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DOE OSTI2023

Alfvén eigenmode stability in a JET afterglow deuterium plasma and projections to deuterium–tritium plasmas

Abstract The performance of fusion devices relies strongly on the good confinement of energetic particles (EPs). Therefore, the investigation of EP transport by magnetohydrodynamic instabilities is one of the key aspects in the development of plasma scenarios. Alfvénic instabilities in particular can lead to significant losses of alpha particles that are essential for plasma self-heating. A so-called afterglow scheme has been developed to study the destabilization of Alfvén eigenmodes (AEs) by alpha particles and associated EP transport in the JET tokamak. In this work, the linear stability of AEs is discussed for the partial afterglow phase in a JET deuterium plasma discharge and for the full afterglow phase in a projected deuterium–tritium (DT) plasma. Thanks to recent upgrades in the tokamak transport code TRANSP, one can account for the contributions of different EP species to mode stability. Analysis of deuterium plasmas shows that AE growth rates are extremely sensitive to the energy and distribution of fast ions. An increase in fast ion energy can lead to more unstable AEs. In the afterglow phase of projected DT plasmas, it is EPs that mostly drive the AEs. However, the drive by alpha particles is comparable to that by beam ions and their contribution to the net growth rate might be hard to separate. According to the discussed projections, the destabilization of AEs might be ineffective because the background plasma damping significantly exceeds the EP drive. In this case, the development of an alternative plasma scenario that allows us to overcome such damping would be required in future experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Optimization of the N ∥ Upshift in the DIII-D high field side lower hybrid current drive experiment

High field side lower hybrid current drive (LHCD) is one potential candidate for efficient non-inductive current drive in tokamak power plants, and the first test of this technology will occur on the DIII-D tokamak during the 2024 campaign. Previous LFS launch experiments operated in the multi-pass regime and relied on scrape-off layer interactions to close the spectral gap. In the DIII-D experiment, single-pass damping is achievable via an upshift in the parallel refractive index N ∥ caused by mode converting twice (slow → fast → slow). This mode conversion affects the ray trajectories and can lead to enhanced N ∥ upshift depending on where mode conversion occurs. Compared to multi-pass absorption experiments, the optimization of launched N ∥ and plasma parameters can be counter-intuitive: increased density may increase efficiency and smaller N ∥,launch tend to damp closer to the separatrix. A hard x-ray camera installed to measure the bremsstrahlung (50–250 keV) radiation from LHCD-generated fast electrons is capable of verifying the trends reporting in this paper through comparison to the ray-tracing/Fokker–Planck codes GENRAY/CQL3D.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

RF antenna helicity dependent particle heating in a helicon source

Experiments have demonstrated that ion phenomena, such as the lower hybrid resonance, play an important role in helicon source operation. Damping of the slow branch of the bounded whistler wave at the edge of a helicon source (i.e. the Trivelpiece-Gould mode) has been correlated with the creation of energetic electrons, heating of ions at the plasma edge, and anisotropic ion heating. Here we present ion velocity distribution function measurements, electron density and temperature measurements, and magnetic fluctuation measurements on both sides of an m = |1| helical antenna in a helicon source as a function of the driving frequency, magnetic field strength, and magnetic field orientation relative to the antenna helicity. Significant electron and ion heating (up to two times larger) occurs on the side of the antenna consistent with the launch of the m = +1 mode. The electron and ion heating occurs within one electron skin depth of the plasma edge, where slow wave damping is expected. The source parameters for enhanced particle heating are also consistent with lower hybrid resonance effects, which can only occur for Trivelpiece-Gould wave excitation.

