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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Dependence of ion-cyclotron range of frequencies instabilities on species mix and fast-ion distribution: I. Stability

Ion cyclotron emission (ICE) driven by fast ions has the potential to be a reactor relevant diagnostic of confined and escaping fast ions; moreover, controlled experiments in magnetic fusion devices can shed light on similar magnetospheric instabilities below and above the ion cyclotron frequency f ci . Dedicated DIII-D experiments studied instabilities below f ci and at cyclotron harmonics l f ci by injecting thirteen different neutral beam populations into plasmas with different thermal compositions of H, D, and 3He at five different values of toroidal field. High-frequency magnetic loops diagnose mode properties. Each beam type is individually injected for an approximate slowing-down time (~100 ms), resulting in a database of 2529 conditions that are analyzed in frequency bands corresponding to ICE harmonics and < f ci global Alfvén eigenmodes. The sub-cyclotron modes are more unstable at low field and in plasmas with large H concentration. For D injection, first harmonic ICE at f cD is more unstable in hydrogen plasmas but, for H injection, the converse is true (ICE at f cH is more unstable in D), suggesting that thermal same-species ions damp fundamental ICE. ICE stability also depends upon the pitch-angle anisotropy gradient and upon the ‘bump-on-tail’ gradient ∂f/∂v. Although the frequency of unstable ICE in these plasmas always occurs near the central cyclotron frequency, the precise value also depends on the Alfvén speed and beam direction, consistent with the idea that instability occurs for modes that simultaneously satisfy ω ≃ 2πlf ci , the magnetosonic dispersion relation, and the Doppler-shifted resonance condition.

electromagnetic ion cyclotron instabilities↗
DOE OSTI2025

Dependence of ion-cyclotron range of frequencies instabilities on species mix and fast-ion distribution: III. Novel sub-cyclotron modes

Dedicated DIII-D experiments studied instabilities above and below the ion cyclotron frequency by injecting thirteen different neutral beam populations into L-mode plasmas with different thermal compositions of H, D, and 3 He at five different values of toroidal field. Two companion papers describe the results of these experiments in detail. This paper focuses on data and analysis of two instabilities that occur at ${\sim}0.6$ of the deuterium and hydrogen cyclotron frequencies $f_\mathrm {cD}$ and $f_\mathrm {cH}$ in mixed hydrogen and deuterium plasmas. The modes below $f_\mathrm {cD}$ are often driven unstable by deuterium beams but are rarely destabilized by hydrogen beams. The modes below $f_\mathrm {CD}$ are reported here for the first time in a fusion plasma. These $\mathrm{sub-}f_\mathrm {cH}$ modes are only driven by deuterium beams but, unlike the $\mathrm{sub-}f_\mathrm {cD}$ modes, they are only unstable in plasmas with deuterium concentrations that are ${\lesssim}20\%$; they also have a smaller amplitude than the sub-deuterium modes. Addition of fully-ionized 3 He to the plasma has little effect on the sub-cyclotron deuterium modes but is stabilizing for the sub-cyclotron hydrogen modes. The modes are excited in the core and have toroidal mode numbers around 20. These trends are compared with calculations of the growth rate in a simplified model. The theory successfully predicts global Alfvén eigenmode instability with frequencies and mode numbers close to experimental values, the stronger amplitude of the sub-deuterium modes, and the species-mix dependence of the sub-hydrogen modes. Increased damping associated with the ion-ion hybrid, cutoff, and crossover frequencies plausibly accounts for the stabilization of the $\mathrm{sub-}f_\mathrm {cH}$ modes when 3 He is puffed. However, the relative stability of $\mathrm{sub-}f_\mathrm {cH}$ modes during hydrogen injection remains unexplained.

