Fast-ion Velocity Distribution Research Articles

A linear parameters study of ion cyclotron emission using drift ring beam distribution

Ion Cyclotron Emission (ICE) holds great potential as a diagnostic tool for fast ions in fusion devices. The theory of Magnetoacoustic Cyclotron Instability (MCI), as an emission mechanism for ICE, states that MCI is driven by a velocity distribution of fast ions that approximates to a drift ring beam. In this study, the influence of key parameters (velocity spread of the fast ions, number density ratio, and instability propagation angle) on the linear MCI is systematically investigated using the linear kinetic dispersion relation solver BO (Xie 2019 Comput. Phys. Commun. 244 343). The computational spectra region considered extends up to 40 times the ion cyclotron frequency. By examining the influence of these key parameters on MCI, several novel results have been obtained. In the case of MCI excited by super-Alfvénic fast ions (where the unique perpendicular speed of fast ion is greater than the perpendicular phase velocity of the fast Alfvén waves), the parallel velocity spread significantly affects the bandwidth of harmonics and the continuous spectrum, while the perpendicular velocity spread has a decisive effect on the MCI growth rate. As the velocity spread increases, the linear relationship between the MCI growth rate and the square root of the number density ratio transitions to a linear relationship between the MCI growth rate and the number density ratio. This finding provides a linear perspective explanation for the observed linear relation between fast ion number density and ICE intensity in JET. Furthermore, high harmonics are more sensitive to changes in propagation angle than low harmonics because a decrease in the propagation angle alters the dispersion relation of the fast Alfvén wave. In the case of MCI excited by sub-Alfvénic fast ions (where the unique perpendicular speed of fast ion is less than the perpendicular phase velocity of the fast Alfvén waves), a significant growth rate increase occurs at high harmonics due to the transition of sub-Alfvénic fast ions to super-Alfvénic fast ions. Similarly, for MCI excited by greatly sub-Alfvénic fast ions (where the unique perpendicular speed of fast ion is far less than the perpendicular phase velocity of the fast Alfvén waves), the growth rate at high harmonics also experiences a drastic increase compared to the low harmonic, thereby expanding the parameter range of the velocity spread.

Investigation of gyrotron-based collective Thomson scattering for fast ion diagnostics in a compact high-field tokamak

As a promising method for fast ion diagnostics, collective Thomson scattering (CTS) can measure the one-dimensional velocity distribution of fast ions with high spatial and temporal resolution. The feasibility of diagnosing fast ions in a compact high-field tokamak by CTS was studied in this work, and the results showed that a wide range of probing frequencies could be applied. A high-frequency case and a low-frequency case were mainly considered for fast ion diagnostics in a compact high-field tokamak. The use of a high probing frequency could effectively avoid the refraction effect of the beams, while the application of a low probing frequency allows greater flexibility in the selection of scattering angle which may help to improve the spatial resolution. Based on typical plasma conditions (B 0 = 12.2 T, n e0 = 4.3 × 1020 m−3, T e0 = 22.2 keV, T i0 = 19.8 keV) for a compact high-field tokamak, a 220 GHz CTS diagnostic that utilizes a small scattering angle of θ = 30° and a 160 GHz CTS diagnostic that utilizes an orthogonal geometry were proposed. Further study showed that the high-frequency case could operate in a wider range of plasma conditions and provide more information on fast ions while the low-frequency case could achieve higher spatial resolution of the poloidal direction.