wave modes↗

DOE OSTI2025

Modeling of the high column density systems in the Lyman-Alpha forest

The Lyman-α forests observed in the spectra of high-redshift quasars can be used as a tracer of the cosmological matter density to study baryon acoustic oscillations (BAO) and the Alcock-Paczynski effect. Extraction of cosmological information from these studies requires modeling of the forest correlations. While the models depend most importantly on the bias parameters of the intergalactic medium (IGM), they also depend on the numbers and characteristics of high-column-density systems (HCDs) ranging from Lyman-limit systems with column densities log N HI /1cm -2 > 17 to damped Lyman-α systems (DLAs) with log N HI /1cm -2 > 20.2. These HCDs introduce broad damped absorption characteristic of a Voigt profile. Consequently they imprint a component on the power spectrum whose modes in the radial direction are suppressed, leading to a scale-dependent bias. Using mock data sets of known HCD content, we test a model that describes this effect in terms of the distribution of column densities of HCDs, the Fourier transforms of their Voigt profiles and the bias of the halos containing the HCDs. Our results show that this physically well-motivated model describes the effects of HCDs with an accuracy comparable to that of the ad-hoc models used in published forest analyses. We also discuss the problems of applying the model to real data, where the HCD content and their bias is uncertain.

Lyman alpha forest↗

DOE OSTI2026

Photogalvanic Effects in Surface States of Topological Insulators under Perpendicular Magnetic Fields

We present a theoretical study of the nonlinear magneto-optical shift conductivity in the surface states of the prototypical topological insulator Bi$_2$Se$_3$ under a perpendicular quantizing magnetic field. By describing the electronic states as Landau levels and using a perturbative approach, we derive the microscopic expression for the shift conductivity $\sigma^{(2);\alpha\beta\gamma}(-\omega,\omega)$, where $\alpha,\beta,\gamma=\pm$ stand for the circular polarization of light and $\omega$ is the light frequency; the spectra are further decomposed into contributions from the interband and intraband optical transitions, for which the selection rules are identified. Considering that the system possesses $C_3$ point group of symmetry, the nonzero components of the conductivity tensor are $\sigma^{(2);-++}=[\sigma^{(2);+--}]^\ast$. Therefore, a pure circularly polarized light generates zero shift current. In the clean limit, the conductivities are nonzero only for discrete photon energies because of the discrete Landau levels and energy conservation, and they become Lorentzian lineshapes with the inclusion of damping, which relaxes the condition of energy conservation. The dependence of the spectra on the damping parameters, the magnetic fields, and the chemical potentials is investigated in detail. Our results reveal that the shift current is highly tunable by the chemical potential and the magnetic field. Furthermore, these results underscore the potential of topological insulators for tunable, strong nonlinear magneto-optical applications.

Landau level↗

DOE OSTI2020

Investigation of mode activity in NBI-heated experiments of Wendelstein 7-X

The 2018 operation phase (OP 1.2b) of the stellarator Wendelstein 7-X (W7-X) included, for the first time, neutral beam injection (NBI) to heat the plasma. Since the injection geometry at W7-X is not parallel, this generates both passing and trapped fast particles. During longer phases of NBI injection, with the primary purpose to study the heating efficiency of this system, Alfvén eigenmodes (AEs) were observed by a number of diagnostics, including the phase contrast imaging (PCI) system, the magnetic pick-up coils (Mirnov coils), and the soft x-ray multi-camera tomography system (XMCTS). Alfvén eigenmodes are of great interest for future fusion reactors as it has been shown that the resonant interaction of fast ions with self-excited AEs can lead to enhanced transport of fast ions and potentially to energy losses. This is especially true for so-called gap-modes, Alfvén eigenmodes with frequencies in gaps of the continuous spectrum, since they lack continuum damping. These modes are commonly known to be excited by fast ions, but other destabilizing mechanisms, e.g. the electron-pressure gradient are also possible. In this article we present a first analysis of the experimentally observed frequencies from the theoretical side. The calculation of shear Alfvén wave continua for selected cases and the assignment of observed frequencies to the gaps of the continuous spectra are presented. Using the ideal-MHD code CKA (Könies A. 2007 10th IAEA TM on Energetic Particles in Magnetic Confinement System), we find gap modes that match the experimental measurements in terms of the observed frequencies. We emphasize the crucial roles played by the coupling of sound and Alfvén waves as well as of the Doppler shift arising as a consequence of the radial electric field in W7-X. We employ the perturbative gyrokinetic code CKA-EUTERPE (Feh´er 2013 Simulation of the interaction between Alfv´en waves and fast particles), using a slowing-down distribution function for the fast ions as calculated by the Monte-Carlo particle following code ASCOT (Hirvijoki et al 2014 Comput. Phys. Commun. 185 1310–21) to assess the fast-ion drive. Here we find that the fast-ion drive is insufficient to overcome the background-plasma damping. The fact that unstable modes were observed experimentally may point to problems with the modelling or indicate the existence of other destabilizing mechanisms, e.g. associated with the electron-pressure gradient (Windisch et al 2017 Plasma Phys. Control. Fusion 59 105002) that sensitively depend on the profiles of the background plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Experimental studies of plasma-antenna coupling with the JET Alfvén Eigenmode Active Diagnostic