electromagnetic ion cyclotron instability↗
DOE OSTI2022

Application of simulations and theory of sub-cyclotron frequency modes to DIII-D

Theoretical and numerical study of Alfvén eigenmodes (AEs) in the sub-cyclotron frequency range explains the observed frequency scaling with beam parameters in experiments across different devices. Global Alfvén (GAEs) and compressional Alfvén eigenmodes (CAEs) are frequently excited during neutral beam injection (NBI) in the National Spherical Torus Experiment (NSTX/NSTX-U), as well as other beam-heated devices such as MAST and DIII-D. These modes are driven unstable through the Doppler shifted cyclotron resonance with the NBI ions and can be excited in ITER due to super-Alfvénic velocities and anisotropy of the fast ion distribution. Numerical models and theory for sub-cyclotron frequency modes, previously developed and used to study the excitation of GAEs/CAEs in the NSTX(-U), have been successfully applied to explain the DIII-D observations. Simulations for DIII-D demonstrate that the modes with ω/ω ci ≈ 0.6, previously mis-identified as compressional Alfvén eigenmodes, have shear polarization and should be identified as the GAEs. Simulation results match the observed frequencies and estimated toroidal mode numbers in DIII-D experiments. Good agreement is found between scaling of the experimentally observed GAE frequencies with NBI parameters for NSTX, NSTX-U and DIII-D and scaling predicted by the theory and simulations. Here, the DIII-D simulation results also demonstrate that GAEs can be excited for larger aspect-ratio devices and smaller (sub- Alfvénic) beam injection velocities, therefore they can be unstable in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Stability of beta-induced Alfvén eigenmodes (BAE) in DIII-D

Although the stability of ellipticity, toroidal and reversed-shear Alfvén eigenmodes (EAE, TAE, RSAE) are relatively well understood, less is known about the stability of lower-frequency modes such as the beta-induced Alfvén eigenmode (BAE) but, because they are often unstable in present devices and are implicated in fast-ion transport, understanding their stability is vital. BAE stability is studied in primarily weak or reversed shear DIII-D plasmas with sub-Alfvénic deuterium beams. Modes are classified based on electron cyclotron emission, beam emission spectroscopy, magnetics, and interferometer data. The study is limited to the initial two seconds of the discharge, where the evolving q profile provides an effective scan of the dependence of stability upon q. In a dedicated experiment, BAEs are unstable at times in the discharge when the minimum of the safety factor q min is close to a rational number. The observed mode frequencies are usually close to analytic estimates of the BAE accumulation point and the eigenfunction peaks in the vicinity of q min . Unstable BAEs usually occur in bursts that chirp rapidly in frequency. To isolate the importance of thermal and beam gradients in driving the modes, the beam and electron cyclotron heating power is altered for 50–100 ms durations in reproducible discharges. As expected from the resonance condition, BAEs depend sensitively on the beam power and injection geometry. Modes only persist for ~25 ms because the anisotropic beam population only interacts strongly with the modes over a relatively narrow range of q. Lastly, a database of over 1000 beam-heated discharges shows that BAEs are more likely to be unstable when the poloidal beta exceeds 0.5.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Simultaneous measurements of unstable and stable Alfvén eigenmodes in JET

Here, we report the novel experimental observation of both unstable and stable toroidicity-induced Alfvén eigenmodes (TAEs) measured simultaneously in a JET tokamak plasma. The three-ion-heating scheme (D-DNBI-3He) is employed to accelerate deuterons to MeV energies, thereby destabilizing TAEs with toroidal mode numbers n = 3–5, each decreasing in mode amplitude. At the same time, the Alfvén eigenmode active diagnostic resonantly excites a stable n = 6 TAE with total normalized damping rate –γ/ω 0 ≈ 1%–4%. Hybrid kinetic-MHD modeling with codes NOVA-K and MEGA both find eigenmodes with similar frequencies, mode structures, and radial locations as in experiment. NOVA-K demonstrates good agreement with the n = 3, 4, and 6 TAEs, matching the damping rate of the n = 6 mode within uncertainties and identifying radiative damping as the dominant contribution. Improved agreement is found with MEGA for all modes: the unstable n = 3–5 and stable n = 2, 6 modes, with the latter two stabilized by higher intrinsic damping and lower fast ion drive, respectively. While some discrepancies remain to be resolved, this unique validation effort gives us confidence in TAE stability predictions for future fusion devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Measurements of the polarization of several instabilities in the DIII-D tokamak

