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Experiments in the DIII-D tokamak show that many overlapping small-amplitude Alfvén 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.

Electron cyclotron emission (ECE) imaging is a passive radiometric technique that measures electron temperature fluctuations; and microwave imaging reflectometry (MIR) is an active radar imaging technique that measures electron density fluctuations. Microwave imaging diagnostic instruments employing these techniques have made important contributions to fusion science and have been adopted at major fusion facilities worldwide including DIII-D, EAST, ASDEX Upgrade, HL-2A, KSTAR, LHD, and J-TEXT. In this paper, we describe the development status of three major technological advancements: custom mm-wave integrated circuits (ICs), digital beamforming (DBF), and synthetic diagnostic modeling (SDM). These have the potential to greatly advance microwave fusion plasma imaging, enabling compact and low-noise transceiver systems with real-time, fast tracking ability to address critical fusion physics issues, including ELM suppression and disruptions in the ITER baseline scenario, naturally ELM-free states such as QH-mode, and energetic particle confinement (i.e. Alfvén eigenmode stability) in highperformance regimes that include steady-state and advanced tokamak scenarios. Furthermore, these systems are fully compatible with today's most challenging non-inductive heating and current drive systems and capable of operating in harsh environments, making them the ideal approach for diagnosing long-pulse and steady-state tokamaks.

Experiments on the DIII-D tokamak have identified how multiple simultaneous Alfvén eigenmodes (AEs) lead to overlapping wave-particle resonances and stochastic fast-ion transport in fusion grade plasmas [C. S. Collins et al., Phys. Rev. Lett. 116, 095001 (2016)]. The behavior results in a sudden increase in fast-ion transport at a threshold that is well above the linear stability threshold for Alfvén instability. A novel beam modulation technique [W. W. Heidbrink et al., Nucl. Fusion 56, 112011 (2016)], in conjunction with an array of fast-ion diagnostics, probes the transport by measuring the fast-ion flux in different phase-space volumes. Well above the threshold, simulations that utilize the measured mode amplitudes and structures predict a hollow fast-ion profile that resembles the profile measured by fast-ion Dα spectroscopy; the modelling also successfully reproduces the temporal response of neutral-particle signals to beam modulation. The use of different modulated sources probes the details of phase-space transport by populating different regions in phase space and by altering the amplitude of the AEs. Both effects modulate the phase-space flows.

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 Alfvén 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.

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfvénic 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 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 Alfvén 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 Alfvénic 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.

A recent DIII-D experiment investigating the impact of electron cyclotron heating (ECH) on neutral beam driven reversed shear Alfvén eigenmode (RSAE) activity is presented. The experiment includes variations of ECH injection location and timing, current ramp rate, beam injection geometry (on/off-axis), and neutral beam power. Essentially all variations carried out in this experiment were observed to change the impact of ECH on AE activity significantly. In some cases, RSAEs were observed to be enhanced with ECH near the off-axis minimum in magnetic safety factor (), in contrast to the original DIII-D experiments where the modes were absent when ECH was deposited near . It is found that during intervals when the geodesic acoustic mode (GAM) frequency at is elevated and the calculated RSAE minimum frequency, including contributions from thermal plasma gradients, is very near or above the nominal TAE frequency (f TAE), RSAE activity is not observed or RSAEs with a much reduced frequency sweep range are found. This condition is primarily brought about by ECH modification of the local electron temperature (T e) which can raise both the local T e at as well as its gradient. A q-evolution model that incorporates this reduction in RSAE frequency sweep range is in agreement with the observed spectra and appears to capture the relative balance of TAE or RSAE-like modes throughout the current ramp phase of over 38 DIII-D discharges. Detailed ideal MHD calculations using the NOVA code show both modification of plasma pressure and pressure gradient at play an important role in modifying the RSAE activity. Analysis of the ECH injection near the case where no frequency sweeping RSAEs are observed shows the typical RSAE is no longer an eigenmode of the system. What remains is an eigenmode with poloidal harmonic content reminiscent of the standard RSAE, but absent of the typical frequency sweeping behavior. The remaining eigenmode is also often strongly coupled to gap TAEs. Analysis with the non-perturbative gyro fluid code TAEFL confirms this change in RSAE activity and also shows a large drop in the resultant mode growth rates.