Here, this paper presents a dedicated study of plasma-antenna (PA) coupling with the Alfvén Eigenmode Active Diagnostic (AEAD) in JET. Stable AEs and their resonant frequencies f, damping rates γ < 0, and toroidal mode numbers n are measured for various PA separations and limiter versus X-point magnetic configurations. Two stable AEs are observed to be resonantly excited at distinct low and high frequencies in limiter plasmas. The values of f and n do not vary with PA separation. However, |γ| increases with PA separation for the low-f, but not high-f, mode, yet this may be due to slightly different edge conditions. The high-f AE is detected throughout the transition from limiter to X-point configuration, though its damping rate increases; the low-f mode, on the other hand, becomes unidentifiable. The linear, resistive MHD code CASTOR is used to simulate the frequency scan of an AEAD-like external antenna. For the limiter pulses, the high-f mode is determined to be an n = 0 GAE, while the low-f mode is likely an n = 2 TAE. During the transition from limiter to X-point configuration, CASTOR indicates that n = 1 and 2 EAEs are excited in the edge gap. These results extend previous experimental studies in JET and Alcator C-Mod; validate the computational work performed by Dvornova et al; and provide guidance for the optimization of PA coupling in upcoming JET energetic particle experiments, for which the AEAD will aim to identify the contribution of alpha particles to AE drive during the DT campaign.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Study of the Alfven eigenmodes stability in CFQS plasma using a Landau closure model

The aim of this study is to analyze the stability of the Alfven eigenmodes (AE) in the Chinese First Quasi-axisymmetric Stellarator (CFQS). The AE stability is calculated using the code FAR3d that solves the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moment for the energetic particles (EP) species including the effect of the helical couplings and acoustic modes. The Landau damping and resonant destabilization effects are added in the model by a given closure relation. The simulation results indicate the destabilization of n = 1 to 4 AEs by EP during the slowing down process, particularly n = 1 and n = 2 toroidal AEs (TAE), n = 3 elliptical AE (EAE) and n = 4 non circular AE (NAE). If the resonance is caused by EPs with an energy above 17 keV (weakly thermalized EP), n = 2 EAEs and n = 3 NAEs are unstable. On the other hand, EPs with an energy below 17 keV (late thermalization stage) lead to the destabilization of n = 3 and n = 4 TAEs. The simulations for an off-axis NBI injection indicate the further destabilization of n = 2 to 4 AEs although the growth rate of the n = 1 AEs slightly decreases, so no clear optimization trend with respect to the NBI deposition region is identified. In addition, n = 2, 4 helical AE (HAE) are unstable above an EP β threshold. Also, if the thermal β of the simulation increases (higher thermal plasma density) the AE stability of the plasma improves. Overall, the simulations including the effect of the finite Larmor radius and electron-ion Landau damping show the stabilization of the n = 1 to 4 EAE/NAEs as well as a decrease of the growth rate and frequency of the n = 1 to 4 BAE/TAEs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Modification of favorable average curvature effect by changing parallel sound wave behavior in tokamak plasmas

