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DOE OSTI2022

A Nonlocal Magneto-curvature Instability in a Differentially Rotating Disk

A global mode is shown to be unstable to nonaxisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic fields where local standard magnetorotational instability (MRI) becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfvén-continuum-driven unstable modes. As its mode structure and relative dominance over MRI are inherently determined by the global spatial curvature as well as the flow shear in the presence of a magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from MRI-driven turbulence to a state dominated by global nonaxisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at a higher magnetic field than predicted by local models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media

In classical Hermitian continuous media, the spectral-flow index of topological modes is linked to the bulk topology via index theorem. However, the interface between two bulks is usually non-Hermitian due to the inhomogeneities of system parameters. We show that the connection between topological modes and bulk topology still exists despite the non-Hermiticity at the interface if the system is endowed with PT symmetry. The theoretical framework developed is applied to the Hall magnetohydrodynamic model to identify a topological mode called topological Alfvén sound wave in magnetized plasmas. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Excitation of toroidally localized harmonics of global Alfvén eigenmodes

Abstract The spherical tokamak NSTX and the upgraded, higher toroidal field, NSTX-U, routinely create plasmas with large un-thermalized populations of super-Alfvénic fast ions. This population of non-thermal energetic ions excites a broad spectrum of Alfvénic waves, from the lower frequency (≈30 kHz–≈200 kHz) toroidal Alfvén eigenmodes (Cheng and Chance 1986 Phys. Fluids 29 3695), to the higher frequency (400 kHz–3 MHz) global Alfvén eigenmodes (GAEs) and compressional Alfvén eigenmodes (Goedbloed 1975 Phys. Fluids 18 1258). In this paper we present evidence that the GAE non-linearly excite modes, presumably GAE, at frequencies consistent with non-linear or 3-wave coupling. The observation of the excitation of 2 nd harmonic GAE through the intrinsic non-linearity of Global Alfvén modes demonstrates that the non-linear terms can act as an exciter-antenna inside the plasma, broadcasting at harmonics of the mode frequency and with concomitantly shorter wavelengths. As with experiments using external antenna to excite otherwise weakly stable Alfvénic modes, this data can provide information about the stability of modes at harmonics of the GAE. It may also provide information on the nature of the non-linearities in the wave dispersion equation or a direct measure of the mode amplitude (Smith et al 2006 Phys. Plasmas 13 042504). We also report that the short wavelength 2 nd harmonic GAE can be strongly toroidally localized. The observation that the shorter wavelength ( n ≈ 20) 2 nd harmonic modes can be toroidally localized potentially has implications for the impact of fast-ion driven instabilities on fast-ion confinement in ITER and future fusion reactors (Gorelenkov et al 2014 Nucl. Fusion 54 125001).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Self-Consistent Simulation of the Excitation of Compressional Alfvén Eigenmodes and Runaway Electron Diffusion in Tokamak Disruptions

Alfvénic modes in the current quench (CQ) stage of the tokamak disruption have been observed in experiments. In DIII-D the excitation of these modes is associated with the presence of high-energy runaway electrons (REs), and a strong mode excitation is often associated with the failure of RE plateau formation. In this work we present results of self-consistent kinetic-MHD simulations of RE-driven compressional Alfvén eigenmodes (CAEs) in DIII-D disruption scenarios, providing an explanation of the CQ modes. Simulation results reveal that high energy trapped REs can have resonance with the Alfvén mode through their toroidal precession motion, and the resonance frequency is proportional to the energy of REs. The mode frequencies and their relationship with the RE energy are consistent with experimental observations. Further, the perturbed magnetic fields from the modes can lead to spatial diffusion of REs including the nonresonant passing ones, thus providing the theoretical basis for a potential approach for RE mitigation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Strong Turbulent Alfvén Wave Interactions in a Laboratory Plasma (Final Scientific/Technical Report)