Tomography of fast ion distribution function under neutral beam injection and ion cyclotron resonance heating on EAST

In magnetic confinement fusion devices, velocity-space tomography of fast-ion velocity distribution function is crucial for investigating fast-ion distribution and transport. In the neutral beam injection (NBI) and ion cyclotron resonance heating (ICRF) synergistic heating experiments in Experimental Advanced Superconducting Tokamak (EAST), high-energy particles with energy exceeding the particle energy in NBI are observed. Simulations of synergistic effect on fast-ion velocity distribution function given by TRANSP also show the existence of particles with energy higher than the particle energy in NBI. To investigate the behaviors of fast ion distribution and calculate the velocity distribution functions under different heating conditions, the first-order Tikhonov regularization tomographic inversion method with higher inversion accuracy is introduced by comparing various regularization techniques. The limitations of the dual-view fast-ion D<sub>α</sub> (FIDA) diagnostic measurements in velocity space are addressed by incorporating prior information such as null measurement and the known peaks and effectively mitigate the occurrence of artifacts. This method is first employed in the case of NBI heating. The NBI peak is successfully reconstructed at the expected location in velocity space, which shows significant improvement in the inversion results. In order to further validate the synergistic effect of NBI-ICRF heating and study the mechanism of fast ion distribution under synergistic heating, the combination of FIDA and neutron emission spectrometer (NES) is applied to the first-order Tikhonov regularization tomographic inversion method for enhancing the coverage of velocity space, through which the issue of artifacts in the inversion results is significantly improved, and thus the precision of the obtained fast-ion velocity distribution functions is enhanced. Based on the benefit described above, the method of combining NES diagnosis and FIDA diagnosis is used to obtain fast-ion velocity distribution functions in the NBI and ICRF synergistic heating discharge. The synergistic heating effect is manifested in the fast-ion velocity distribution. The availability of this inversion method in reconstructing fast-ion velocity distribution functions during high-performance operation of NBI-ICRF synergistic heating in the EAST experiment is confirmed. In the next-step EAST research, high performance discharge will demand more efficiency NBI and ICRF synergistic heating, the present work builds the stage for investigating the underlying mechanism of synergistic heating and the intricate behaviors associated with fast ion distribution and transport.

Simulations of neutral beam injection and ion cyclotron resonance heating synergy in high power EAST scenarios.

The EAST plasmas heated with deuterium neutral beam injection and ion cyclotron resonance heating (ICRH) have been simulated by the TRANSP code. The analysis has been conducted using the full wave solver TORIC5, the radio frequency (RF)-kick operator, and NUBEAM to model the RF heating effects on fast ion velocity distribution. In this work, we present several simulated results compared with experiments for high power EAST scenarios, indicating that the interactions between ICRH and fast ions can significantly accelerate fast ions, which are confirmed by the increased neutron yield and broadened neutron emission spectrum measurements.

Collective Thomson scattering diagnostic with in situ calibration system for velocity space analysis in large helical device.

A collective Thomson scattering (CTS) diagnostic with a ±3 GHz band around a 77 GHz gyrotron probe beam was developed to measure the velocity distribution of bulk and fast ions in high-temperature plasmas. We propose a new in situ calibration method for a CTS diagnostic system combined with a raytracing code. The method is applied in two situations for electron cyclotron emission in plasmas and in a CTS diagnostic with a modulated probe beam. Experimental results highlight the importance of refraction correction in probe and receive beams. The CTS spectrum is measured with the in situ calibrated CTS receiver and responds to fast ions originating from a tangential neutral beam with an energy of 170 keV and from a perpendicular beam with an energy of 60 keV, both in the large helical device. From a velocity space analysis model, the results elucidate the measured anisotropic CTS spectrum caused by fast ions. The calibration methods and analyses demonstrated here are essential for CTS, millimeter-wave diagnostics, and electron cyclotron heating required under fusion reactor conditions.

Development of a 105 GHz fast ion collective Thomson scattering diagnostic on HL-2A tokamak

Collective Thomson Scattering (CTS) diagnostic technique has great potential in measuring velocity distribution of fast ions in magnetically confined fusion devices. Here we present design and development of a 105 GHz fast ion CTS system on HL-2A tokamak. The gyrotron with high power transmission/antenna is used to generate a probe beam. To better focus the scattering beam and effectively avoid the stray contamination, a W-band Cassegrain antenna is utilized to receive the scattering beam from the central chord. The scattering signal is estimated at 10–30 eV and the frequency broadening is less than 2 GHz for typical HL-2A plasmas. To pick out the weak signals, a multi-channel receiver system with working frequency of 103–107 GHz is developed. The steerable direction of probe beam enables that the scattering volume can move from core to edge, with which the spatial resolution range varies from 70 mm at low field side to 260 mm at high field side.

