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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.

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.

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.

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.

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.

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 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.

Author(s): Menard, JE; Allain, JP; Battaglia, DJ; Bedoya, F; Bell, RE; Belova, E; Berkery, JW; Boyer, MD; Crocker, N; Diallo, A; Ebrahimi, F; Ferraro, N; Fredrickson, E; Frerichs, H; Gerhardt, S; Gorelenkov, N; Guttenfelder, W; Heidbrink, W; Kaita, R; Kaye, SM; Kriete, DM; Kubota, S; Leblanc, BP; Liu, D; Lunsford, R; Mueller, D; Myers, CE; Ono, M; Park, JK; Podesta, M; Raman, R; Reinke, M; Ren, Y; Sabbagh, SA; Schmitz, O; Scotti, F; Sechrest, Y; Skinner, CH; Smith, DR; Soukhanovskii, V; Stoltzfus-Dueck, T; Yuh, H; Wang, Z; Waters, I; Ahn, JW; Andre, R; Barchfeld, R; Beiersdorfer, P; Bertelli, N; Bhattacharjee, A; Brennan, D; Buttery, R; Capece, A; Canal, G; Canik, J; Chang, CS; Darrow, D; Delgado-Aparicio, L; Domier, C; Ethier, S; Evans, T; Ferron, J; Finkenthal, M; Fonck, R; Gan, K; Gates, D; Goumiri, I; Gray, T; Hosea, J; Humphreys, D; Jarboe, T; Jardin, S; Jaworski, MA; Koel, B; Kolemen, E; Ku, S; La Haye, RJ; Levinton, F; Luhmann, N; Maingi, R; Maqueda, R; McKee, G; Meier, E; Myra, J; Perkins, R | Abstract: 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.

Author(s): Collins, CS; Heidbrink, WW; Podesta, M; White, RB; Kramer, GJ; Pace, DC; Petty, CC; Stagner, L; Van Zeeland, MA; Zhu, YB | Abstract: Experiments in the DIII-D tokamak show that many overlapping small-amplitude Alfven eigenmodes (AEs) cause fast-ion transport to sharply increase above a critical threshold in beam power, leading to fast-ion density profile resilience and reduced fusion performance. The threshold is above the AE linear stability limit and varies between diagnostics that are sensitive to different parts of fast-ion phase-space. Comparison with theoretical analysis using the nova and orbit codes shows that, for the neutral particle diagnostic, the threshold corresponds to the onset of stochastic particle orbits due to wave-particle resonances with AEs in the measured region of phase space. The bulk fast-ion distribution and instability behavior was manipulated through variations in beam deposition geometry, and no significant differences in the onset threshold outside of measurement uncertainties were found, in agreement with the theoretical stochastic threshold analysis. Simulations using the 'kick model' produce beam ion density gradients consistent with the empirically measured radial critical gradient and highlight the importance of including the energy and pitch dependence of the fast-ion distribution function in critical gradient models. The addition of electron cyclotron heating changes the types of AEs present in the experiment, comparatively increasing the measured fast-ion density and radial gradient. These studies provide the basis for understanding how to avoid AE transport that can undesirably redistribute current and cause fast-ion losses, and the measurements are being used to validate AE-induced transport models that use the critical gradient paradigm, giving greater confidence when applied to ITER.

At the power levels required for significant heating and current drive in magnetically-confined toroidal plasma, modification of the particle distribution function from a Maxwellian shape is likely (Stix 1975 Nucl. Fusion 15 737), with consequent changes in wave propagation and in the location and amount of absorption. In order to study these effects computationally, both the finite-Larmor-radius and the high-harmonic fast wave (HHFW), versions of the full-wave, hot-plasma toroidal simulation code TORIC (Brambilla 1999 Plasma Phys. Control. Fusion 41 1 and Brambilla 2002 Plasma Phys. Control. Fusion 44 2423), have been extended to allow the prescription of arbitrary velocity distributions of the form . For hydrogen (H) minority heating of a deuterium (D) plasma with anisotropic Maxwellian H distributions, the fractional H absorption varies significantly with changes in parallel temperature but is essentially independent of perpendicular temperature. On the other hand, for HHFW regime with anisotropic Maxwellian fast ion distribution, the fractional beam ion absorption varies mainly with changes in the perpendicular temperature. The evaluation of the wave-field and power absorption, through the full wave solver, with the ion distribution function provided by either a Monte-Carlo particle and Fokker–Planck codes is also examined for Alcator C-Mod and NSTX plasmas. Non-Maxwellian effects generally tend to increase the absorption with respect to the equivalent Maxwellian distribution.