Turbulence is a fundamental and widespread aspect of plasma behavior, occurring in nearly every natural plasma system that is observed, from clusters of distant galaxies to plasmas within the solar system. Plasma continuously streaming from the sun, known as the solar wind, has been particularly fruitful in understanding plasma turbulence due to the availability of spacecraft data. An ensuring mystery in solar wind turbulence is the unexpected observation of residual energy – there is excess energy in the magnetic fluctuations compared to the velocity fluctuations even though an Alfvén wave in Magnetohydrodynamics has equal amounts of energy in each. The project studied strong non-linear interaction between counter-propagating Alfvén waves in the lab for the first time. Dr. Mel Abler, who was hired as a postdoctoral researcher under this grant, obtained the first observation of residual energy in a counter-propagating Alfvén wave interaction. Dr. Abler showed experimentally that the interaction of two counter-propagating Alfvén waves produces daughter modes that are not not normal modes of the system and only exist in the presence of the nonlinear drive. These Alfvén quasimodes contain either negative residual energy (more energy in magnetic fluctuations) or positive residual energy (more energy in velocity fluctuations).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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

Simulation of Alfvénic avalanche onset in NSTX

In some tokamak discharges, a number of Alfvén eigenmodes (AEs) have been observed to cause a large-scale collapse of the high energy particle distribution, a phenomenon referred to as an avalanche. We examine the necessary conditions for an avalanche using the available experimental information from NSTX on the equilibrium and mode properties for two cases, one with a measurable but benign AE activity and one with an AE activity leading up to an avalanche. To produce an avalanche, the modes present in the discharge must possess resonances that can overlap with a modest increase in instability magnitude, providing a path to global particle stochastic motion. In this paper, we find that the modes present in the avalanche-free discharge do not provide such a path even at a very large amplitude. During the discharge which subsequently produces an avalanche, the high energy population is growing and the Alfvén frequency is dropping due to increasing density, and we find that both these changes, producing a small increased drive or an increased resonance width for the Alfvén modes, can lead in this case to uncontrolled mode growth and large-scale beam particle loss.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Gyrokinetic simulation of low-frequency Alfvénic modes in DIII-D tokamak

Global gyrokinetic simulations find that a beta-induced Alfvén eigenmode (BAE) and a Low frequency mode (LFM) coexist in the DIII-D tokamak experiments. The LFM can be excited without fast ions and has a frequency inside the gap of the beta-induced Alfvén-acoustic eigenmode (BAAE). The mode structure of the LFM from simulations and many of its parametric dependencies are consistent with experimental observations. For the BAE, the simulated mode structure is consistent with experiment but the frequency is lower than experiment. An antenna scan shows that the LFM is NOT the conventioanl BAAE; rather, it is an interchange-like electromagnetic mode excited by non-resonant drive of pressure gradients. The compressible magnetic perturbations significantly increase the growth rates of the BAE and LFM. On the other hand, effects of trapped electrons and equilibrium current have modest effects on the BAE and LFM. Finally, radial transfer of wave energy is different between the BAE and LFM, resulting in their respective triangular and elliptic mode shapes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Measurement of the Alfvén Wave Parametric Decay Instability Growth Rate

Alfvén waves, a fundamental mode of magnetized plasmas, are ubiquitous in space and laboratory plasmas. The nonlinear behavior of these modes is thought to play a key role in important problems in space plasma, such as the heating of the solar corona and solar wind turbulence. In particular, theoretical predictions show that these Alfvén waves may be unstable to various parametric instabilities, but space observations of these processes are limited. We demonstrate the first measurement of the Alfvén wave parametric decay instability (PDI) growth rate. Experiments are conducted on the Large Plasma Device at UCLA in which a high amplitude 𝛿⁢𝐵/𝐵 0 ∼ 0.7% pump Alfvén wave is launched from one end of the device and a smaller seed Alfvén wave is launched from the other side. When the frequency of the seed wave is chosen to match the backward wave expected from PDI, damping of the seed wave is reduced. We compare this reduction in damping to the theoretically expected PDI growth rate while accounting for acoustic mode damping. Results show agreement between measurements and theoretical predictions. As a result, this not only provides critical validation for PDI theories and simulations that could help interpret future space observations but also suggests a new way of studying similar nonlinear wave phenomena.