Identification of slow-wave ion cyclotron emission on JT-60U

Ion cyclotron emissions (ICEs) are generally considered to be emissions of fast waves driven by velocity-space instabilities due to fast ions. However, on JT-60U, measured properties of ICEs observed at frequencies lower than the bulk ion cyclotron frequency (L-ICEs) do not match the fast-wave dispersion relation, indicating the possibility of L-ICEs being slow-wave emissions. In this paper, we show that L-ICE observation on JT-60U can be explained in terms of a slow-wave emission driven by fast ions, i.e. a slow-wave ICE. To investigate whether the slow wave can be driven by fast ions, its linear growth rate has been calculated in a typical discharge using a wave dispersion code. This wave dispersion code is capable of performing calculations with an arbitrary spatially-localized velocity distribution. For the growth rate calculation, we have directly used fast ion velocity distributions evaluated by an orbit following Monte-Carlo simulation. It is found that negative-ion-source neutral beam (N-NB) injected fast ions can destabilize the slow wave. Its frequency and wavenumber at high linear growth rates are close to experimental observations of L-ICE. In addition, observed L-ICE frequencies agree reasonably well with frequencies based on the slow-wave dispersion relation at measured toroidal wavenumbers in several discharges. Moreover, the observed frequencies also agree with the Doppler-shifted cyclotron resonance frequencies for the N-NB injected ion. Therefore, L-ICE in JT-60U is identified as a slow-wave ICE driven by the N-NB injected fast ions and distinguished from other ICEs through a measurement of its frequency and wavenumber.

Determining 1D fast-ion velocity distribution functions from ion cyclotron emission data using deep neural networks

The relationship between simulated ion cyclotron emission (ICE) signals s and the corresponding 1D velocity distribution function fv⊥ of the fast ions triggering the ICE is modeled using a two-layer deep neural network. The network architecture (number of layers and number of computational nodes in each layer) and hyperparameters (learning rate and number of learning iterations) are fine-tuned using a bottom-up approach based on cross-validation. Thus, the optimal mapping gs;θ of the neural network in terms of the number of nodes, the number of layers, and the values of the hyperparameters, where θ is the learned model parameters, is determined by comparing many different configurations of the network on the same training and test set and choosing the best one based on its average test error. The training and test sets are generated by computing random ICE velocity distribution functions f and their corresponding ICE signals s by modeling the relationship as the linear matrix equation Wf = s. The simulated ICE signals are modeled as edge ICE signals at LHD. The network predictions for f based on ICE signals s are on many simulated ICE signal examples closer to the true velocity distribution function than that obtained by 0th-order Tikhonov regularization, although there might be qualitative differences in which features one technique is better at predicting than the other. Additionally, the network computations are much faster. Adapted versions of the network can be applied to future experimental ICE data to infer fast-ion velocity distribution functions.

Fast-ion velocity-space tomography using slowing-down regularization in EAST plasmas with co- and counter-current neutral beam injection

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.

Tomography of the positive-pitch fast-ion velocity distribution in DIII-D plasmas with Alfvén eigenmodes and neoclassical tearing modes

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.

Collective Thomson Scattering Diagnostic for Wendelstein 7-X at 175 GHz

The Collective Thomson Scattering (CTS) diagnostic measures the scattering spectrum of incident radiation off collective fluctuations in plasmas. In Wendelstein 7-X (W7-X) the diagnostic uses a 140 GHz heating gyrotron as a source of the probing radiation. At this frequency, the CTS spectra are heavily affected by the electron cyclotron emission, and the microwave beam propagation is restricted at typical W7-X plasma parameters. The diagnostic was successfully commissioned in the last experimental campaign and demonstrated ion temperature measurements. However, the signal-to-noise ratio was too low for measuring other quantities such as the fast-ion velocity distribution function or the fuel ion ratio. Currently, the W7-X CTS diagnostic is undergoing an upgrade to a frequency of 175 GHz. This will increase the sensitivity of the diagnostic, since the noise due to electron cyclotron emission will be reduced, and it will relax the constraints on microwave beam propagation in W7-X. Here we present the salient features of the upgraded CTS system and discuss its prospects for both thermal-ion and fast-ion measurements.

