Search

Fast ions in fusion plasmas often leave characteristic signatures in the plasma neutron emission. Measurements of this emission are subject to the phase-space sensitivity of the diagnostic, which can be mapped using weight functions. In this paper, we present orbit weight functions for the TOFOR and NE213 neutron diagnostics at the Joint European Torus, mapping their phase-space sensitivity in 3D orbit space. Both diagnostics are highly sensitive to fast ions that spend a relatively large fraction of their orbit transit times inside the viewing cone of the diagnostic. For most neutron energies, TOFOR is found to be relatively sensitive to potato orbits and heavily localized counter-passing orbits, as well as trapped orbits whose “banana tips” are inside the viewing cone of TOFOR. For the NE213-scintillator, the sensitivity is found to be relatively high for stagnation orbits.

Radially resolved hydrogenic isotope fraction measurement capabilities have been developed for DIII-D using the main-ion charge exchange recombination (MICER) spectroscopy system in preparation for mixed hydrogen and deuterium experiments. Constraints on the hydrogenic ion temperatures and velocities based on measurements of the impurity ion properties are required to accurately fit the spectrum. Corrections for cross sectional distortions, spatial smearing due to the halo, and a neoclassical offset between the impurity and hydrogenic toroidal rotation are applied to the constraints prior to fitting the MICER spectrum. Extensive atomic physics calculations have been performed using the FIDASIM code, which has recently been improved to allow simulations using mixtures of hydrogenic species. These results demonstrate that for the same plasma parameters, the Dα emission is 20%–30% brighter than Hα due to differences in rate coefficients associated with the different ion thermal velocities for the same temperature and therefore must be taken into consideration when calculating absolute densities. However, despite these differences, the absolute error when estimating the hydrogen isotope fraction [nH/(nH + nD)] by using the Hα radiance fraction [LHα/(LHα + LDα)] is typically less than 5% due to the way the fraction is formed, making the radiance fraction a reasonably accurate estimate of the isotope fraction for most cases.

We demonstrate 2D reconstructions of the fast-ion velocity distribution from two-view fast-ion D-alpha (FIDA) measurements at the EAST tokamak. By expressing the distribution in a basis relying on the fast-ion slowing-down process in fusion plasmas, the smoothness and velocity-space resolution of reconstructions are improved. We reconstruct distributions of fast ions born from simultaneous co- and counter-current neutral beam injection and detect the expected distinct change in fast-ion birth pitch when comparing discharges utilizing different neutral beam injectors. For purely co-current injection, we find a good agreement between TRANSP-predicted and reconstructed fast-ion densities, pressures and current densities for energies above 20 keV. We furthermore illustrate the improvement of the reconstructed high-energy range (> 40 keV) of the distribution by combining FIDA with neutron emission spectroscopy measurements with the compact single-plate EJ301 scintillator.

FIDASIM is a code that models signals produced by charge-exchange reactions between neutrals and ions (both fast and thermal) in magnetically confined plasmas. With the ion distribution function as input, the code predicts the efflux to a neutral particle analyzer diagnostic and the photon radiance of Balmer-alpha light to a fast-ion Dα diagnostic, in addition to many other related quantities. A new, parallelized version of the Monte Carlo code FIDASIM has been developed in Fortran90 that is substantially faster than the original interactive data language version. Modified algorithms include more accurate treatments of the time dependent collisional-radiative equations that describe neutral energy levels, of the cloud of ‘halo’ neutrals that surround the injected neutral beam, and of finite Larmor radius effects. Enhanced physics capabilities include modelling ‘passive’ signals from cold edge neutrals, the ability to treat general three-dimensional magnetic confinement configurations, and calculations of diagnostic-specific weight functions that enable tomographic reconstructions of the fast-ion distribution function. Neutral beam attenuation, beam emission, and fast-ion birth profiles are also modelled. The new algorithms have been successfully validated against experimental data and new features have been tested through benchmarks between two independently developed versions of the code.