Recently, a method to infer the polarization of modes with frequencies much less than the ion cyclotron frequency was published [X.D. Du et al., Phys. Rev. Lett. 132 (2024) 215101]. The method uses measurements of electron temperature and density fluctuations δTₑ and δnₑ at the same spatial position to infer the local ratio of “acoustic polarization,” |δϕ ∥ |/(|δϕ ∥ |+|δψ|), where δϕ ∥ is the effective parallel potential and δψ is related to the parallel magnetic vector potential A ∥ . This paper summarizes key formulas, with emphasis on their range of validity, and elaborates on the workflow required to infer the acoustic polarization from experimental data. The drift-acoustic polarization of ellipticity-induced, toroidicity-induced, and reversed shear Alfvén eigenmodes is nearly zero, as expected for modes with predominately shear-Alfvénic polarization. The polarization of beta-induced Alfvén eigenmodes contains an acoustic component that increases with poloidal wave number. “Low frequency modes,” (instabilities that appear transiently when the minimum of the safety factor qₘᵢₙ passes through rational values) have large and highly variable acoustic polarization. In both experiment and simulation, fishbones have non-zero acoustic polarization that increases as the mode chirps down in frequency.

Alfven eigenmode↗
DOE OSTI2022

Fast Particle-Wave Interactions and Alfvén Eigenmodes in JET Tokamak Plasmas

This document serves as the closeout report of DOE Grant Award No. DE-FG02-99ER54563 with project period 1 April 2015 through 31 March 2020. The project comprised the international collaboration between MIT and EU scientists on the JET facility to improve our understanding of the physics of energetic particle-wave interactions by measuring the damping rates of stable Alfvén Eigenmodes (AEs) and unstable energetic particle driven modes. More specifically, this project involved the continued participation of MIT, the Culham Centre for Fusion Energy, the Swiss Plasma Center, and theorists from various European laboratories and from UC Irvine. Past contributions from the University of São Paulo are gratefully acknowledged. The Alfvén Eigenmode Active Diagnostic (AEAD) on JET discharges was successfully upgraded in this period and has extracted physically useful information, in primarily deuterium plasma discharges. It is expected that such experiments would be continued during the DT campaign in CY 2021 to assess the damping rates of similar modes in the presence of alpha particles, a product of fusing burning plasma. Only JET would carry out such experiments in the near term in the world. It is important to note that this collaboration was continued under DOE Grant Award No. DE-SC0014264 from 1 April 2020 through the present. In this grant period, the AEAD was upgraded with a set of individual amplifiers for each of a set of six antennas in two toroidally opposite locations. These new amplifiers allowed targeted selection of the antennas’ toroidal spectrum for AEs of interest with toroidal mode number | n | ≤ 20. The resonant detection and measurement of the damping rates of AEs was obtained from magnetic probes that could be compared with theory and simulations. This is a key topic of investigation for ITER and all other next-step fusion experiments, where such modes will interact with energetic particles produced by fusion reactions (alpha particles), Neutral Beam Injection (NBI) and Ion Cyclotron Resonance Heating (ICRH). The majority of the observations during this period were of Toroidal Alfvén Eigenmodes (TAEs) as these are most commonly observed on JET; a number of measurements were made during dedicated TAE experiments. However, a new set of lower frequency band filters were procured with the goal of studying Geodesic Acoustic Modes (GAMs), Beta (Acoustic) AEs (BAE/BAAEs), and Reverse Shear AEs (RSAEs), also predicted by theory. Commissioning and optimizations were successfully completed in this period, and the diagnostic has been in operation during the more recent JET campaigns. Initial results have been obtained in dedicated TAE experiments and successfully compared to drift-kinetic theory. A wide range of theoretical studies have been undertaken in support of the upcoming JET campaigns experiments. To supplement the ongoing use of ideal MHD codes, such as MISHKA during the studies of TAEs, gyrokinetic simulations of low frequency AEs were performed in collaboration with UC Irvine. The Gyrokinetic Toroidal Code (GTC) was used to determine the structure, frequencies and stability of AEs in JET plasmas. Thus, a solid scientific foundation has been laid for future DT campaigns in JET in the 2021 operation period when the damping rates of relevant modes in the presence of alpha particles could be assessed.