Alfvén waves↗
DOE OSTI2026

Spherical tokamak physics research in preparation for the operation of NSTX-U

The National Spherical Torus Experiment Upgrade (NSTX-U) is preparing to resume operation, representing a crucial step toward realizing compact, cost-effective fusion pilot plants. In advance of this, extensive modeling and data analysis have been conducted to advance the physics basis for low-aspect-ratio, high-performance plasma regimes, focusing on three core objectives: confinement and stability, power and particle handling, and steady-state operation. Significant progress has been made in understanding the electron temperature flattening in high-β plasmas, which is shown to be driven by a complex interplay of magnetohydrodynamic instabilities (e.g. non-resonant infernal modes), fast-ion-driven Alfvén eigenmodes, and electron and ion-scale micro-instabilities, particularly Kinetic Ballooning Modes (KBMs), whose destabilization is strongly dependent on parallel magnetic field fluctuations (δB ∥ ). Furthermore, a new gyrokinetic critical pedestal model was developed, accurately predicting pedestal structure by identifying KBMs as the primary stability limit, offering a critical constraint for future high-confinement scenarios. To address the challenge of high heat flux, novel liquid lithium plasma-facing components were modeled. The analysis confirmed that lithium vapor shielding is a self-regulating mechanism for heat mitigation, while also emphasizing that strong main ion parallel flow is essential to minimize core lithium contamination. Finally, progress toward steady-state operation was anchored by developing the required physics basis and control tools. This includes predictive modeling for reversed magnetic shear sustainment, demonstrating that magnetic island-induced bootstrap current reduction is negligible in STs, and advancing real-time control and disruption avoidance capabilities. The development of high-speed surrogate models (e.g. MMMNet) provides computationally efficient tools vital for non-inductive scenario optimization and integrated, low-disruptivity operations planned for NSTX-U.

NSTX-U↗
DOE OSTI2022

Plasma shape effects on the Alfvén eigenmode spectrum through Alfvén slow-magnetosonic wave coupling

In this report the effect of the plasma shaping (triangularity and elongation) on the continuous spectrum, frequency gaps, and number of eigenmodes is studied. The plasma shaping affects the coupling between Alfvén and slow magnetosonic waves via the geodesic magnetic curvature and the plasma pressure. The Alfvén-slow coupling creates a large number of new gaps in the continuous spectrum below the Alfvén frequency where discrete modes can reside. In ideal magnetohydrodynamic simulations a large number (a few hundred or more) of potential eigenmodes are found. The number of eigenmodes is correlated with the maximum geodesic curvature and a minimum number of possible discrete eigenmodes is found at a negative triangularity of -0.3. It is hypothesized that these possible eigenmodes form a low amplitude and dense discrete spectrum, which can be studied experimentally.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Enabling integrated AI control on DIII-D: a control system design with state-of-the-art experiments

We present the design and application of a general algorithm for Prediction And Control using MAchiNe learning (PACMAN) in DIII-D. Machine learning (ML)-based predictors and controllers have shown great promise in achieving regimes in which traditional controllers fail, such as tearing mode (TM) free scenarios, ELM-free scenarios and stable advanced tokamak conditions. The architecture presented here was deployed on DIII-D to facilitate the end-to-end implementation of advanced control experiments, from diagnostic processing to final actuation commands. This paper describes the detailed design of the algorithm and explains the motivation behind each design point. We also describe several successful ML control experiments in DIII-D using this algorithm, including a reinforcement learning controller targeting advanced non-inductive plasmas, a wide-pedestal quiescent H-mode ELM predictor, an Alfvén Eigenmode controller, a Model Predictive Control plasma profile controller and a state-machine TM predictor-controller. There is also discussion on guiding principles for real-time ML controller design and implementation.