Abstract The favorable average curvature effect, also known as the GGJ effect (Glasser et al 1975 Phys. Fluids 18 875), is intrinsically associated with parallel sound wave propagation in a tokamak plasma. This work investigates how the GGJ effect is modified by changing the parallel sound wave behavior. Two physics models beyond the standard single fluid theory, i.e. an anisotropic thermal transport model and a parallel sound wave damping model, are employed to change parallel sound waves in a toroidal plasma, and the consequence on the GGJ effect is demonstrated for two important classes of problems, i.e. the resistive plasma response to the applied resonant magnetic perturbation and the stability of the tearing mode. Toroidal modeling reveals that the GGJ effect is significantly altered by both of the aforementioned physics effects. Compared to the thermal transport physics, which completely removes the GGJ effect, the sound wave damping effect only offers partial mitigation. The differences between these two models are further illustrated in terms of the radial structure of the shielding current and the eigenfunction of the tearing instability. In particular, a fundamental reason for complete suppression of the GGJ effect by the thermal transport is identified as an extra toroidal coupling of the poloidal harmonics.

Physics↗

DOE OSTI2021

Chirping ion cyclotron emission (ICE) on NSTX-U

In this work, we report on the discovery on NSTX-U of a qualitatively new type of non-thermal emission from plasmas in the ion-cyclotron frequency range (ICE). This new type of ICE is weakly damped, γ damp /ω ICE ≈ 0.14%, low order eigenmodes, excited by a fast ion population radially located near an internal transport barrier. The ICE appears as repetitive bursts with durations of ≈1 ms, and the bursts exhibit frequency chirps upwards and/or downwards with maximum δf/f ≈ 1%. We refer to this chirping ICE as ch-ICE. The bursts are longer than the typical ICE bursts of ≈100 μs reported previously for NSTX and NSTX-U, for simplicity, NSTX(-U). The chirping resembles that seen in modeling of weakly unstable fast particle driven instabilities (cf, Berk et al 1997 Phys. Lett. A 234 213). These data also provide some preliminary indications of non-linear coupling between the ch-ICE harmonics. Despite extensive experimental and theoretical studies of ICE, theoretical understanding of ICE remains qualitative at best. The detailed experimental observations of ICE from NSTX(-U) find a wide variation in the ICE characteristics. The new observations of ch-ICE presented here, combined with the characteristics of ICE on NSTX(-U) previously reported (Fredrickson et al 2019 Phys. Plasmas 26 032111), could guide the development of more complete theoretical models of ICE.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Scoping study of lower hybrid current drive for CFETR

The paper assesses the applicability of lower hybrid current drive (LHCD) for two potential operating scenarios for the China Fusion Engineering Test Reactor (CFETR): the “hybrid” scenario in which some of the plasma current is sustained by the Ohmic transformer, and the fully non-inductive “steady state” scenario. Here, the πScope workflow engine was used to set up a large number of ray tracing/Fokker-Planck simulations (> 10 4 ) with parametric scans in the antenna poloidal position and launched parallel refractive index (n || ) for both the hybrid and steady state scenarios. Modeling predicts efficient off-axis current drive (1.3 MA for 20 MW launched power) with a peak near ρ of 0.6-0.65 for waves launched from the high field side (HFS). Waves launched from the low field side (LFS) damp at larger radius (ρ > 0.73) with similar efficiency to HFS launch. Stability analysis of the CFETR scenarios favors current drive profiles peaked near the mid-radius, suggesting that HFS launch is preferable due to the current drive location. The effect of wave scattering from density blobs in the edge/scrape-off-layer region was assessed through rotation of the perpendicular wavenumber at the ray origin. Simulations show that this effect can be quite large both in efficiency and damping location, however by adjusting the launched n|| much of the unperturbed performance can be recovered.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Suppression of toroidal Alfvén eigenmodes by the electron cyclotron current drive in KSTAR plasmas