Observations on the National Spherical Torus Experiment (NSTX) indicate that externally applied non-axisymmetric magnetic perturbations (MP) can reduce the amplitude of toroidal Alfvén eigenmodes (TAE) and global Alfvén eigenmodes (GAE) in response to pulsed n = 3 non-resonant fields. From full-orbit following Monte Carlo simulations with the one- and two-fluid resistive MHD plasma response to the magnetic perturbation included, it was found that in response to MP pulses the fast-ion losses increased and the fast-ion drive for the GAEs was reduced. The MP did not affect the fast-ion drive for the TAEs significantly but the Alfvén continuum at the plasma edge was found to be altered due to the toroidal symmetry breaking which leads to coupling of different toroidal harmonics. The TAE gap was reduced at the edge creating enhanced continuum damping of the global TAEs, which is consistent with the observations. The results suggest that optimized non-axisymmetric MP might be exploited to control and mitigate Alfvén instabilities by tailoring the fast-ion distribution function and/or continuum structure.

Experiments in the DIII-D tokamak show that fast-ion transport suddenly becomes stiff above a critical threshold in the presence of many overlapping small-amplitude Alfvén eigenmodes (AEs). The threshold is phase-space dependent and occurs when particle orbits become stochastic due to resonances with AEs. Above threshold, equilibrium fast-ion density profiles are unchanged despite increased drive, and intermittent fast-ion losses are observed. Fast-ion Dα spectroscopy indicates radially localized transport of the copassing population at radii that correspond to the location of midcore AEs. The observation of stiff fast-ion transport suggests that reduced models can be used to effectively predict alpha profiles, beam ion profiles, and losses to aid in the design of optimized scenarios for future burning plasma devices.

Fast-ion transport caused by the combination of MHD and a mock-up test-blanket module (TBM) coil is measured in the DIII-D tokamak. The primary diagnostic is an infrared camera that measures the heat flux on the tiles surrounding the coil. The combined effects of the TBM and four other potential sources of transport are studied: neoclassical tearing modes, Alfn eigenmodes, sawteeth, and applied resonant magnetic perturbation fields for the control of edge localized modes. A definitive synergistic effect is observed at sawtooth crashes where, in the presence of the TBM, the localized heat flux at a burst increases from 0.36 ± 0.27 to 2.6 ±0.5 MW m-2.

Measurements show fast ion losses correlated with applied three-dimensional (3D) fields in a variety of plasmas ranging from L-mode to resonant magnetic perturbation (RMP) edge localized mode (ELM) suppressed H-mode discharges. In DIII-D L-mode discharges with a slowly rotating n = 2 magnetic perturbation, scintillator detector loss signals synchronized with the applied fields are observed to decay within one poloidal transit time after beam turnoff indicating they arise predominantly from prompt loss orbits. Full orbit following using M3D-C1 calculations of the perturbed fields and kinetic profiles reproduce many features of the measured losses and points to the importance of the applied 3D field phase with respect to the beam injection location in determining the overall impact on prompt beam ion loss. Modeling of these results includes a self-consistent calculation of the 3D perturbed beam ion birth profiles and scrape-off-layer ionization, a factor found to be essential to reproducing the experimental measurements. Extension of the simulations to full slowing down timescales, including fueling and the effects of drag and pitch angle scattering, show the applied n = 3 RMPs in ELM suppressed H-mode plasmas can induce a significant loss of energetic particles from the core. With the applied n = 3 fields, up to 8.4% of the injected beam power is predicted to be lost, compared to 2.7% with axisymmetric fields only. These fast ions, originating from minor radii ρ > 0.7, are predicted to be primarily passing particles lost to the divertor region, consistent with wide field-of-view infrared periscope measurements of wall heating in n = 3 RMP ELM suppressed plasmas. Edge fast ion Dα (FIDA) measurements also confirm a large change in edge fast ion profile due to the n = 3 fields, where the effect was isolated by using short 50 ms RMP-off periods during which ELM suppression was maintained yet the fast ion profile was allowed to recover. The role of resonances between fast ion drift motion and the applied 3D fields in the context of selectively targeting regions of fast ion phase space is also discussed.

