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.

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 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.

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 ⌈.

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.

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.

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.

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.

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.