency the radial and poloidal correlation lengths and propagation velocities and the power and frequency spectral density.

The Mega Ampère Spherical Tokamak (MAST) programme is strongly focused on addressing key physics issues in preparation for operation of ITER as well as providing solutions for DEMO design choices. In this regard, MAST has provided key results in understanding and optimizing H-mode confinement, operating with smaller edge localized modes (ELMs), predicting and handling plasma exhaust and tailoring auxiliary current drive. In all cases, the high-resolution diagnostic capability on MAST is complemented by sophisticated numerical modelling to facilitate a deeper understanding. Mitigation of ELMs with resonant magnetic perturbations (RMPs) with toroidal mode number n RMP = 2, 3, 4, 6 has been demonstrated: at high and low collisionality; for the first ELM following the transition to high confinement operation; during the current ramp-up; and with rotating n RMP = 3 RMPs. n RMP = 4, 6 fields cause less rotation braking whilst the power to access H-mode is less with n RMP = 4 than n RMP = 3, 6. Refuelling with gas or pellets gives plasmas with mitigated ELMs and reduced peak heat flux at the same time as achieving good confinement. A synergy exists between pellet fuelling and RMPs, since mitigated ELMs remove fewer particles. Inter-ELM instabilities observed with Doppler backscattering are consistent with gyrokinetic simulations of micro-tearing modes in the pedestal. Meanwhile, ELM precursors have been strikingly observed with beam emission spectroscopy (BES) measurements. A scan in beta at the L–H transition shows that pedestal height scales strongly with core pressure. Gyro-Bohm normalized turbulent ion heat flux (as estimated from the BES data) is observed to decrease with increasing tilt of the turbulent eddies. Fast ion redistribution by energetic particle modes depends on density, and access to a quiescent domain with ‘classical’ fast ion transport is found above a critical density. Highly efficient electron Bernstein wave current drive (1 A W−1) has been achieved in solenoid-free start-up. A new proton detector has characterized escaping fusion products. Langmuir probes and a high-speed camera suggest filaments play a role in particle transport in the private flux region whilst coherence imaging has measured scrape-off layer (SOL) flows. BOUT++ simulations show that fluxes due to filaments are strongly dependent on resistivity and magnetic geometry of the SOL, with higher radial fluxes at higher resistivity. Finally, MAST Upgrade is due to begin operation in 2016 to support ITER preparation and importantly to operate with a Super-X divertor to test extended leg concepts for particle and power exhaust.

The National Spherical Torus Experiment (NSTX) is currently being upgraded to operate at twice the toroidal field and plasma current (up to 1 T and 2 MA), with a second, more tangentially aimed neutral beam (NB) for current and rotation control, allowing for pulse lengths up to 5 s. Recent NSTX physics analyses have addressed topics that will allow NSTX-Upgrade to achieve the research goals critical to a Fusion Nuclear Science Facility. These include producing stable, 100% non-inductive operation in high-performance plasmas, assessing plasma–material interface (PMI) solutions to handle the high heat loads expected in the next-step devices and exploring the unique spherical torus (ST) parameter regimes to advance predictive capability. Non-inductive operation and current profile control in NSTX-U will be facilitated by co-axial helicity injection (CHI) as well as radio frequency (RF) and NB heating. CHI studies using NIMROD indicate that the reconnection process is consistent with the 2D Sweet–Parker theory. Full-wave AORSA simulations show that RF power losses in the scrape-off layer (SOL) increase significantly for both NSTX and NSTX-U when the launched waves propagate in the SOL. Toroidal Alfven eigenmode avalanches and higher frequency Alfven eigenmodes can affect NB-driven current through energy loss and redistribution of fast ions. The inclusion of rotation and kinetic resonances, which depend on collisionality, is necessary for predicting experimental stability thresholds of fast growing ideal wall and resistive wall modes. Neutral beams and neoclassical toroidal viscosity generated from applied 3D fields can be used as actuators to produce rotation profiles optimized for global stability. DEGAS-2 has been used to study the dependence of gas penetration on SOL temperatures and densities for the MGI system being implemented on the Upgrade for disruption mitigation. PMI studies have focused on the effect of ELMs and 3D fields on plasma detachment and heat flux handling. Simulations indicate that snowflake and impurity seeded radiative divertors are candidates for heat flux mitigation in NSTX-U. Studies of lithium evaporation on graphite surfaces indicate that lithium increases oxygen surface concentrations on graphite, and deuterium–oxygen affinity, which increases deuterium pumping and reduces recycling. In situ and test-stand experiments of lithiated graphite and molybdenum indicate temperature-enhanced sputtering, although that test-stand studies also show the potential for heat flux reduction through lithium vapour shielding. Non-linear gyro kinetic simulations have indicated that ion transport can be enhanced by a shear-flow instability, and that non-local effects are necessary to explain the observed rapid changes in plasma turbulence. Predictive simulations have shown agreement between a microtearing-based reduced transport model and the measured electron temperatures in a microtearing unstable regime. Two Alfven eigenmode-driven fast ion transport models have been developed and successfully benchmarked against NSTX data. Upgrade construction is moving on schedule with initial physics research operation of NSTX-U planned for mid-2015.