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Due to the usually complicated and anisotropic nature of the fast-ion distribution function, diagnostic velocity-space weight functions, which indicate the sensitivity of a diagnostic to different fast-ion velocities, are used to facilitate the analysis of experimental data. Additionally, when velocity-space weight functions are discretized, a linear equation relating the fast-ion density and the expected diagnostic signal is formed. In a technique known as velocity-space tomography, many measurements can be combined to create an ill-conditioned system of linear equations that can be solved using various computational methods. However, when velocity-space weight functions (which by definition ignore spatial dependencies) are used, velocity-space tomography is restricted, both by the accuracy of its forward model and also by the availability of spatially overlapping diagnostic measurements. In this work, we extend velocity-space weight functions to a full 6D generalized coordinate system and then show how to reduce them to a 3D orbit-space without loss of generality using an action-angle formulation. Furthermore, we show how diagnostic orbit-weight functions can be used to infer the full fast-ion distribution function, i.e., orbit tomography. In depth derivations of orbit weight functions for the neutron, neutral particle analyzer, and fast-ion D-α diagnostics are also shown.

A numerical study is performed on the coherent beam ion prompt losses driven by Alfvén eigenmodes (AEs) in DIII-D plasmas using realistic parameters and beam ion deposition profiles. The synthetic signal of a fast-ion loss detector (FILD) is calculated for a single AE mode. The first harmonic of the calculated FILD signal is linearly proportional to the AE amplitude with the same AE frequency in agreement with the experimental measurement. The calculated second harmonic is proportional to the square of the first harmonic for typical AE amplitudes. The coefficient of quadratic scaling is found to be sensitive to the AE mode width. The second part of this work considers the AE drive due to coherent prompt loss. It is shown that the loss-induced mode drive is much smaller than the previous estimate and can be ignored for mode stability.

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.

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.

A first-ever demonstration of controlling power and torque injection through time evolution of neutral beam energy has been achieved in recent experiments at the DIII-D tokamak (Luxon 2002 Nucl. Fusion 42 614). Pre-programmed waveforms for the neutral beam energy produce power and torque inputs that can be separately and continuously controlled. Previously, these inputs were tailored using on/off modulation of neutral beams resulting in large perturbations (e.g. power swings of over 1 MW). The new method includes, importantly for experiments, the ability to maintain a fixed injected power while varying the torque. In another case, different beam energy waveforms (in the same plasma conditions) produce significant changes in the observed spectrum of beam ion-driven instabilities. Measurements of beam ion loss show that one energy waveform results in the complete avoidance of coherent losses due to Alfvénic instabilities. This new method of neutral beam operation is intended for further application in a variety of DIII-D experiments including those concerned with high-performance steady state scenarios, fast particle effects, and transport in the low torque regime. Developing this capability would provide similar benefits and improved plasma control for other magnetic confinement fusion facilities.

A first-ever demonstration of controlling power and torque injection through time evolution of neutral beam energy has been achieved in recent experiments at the DIII-D tokamak (Luxon 2002 Nucl. Fusion 42 614). Pre-programmed waveforms for the neutral beam energy produce power and torque inputs that can be separately and continuously controlled. Previously, these inputs were tailored using on/off modulation of neutral beams resulting in large perturbations (e.g. power swings of over 1 MW). The new method includes, importantly for experiments, the ability to maintain a fixed injected power while varying the torque. In another case, different beam energy waveforms (in the same plasma conditions) produce significant changes in the observed spectrum of beam ion-driven instabilities. Measurements of beam ion loss show that one energy waveform results in the complete avoidance of coherent losses due to Alfvénic instabilities. This new method of neutral beam operation is intended for further application in a variety of DIII-D experiments including those concerned with high-performance steady state scenarios, fast particle effects, and transport in the low torque regime. Developing this capability would provide similar benefits and improved plasma control for other magnetic confinement fusion facilities.