By arranging the particle first banana orbits to pass near a distant detector, the light ion beam probe (LIBP) utilizes orbital deflection to probe internal fields and field fluctuations. The LIBP technique takes advantage of (1) the in situ, known source of fast ions created by beam-injected neutral particles that naturally ionize near the plasma edge and (2) various commonly available diagnostics as its detector. These born trapped particles can traverse the plasma core on their inner banana leg before returning to the plasma edge. Orbital displacements (the forces on fast ions) caused by internal instabilities or edge perturbing fields appear as modulated signal at an edge detector. Adjustments in the q-profile and plasma shape that determine the first orbit, as well as the relative position of the source and detector, enable studies under a wide variety of plasma conditions. This diagnostic technique can be used to probe the impact on fast ions of various instabilities, e.g., Alfvén eigenmodes (AEs) and neoclassical tearing modes, and of externally imposed 3D fields, e.g., magnetic perturbations. To date, displacements by AEs and by externally applied resonant magnetic perturbation fields have been measured using a fast ion loss detector. Comparisons with simulations are shown. In addition, nonlinear interactions between fast ions and independent AE waves are revealed by this technique.

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 Alfvén 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.

Two key insights into interactions between Alfvén eigenmodes (AEs) and energetic particles in the plasma core are gained from measurements and modeling of first-orbit beam-ion loss in DIII-D. First, the neutral beam-ion first-orbit losses are enhanced by AEs and a single AE can cause large fast-ion displacement. The coherent losses are from born trapped full energy beam-ions being non-resonantly scattered by AEs onto loss orbits within their first poloidal transit. The loss amplitudes scale linearly with the mode amplitude but the slope is different for different modes. The radial displacement of fast-ions by individual AEs can be directly inferred from the measurements. Second, oscillations in the beam-ion first-orbit losses are observed at the sum, difference, and harmonic frequencies of two independent AEs. These oscillations are not plasma modes and are absent in magnetic, density, and temperature fluctuations. The origin of the non-linearity as a wave-particle coupling is confirmed through bi-coherence analysis, which is clearly observed because the coherences are preserved by the first-orbit loss mechanism. An analytic model and full orbit simulations show that the non-linear features seen in the loss signal can be explained by a non-linear interaction between the fast ions and the two independent AEs. © 2014 AIP Publishing LLC.

Energy and pitch angle resolved measurements of escaping neutral beam ions (E ≈ 80 keV) have been made during DIII-D L-mode discharges with applied, slowly rotating, n = 2 magnetic perturbations. Data from separate scintillator detectors (FILDs) near and well below the plasma midplane show fast-ion losses correlated with the internal coil (I-coil) fields. The dominant fast-ion loss signals are observed to decay within one poloidal transit time after beam turn-off indicating they are primarily prompt loss orbits. Also, during application of the rotating I-coil fields, outboard midplane edge density and bremsstrahlung emission profiles exhibit a radial displacement of up to δR ≈ 1 cm. Beam deposition and full orbit modeling of these losses using M3D-C1 calculations of the perturbed kinetic profiles and fields reproduce many features of the measured losses. In particular, the predicted phase of the modulated loss signal with respect to the I-coil currents is in close agreement with FILD measurements as is the relative amplitudes of the modulated losses for the co and counter-current beam used in the experiment. These simulations show modifications to the beam ion birth profile and subsequent prompt loss due to changes in the edge density; however, the dominant factor causing modulation of the losses to the fast-ion loss detectors is the perturbed magnetic field (δB/B ≈ 10-3 in the plasma). Calculations indicate total prompt loss to the DIII-D wall can increase with application of the n = 2 perturbation by up to 7% for co-current injected beams and 3% for counter-current injected beams depending on phase of the perturbation relative to the injected beam. © 2014 IOP Publishing Ltd.

Energy and pitch angle resolved measurements of escaping neutral beam ions (E ≈ 80 keV) have been made during DIII-D L-mode discharges with applied, slowly rotating, n = 2 magnetic perturbations. Data from separate scintillator detectors (FILDs) near and well below the plasma midplane show fast-ion losses correlated with the internal coil (I-coil) fields. The dominant fast-ion loss signals are observed to decay within one poloidal transit time after beam turn-off indicating they are primarily prompt loss orbits. Also, during application of the rotating I-coil fields, outboard midplane edge density and bremsstrahlung emission profiles exhibit a radial displacement of up to δR ≈ 1 cm. Beam deposition and full orbit modeling of these losses using M3D-C1 calculations of the perturbed kinetic profiles and fields reproduce many features of the measured losses. In particular, the predicted phase of the modulated loss signal with respect to the I-coil currents is in close agreement with FILD measurements as is the relative amplitudes of the modulated losses for the co and counter-current beam used in the experiment. These simulations show modifications to the beam ion birth profile and subsequent prompt loss due to changes in the edge density; however, the dominant factor causing modulation of the losses to the fast-ion loss detectors is the perturbed magnetic field (δB/B ≈ 10-3 in the plasma). Calculations indicate total prompt loss to the DIII-D wall can increase with application of the n = 2 perturbation by up to 7% for co-current injected beams and 3% for counter-current injected beams depending on phase of the perturbation relative to the injected beam. © 2014 IOP Publishing Ltd.