Progress in characterizing the edge stability and properties of the microinstabilities responsible for enhanced transport in the pedestal region is reported. The stability of the pedestal is characterized in high performance discharges on National Spherical Torus Experiment. These high performance plasmas are found to be ideal kink-peeling and ideal infinite-n ballooning unstable prior to the onset of edge-localized modes (ELM). The spatial structure of turbulence present during an ELM cycle in the pedestal region indicates poloidal spatial scales propagating in the ion diamagnetic drift direction at the pedestal top, and radial spatial scales . These propagating spatial scales are found to be poloidally elongated and consistent with ion-scale microturbulence. Both global and local gyrokinetic simulations have been performed to identify the microturbulence structure. The local gyrokinetic analysis indicates the presence of a linearly unstable hybrid kinetic ballooning mode and trapped electron mode with spatial scale and propagation direction consistent with experimental observations. In the global gyrokinetic analysis, the nonlinearly saturated potential fluctuations show radial and poloidal correlation lengths in agreement with experimental density fluctuation correlation length measurements.

Remarkable progress has been made in diagnosing energetic particle instabilities on present-day machines and in establishing a theoretical framework for describing them. This overview describes the much improved diagnostics of Alfven instabilities and modelling tools developed world-wide, and discusses progress in interpreting the observed phenomena. A multi-machine comparison is presented giving information on the performance of both diagnostics and modelling tools for different plasma conditions outlining expectations for ITER based on our present knowledge., 37 pages, 20 figures

Tokamak plasmas can feature a large population of energetic particles (EP) from neutral beam injection or fusion reactions. In turn, energetic particles can drive instabilities, which affect the driving EP population leading to a distortion of the original EP distribution function and of quantities that depend on it. The latter include, for example, neutral beam (NB) current drive and plasma heating through EP thermalization. Those effects must be taken into account to enable reliable and quantitative simulations of discharges for present devices as well as predictions for future burning plasmas. Reduced models for EP transport are emerging as an effective tool for long time-scale integrated simulations of tokamak plasmas, possibly including the effects of instabilities on EP dynamics. Available models differ in how EP distribution properties are modified by instabilities, e.g. in terms of gradients in real or phase space. It is therefore crucial to assess to what extent different assumptions in the transport models affect predicted quantities such as EP profile, energy distribution, NB driven current and energy/momentum transfer to the thermal populations. A newly developed kick model, which includes modifications of the EP distribution by instabilities in both real and velocity space, is used in this work to investigate these issues. Coupled to TRANSP simulations, the kick model is used to analyze NB-heated NSTX and DIII-D discharges featuring unstable Alfvén eigenmodes (AEs). Results show that instabilities can strongly affect the EP distribution function, and modifications propagate to macroscopic quantities such as NB-driven current profile and NB power transferred to the thermal plasma species. Those important aspects are only qualitatively captured by simpler fast ion transport models that are based on radial diffusion of energetic ions only.

The redistribution and potential loss of energetic particles due to MHD modes can limit the performance of fusion plasmas by reducing the plasma heating rate. In this work, we present validation studies of the 1.5D critical gradient model (CGM) for Alfven eigenmode (AE) induced EP transport in NSTX and DIII-D neutral beam heated plasmas. In previous comparisons with a single DIII-D L-mode case, the CGM model was found to be responsible for 75% of measured AE induced neutron deficit [1]. A fully kinetic HINST is used to compute mode stability for the non-perturbative version of CGM (or nCGM). We have found that AEs show strong local instability drive up to violating assumptions of perturbative approaches used in NOVA-K code. We demonstrate that both models agree with each other and both underestimate the neutron deficit measured in DIII-D shot by approximately a factor of 2. On the other hand in NSTX the application of CGM shows good agreement for the measured flux deficit predictions. We attempt to understand these results with the help of the so-called kick model which is based on the guiding center code ORBIT. The kick model comparison gives important insight into the underlying velocity space dependence of the AE induced EP transport as well as it allows the estimate of the neutron deficit in the presence of the low frequency Alfvenic modes. Within the limitations of used models we infer that there are missing modes in the analysis which could improve the agreement with the experiments.

Measured fast-ion D α (FIDA) data from an extensive NSTX database are compared to ‘classical’ predictions that neglect transport by instabilities. Even in the absence of appreciable MHD, in many cases, the profile peaks at smaller major radius and the profile is broader than the predictions. Abrupt large-amplitude MHD events flatten the FIDA profile, as do most toroidal Alfvén eigenmode (TAE) avalanche events. Generally, the onset of a long-lived mode also flattens the FIDA profile.