In toroidal magnetic fusion devices, fast-ion D-alpha diagnostic (FIDA) is a powerful method to study the fast-ion feature. The fast-ion characteristics can be inferred from the Doppler shifted spectrum of Dα light according to charge exchange recombination process between fast ions and probe beam. Since conceptual design presented in the last HTPD conference, significant progress has been made to apply FIDA systems on the Experimental Advanced Superconducting Tokamak (EAST). Both co-current and counter-current neutral beam injectors are available, and each can deliver 2-4 MW beam power with 50-80 keV beam energy. Presently, two sets of high throughput spectrometer systems have been installed on EAST, allowing to capture passing and trapped fast-ion characteristics simultaneously, using Kaiser HoloSpec transmission grating spectrometer and Bunkoukeiki FLP-200 volume phase holographic spectrometer coupled with Princeton Instruments ProEM 1024B eXcelon and Andor DU-888 iXon3 1024 CCD camera, respectively. This paper will present the details of the hardware descriptions and experimental spectrum.

To investigate the fast ion behavior, a fast ion D-alpha (FIDA) diagnostic system has been installed on EAST. Fast ion features can be inferred from the Doppler shifted spectrum of Balmer-alpha light from energetic hydrogenic atoms. This paper will focus on the validation of FIDA measurements performed using MHD-quiescent discharges in 2015 campaign. Two codes have been applied to calculate the Dα spectrum: one is a Monte Carlo code, Fortran 90 version FIDASIM, and the other is an analytical code, Simulation of Spectra (SOS). The predicted SOS fast-ion spectrum agrees well with the measurement; however, the level of fast-ion part from FIDASIM is lower. The discrepancy is possibly due to the difference between FIDASIM and SOS velocity distribution function. The details will be presented in the paper to primarily address comparisons of predicted and observed spectrum shapes/amplitudes.

A compact and multi-view solid state neutral particle analyzer (SSNPA) diagnostic based on silicon photodiode arrays has been successfully tested on the National Spherical Torus Experiment-Upgrade. The SSNPA diagnostic provides spatially, temporally, and pitch-angle resolved measurements of fast-ion distribution by detecting fast neutral flux resulting from the charge exchange (CX) reactions. The system consists of three 16-channel subsystems: t-SSNPA viewing the plasma mid-radius and neutral beam (NB) line #2 tangentially, r-SSNPA viewing the plasma core and NB line #1 radially, and p-SSNPA with no intersection with any NB lines. Due to the setup geometry, the active CX signals of t-SSNPA and r-SSNPA are mainly sensitive to passing and trapped particles, respectively. In addition, both t-SSNPA and r-SSNPA utilize three vertically stacked arrays with different filter thicknesses to obtain coarse energy information. The experimental data show that all channels are operational. The signal to noise ratio is typically larger than 10, and the main noise is x-ray induced signal. The active and passive CX signals are clearly observed on t-SSNPA and r-SSNPA during NB modulation. The SSNPA data also indicate significant losses of passing particles during sawteeth, while trapped particles are weakly affected. Fluctuations up to 120 kHz have been observed on SSNPA, and they are strongly correlated with magnetohydrodynamics instabilities.

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.

Fast ion pressure profiles flattened by multiple Alfvén eigenmodes (AEs) are investigated for various neutral beam deposition powers in a multi-phase simulation, which is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic fluid. Monotonic degradation of fast ion confinement and fast ion profile stiffness is found with increasing beam deposition power. The confinement degradation and profile stiffness are caused by a sudden increase in fast ion transport flux brought about by AEs for fast ion pressure gradients above a critical value. The critical pressure gradient and the corresponding beam deposition power depend on the radial location. The fast ion pressure gradient stays moderately above the critical value, and the profiles of the fast ion pressure and fast ion transport flux spread radially outward from the inner region, where the beam is injected. It is found that the square root of the MHD fluctuation energy is proportional to the beam deposition power. Analysis of the time evolutions of the fast ion energy flux profiles reveals that intermittent avalanches take place with contributions from the multiple eigenmodes. Surface of section plots demonstrate that the resonance overlap of multiple eigenmodes accounts for the sudden increase in fast ion transport with increasing beam power. The critical gradient and critical beam power for the profile stiffness are substantially higher than the marginal stability threshold.