Infrared imaging of hot spots induced by localized magnetic perturbations using the test blanket module (TBM) mock-up on DIII-D is in good agreement with beam-ion loss simulations. The hot spots were seen on the carbon protective tiles surrounding the TBM as they reached temperatures over 1000 °C. The localization of the hot spots on the protective tiles is in fair agreement with fast-ion loss simulations using a range of codes: ASCOT, SPIRAL and OFMCs while the codes predicted peak heat loads that are within 30% of the measured ones. The orbit calculations take into account the birth profile of the beam ions as well as the scattering and slowing down of the ions as they interact with the localized TBM field. The close agreement between orbit calculations and measurements validate the analysis of beam-ion loss calculations for ITER where ferritic material inside the tritium breeding TBMs is expected to produce localized hot spots on the first wall. © 2013 IAEA, Vienna.

Prompt neutral beam-ion loss due to non-resonant scattering caused by toroidicity-induced and reversed shear Alfvén eigenmodes (TAE/RSAEs) have been observed in DIII-D. The coherent losses are of full-energy beam ions born on unperturbed trapped orbits that would carry them close to a fast-ion loss detector (FILD) within one poloidal transit. However, in the presence of AEs, the particles are expelled from the plasma before completing their first poloidal orbits. The loss signals on FILD emerge within 100 μs after the beam switch-on (which is the time scale of a single poloidal transit) and oscillate at mode frequencies. Time-resolved loss measurements show a linear dependence on the AE fluctuation amplitude and a radial 'kick' of ∼10 cm by an n = 2 RSAE at δB/B 1 × 10-3 can be directly inferred from the measurements. Full-orbit modelling of the fast-ion displacement caused by the AEs is in good quantitative agreement with the measurements. Direct interactions of the mode and the beam-ion orbit can account for a large fraction of fast-ion losses observed in such DIII-D discharges. The first orbit non-resonant loss mechanism may also contribute to enhanced localized losses in ITER and future reactors. A new diagnostic method of the radial displacement is inspired by these findings and can be used to study the interaction between fast ions and various MHD modes as well as three-dimensional fields. © 2013 IAEA, Vienna.

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 Alfvén 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. © 2013 IAEA, Vienna.

The application of static magnetic field perturbations to a tokamak plasma is observed to alter the dynamics of high-frequency bursting Alfvén modes that are driven unstable by energetic ions. In response to perturbations with an amplitude of δB/B∼0.01 at the plasma boundary, the mode amplitude is reduced, the bursting frequency is increased, and the frequency chirp is smaller. For modes of weaker bursting character, the magnetic perturbation induces a temporary transition to a saturated continuous mode. Calculations of the perturbed distribution function indicate that the 3D perturbation affects the orbits of fast ions that resonate with the bursting modes. The experimental evidence represents an important demonstration of the possibility of controlling fast-ion instabilities through "phase-space engineering" of the fast-ion distribution function, by means of externally applied perturbation fields.

We report the first observation of prompt neutral beam-ion losses due to nonresonant scattering induced by toroidal and reversed shear Alfvén eigenmodes in the DIII-D tokamak. The coherent losses are of full energy beam ions expelled from the plasma on their first poloidal orbit. The first-orbit loss mechanism causes enhanced, concentrated losses on the first wall exceeding nominal levels of prompt losses. The loss amplitude scales linearly with the mode amplitude. The data provide a novel and direct measure of the radial excursion or scatter of particles induced by individual modes and may shed light on the mechanism for the scattering of energetic particles in interstellar medium.