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

A recently developed imaging neutral particle analyzer (INPA) on the DIII-D tokamak [X.D. Du et al., Nucl. Fusion 58, 082006 (2018)] enables fast ion velocity-space tomography of high fidelity at the interrogated phase space. To accomplish this, the spatial and energy depending fast (E < 80keV ) neutral flux towards the INPA stripping foils is calculated with FIDASIM and a newly developed code INPASIM simulates the INPA instrumental response to this neutral flux. Included in INPASIM is the neutral-foil interaction, the Larmor orbit tracing between the foil and the phosphor, the phosphor response to the incident ion flux as well as camera focusing. Benefiting from heavy, localized velocity-space weights and excellent signal to noise, computed tomography using the Ridge regression method is able to successfully reconstruct fine-scale velocity-space structures produced by multiple neutral beams separated by as small as ~ 3 keV in tests. Applying the inversion method to a sawtooth crash event reveals a significant profile flattening of confined passing particles across q = 1 flux surface, as well as a redistribution of fast ions into the trapped orbits at the plasma edge close to the last closed flux surface.

All the information about a plasma species is encoded in its distribution function. While it would be helpful to measure the distribution function directly, it is only possible to measure its moments. If the form of the distribution function is not known a priori, it can be difficult to interpret diagnostic signals. This is particularly true in fast-ion physics, where diagnostics that nominally view the same thing, the fast-ion distribution function, give seemingly discordant measurements. The process of going from a fast-ion distribution to a measurement and the reverse process of going from a set of measurements to a fast-ion distribution are the main topics of this thesis.Chapters 2-3 concern the modeling of fast-ion diagnostics. Here we derive functions that translate the information about a fast ion into measurable quantities, i.e. forward models. This is done for three diagnostics: the neutral particle analyzer (NPA), fast ion D-α (FIDA) spectroscopy, and neutron scintillators. Chapter 3 discusses the development of FIDASIM, the practical implementation of the forward models.Chapter 4 deals with diagnostic velocity-space weight functions, an ansatz which is used to aid in the interpretation of experimental measurements and as an approximate forward model of the diagnostic. From the forward models discussed in Chapter 2, we derive weight functions in a full 6D generalized coordinate system, from which we also derive the velocity-space weight functions. Using an action-angle formulation, orbit-space weight functions, which can be used to exactly represent a diagnostic's forward model in a linear form, are derived.Chapters 5-6 detail how to use weight functions to infer the fast-ion distribution function from experimental measurements. Orbit weight functions, in particular, facilitate the inference of the entire distribution function, using any fast-ion diagnostic that views the plasma. Benchmarks with synthetic data and a reconstruction of a classical distribution from experimental measurements, show that systematic errors and intrinsic biases in the inference methods are the main impediments to accurately inferring the fast-ion distribution function. However, experimental studies of the redistribution of fast ions by sawtooth crashes at ASDEX Upgrade demonstrate that the effects of systematic error and biases become less important when only considering relative changes in the distribution function.

A novel imaging neutral particle analyzer (INPA) which provides energy-resolved radial profiles of confined fast ions on the DIII-D tokamak is discussed. The INPA measures charge-exchanged energetic neutrals by viewing an "active" neutral beam through a 1D pinhole camera with a rear collimating slit that defines the neutral particle collection sightlines. The incident neutrals are ionized by 10 nm thick carbon stripping foils and the local tokamak magnetic field acts as a magnetic spectrometer to disperse ions onto a phosphor scintillator. A fast (160 Hz) CCD camera provides 2D images of the escaping neutrals mapped to energy and radial position in the plasma. The INPA typically probes passing orbits with an energy resolution of ≈7.5 keV (E= 20−80 keV) and a spatial resolution that ranges from 4 cm half width at half max (HWHM) in the core to 3 cm at the plasma edge. The INPA clearly resolves fast ion transport in localized regions of phase space due to individual sawteeth and a replenishing before each event. Extension to proton and triton DD fusion product measurements in high-performance DIII-D plasmas is analyzed and simulations show peak signals which are 10−6 lower than that from neutral beam ions for the same configuration. Possible modifications to increase fusion product signals are discussed along with upgrades to improve the overall diagnostic performance.

A tangential Fast-Ion D Alpha (FIDA) diagnostic is applied to the Large Helical Device (LHD) in order to observe energetic distribution of toroidal circulating energetic particles which are produced by tangential Negative Neutral Beams (NNB). A perpendicular Positive NB (PNB) is used as the diagnostic probe beam of the tangential-FIDA diagnostic in this observation geometry. In order to assess the appropriateness of the tangential-FIDA diagnostic, the experimental result was compared with a Silicon-diode-based Fast Neutral Analyzer (Si-FNA) which was installed on the same line of sight. As a result of the comparison, the tangential-FIDA and the Si-FNA experimental data obtained good linearity in the energy region from 60 keV to 180 keV. In addition, an enhanced FIDASIM was applied for analyzing the FIDA on the three-dimensional magnetic configuration fusion device.