Fast-ion signals produced by a modulated neutral beam are used to infer fast-ion transport. The measured quantity is the divergence of perturbed fast-ion flux from the phase-pace volume measured by the diagnostic, δ ⌈Since velocity-space transport often contributes to this divergence, the phase-space sensitivity of the diagnostic (or weight function) plays a crucial role in the interpretation of the signal. The source and sink make major contributions to the signal but their effects are accurately modelled by calculations that employ an exponential decay term for the sink. Recommendations for optimal design of a fast-ion transport experiment are given, illustrated by results from DIII-D measurements of fast-ion transport by Alfvn eigenmodes. The signal-to-noise ratio of the diagnostic, systematic uncertainties in the modeling of the source and sink, and the non-linearity of the perturbation all contribute to the error in δ ⌈.

Full function integrated, compact solid state neutral particle analyzers (ssNPA) based on absolute extreme ultraviolet silicon photodiode have been successfully implemented on the experimental advanced superconducting tokamak to measure energetic particle. The ssNPA system has been operated in advanced current mode with fast temporal and spatial resolution capabilities, with both active and passive charge exchange measurements. It is found that the ssNPA flux signals are increased substantially with neutral beam injection (NBI). The horizontal active array responds to modulated NBI beam promptly, while weaker change is presented on passive array. Compared to near-perpendicular beam, near-tangential beam brings more passive ssNPA flux and a broader profile, while no clear difference is observed on active ssNPA flux and its profile. Significantly enhanced intensities on some ssNPA channels have been observed during ion cyclotron resonant heating.

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.

Velocity-space tomography of the fast-ion distribution function in a fusion plasma is usually a photon-starved tomography method due to limited optical access and signal-to-noise ratio of fast-ion Dα (FIDA) spectroscopy as well as the strive for high-resolution images. In high-definition tomography, prior information makes up for this lack of data. We restrict the target velocity space through the measured absence of FIDA light, impose phase-space densities to be non-negative, and encode the known geometry of neutral beam injection (NBI) sources. We further use a numerical simulation as prior information to reconstruct where in velocity space the measurements and the simulation disagree. This alternative approach is demonstrated for four-view as well as for two-view FIDA measurements. The high-definition tomography tools allow us to study fast ions in sawtoothing plasmas and the formation of NBI peaks at full, half and one-third energy by time-resolved tomographic movies.

Spectra of passive fast-ion D-alpha (FIDA) light from beam ions that charge exchange with background neutrals are measured and simulated. The fast ions come from three sources: ions that pass through the diagnostic sightlines on their first full orbit, an axisymmetric confined population, and ions that are expelled into the edge region by instabilities. A passive FIDA simulation (P-FIDASIM) is developed as a forward model for the spectra of the first-orbit fast ions and consists of an experimentally-validated beam deposition model, an ion orbit-following code, a collisional-radiative model, and a synthetic spectrometer. Model validation consists of the simulation of 86 experimental spectra that are obtained using 6 different neutral beam fast-ion sources and 13 different lines of sight. Calibrated spectra are used to estimate the neutral density throughout the cross-section of the tokamak. The resulting 2D neutral density shows the expected increase toward each X-point with average neutral densities of 8×109cm-3 at the plasma boundary and 1×1011cm-3 near the wall. Fast ions that are on passing orbits are expelled by the sawtooth instability more readily than trapped ions. In a sample discharge, approximately 1% of the fast-ion population is ejected into the high neutral density region per sawtooth crash.

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.

Velocity-space tomography has been used to infer 2D fast-ion velocity distribution functions. Here we compare the performance of five different tomographic inversion methods: truncated singular value decomposition, maximum entropy, minimum Fisher information and zerothand first-order Tikhonov regularization. The inversion methods are applied to fast-ion Dα measurements taken just before and just after a sawtooth crash in the ASDEX Upgrade tokamak as well as to synthetic measurements from different test distributions. We find that the methods regularizing by penalizing steep gradients or maximizing entropy perform best. We assess the uncertainty of the calculated inversions taking into account photon noise, uncertainties in the forward model as well as uncertainties introduced by the regularization which allows us to distinguish regions of high and low confidence in the tomographies. In high confidence regions, all methods agree that ions with pitch values close to zero, as well as ions with large pitch values, are ejected from the plasma center by the sawtooth crash, and that this ejection depletes the ion population with large pitch values more strongly.