Advanced operation scenarios such as high poloidal beta ( β P ) or high q min are promising concepts to achieve the steady-state high-performance fusion plasmas. However, those scenarios are prone to substantial Alfvénic activity, causing fast-ion transport and losses. Recent experiments with the advanced operation scenario on KSTAR tokamak have shown that the electron cyclotron current drive (ECCD) is able to mitigate and suppress the beam-ion driven toroidal Alfvén eigenmodes (TAEs) for over several tens of global energy confinement time. Co-current directional intermediate off-axis ECCD lowers the central safety factor slightly and tilts the central q -profile shape so that the continuum damping in the core region increases. Besides, the rise of central plasma pressure and increased thermal-ion Landau damping contribute to TAE stabilization. While the TAEs are suppressed, neutron emission rate and total stored energy increase by approximately 45% and 25%, respectively. Fast-ion transport estimated by TRANSP calculations approaches the classical level during the TAE suppression period. Substantial reduction in fast-ion loss and neutron deficit is also observed. Subsequently, enhancement of fast-ion confinement by suppressing the TAEs leads to an increase of non-inductive current fraction and will benefit the sustainment of the long-pulse high-performance discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Analysis of the ECH effect on EPM/AE stability in Heliotron J plasma using a Landau closure model

The aim of the present study is to analyze the effect of the electron cyclotron heating (ECH) on the linear stability of Alfvén eigenmodes (AEs) and energetic particle modes (EPMs) triggered by energetic ions in Heliotron J plasma. The analysis is performed using the FAR3d code that solves a reduced MHD model to describe the thermal plasma coupled with a gyrofluid model for the energetic particle (EP) species. The simulations reproduce the AE/EPM stability trends observed in the experiments as the electron temperature (T e ) increases, modifying the thermal plasma β, EP β and EP slowing-down time. Particularly, the $n/m = 1/2$ EPM and $2/4$ Global AE are stabilized in the low-bumpiness (LB) configuration due to an enhancement of the continuum, finite Larmor radius and e-i Landau damping effects as the thermal β increases. On the other hand, a larger ECH injection power cannot stabilize the AE/EPM in medium-bumpiness and high-bumpiness (HB) configurations because the damping effects are weaker compared to the LB case, unable to balance the further destabilization induced by an enhanced EP resonance as the EP slowing-down time and EP β increases with T e .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Resonance in radio frequency sheath admittance and enhanced impurity emission near the ion cyclotron frequency

Ion cyclotron resonance heating (ICRH) is of considerable interest among all auxiliary heating techniques, because it transfers power directly to ions, targets the high-density core, and involves the cheapest radio-frequency (RF) components. During ICRH operation, RF sheaths form on the ICRH antenna itself, nearby hardware, and far-field surfaces. These sheaths are associated with large hot-spot formation and impurity emissions. This work presents high-resolution numerical modelling of RF sheaths in nuclear fusion scenarios using hPIC2, a Debye-scale particle-in-cell code. The modelling reveals a new RF sheath phenomenon which occurs when the RF is resonant with a species ion cyclotron frequency or harmonic in an oblique magnetic field. This resonance of the RF sheath causes modifications of the energy-angle distributions of the ions impacting on the walls, with consequent increase in wall impurity emission. Due to the 1/ R scaling of the magnetic field in a tokamak, such cases are possible on divertor or vacuum chamber surfaces, depending on the geometry of the tokamak and the RF heating scenario. A simple physics interpretation using a driven damped harmonic oscillator is proposed, where the ion sheath transit time plays the role of damping the RF sheath admittance. Critically, the resonance leads to increased ion heat flux at the wall as well as increased physical sputtering, despite a lack of increase in RF rectified sheath potential.

ICRH antenna↗

DOE OSTI2025

Design workflow of a symmetric traveling wave antenna for fast ion production on DD tokamaks

Initial computational plasma physics scoping and a finite element method antenna modeling design workflow for a symmetric center-fed high-field side high harmonic fast wave traveling wave array (TWA) antenna are reported here. The TWA is designed to generate a test population of fast deuterium ions in an existing D–D tokamak by heating neutral beam deuterium ions, accelerating them from 80 keV to several hundred keV. The resulting fast particles are tailored to mimic key reactor energetic particle parameters with regards to exciting Alfven eigenmode instabilities, allowing for a D–D tokamak like DIII-D or ASDEX-U to replicate reactor-relevant conditions experimentally. Initial scenario scoping for high single-pass absorption as well as good preferential fast ion damping relative to electron damping was completed using the ray-tracing/Fokker–Planck codes GENRAY and CQL3D. Python RF network analysis packages were used to create a custom TWA optimization tool to inform a COMSOL flat antenna design, and Petra-M was used to study cold plasma effects. The TWA produced by this workflow has several novel features when compared to previous TWA studies, including symmetric center feeding, and passive end straps for image current cancellation for reduced impurity production. We show here that the antenna design workflow can readily produce TWA antennas optimized for reflection coefficient, image current cancellation, and launched power spectrum shape; and that a population of fast ions can be generated in the correct region of parameter space, warranting future more detailed studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Alfvén eigenmode-driven zonal modes saturate and heat thermal ions by cross-scale interactions