Neutral beam injection (NBI) is one of the primary tools foreseen for heating, current drive (CD) and q-profile control in future fusion reactors such as ITER and a Fusion Nuclear Science Facility. However, fast ions from NBI may also provide the drive for energetic particle-driven instabilities (e.g. Alfvenic modes (AEs)), which in turn redistribute fast ions in both space and energy, thus hampering the control capabilities and overall efficiency of NB-driven current. Based on experiments on the NSTX tokamak (M. Ono et al 2000 Nucl. Fusion 40 557), the effects of AEs and other low-frequency magneto-hydrodynamic instabilities on NB-CD efficiency are investigated. A new fast ion transport model, which accounts for particle transport in phase space as required for resonant AE perturbations, is utilized to obtain consistent simulations of NB-CD through the tokamak transport code TRANSP. It is found that instabilities do indeed reduce the NB-driven current density over most of the plasma radius by up to ~50%. Moreover, the details of the current profile evolution are sensitive to the specific model used to mimic the interaction between NB ions and instabilities. Implications for fast ion transport modeling in integrated tokamak simulations are briefly discussed.

Author(s): Chen, X; Kramer, GJ; Heidbrink, WW; Fisher, RK; Pace, DC; Petty, CC; Podesta, M; Van Zeeland, MA | Abstract: A new non-linear feature has been observed in fast-ion loss from tokamak plasmas in the form of oscillations at the sum, difference and second harmonic frequencies of two independent Alfven eigenmodes (AEs). Full orbit calculations and analytic theory indicate this non-linearity is due to coupling of fast-ion orbital response as it passes through each AE - a change in wave-particle phase k•r by one mode alters the force exerted by the next. The loss measurement is of barely confined, non-resonant particles, while similar non-linear interactions can occur between well-confined particles and multiple AEs leading to enhanced fast-ion transport. © 2014 IAEA, Vienna.

Developing a reactor-compatible divertor has been identified as a particularly challenging technology problem for magnetic confinement fusion. Application of lithium (Li) in NSTX resulted in improved H-mode confinement, H-mode power threshold reduction, and other plasma performance benefits. During the 2010 NSTX campaign, application of a relatively modest amount of Li (300 mg prior to the discharge) resulted in a ∼50% reduction in heat load on the liquid lithium divertor (LLD) attributable to enhanced divertor bolometric radiation. These promising Li results in NSTX and related modelling calculations motivated the radiative LLD concept proposed here. Li is evaporated from the liquid lithium (LL) coated divertor strike-point surface due to the intense heat flux. The evaporated Li is readily ionized by the plasma due to its low ionization energy, and the poor Li particle confinement near the divertor plate enables ionized Li ions to radiate strongly, resulting in a significant reduction in the divertor heat flux. This radiative process has the desired effect of spreading the localized divertor heat load to the rest of the divertor chamber wall surfaces, facilitating the divertor heat removal. The LL coating of divertor surfaces can also provide a ‘sacrificial’ protective layer to protect the substrate solid material from transient high heat flux such as the ones caused by the edge localized modes. By operating at lower temperature than the first wall, the LL covered large divertor chamber wall surfaces can serve as an effective particle pump for the entire reactor chamber, as impurities generally migrate towards lower temperature LL divertor surfaces. To maintain the LL purity, a closed LL loop system with a modest circulating capacity (e.g., ∼1 l s−1 for ∼1% level ‘impurities’) is envisioned for a steady-state 1 GW-electric class fusion power plant.

Previous pedestal turbulence measurements in the National Spherical Torus Experiment assessed the spatial and temporal properties of turbulence in the steep gradient region of H-mode pedestals during edge localized mode (ELM)-free, MHD-quiescent periods. Here, we extend the analysis to fluctuation amplitudes and compare observations to pedestal turbulence simulations. Measurements indicate normalized fluctuation amplitudes are about 1–5% in the steep gradient region. Regression analysis indicates fluctuation amplitudes scale positively with electron density gradient, collisionality, and poloidal beta, and scale negatively with magnetic shear, electron density, ion temperature gradient (ITG), toroidal flow and radial electric field. The scalings are most consistent with trapped electron mode, kinetic ballooning mode, or microtearing instabilities, but, notably, least consistent with ITG turbulence. Gyrokinetic simulations of pedestal turbulence with realistic pedestal profiles show collisional instabilities with growth rates that increase at higher density gradient and decrease at higher ITG, in qualitative agreement with observed scalings. Finally, Braginskii fluid simulations of pedestal turbulence do not reproduce scalings from measurements and gyrokinetic simulations, and suggest electron dynamics can be a critical factor for accurate pedestal turbulence simulations.