Effects of the energetic-ion-driven Geodesic Acoustic modes (GAM and E-GAM) on the toroidally passing energetic ions and the concomitant change of the neutron yield of beam-plasma fusion reactions in tokamaks are considered. It is shown that due to large perturbations of the plasma density, the resonant energetic ions driving the instability can be considerably slowed down for a few tens of the particle transit periods, which is much less than the collisional slowing down time. The time of the collisionless slowing down is actually determined by the period of the particle motion within the resonance island arising because of the GAM / E-GAM. Being trapped in the island, the resonant particles can not only lose their energy but also gain it. One more effect of GAMs is the flattening on the distribution function of the resonant particles. Due to conservation of the canonical angular momentum during a GAM / E-GAM instability, the change of the particle energy is accompanied by a radial displacement of the resonant particle for a distance up to the poloidal Larmor radius of energetic ions. The particles are displaced inwards or outwards, depending on the direction of their motion along the magnetic field. Expressions describing the change of the neutron yield due to GAM modes are derived. It is found that the distortion of the velocity distribution of the resonant particles can lead to a considerable drop of the neutron emission even when effects of the particle radial displacement are small. The developed theory is applied to an E-GAM experiment on the DIII-D tokamak. Relations for the period of the motion within the resonance island of passing (both well passing and marginally passing) particles and the width of the resonance of the energetic particles with GAM modes and low-frequency Alfvé modes are derived.

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.

Neutral-beam ions that are deflected onto loss orbits by Alfvén eigenmodes (AE) on their first bounce orbit and are detected by a fast-ion loss detector (FILD) satisfy the "local resonance" condition proposed by Zhang et al. [Nucl. Fusion 55, 22002 (2015)]. This theory qualitatively explains FILD observations for a wide variety of AE-particle interactions. When coherent losses are measured for multiple AE, oscillations at the sum and difference frequencies of the independent modes are often observed in the loss signal. The amplitudes of the sum and difference peaks correlate weakly with the amplitudes of the fundamental loss-signal amplitudes but do not correlate with the measured mode amplitudes. In contrast to a simple uniform-plasma theory of the interaction [Chen et al., Nucl. Fusion 54, 083005 (2014)], the loss-signal amplitude at the sum frequency is often larger than the loss-signal amplitude at the difference frequency, indicating a more detailed computation of the orbital trajectories through the mode eigenfunctions is needed.

A 3D halo neutral code developed at the Princeton Plasma Physics Laboratory and implemented for analysis using the TRANSP code is applied to projected National Spherical Torus eXperiment-Upgrade (NSTX-U plasmas). The legacy TRANSP code did not handle halo neutrals properly since they were distributed over the plasma volume rather than remaining in the vicinity of the neutral beam footprint as is actually the case. The 3D halo neutral code uses a 'beam-in-a-box' model that encompasses both injected beam neutrals and resulting halo neutrals. Upon deposition by charge exchange, a subset of the full, one-half and one-third beam energy components produce first generation halo neutrals that are tracked through successive generations until an ionization event occurs or the descendant halos exit the box. The 3D halo neutral model and neutral particle analyzer (NPA) simulator in the TRANSP code have been benchmarked with the Fast-Ion D-Alpha simulation (FIDAsim) code, which provides Monte Carlo simulations of beam neutral injection, attenuation, halo generation, halo spatial diffusion, and photoemission processes. When using the same atomic physics database, TRANSP and FIDAsim simulations achieve excellent agreement on the spatial profile and magnitude of beam and halo neutral densities and the NPA energy spectrum. The simulations show that the halo neutral density can be comparable to the beam neutral density. These halo neutrals can double the NPA flux, but they have minor effects on the NPA energy spectrum shape. The TRANSP and FIDAsim simulations also suggest that the magnitudes of beam and halo neutral densities are relatively sensitive to the choice of the atomic physics databases.

Recent EAST/DIII-D joint experiments on the high poloidal beta tokamak regime in DIII-D have demonstrated fully noninductive operation with an internal transport barrier (ITB) at large minor radius, at normalized fusion performance increased by 30% relative to earlier work (Politzer et al 2005 Nucl. Fusion 45 417). The advancement was enabled by improved understanding of the 'relaxation oscillations', previously attributed to repetitive ITB collapses, and of the fast ion behavior in this regime. It was found that the 'relaxation oscillations' are coupled core-edge modes amenable to wall-stabilization, and that fast ion losses which previously dictated a large plasma-wall separation to avoid wall over-heating, can be reduced to classical levels with sufficient plasma density. By using optimized waveforms of the plasma-wall separation and plasma density, fully noninductive plasmas have been sustained for long durations with excellent energy confinement quality, bootstrap fraction ≥80%, βN ≤ 4, βP ≥ 3, and βT ≥ 2%. These results bolster the applicability of the high poloidal beta tokamak regime toward the realization of a steady-state fusion reactor.