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 OSTI2024

Three-wave coupling observed between a shear Alfvén wave and a kink-unstable magnetic flux rope

Results from a laboratory experiment are presented in which, for the first time, a shear Alfvén wave is launched using an antenna in a current-carrying plasma column that is tailored to be either stable or unstable to the kink oscillation. As the plasma is driven kink unstable, the frequency power spectrum of the Alfvén wave evolves from a single peak to a peak with multiple sidebands separated by integer multiples of the kink frequency. The main sidebands (one on either side of the launched wave peak in the power spectrum) are analyzed using azimuthal wavenumber matching, perpendicular and parallel wavenumber decomposition, and bispectral time series analysis. The dispersion relation and three-wave matching conditions are satisfied, given each sideband is a propagating Alfvén wave that results from the interaction of the pump Alfvén wave and the co-propagating component of a half-wavelength, standing kink mode. The interaction is shown to generate smaller perpendicular wavelength Alfvén waves that drive energy transport to scales that will approach the dissipation scale of k⊥ρs=1, with k⊥ being the perpendicular wavenumber and ρs being the ion gyroradius at the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Planar Collisionless Shock Simulations with the Semi-implicit Particle-in-cell Model FLEKS

This study investigates the applicability of the semi-implicit particle-in-cell code FLexible Exascale Kinetic Simulator (FLEKS) to heliospheric shock simulations. We examine one- and two-dimensional local planar shock simulations, initialized using MHD states with upstream conditions representative of plasmas in the hypersonic, β ∼ 1 regime, for both quasi-perpendicular and quasi-parallel configurations. The refined algorithm in FLEKS proves robust, enabling accurate shock simulations with a grid resolution on the order of the electron inertial length d e . Our simulations successfully capture key shock features, including shock structures (foot, ramp, overshoot, and undershoot), upstream and downstream waves (fast magnetosonic, whistler, Alfvén ion-cyclotron, and mirror modes), and non-Maxwellian particle distributions. Crucially, we find that at least two spatial dimensions are critical for accurately reproducing downstream-wave physics in quasi-perpendicular shocks and capturing the complex dynamics of quasi-parallel shocks, including surface rippling, shocklets, short, large-amplitude magnetic structures, magnetic reconnection, and jets. Furthermore, our parameter studies demonstrate the impact of mass ratio and grid resolution on shock physics. This work provides valuable guidance for selecting appropriate physical and numerical parameters for shock simulations using a semi-implicit PIC method, paving the way for incorporating kinetic shock processes into large-scale collisionless plasma simulations with the MHD-AEPIC model.

plasma astrophysics↗
DOE OSTI2021

Alfven eigenmodes and fast ion transport in negative triangularity DIII-D plasmas

The first energetic particle experiments in negative triangularity tokamak plasmas have been carried out on DIII-D. Alfvén eigenmode (AE) activity and associated fast ion transport comparable to that in positive triangularity is observed during the current ramp portion of all plasmas with early beam heating indicating negative triangularity does not confer a special advantage with respect to AE induced transport. In these discharges, a range of mode activity driven by the sub-Alfvénic (Vbeam/VA < 0.5) 80 kV neutral beams is found including beta induced Alfvén acoustic eigenmodes, beta induced Alfvén eigenmodes, reversed shear Alfvén eigenmodes (RSAEs) and toroidicity induced Alfvén eigenmodes (TAEs). Mode intermittency and possibly chirping appears to be more common than comparable positive triangularity and/or oval discharges but overall, the unstable spectra and mode amplitudes observed on magnetics, CO2 interferometry, and electron cyclotron emission in a set of matched positive and negative triangularity cases at moderate beam power is similar. Large levels of Alfvén eigenmode induced fast ion transport are found in both positive and negative triangularity with up to 70% central fast ion pressure deficits relative to classical predictions early during the current ramp phase for discharges with 3 MW injected 80 kV neutral beam power. The deficit in both cases is reduced toward zero as the current penetrates and eventually reaches classical levels during current flattop with qmin ≈ 1. Fast ion transport in negative triangularity plasmas measured using a beam modulation technique show very similar levels to those measured in oval plasmas over the range of tested beam powers (Pbeam ≈ 2–7 MW). This similarity is found despite quite different unstable spectra in the highest beam power case where a mixture of coherent and quasi-coherent modes in the TAE frequency range are observed in negative triangularity and a spectrum of more typical narrowband TAEs and RSAEs is observed for the oval plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Microturbulence-mediated route for energetic ion transport and Alfvénic mode amplitude oscillations in tokamaks