The numerical methods used in the full particle-orbit following SPIRAL code are described and a number of physics studies performed with the code are presented to illustrate its capabilities. The SPIRAL code is a test-particle code and is a powerful numerical tool to interpret and plan fast-ion experiments in tokamaks. Gyro-orbit effects are important for fast ions in low-field machines such as NSTX and to a lesser extent in DIII-D. A number of physics studies are interlaced between the description of the code to illustrate its capabilities. Results on heat loads generated by a localized error-field on the DIII-D wall are compared with measurements. The enhanced Triton losses caused by the same localized error-field are calculated and compared with measured neutron signals. Magnetohydrodynamic (MHD) activity such as tearing modes and toroidicity-induced Alfvén eigenmodes (TAEs) have a profound effect on the fast-ion content of tokamak plasmas and SPIRAL can calculate the effects of MHD activity on the confined and lost fast-ion population as illustrated for a burst of TAE activity in NSTX. The interaction between ion cyclotron range of frequency (ICRF) heating and fast ions depends solely on the gyro-motion of the fast ions and is captured exactly in the SPIRAL code. A calculation of ICRF absorption on beam ions in ITER is presented. The effects of high harmonic fast wave heating on the beam-ion slowing-down distribution in NSTX is also studied. © 2013 IOP Publishing Ltd.

We report the first experimental observations of fast-ion loss in a tokamak due to energetic particle driven geodesic acoustic modes (EGAMs). A fast-ion loss detector installed on the DIII-D tokamak observes bursts of beam ion losses coherent with the EGAM frequency. The EGAM activity results in a significant loss of beam ions, comparable to the first orbit losses. The pitch angles and energies of the measured fast-ion losses agree with predictions from a full orbit simulation code SPIRAL, which includes scattering and slowing-down. © 2012 IAEA, Vienna.

Neutral beam injection into reversed-magnetic shear DIII-D plasmas produces a variety of Alfvénic activity including toroidicity-induced Alfvén eigenmodes (TAEs) and reversed shear Alfvén eigenmodes (RSAEs). With measured equilibrium profiles as inputs, the ideal MHD code NOVA is used to calculate eigenmodes of these plasmas. The postprocessor code NOVA-K is then used to perturbatively calculate the actual stability of the modes, including finite orbit width and finite Larmor radius effects, and reasonable agreement with the spectrum of observed modes is found. Using experimentally measured mode amplitudes, fast ion orbit following simulations have been carried out in the presence of the NOVA calculated eigenmodes and are found to reproduce the dominant energy, pitch and temporal evolution of the losses measured using a large bandwidth scintillator diagnostic. The same analysis techniques applied to a DT 8 MA ITER steady-state plasma scenario with reversed-magnetic shear and both beam ion and alpha populations show Alfvén eigenmode instability. Both RSAEs and TAEs are found to be unstable with maximum growth rates occurring for toroidal mode number n=6 and the majority of the drive coming from fast ions injected by the 1MeV negative ion beams. AE instability due to beam ion drive is confirmed by the non-perturbative code TAEFL. Initial fast ion orbit following simulations using the unstable modes with a range of amplitudes (δB/B=10 -510 -3) have been carried out and show negligible fast ion loss. The lack of fast ion loss is a result of loss boundaries being limited to large radii and significantly removed from the actual modes themselves. © 2012 IAEA, Vienna.

Chirping toroidicity-induced Alfvén eigenmodes (TAEs) are destabilized during neutral beam injection on the National Spherical Torus Experiment (NSTX (Ono M. et al 2000 Nucl. Fusion 40 557)) by super-Alfvénic ions with velocities up to five times larger than the Alfvén velocity. TAEs exhibit repeated bursts in amplitude and down-chirps in frequency. Larger bursts, so-called TAE avalanches, are eventually observed and correlate with a loss of fast ions up to 30% over ∼1ms. Frequency, amplitude and radial structure of TAEs are characterized via magnetic pickup coils and a multi-channel reflectometer system. The modes have a broad radial structure, which appears to be unaffected by the large frequency and amplitude variations. However, the large mode amplitude does impact the modes' dynamics by favouring the coupling among different modes. In addition, the coupling involves kink-like modes and can therefore degrade the thermal plasma confinement. In spite of the non-linear regime characterizing the TAE dynamics, the measured properties are found to be in reasonable agreement with solutions from the ideal MHD code NOVA. © 2012 IAEA, Vienna.

From numerical simulation and analytical modeling it is shown that fast ions can resonate with plasma waves at fractional values of the particle drift-orbit transit frequency when the plasma wave amplitude is sufficiently large. The fractional resonances, which are caused by a nonlinear interaction between the particle orbit and the wave, give rise to an increased density of resonances in phase space which reduces the threshold for stochastic transport. The effects of the fractional resonances on spatial and energy transport are illustrated for an energetic particle geodesic acoustic mode but they apply equally well to other types of MHD activity.