Interactions between electromagnetic waves and the most energetic ions in a plasma can perturb the orbits of those ions enough to expel them from the confining magnetic field.

Some neutral-beam ions are deflected onto loss orbits by Alfvén eigenmodes on their first bounce orbit. The resonance condition for these ions differs from the usual resonance condition for a confined fast ion. Estimates indicate that particles on single-pass loss orbits transfer enough energy to the wave to alter mode stability.

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.

A multi-phase simulation, which is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic (MHD) fluid including neutral beam injection, slowing-down, and pitch angle scattering, is applied to DIII-D discharge #142111 where the fast ion spatial profile is significantly flattened due to multiple Alfvén eigenmodes (AEs). The large fast ion pressure profile flattening observed experimentally is successfully reproduced by these first of a kind comprehensive simulations. Temperature fluctuations due to three of the dominant toroidal Alfvén eigenmodes in the simulation results are compared in detail with electron cyclotron emission measurements in the experiment. It is demonstrated that the temperature fluctuation profile and the phase profile are in very good agreement with the measurement, and the amplitude is also in agreement within a factor of two. This level of agreement validates the multi-phase hybrid simulation for the prediction of AE activity and alpha particle transport in burning plasmas.

Results from experiments on DIII-D [J. L. Luxon, Fusion Sci. Technol. 48, 828 (2005)] aimed at developing high β steady-state operating scenarios with high- q min confirm that fast-ion transport is a critical issue for advanced tokamak development using neutral beam injection current drive. In DIII-D, greater than 11 MW of neutral beam heating power is applied with the intent of maximizing β N and the noninductive current drive. However, in scenarios with q min > 2 that target the typical range of q 95 = 5-7 used in next-step steady-state reactor models, Alfvén eigenmodes cause greater fast-ion transport than classical models predict. This enhanced transport reduces the absorbed neutral beam heating power and current drive and limits the achievable βN. In contrast, similar plasmas except with q min just above 1 have approximately classical fast-ion transport. Experiments that take q min > 3 plasmas to higher β P with q 95 = 11-12 for testing long pulse operation exhibit regimes of better than expected thermal confinement. Compared to the standard high- q min scenario, the high β P cases have shorter slowing-down time and lower ∇ β fast, and this reduces the drive for Alfvénic modes, yielding nearly classical fast-ion transport, high values of normalized confinement, β N, and noninductive current fraction. These results suggest DIII-D might obtain better performance in lower- q 95, high- q min plasmas using broader neutral beam heating profiles and increased direct electron heating power to lower the drive for Alfvén eigenmodes.

The detection of fast particle-driven waves in the ion cyclotron frequency range (ion cyclotron emission or ICE) could provide a passive, non-invasive diagnostic of confined and escaping fast particles (fusion α-particles and beam ions) in ITER, and would be compatible with the high radiation environment of deuterium-tritium plasmas in that device. Recent experimental results from ASDEX Upgrade and DIII-D demonstrate the efficacy of ICE as a diagnostic of different fast ion species and of fast ion losses, while recent particle-in-cell (PIC) and hybrid simulations provide a more exact comparison with measured ICE spectra and open the prospect of exploiting ICE more fully as a fast ion diagnostic in future experiments. In particular the PIC/hybrid approach should soon make it possible to simulate the nonlinear physics of ICE in full toroidal geometry. Emission has been observed previously at a wide range of poloidal angles, so there is flexibility in the location of ICE detectors. Such a detector could be implemented in ITER by installing a small toroidally orientated loop near the plasma edge or by adding a detection capability to the ion cyclotron resonance heating (ICRH) antennae. In the latter case, the antenna could be used simultaneously to heat the plasma and detect ICE, provided that frequencies close to those of the ICRH source are strongly attenuated in the detection system using a suitable filter. Wavenumber information, providing additional constraints on the fast ion distribution exciting the emission, could be obtained by measuring ICE using a toroidally distributed array of detectors or different straps of the ICRH antenna.