The new regimes of Alfvén eigenmode (AE) induced fast ion transport in tokamak plasmas are reported, in which microturbulence plays the role of a mediator of fast ion relaxation. Coulomb collisional scattering alone leads to small AE amplitudes and does not reproduce the steady state regimes observed in experiments. We show that in nonlinear regimes the sufficiently large effective pitch angle scattering due to microturbulence can lead to steady state AE amplitude evolution. This indicates a new route for fast ion losses, which is beyond the scenarios described in “Energetic ion transport by microturbulence is insignificant in tokamaks”. As a result, microturbulence can significantly increase the amplitude of AEs in predictive simulations of burning plasma experiments such as ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Alpha particle driven Alfvénic instabilities in ITER post-disruption plasmas

Fusion-born alpha particles in ITER disruption simulations are investigated as a possible drive of Alfvénic instabilities. The ability of these waves to expel runaway electron (RE) seed particles is explored in the pursuit of a passive, inherent RE mitigation scenario. The spatiotemporal evolution of the alpha particle distribution during the disruption is calculated using the linearized Fokker–Planck solver CODION coupled to a fluid disruption simulation. These simulations are done in the limit of no alpha particle transport during the thermal quench, which can be seen as a most pessimistic situation where there is also no RE seed transport. Under these assumptions, the radial anisotropy of the resulting alpha population provides free energy to drive Alfvénic modes during the quench phase of the disruption. We use the linear gyrokinetic magnetohydrodynamic code LIGKA to calculate the Alfvén spectrum and find that the equilibrium is capable of sustaining a wide range of modes. The self-consistent evolution of the mode amplitudes and the alpha distribution is calculated utilizing the wave-particle interaction tool HAGIS. Intermediate mode number (n = 7–15, 22–26) toroidal Alfvén eigenmodes are shown to saturate at an amplitude of up to δB/B ≈ 0.1% in the spatial regimes crucial for RE seed formation. We find that the mode amplitudes are predicted to be sufficiently large to permit the possibility of significant radial transport of REs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Characteristics of grassy ELMs and their impact on the divertor heat flux width

We report BOUT++ turbulence simulations are conducted for a 60 s steady-state long pulse high β p EAST grassy ELM discharge. BOUT++ linear simulations show that the unstable mode spectrum covers a range of toroidal mode numbers from low-n (n = 10–15) peeling–ballooning modes (P–B) to high-n (n = 40–80) drift-Alfvén instabilities. Nonlinear simulations show that the ELM crash is triggered by low-n peeling modes and fluctuation is generated at the peak pressure gradient position and radially spread outward into the scrape-off-layer, even though the drift-Alfvén instabilities dominate the linear growth phase. However, drift-Alfvén turbulence delays the onset of the grassy ELM and enhances the energy loss with the fluctuation extending to pedestal top region. Simulations further show that if the peeling drive is removed, the fluctuation amplitude drops by an order of magnitude and the ELM crashes disappear. The divertor heat flux width is ~2 times larger than the estimates based on the HD model and the Eich's ITPA multi-tokamak scaling (or empirical Eich scaling) due to the strong radial turbulence transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Long range frequency chirping of Alfvén eigenmodes

In this work, a theoretical framework has been developed for an NBI scenario to model the hard non-linear evolution of global Alfvén eigenmodes (GAEs) where the adiabatic motion of phase-space structures (holes and clumps), associated with frequency chirping, occurs in generalized phase-space of slowing down energetic particles. The radial profile of the GAE is expanded using finite elements, which allows an update of the mode structure as the mode frequency chirps. Constants of motion are introduced to track the dynamics of energetic particles during frequency chirping by implementing proper action-angle variables and canonical transformations which reduce the dynamics essentially to 1D. Consequently, we specify whether the particles are drifting inward/outward as the frequency deviates from the initial MHD eigenfrequency. Using the principle of least action, we have derived the non-linear equation describing the evolution of the radial profile by varying the total Lagrangian of the system with respect to the weights of the finite elements. For the choice of parameters in this work, it is shown that the peak of the radial profile is shifted and also broadens due to frequency chirping. The time rate of frequency change is also calculated using the energy balance and we show that the adiabatic condition remains valid once it is satisfied. This model clearly illustrates the theoretical treatment to study the long-range adiabatic frequency sweeping events observed for Alfvén gap modes in real experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Beam modulation and bump-on-tail effects on Alfvén eigenmode stability in DIII-D