In scenarios where a sustained energetic particle source strongly drives toroidal Alfvén eigenmodes (TAE), and phase-space transport is insufficient to saturate TAE, this novel theory of TAE-zonal mode (ZM)-turbulence—self-regulated by cross-scale interactions (including collisionless ZF damping) – merits consideration. Zonal modes are driven by Reynolds and Maxwell stresses, without the onset of modulational instability. TAE evolution in the presence of ZMs conserves energy and closes the system feedback loop. The saturated zonal shears can be sufficient to suppress ambient drift-ion temperature gradient (ITG) turbulence, achieving an enhanced core confinement regime. The saturated state is regulated by linear and turbulent zonal flow drag. This regulation leads to bursty TAE spectral oscillations, which overshoot while approaching saturation. Heating by both collisional and collisionless ZM damping deposits alpha particle energy into the thermal plasma, achieving effective alpha channeling. This theory offers a mechanism for EP-induced transport barrier formation, and predicts a novel thermal ion heating mechanism.

ITB↗

DOE OSTI2022

Aeroservoelastic Stability of a Floating Wind Turbine

The problem of negative damping undermines the aeroservoelastic stability of floating offshore wind turbines. The negative damping problem is most prevalent around rated wind speed, where the sensitivity of thrust to wind speed is the largest. This paper investigates the implementation of peak shaving, a controller feature that limits the rated thrust by pitching the blades before rated wind speed is reached. Two controller designs are investigated: a de-tuned controller and a nacelle-feedback controller. A time-domain metric is defined, inspired by Lyapunov theory, in order to compute and assess the stability of floating offshore wind turbines. The model of the International Energy Agency 15-MW reference wind turbine mounted on the University of Maine VolturnUS-S floater is simulated in HAWC2 with the National Renewable Energy Laboratory reference open-source controller. Peak shaving is applied to the two controller designs and stability is assessed. According to the chosen metric, peak shaving does not improve the stability of the system. This is due to the trade-off between loads and error tracking: although the loads and displacements in the fore-aft direction of the turbine are reduced, the rotor-speed tracking is poorer, which increases the shaft torsion fatigue load.

17 WIND ENERGY↗

DOE OSTI2021

Recovery of coincident frequency domain multiplexed detector pulses using sequential deconvolution

Multiplexing of radiation detector signals into a single channel significantly reduces the need for a large number of digitizer channels, which reduces the cost and the power consumption of a data acquisition system. We previously demonstrated frequency domain multiplexing by convolution using a prototype system that multiplexed two EJ-309 organic scintillators signals into a single channel. Each detector pulse was converted to a damped sinusoid which was then combined into a single channel. The combined signal was digitized and the original detector signal was recovered from the damped sinusoid by deconvolution. In this paper, we demonstrate the recovery of multiple detector signals that arrive during the same digitized record via a new sequential deconvolution method. Here, when two detectors produce signals in the same digitized record and their pulses do not overlap in time, we found that the charge, arrival time, and particle type can be estimated fairly precisely for the first pulse, but the second pulse exhibits substantial degradation in the precision of the estimated charge and arrival time. When the pulses overlap in time, we demonstrate both theoretically and experimentally that the part of the first pulse that does not overlap with the second can be recovered accurately, so the arrival time and amplitude of the first pulse can be estimated fairly precisely, but not the charge or particle type. None of these quantities can be estimated precisely for the second pulse when the two pulses overlap.

47 OTHER INSTRUMENTATION↗