Linear properties of the toroidal Alfvén eigenmode (TAE) excited by energetic particles (EP) in a DIII-D tokamak experiment have been studied in global gyrokinetic particle simulations treating self-consistently kinetic effects of EP, thermal ions, and electrons. Simulation results of the TAE frequency and mode structure agree very well with the experimental measurements. The non-perturbative EP contribution induces a radial localization of the TAE mode structure, a break-down of mode radial symmetry, as well as a frequency dependence on the toroidal mode number. The simulations further demonstrate the dependence of the growth rate and mode structure on EP pressure gradients. The in-out asymmetry of the mode structure and the experimental identification of the poloidal harmonics have also been clarified.

Doppler tomography is a well-known method in astrophysics to image the accretion flow, often in the shape of thin discs, in compact binary stars. As accretion discs rotate, all emitted line radiation is Doppler-shifted. In fast-ion Dα (FIDA) spectroscopy measurements in magnetically confined plasma, the Dα-photons are likewise Doppler-shifted ultimately due to gyration of the fast ions. In either case, spectra of Doppler-shifted line emission are sensitive to the velocity distribution of the emitters. Astrophysical Doppler tomography has lead to images of accretion discs of binaries revealing bright spots, spiral structures and flow patterns. Fusion plasma Doppler tomography has led to an image of the fast-ion velocity distribution function in the tokamak ASDEX Upgrade. This image matched numerical simulations very well. Here we discuss achievements of the Doppler tomography approach, its promise and limits, analogies and differences in astrophysical and fusion plasma Doppler tomography and what can be learned by comparison of these applications.

Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.

Full function integrated, compact silicon photodiode based solid state neutral particle analyzers (ssNPA) have been developed for energetic particle (EP) relevant studies on the Experimental Advanced Superconducting Tokamak (EAST). The ssNPAs will be mostly operated in advanced current mode with a few channels to be operated in conventional pulse-counting mode, aiming to simultaneously achieve individually proved ultra-fast temporal, spatial, and spectral resolution capabilities. The design details together with considerations on EAST specific engineering realities and physics requirements are presented. The system, including a group of single detectors on two vertical ports and two 16-channel arrays on a horizontal port, can provide both active and passive charge exchange measurements. ssNPA detectors, with variable thickness of ultra thin tungsten dominated foils directly deposited on the front surface, are specially fabricated and utilized to achieve about 22 keV energy resolution for deuterium particle detection.

A new compact, multi-channel Solid State Neutral Particle Analyzer (SSNPA) diagnostic based on silicon photodiode array has been designed and is being fabricated for the National Spherical Torus Experiment-Upgrade (NSTX-U). The SSNPA system utilizes a set of vertically stacked photodiode arrays in current mode viewing the same plasma region with different filter thickness to obtain fast temporal resolution (∼120 kHz bandwidth) and coarse energy information in three bands of >25 keV, >45 keV, and >65 keV. The SSNPA system consists of 15 radial sightlines that intersect existing on-axis neutral beams at major radii between 90 and 130 cm, 15 tangential sightlines that intersect new off-axis neutral beams at major radii between 120 and 145 cm. These two subsystems aim at separating the response of passing and trapped fast ions. In addition, one photodiode array whose viewing area does not intersect any neutral beams is used to monitor passive signals produced by fast ions that charge exchange with background neutrals.

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.

To investigate the fast ion behavior, a fast ion D-alpha (FIDA) diagnostic system has been planned and is presently under development on Experimental Advanced Superconducting Tokamak. The greatest challenges for the design of a FIDA diagnostic are its extremely low intensity levels, which are usually significantly below the continuum radiation level and several orders of magnitude below the bulk-ion thermal charge-exchange feature. Moreover, an overlaying Motional Stark Effect (MSE) feature in exactly the same wavelength range can interfere. The simulation of spectra code is used here to guide the design and evaluate the diagnostic performance. The details for the parameters of design and hardware are presented.