Fast beam-ion losses were studied in DIII-D in the presence of a scaled mock-up of two test blanket modules (TBM) for ITER. Heating of the protective tiles on the front of the TBM surface was found when neutral beams were injected and the TBM fields were engaged. The fast-ion core confinement was not significantly affected. Different orbit-following codes predict the formation of a hot spot on the TBM surface arising from beam ions deposited near the edge of the plasma. The codes are in good agreement with each other on the total power deposited at the hot spot, predicting an increase in power with decreasing separation between the plasma edge and the TBM surface. A thermal analysis of the heat flow through the tiles shows that the simulated power can account for the measured tile temperature rise. The thermal analysis, however, is very sensitive to the details of the localization of the hot spot, which is predicted to be different among the various codes. © 2011 IAEA, Vienna.

Neutral beam injection into reversed magnetic shear DIII-D and ASDEX Upgrade plasmas produces a variety of Alfvénic activity including toroidicity-induced Alfvén eigenmodes and reversed shear Alfvén eigenmodes (RSAEs). These modes are studied during the discharge current ramp phase when incomplete current penetration results in a high central safety factor and increased drive due to multiple higher order resonances. Scans of injected 80 keV neutral beam power on DIII-D showed a transition from classical to AE dominated fast ion transport and, as previously found, discharges with strong AE activity exhibit a deficit in neutron emission relative to classical predictions. By keeping beam power constant and delaying injection during the current ramp, AE activity was reduced or eliminated and a significant improvement in fast ion confinement observed. Similarly, experiments in ASDEX Upgrade using early 60 keV neutral beam injection drove multiple unstable RSAEs. Periods of strong RSAE activity are accompanied by a large (peak δS n/Sn ≈ 60%) neutron deficit. Losses of beam ions modulated at AE frequencies were observed using large bandwidth energy and pitch resolving fast ion loss scintillator detectors and clearly identify their role in the process. Modeling of DIII-D loss measurements using guiding center following codes to track particles in the presence of ideal magnetohydrodynamic (MHD) calculated AE structures (validated by comparison to experiment) is able to reproduce the dominant energy, pitch, and temporal evolution of these losses. While loss of both co and counter current fast ions occurs, simulations show that the dominant loss mechanism observed is the mode induced transition of counter-passing fast ions to lost trapped orbits. Modeling also reproduces a coherent signature of AE induced losses and it was found that these coherent losses scale proportionally with the amplitude; an additional incoherent contribution scales quadratically with the mode amplitude. © 2011 American Institute of Physics.

Neutral beam injection into reversed magnetic shear DIII-D plasmas produces a variety of Alfvénic activity including toroidicity and ellipticity induced Alfvén eigenmodes (TAE/EAE, respectively) and reversed shear Alfvén eigenmodes (RSAE) as well as their spatial coupling. These modes are studied during the discharge current ramp phase when incomplete current penetration results in a high central safety factor and strong drive due to multiple higher order resonances. It is found that ideal MHD modelling of eigenmode spectral evolution, coupling and structure are in excellent agreement with experimental measurements. It is also found that higher radial envelope harmonic RSAEs are clearly observed and agree with modelling. Some discrepancies with modelling such as that due to up/down eigenmode asymmetries are also pointed out. Concomitant with the Alfvénic activity, fast ion (FIDA) spectroscopy shows large reductions in the central fast ion profile, the degree of which depends on the Alfvén eigenmode amplitude. Interestingly, localized electron cyclotron heating (ECH) near the mode location stabilizes RSAE activity and results in significantly improved fast ion confinement relative to discharges with ECH deposition on axis. In these discharges, RSAE activity is suppressed when ECH is deposited near the radius of the shear reversal point and enhanced with deposition near the axis. The sensitivity of this effect to deposition power and current drive phasing as well as ECH modulation are presented. © 2009 IAEA, Vienna.

Alfv́n cascade (AC) modes are observed in the National Spherical Torus Experiment [M. Ono, Nucl. Fusion 40, 557 (2000)] reversed shear plasmas over a wide range (up to ∼25% on axis, or ∼11% at minimum q) of Β (ratio of kinetic pressure to magnetic pressure). At low Β, the AC mode spectrum shows characteristics similar to conventional tokamaks. At higher Β, distinct Β and ∇Β effects are observed in the spectrum, including a significant reduction in the relative size of the frequency sweep and a toroidal mode number dependence in the minimum mode frequency. AC mode structure is obtained using reflectometry. Fast-ion loss associated with AC mode activity is observed. AC mode polarization at the plasma edge is consistent with expectation. Magnetohydrodynamic (MHD) spectroscopy is shown to be usable to determine qmin at both low Β and high Β. Observed AC mode structure and frequency are found to be consistent with calculations for the same plasma conditions and geometry using the linear, ideal MHD hybrid kinetic code NOVA-K [C. Z. Cheng, Phys. Rep. 211, 1 (1992)]. © 2008 American Institute of Physics.

Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (q_{min}>or=2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (n[over ]_{e}/n_{e} approximately 1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode.

Neutral beam injection into a plasma with negative central shear produces a rich spectrum of toroidicity-induced and reversed-shear Alfvén eigenmodes in the DIII-D tokamak. The application of fast-ion D α (FIDA) spectroscopy shows that the central fast-ion profile is flattened in the inner half of the discharge. Neutron and equilibrium measurements corroborate the FIDA data. The temporal evolution of the current profile is also strongly modified. Studies in similar discharges show that flattening of the profile correlates with the mode amplitude and that both types of Alfvén modes correlate with fast-ion transport. Calculations by the ORBIT code do not explain the observed fast-ion transport for the measured mode amplitudes, however. Possible explanations for the discrepancy are considered. © 2008 IAEA, Vienna.

Core localized Alfv́n eigenmodes in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] and Joint European Torus (JET) [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] plasmas are driven by deuterium neutral beam ions traveling well below the Alfv́n speed. Modes are observed in reverse magnetic shear discharges with deuterium ion velocities as low as 0.23 and 0.16 of the Alfv́n speed parallel to the magnetic field in DIII-D and JET plasmas, respectively. Ellipticity-induced Alfv́n eigenmodes in DIII-D and toroidicity-induced Alfv́n eigenmodes in JET are excited by deuterium ions traveling well below the fundamental passing ion resonance condition, indicating the role of high-order resonances in driving these modes. NOVA-K analysis reveals many high-order resonances as contributing to the mode drive at high central safety factor due to the correspondingly large poloidal orbit width and the decrease in the perpendicular scale length of the modes. © 2008 American Institute of Physics.

Reversed shear Alfvén eigenmode (RSAE) activity in DIII-D is stabilized by electron cyclotron heating (ECH) applied near the minimum of the magnetic safety factor (qmin) in neutral beam heated discharges with reversed-magnetic shear. The degree of RSAE stabilization, fast ion density and the volume averaged neutron production (Sn) are highly dependent on ECH deposition location relative to qmin. While discharges with ECH stabilization of RSAEs have higher Sn and more peaked fast ion profiles than discharges with significant RSAE activity, neutron production remains strongly reduced (up to 60% relative to TRANSP predictions assuming classical fast ion transport) even when RSAEs are stabilized. © 2008 IOP Publishing Ltd.

Neutral-beam injection into plasmas with negative central shear produces a rich spectrum of toroidicity-induced and reversed-shear Alfvén eigenmodes in the DIII-D tokamak. The first application of fast-ion D_{alpha} (FIDA) spectroscopy to Alfvén-eigenmode physics shows that the central fast-ion profile is anomalously flat in the inner half of the discharge. Neutron and equilibrium measurements corroborate the FIDA data. The current density driven by fast ions is also strongly modified. Calculations based on the measured mode amplitudes do not explain the observed fast-ion transport.

Reversed shear Alfv́n eigenmodes (RSAEs) are typically thought of as being localized near the minima in the magnetic safety factor profile, however, their spatial coupling to global toroidal Alfv́n eigenmodes (TAEs) has been observed in DIII-D discharges. For a decreasing minimum magnetic safety factor, the RSAE frequency chirps up through that of stable and unstable TAEs. Coupling creates a small gap at the frequency degeneracy point forming two distinct global modes. The core-localized RSAE mode structure changes and becomes temporarily global. Similarly, near the mode frequency crossing point, the global TAE extends deeper into the plasma core. The frequency splitting and spatial structure of the two modes throughout the various coupling stages, as measured by an array of internal fluctuation diagnostics, are in close agreement with linear ideal MHD calculations using the NOVA code. The implications of this coupling for eigenmode stability is also investigated and marked changes are noted throughout the coupling process. © 2007 American Institute of Physics.

The spatial structure of toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes in DIII-D is obtained from electron-cyclotron-emission measurements. Peak measured temperature perturbations are of similar magnitude for both toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes and found to be deltaT(e)/T(e) approximately equal to 0.5%. Simultaneous measurements of density fluctuations using beam-emission spectroscopy indicate deltan(e)/n(e) approximately equal to 0.25%. Predictions of the measured temperature and density perturbation profiles as well as deltaT(e)/deltan(e) from the ideal magnetohydrodynamic code NOVA are in close agreement with experiment.