Collective Thomson scattering with 77, 154, and 300 GHz sources in LHD

Collective Thomson scattering (CTS) is one of attractive diagnostics for measuring locally and directly the fuel temperature and the velocity distribution of fast ions in fusion plasmas. A mega-watt class source of millimeter or sub-millimeter waves is required to detect a weak scattered radiation superimposed on background radiation owing to electron cyclotron emissions (ECEs) from plasmas. Based on electron cyclotron resonance heating (ECRH) system with the frequencies of 77 GHz and 154 GHz in the Large Helical Device (LHD), the CTS diagnostic system has been developed to measure bulk ion temperatures from a few keV to ∼10 keV and fast ions originated from 180 keV-neutral beam injection in the LHD. The measured CTS spectra and their time evolutions are analyzed with the electrostatic scattering theory. The bulk ion temperatures obtained from CTS spectra increase with the neutral beam injections and decrease with the heating terminated. The velocity map of simulated fast ions explains that the bumps on tail of measured CTS spectra are caused by the co- and counter- fast ions. A new prescription for anisotropic velocity distribution function is proposed. As for 154 GHz bands, the CTS spectrum broadenings for D and H plasmas are distinguished reasonably at the same temperature, and its ion temperatures are comparable to those of the charge exchange recombination spectroscopy. As reactor-relevant diagnostics, a 300 GHz gyrotron and a corresponding receiver system have been implemented in LHD to access high density plasmas with low background ECEs. The recent progress for CTS diagnostics and their spectrum analysis with the probe frequencies of 77 GHz, 154 GHz, and 300 GHz in the LHD experiments is described.

Optimization of the Collective Thomson scattering diagnostic for future operation

Collective Thomson scattering (CTS) is a microwave diagnostic allowing measurements of a number of plasma parameters such as the bulk ion temperature, the plasma composition, drift velocities and fast ion velocity distribution function. A CTS system has been successfully installed and commissioned on the Wendelstein 7-X (W7-X) stellarator. The measured spectra are analyzed by the means of the CTS forward model eCTS and the Minerva scientific framework enabling the use of Bayesian inference of relevant plasma parameters. Here we discuss the options for further optimization of the CTS diagnostic and focus on two topics of importance for the inference of bulk ion temperature values from CTS spectra: influence of impurities on the CTS spectra and the width of the notch filters that are employed to protect the receiver from high-power radiation. In addition to that we discuss the possibility of effective charge measurements by CTS. We explore the existence of an optimal notch filter width.

Thermo-structural analyses of the in-vessel components of the ITER collective Thomson scattering system

The Collective Thomson Scattering (CTS) diagnostic system will be used at ITER to provide spatial and temporal measurements of fast ion velocity distributions. The diagnostic is based on the CTS principle, where a microwave beam scatters off electrons in the plasma. The scattered radiation is then collected and measured, providing information about the fast ions. The system components are either considered in-vessel or ex-vessel depending on their location in the port plug. In this work, thermo-structural analyses were performed on four in-vessel components using the finite-element method (FEM) and the commercial software ANSYS Mechanical v18.0. The analyses indicate that active cooling will be required for most of the analysed components. The thermal stresses will be used to perform the structural assessment of these components based on the RCC-MR code.