The velocity-space observation regions and sensitivities in fast-ion Dα(FIDA) spectroscopy measurements are often described by so-called weight functions. Here we derive expressions for FIDA weight functions accounting for the Doppler shift, Stark splitting, and the charge-exchange reaction and electron transition probabilities. Our approach yields an efficient way to calculate correctly scaled FIDA weight functions and implies simple analytic expressions for their boundaries that separate the triangular observable regions in (vv, vb)-space from the unobservable regions. These boundaries are determined by the Doppler shift and Stark splitting and could until now only be found by numeric simulation.

A multi-phase simulation that is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic (MHD) fluid is developed to simulate the nonlinear dynamics on the slowing down time scale of the energetic particles. The hybrid simulation code is extended with realistic beam deposition profile, collisions and losses, and is used for both the classical and hybrid phases. The code is run without MHD perturbations in the classical phase, while the interaction between the energetic particles and the MHD fluid is simulated in the hybrid phase. In a multi-phase simulation of DIII-D discharge #142111, the stored beam ion energy is saturated due to Alfvén eigenmodes (AE modes) at a level lower than in the classical simulation. After the stored fast ion energy is saturated, the hybrid simulation is run continuously. It is demonstrated that the fast ion spatial profile is significantly flattened due to the interaction with the multiple AE modes with amplitude v/vA∼ δB/B ∼ O(10-4). The dominant AE modes are toroidal Alfvén eigenmodes (TAE modes), which is consistent with the experimental observation at the simulated moment. The amplitude of the temperature fluctuations brought about by the TAE modes is of the order of 1% of the equilibrium temperature. This is also comparable with electron cyclotron emission measurements in the experiment.

Analysis of neutron and fast-ion Dα data from the DIII-D tokamak shows that Alfvén eigenmode activity degrades fast-ion confinement in many high βN, high qmin, steady-state scenario discharges. (βN is the normalized plasma pressure and qmin is the minimum value of the plasma safety factor.) Fast-ion diagnostics that are sensitive to the co-passing population exhibit the largest reduction relative to classical predictions. The increased fast-ion transport in discharges with strong AE activity accounts for the previously observed reduction in global confinement with increasing qmin; however, not all high qmin discharges show appreciable degradation. Two relatively simple empirical quantities provide convenient monitors of these effects: (1) an 'AE amplitude' signal based on interferometer measurements and (2) the ratio of the neutron rate to a zero-dimensional classical prediction. © 2014 IOP Publishing Ltd.

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.

Diffusion of test-ions in a flux-coil generated, collisional, field-reversed configuration is measured via time-resolved tomographic reconstruction of Ar+ optical emission in the predominantly nitrogen plasma. Azimuthal test ion diffusion across magnetic field lines is found to be classical during the stable period of the discharge. Test ion radial confinement is enhanced by a radial electric field, reducing the observed outward radial transport rate below predictions based solely on classical cross-field diffusion rates. Test ion diffusion is ∼500m2s-1 during the stable period of the discharge. The electric field inferred from plasma potential measurements and from equilibrium calculations is consistent with the observed reduction in argon transport. © 2014 IOP Publishing Ltd.

The CQL3D Fokker-Planck code[1] has been upgraded to include physics of finite-orbit-width (FOW) guiding-center orbits[2,3], as compared with the previous zero-orbit-width (ZOW) model, and a recent first-order orbit calculation[2]. The Fast Ion Diagnostic FIDA[4,5] signal resulting from neutral beam (NBI) and high harmonic fast wave (HHFW) RF power injected into the NSTX spherical tokamak can now be modeled quite accurately, using ion distributions from the CQL3D-Hybrid-FOW code, a rapidly executing variant that includes FOW+gyro-orbit losses to the plasma edge, FOW effects on NBI injection and HHFW diffusion, but does not include neoclassical radial diffusion. Accurate simulation of prompt fast ion (FI) losses is a key feature of the marked modeling improvement relative to previous ZOW results. By comparing NBI-only and NBI+HHFW shots, independent confirmation of the usual 35% edge loss of HHFW in NSTX is obtained. Further, HHFW prompt losses from the plasma core are shown to be 3X as large (>25%) as the NBI-only case. The modulated NBI and time-dependent background plasma variations and charge exchange losses of fast ions are accounted for, and the temporal neutron variation is in approximate agreement with NSTX observations. © 2014 AIP Publishing LLC.