Beam modulation effects on Alfvén eigenmode stability have been investigated in a recent DIII-D experiment and show that variations in neutral beam modulation period can have an impact on the beam driven Alfvén eigenmode spectrum and resultant fast ion transport despite similar time-averaged input power. The experiment was carried out during the current ramp phase of L-mode discharges heated with sub-Alfvénic 50–80 kV deuterium neutral beams that drive a variety of Alfvén eigenmodes unstable. The modulation period of two interleaved beams with different tangency radii was varied from shot to shot in order to modify the relative time dependent mix of the beam pitch angle distribution as well as the persistence of a bump-on-tail feature near the injection energy (a feature confirmed by imaging neutral particle analyzer measurements). As the beam modulation period is varied from 7 ms to 30 ms on/off (typical full energy slowing down time of τ slow ≈ 50 ms at mid-radius), toroidicity-induced Alfvén eigenmodes (TAEs) located in the outer periphery of the plasma become intermittent and coincident with the more tangential beam. Core mode activity changes from reversed shear Alfvén eigenmodes (RSAEs) to a mix of RSAE and beta-induced Alfvén eigenmodes. Discharges with 30 ms on/off period do not have a persistent bump-on-tail feature, have the lowest average mode amplitude and least fast ion transport. Furthermore, detailed analysis of an individual TAE using TRANSP kick modeling (Monte Carlo evolution of the distribution function with probabilistic 'kicks' by the AEs) and the resistive MHD code with kinetic fast ions, MEGA, find no strong role of energy gradient drive due to bump-on-tail features. Instead, the observed TAE modulation with interleaved beams is likely a pitch angle dependent result combined with slowing down of the tangential beam between pulses. For the conditions investigated, bump-on-tail contributions to TAE drive were found to be 5% or less of the total drive at any given time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Perturbative model for the saturation of energetic-particle-driven modes limited by self-generated zonal modes

We present a simplified energy-conserving approach to incorporate wave–wave nonlinear effects within the framework commonly used to describe wave–particle nonlinearities. In particular, the effects of zonal mode (ZM) generation on the determination of the saturation amplitude of energetic particle (EP)-driven Alfvénic instabilities is studied. The model assumes that the zonal perturbations grow at a rate twice that of the original (pump) wave, consistent with a beat-driven (or force-driven) generation mechanism. The evolution and saturation of the mode amplitude are investigated both analytically and numerically within our reduced model assumptions, in both the collisionless and scattering-dominated regimes. These studies underscore the crucial role of sources and sinks in capturing the impact and the role of beat-driven zonal perturbations on mode evolution. In the realistic case of saturation set by sources and sinks, we discuss the role of a finite amplitude ZM in reducing microturbulent particle scattering, thus limiting the energy source for the resonant mode. We then discuss comparisons between the model’s predictions and simulation results. The model reproduces key features observed in gyrokinetic simulations as the reduction in saturated mode amplitude and the onset of wave–wave nonlinear effects as functions of mode growth rate and amplitude. Thanks to its simplicity, it can be readily implemented into codes based on reduced models, thereby improving their predictive capability for strongly driven instabilities.

Alfvén eigenmodes↗
DOE OSTI2024

Eigenmode twist by energy flux during fast-ion driven instabilities

Twisting of the spatial structure of eigenmodes by energy fluxes generated due to the spatial channeling (SC)—the fast-ion energy and momentum transfer across the magnetic field by destabilized modes—is considered. It is revealed that there is a correlation between the direction of the radial wave energy flux, orientation of the mode twist (MT), and the direction of mode rotation. The mode twist parameter is introduced and relations connecting it with the energy flux are established. It is shown the energy flux transforms zeros of the radial profile of the mode amplitude into minima (i.e., zeros disappear). It is found that the radial group velocity and phase velocity of reversed shear Alfvén eigenmodes (RSAEs) have opposite directions. These findings can be used for diagnostics of the energy fluxes during fast-ion driven instabilities and understanding whether the SC degrades or improves plasma performance. Specific calculations are carried out for fast magnetoacoustic modes, FMMs (known also as compressional Alfvén eigenmodes, CAEs), and Alfvén eigenmodes, AEs. A DIII-D experiment where RSAEs were observed is considered. It is concluded that an outward SC took place in this experiment. Peculiarities of various modes are discussed, which may explain why twisting of AEs, but not of FMMs, was observed experimentally in the DIII-D and NSTX tokamaks.

Kolesnichenko, Ya. I. (ORCID:0000000323219681)↗