Bi-Maxwellian, slowing-down, and ring velocity distributions of fast ions in magnetized plasmas

We discuss analytical fast-ion velocity distribution functions which are useful for basic plasma modelling as illustrated for the tokamak ITER. The Maxwellian is by far the most widespread model for ions and electrons in tokamaks and stellarators. The bi-Maxwellian and the drifting (bi-)Maxwellian are extensions allowing for anisotropy and bulk plasma flow, respectively. For example, fast ions generated by wave heating in the ion cyclotron range of frequencies are often described by bi-Maxwellians or so-called tail temperatures. The ring distribution can serve as a basic building block for arbitrary distributions or as a bump-on-tail in stability studies. The isotropic slowing-down distribution is a good model for fusion α-particles. The anisotropic slowing-down distribution occurs for anisotropic particle sources as is typical for neutral beam injection. We physically motivate these distribution functions and present analytical models in various coordinate systems commonly used by theorists and experimentalists. We further calculate 1D projections of the distribution functions onto a diagnostic line-of-sight to gain insight into measurements relying on the Doppler shift.

Velocity-space tomography using prior information at MAST.

Velocity-space tomography provides a way of diagnosing fast ions in a fusion plasma by combining measurements from multiple instruments. We use a toroidally viewing and a vertically viewing fast-ion D-alpha diagnostic installed on the mega-amp spherical tokamak (before the upgrade) to perform velocity-space tomography of the fast-ion distribution function. To make up for the scarce amount of data, prior information is included in the inversions. We impose a non-negativity constraint, suppress the distribution in the velocity-space region associated with null-measurements, and encode the belief that the distribution function does not extend to energies significantly higher than those expected neoclassically. This allows us to study the fast-ion velocity distributions and the derived fast-ion densities before and after a sawtooth crash.

Numerical and semi-analytical treatments of neutral beam current drive in DEMO-FNS

Neutral Beam Current Drive (NBCD) is considered as a highly attractive mechanism for a steady state regime in such contemporary projects as a tokamak based Fusion Neutron Source (FNS) or a DEMO type thermonuclear reactor. In this report numerical calculations of NBCD with a Monte Carlo code NUBEAM are complemented by a semi-analytical treatment of fast ion velocity distribution function. Spectral distributions of fast ions injected with neutral beams to FNS plasma are obtained for DEMO-FNS and a Spherical Tokamak Neutron Source FNS-ST. A detailed comparison of NUBEAM and semi-analytical approaches is presented on the basis of ASTRA transport code provided equilibrium data for different plasma regimes. The applicability of the semi-analytical approach is discussed.

Characterisation of a BC501A compact neutron spectrometer for fusion research.

The compact neutron spectrometer used at the ASDEX Upgrade tokamak is characterised to obtain its response matrix. This paper describes the characterisation procedure and the derived response matrix, based on a campaign at the PTB ion accelerator facility (PIAF) and on the subsequent time-of-flight (TOF) analysis of neutrons from a field with a broad energy distribution. The response of mono-energetic neutrons generated at the PIAF is used as reference for the TOF analysis. The detector's response functions for spectrum deconvolution are obtained by Gaussian broadening of the simulated responses to fit the experimental ones, using a maximum-entropy ansatz. In this way, the response functions are smooth enough to ensure a reliable unfolding of pulse height spectra into neutron emission spectra, which provide information on the fast ion velocity distribution in neutral beam heated tokamak plasmas.

Inversion methods for fast-ion velocity-space tomography in fusion plasmas

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 zeroth- and first-order Tikhonov regularization. The inversion methods are applied to fast-ion 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.

Benchmark and combined velocity-space tomography of fast-ion D-alpha spectroscopy and collective Thomson scattering measurements

We demonstrate the combination of fast-ion D-alpha spectroscopy (FIDA) and collective Thomson scattering (CTS) measurements to determine a common best estimate of the fast-ion velocity distribution function by velocity-space tomography. We further demonstrate a benchmark of FIDA tomography and CTS measurements without using a numerical simulation as common reference. Combined velocity-space tomographies from FIDA and CTS measurements confirm that sawtooth crashes reduce the fast-ion phase-space densities in the plasma center and affect ions with pitches close to one more strongly than those with pitches close to zero.