The edge electron (Te) and ion temperature (Ti) at the time of the L?H transition increase when the X-point radius (RX) is reduced to a high-triangularity shape while maintaining constant edge density. Consequently the L?H power threshold (PLH) is larger for the high-triangularity shape. This supports the prediction that a single-particle loss hole, whose properties are strongly linked to RX and Ti, influences the edge radial electric field (Er) and Er???B flow-shearing rate available for turbulence suppression. Simulations using XGC0, a full-f drift-kinetic neoclassical code, indicate that maintaining a constant Er???B flow-shearing rate does require a larger heat flux and edge Ti as RX decreases. NSTX also observes a decrease in PLH when the divertor recycling is decreased using lithium coatings. However, the edge Te and Ti at the L?H transition appear independent of the divertor recycling for a constant shape. XGC0 calculations demonstrate that more heat flux is needed to maintain the edge Ti and the Er???B flow-shearing rate as the contribution of divertor recycling to the overall neutral fuelling rate increases.

Liquid metal plasma-facing components (PFCs) have been proposed as a means of solving several problems facing the creation of economically viable fusion power reactors. To date, few demonstrations exist of this approach in a diverted tokamak and we here provide an overview of such work on the National Spherical Torus Experiment (NSTX). The Liquid Lithium Divertor (LLD) was installed and operated for the 2010 run campaign using evaporated coatings as the filling method. The LLD consisted of a copper-backed structure with a porous molybdenum front face. Nominal Li filling levels by the end of the run campaign exceeded the porosity void fraction by 150%. Despite a nominal liquid level exceeding the capillary structure and peak current densities into the PFCs exceeding 100 kA m−2, no macroscopic ejection events were observed. In addition, no substrate line emission was observed after achieving lithium-melt temperatures indicating the lithium wicks and provides a protective coating on the molybdenum porous layer. Impurity emission from the divertor suggests that the plasma is interacting with oxygen-contaminated lithium whether diverted on the LLD or not. A database of LLD discharges is analysed to consider whether there is a net effect on the discharges over the range of total deposited lithium in the machine. Examination of H-97L indicates that performance was constant throughout the run, consistent with the hypothesis that it is the quality of the surface layers of the lithium that impact performance. The accumulation of impurities suggests a fully flowing liquid lithium system to obtain a steady-state PFC on timescales relevant to NSTX.

Fast-wave heating and current drive efficiencies can be reduced by a number of processes in the vicinity of the antenna and in the scrape off layer (SOL). On NSTX from around 25% to more than 60% of the high-harmonic fast-wave power can be lost to the SOL regions, and a large part of this lost power flows along SOL magnetic field lines and is deposited in bright spirals on the divertor floor and ceiling. We show that field-line mapping matches the location of heat deposition on the lower divertor, albeit with a portion of the heat outside of the predictions. The field-line mapping can then be used to partially reconstruct the profile of lost fast-wave power at the midplane in front of the antenna, and the losses peak close to the last closed flux surface (LCFS) as well as the antenna. This profile suggests a radial standing-wave pattern formed by fast-wave propagation in the SOL, and this hypothesis will be tested on NSTX-U. Advanced RF codes must reproduce these results so that such codes can be used to understand this edge loss and to minimize RF heat deposition and erosion in the divertor region on ITER.

Microturbulence is considered to be a major candidate in driving anomalous transport in fusion plasmas, and the equilibrium E × B shear generated by externally driven flow can be a powerful tool to control microturbulence in future fusion devices such as FNSF and ITER. Here we present the first observation of the change in electron-scale turbulence wavenumber spectrum (measured by a high-k scattering system) and thermal transport responding to continuous E × B shear ramp-up in an NSTX centre-stack limited and neutral beam injection-heated L-mode plasma. It is found that while linear stability analysis shows that the maximum electron temperature gradient mode linear growth rate far exceeds the observed E × B shearing rate in the measurement region of the high-k scattering system, the unstable ion temperature gradient (ITG) modes are susceptible to E × B shear stabilization. We observed that as the E × B shearing rate is continuously ramped up in the high-k measurement region, the ratio between the E × B shearing rate and maximum ITG mode growth rate continuously increases (from about 0.2 to 0.7) and the maximum power of the measured electron-scale turbulence wavenumber spectra decreases. Meanwhile, electron and ion thermal transport is also reduced in the outer half of the plasmas as long as magnetohydrodynamic activities are not important and the L-mode plasmas eventually reach H-mode-like confinement. Linear and nonlinear gyrokinetic simulations are presented to address the experimental observations.