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-space volume measured by the diagnostic, ∇ ⋅ Γ ∼ . 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 Alfvén 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 ∇ ⋅ Γ ∼ .

Author(s): Salewski, M; Geiger, B; Jacobsen, AS; Hansen, PC; Heidbrink, WW; Korsholm, SB; Leipold, F; Madsen, J; Moseev, D; Nielsen, SK; Nocente, M; Odstrcil, T; Rasmussen, J; Stagner, L; Stejner, M; Weiland, M | Abstract: 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.

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

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

Recent completion of the thirty two channel main-ion (deuterium) charge exchange recombination spectroscopy (CER) diagnostic on DIII-D [J.L. Luxon, Nucl. Fusion 42 (2002) 614] enables detailed comparisons between impurity and main-ion temperature, density, and toroidal rotation. Sixteen sightlines cover the core of the plasma and another sixteen are densely packed towards the edge, providing high resolution measurements of the pedestal and steep gradient edge region of H-mode plasmas. The complexities of the Dα spectrum require fitting with a comprehensive model, as well as using iterative collisional radiative modeling to determine the underlying thermal deuterium ion properties. Large differences in the structure and magnitude of impurity (C6+) and main-ion (D+) toroidal rotation profiles are seen in the H-mode pedestal. Additionally the D+ temperature can be half the value of the C6+ temperature at the separatrix and shows more of a pedestal structure. Typically only the impurity properties are measured and the main-ion properties are either assumed to be the same, or inferred using neoclassical models, which require validation in the steep gradient region. These measured differences have implications for transport model validation, intrinsic rotation studies, pedestal stability, and the boundary conditions for scrape off layer and plasma material interactions studies.

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 ...

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

Experiments on the DIII-D tokamak have identified how multiple simultaneous Alfven 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 Alfven 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.

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.

Analysis of neutron and fast-ion Dαdata from the DIII-D tokamak shows that Alfvén eigenmode activity degrades fast-ion confinement in many high βN, high qmin, steady-state scenario discharges. (βNis the normalized plasma pressure and qminis 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 qmindischarges 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.

Recent completion of a thirty two channel main-ion (deuterium) charge exchange recombination spectroscopy (CER) diagnostic on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] enables detailed comparisons between impurity and main-ion temperature, density, and toroidal rotation. In a H-mode DIII-D discharge, these new measurement capabilities are used to provide the deuterium density profile, demonstrate the importance of profile alignment between Thomson scattering and CER diagnostics, and aid in determining the electron temperature at the separatrix. Sixteen sightlines cover the core of the plasma and another sixteen are densely packed towards the plasma edge, providing high resolution measurements across the pedestal and steep gradient region in H-mode plasmas. Extracting useful physical quantities such as deuterium density is challenging due to multiple photoemission processes. These challenges are overcome using a detailed fitting model and by forward modeling the photoemission using the FIDASIM code, which implements a comprehensive collisional radiative model.

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.

The first measurements of fast-ion D-alpha (FIDA) radiation have been acquired on C-2U, Tri Alpha Energy’s advanced, beam-driven field-reversed configuration (FRC). These measurements are also forward modeled by FIDASIM. This is the first measurement and simulation of FIDA carried out on an FRC topology. FIDA measurements are made of Doppler-shifted Balmer-alpha light from neutralized fast ions using a bandpass filter and photomultiplier tube. One adjustable line-of-sight measured signals at eight locations and eight times during the FRC lifetime over 26 discharges. Filtered signals include only the highest energy ions (>6 keV) and share some salient features with the FIDASIM result. Highly Doppler-shifted beam radiation is also measured with a high-speed camera and is spatially well-correlated with FIDASIM.

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

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.

Author(s): Jacobsen, AS; Stagner, L; Salewski, M; Geiger, B; Heidbrink, WW; Korsholm, SB; Leipold, F; Nielsen, SK; Rasmussen, J; Stejner, M; Thomsen, H; Weiland, M | Abstract: 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.