Low and high frequency beam ion driven instabilities in the National Spherical Tokamak Experiment (NSTX) plasma were analyzed. Low frequency magnetohydrodynamics (MHD) activities in ∼100 kHz frequency range on NSTX were often observed and identified as the TAEs driven by beam ions. It was shown that there was a large uncertainty in the experimental plasma parameters upon which the numerical model was based for the low-n TAE instabilities. The analysis helps to validate the NOVA/NOVA-K predictions that TAEs will be unstable in ITER if driven by fusion alphas in a plasma with T i0>20 KeV.

A superheterodyne reflectometer could provide a direct and inexpensive measurement of ion species mixes with different charge-to-mass ratios. Using the cold plasma dispersion relation, the ion-ion hybrid cutoff frequency is uniquely determined by the density ratio and cyclotron frequencies of the two different species. The phase of a 20 MHz wave that travels from the launching point to the cutoff layer to the receiving antenna provides a direct measure of the hydrogen : deuterium species mix. In the first experiment, a fast Alfvén wave is launched perpendicular to a hydrogen-deuterium plasma from the low field side of the DIII-D tokamak. Quantitative measurements observe a hydrogen concentration range of 3-67% and a maximum penetration depth of 0.60m. Corroborative values are obtained from two independent diagnostics. In the second experiment, the fast Alfvén wave is launched from the high field side (HFS) during a hydrogen puffing experiment. The results suggest that a wave launched from the HFS is able to tunnel through the resonance-layer and reflect back to the receiving antenna.

A superheterodyne reflectometer could provide a direct and inexpensive measurement of ion species mixes with different charge-to-mass ratios. Using the cold plasma dispersion relation, the ion-ion hybrid cutoff frequency is uniquely determined by the density ratio and cyclotron frequencies of the two different species. The phase of a 20 MHz wave that travels from the launching point to the cutoff layer to the receiving antenna provides a direct measure of the hydrogen : deuterium species mix. In the first experiment, a fast Alfvén wave is launched perpendicular to a hydrogen-deuterium plasma from the low field side of the DIII-D tokamak. Quantitative measurements observe a hydrogen concentration range of 3-67% and a maximum penetration depth of 0.60m. Corroborative values are obtained from two independent diagnostics. In the second experiment, the fast Alfvén wave is launched from the high field side (HFS) during a hydrogen puffing experiment. The results suggest that a wave launched from the HFS is able to tunnel through the resonance-layer and reflect back to the receiving antenna.

The stability of α-particle driven shear Alfvén eigenmodes (AE) for nominal burning plasma (BP) parameters in the proposed international tokamak experimental reactor (ITER), fusion ignition research experiment (FIRE) and IGNITOR tokamaks is studied. JET plasma, where fusion as were generated in tritium experiments, is also studied to compare the numerical predictions with the existing experiments. An analytic assessment of toroidal AE (TAB) stability is first presented, where the α-particle β due to the fusion reaction rate and electron drag is simply and accurately estimated in plasmas with central temperature in the range of 7-20 keV. In this assessment the hot particle drive is balanced against ion-Landau damping of the background douterons, and electron collision effects and stability boundaries are determined. Then two numerical studies of AE instability are presented. In one, the HIgh-n STability (HINST) code is used to predict the instabilities of low and moderately high frequency Alfvén modes. HINST computes the non-perturbative solutions of the AE including effects of ion finite Larmor radius, orbit width, trapped electrons etc. The stability calculations are repeated using the global code NOVAK. We show that for these plasmas the spectrum of the least stable AE modes is at medium-/high-n numbers. In HINST, TAEs are locally unstable due to the α pressure gradient in all the devices under consideration except IGNITOR. However, NOVAK calculations show that the global mode structure enhances the damping mechanisms and produces stability for the nominal FIRE proposal and near-marginal stability for the nominal ITER proposal. NBI ions produce a strong stabilizing effect for JET. However, in ITER, the beam energies needed to penetrate to the core must be high (∼1 MeV) so that a diamagnetic drift frequency comparable to that of α-particles is produced by the beam ions which induces a destabilizing effect. A serious question remains whether the perturbation theory used in NOVAK overestimates the stability predictions, so that it is premature to conclude that the nominal operation of all three BP proposals without neutral beam injection are stable (or marginally stable) to AEs.