Core transport of intrinsic carbon and lithium impurities is analysed in H-mode discharges in NSTX. The application of lithium coatings on graphite plasma-facing components led to high-performance H-mode discharges with edge localized mode (ELM) suppression and resulted in core carbon accumulation. Lithium ions did not accumulate and had densities less than 1% of carbon densities. Core transport codes NCLASS, NEO and MIST are used to assess the impact of lithium evaporative coatings on impurity transport. The disappearance of ELMs, due to changes in the electron pressure profiles, together with modifications in neoclassical transport, due to changes in main ion temperature and density profiles, explains the core carbon accumulation in discharges with lithium coatings. Residual anomalous transport in the pedestal region is needed to explain the experimental carbon density profile shape and evolution. The enhancement in neoclassical lithium particle diffusivities due to the high carbon concentration is partially responsible for the low lithium core concentration.

Fast-ions (e.g. fusion alphas and neutral beam ions) will excite a wide range of instabilities in ITER and a Fusion Nuclear Science Facility device. Among the possible instabilities are high frequency Alfv?n eigenmodes (AEs) excited through Doppler-shifted cyclotron resonance with beam ions. High frequency AEs cause fast-ion transport, correlate with enhanced electron thermal transport and are postulated to contribute to ion heating. These high frequency modes have historically been identified as a mixture of compressional (CAE) and global (GAE) Alfv?n eigenmodes, but distinguishing between the CAEs and GAEs has sometimes proven difficult. Identification is essential for understanding the extent of their effect, since the two types of modes have very different effects on resonant particle orbits. The effect on plasma performance of high frequency AEs is investigated in NSTX, facilitated by a recently upgraded array of 16 fixed-frequency quadrature reflectometers. Detailed measurements of high frequency AE amplitude and eigenmode structure were obtained in a high power (6?MW), beam-heated H-mode plasma that is very similar to those in which high frequency AE activity is shown to correlate with enhanced electron thermal transport. These measurements, which extend from the plasma edge to deep in the core, can be used in modelling the effects of the modes on electron thermal transport. The observed modes are identified by comparison of their frequency and measured toroidal mode numbers with local Alfv?n dispersion relations. The modes identified as CAEs have higher frequencies (predominantly f>??600?kHz) and smaller toroidal mode numbers (|n|???5) than the GAEs (predominantly f??600?kHz, n?=??6 to ?8). Also, they are strongly core localized, in contrast with the GAEs, which also peak towards the plasma centre but have much broader radial extent.

Short toroidal Alfven eigenmode (TAE) avalanche bursts in the National Spherical Torus Experiment (NSTX) cause a drop in the neutron rate and sometimes a loss of neutral beam ions at or near the full injection energy over an extended range of pitch angles. The simultaneous loss of wide ranges of pitch angle suggests stochastic transport of the beam ions occurs. When beam ion orbits are followed with a guiding centre code that incorporates the plasma's magnetic equilibrium plus the measured modes, the predicted ranges of lost pitch angle are similar to those seen in the experiment, with distinct populations of trapped and passing orbits lost. These correspond to domains where the stochasticity extends in the orbit phase space from the region of beam ion deposition to the loss boundary and the trajectories along which modes may transport particles extend from the deposition volume to the loss boundary.

Strong toroidal Alfvén eigenmode (TAE) avalanches on NSTX, the National Spherical Torus Experiment (Ono et al 2000 Nucl. Fusion 40 557) are typically correlated with drops in the neutron rate in the range 5–15%. In previous studies of avalanches in L-mode plasmas, these neutron drops were found to be consistent with modelled losses of fast ions. Here we expand the study to TAE avalanches in NSTX H-mode plasmas with improved analysis techniques. At the measured TAE mode amplitudes, simulations with the ORBIT code predict that fast ion losses are negligible. However, the simulations predict that the TAE scatter the fast ions in energy, resulting in a small (≈5–6%) drop in fast ion β. The net decrease in energy of the fast ions is sufficient to account for about 50% of the drop in neutron rate, redistribution for ≈40%, and fast ion losses account for only ≈10%. This loss of energy from the fast ion population is comparable to the estimated energy lost by damping from the Alfvén wave during the burst. The previously studied TAE avalanches in L-mode are re-evaluated using an improved calculation of the potential fluctuations in the ORBIT code near the separatrix.