machine learning↗
DOE OSTI2021

Stability of superthermal strahl electrons in the solar wind

We present a kinetic stability analysis of the solar wind electron distribution function consisting of the Maxwellian core and the magnetic-field aligned strahl, a superthermal electron beam propagating away from the sun. We use an electron strahl distribution function obtained as a solution of a weakly collisional drift-kinetic equation, representative of a strahl affected by Coulomb collisions but unadulterated by possible broadening from turbulence. This distribution function is essentially non-Maxwellian and varies with the heliospheric distance. The stability analysis is performed with the Vlasov–Maxwell linear solver leopard. We find that depending on the heliospheric distance, the core-strahl electron distribution becomes unstable with respect to sunward-propagating kinetic-Alfvén, magnetosonic, and whistler modes, in a broad range of propagation angles. The wavenumbers of the unstable modes are close to the ion inertial scales, and the radial distances at which the instabilities first appear are on the order of 1 au. However, we have not detected any instabilities driven by resonant wave interactions with the superthermal strahl electrons. Instead, the observed instabilities are triggered by a relative drift between the electron and ion cores necessary to maintain zero electric current in the solar wind frame (ion frame). Contrary to strahl distributions modelled by shifted Maxwellians, the electron strahl obtained as a solution of the kinetic equation is stable. Our results are consistent with the previous studies based on a more restricted solution for the electron strahl.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Magnetic Field Strength from Turbulence Theory. I. Using Differential Measure Approach

The mean plane-of-sky magnetic field strength is traditionally obtained from the combination of polarization and spectroscopic data using the Davis–Chandrasekhar–Fermi (DCF) technique. However, we identify the major problem of the DCF technique to be its disregard of the anisotropic character of MHD turbulence. On the basis of the modern MHD turbulence theory we introduce a new way of obtaining magnetic field strength from observations. Unlike the DCF technique, the new technique uses not the dispersion of the polarization angle and line-of-sight velocities, but increments of these quantities given by the structure functions. To address the variety of astrophysical conditions for which our technique can be applied, we consider turbulence in both media with magnetic pressure higher than the gas pressure, corresponding, e.g., to molecular clouds, and media with gas pressure higher than the magnetic pressure, corresponding to the warm neutral medium. We provide general expressions for arbitrary admixtures of Alfvén, slow, and fast modes in these media and consider in detail particular cases relevant to diffuse media and molecular clouds. We successfully test our results using synthetic observations obtained from MHD turbulence simulations. We demonstrate that our differential measure approach, unlike the DCF technique, can be used to measure the distribution of magnetic field strengths, can provide magnetic field measurements with limited data, and is much more stable in the presence of induced large-scale variations of nonturbulent nature. Furthermore, our study uncovers the deficiencies of earlier DCF research.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Results from the Alfvén Eigenmode Active Diagnostic during the 2019-2020 JET deuterium campaign

This paper presents results of extensive analysis of mode excitation observed during the operation of the Alfvén Eigenmode Active Diagnostic (AEAD) in the JET tokamak during the 2019-2020 deuterium campaign. Here, six of eight toroidally spaced antennas, each with independent power and phasing, were successful in actively exciting stable MHD modes in 479 plasmas. In total, magnetic resonances were detected with up to fourteen fast magnetic probes. In this work, we present the calculations of resonant frequencies $f_0$, damping rates γ < 0, and toroidal mode numbers $\textit{n}$, spanning the parameter ranges $f_0$ ≈ 30–250 kHz, –γ ≈ 0–13 kHz, and $\vert n \vert \leq {30}$. In general, good agreement is seen between the resonant and the calculated toroidal Alfvén Eigenmode frequencies, and between the toroidal mode numbers applied by the AEAD and estimated of the excited resonances. We note several trends in the database: the probability of resonance detection decreases with plasma current and external heating power; the normalized damping rate increases with edge safety factor but decreases with external heating. These results provide key information to prepare future experimental campaigns and to better understand the physics of excitation and damping of Alfvén Eigenmodes in the presence of alpha particles during the upcoming DT campaign, thereby extrapolating with confidence to future tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Toroidal modeling of Alfvén eigenmodes excited by runaway electrons in DIII-D and ITER

The non-perturbative MHD-kinetic hybrid code MARS-K (Liu et al 2014 Phys. Plasmas 21 056105) is updated to include relativistic effects for kinetic fast particles, enabling the code to model excitation of Alfvén eigenmodes (AEs) by runaway electrons (REs) in post-disruption tokamak plasmas. Applying the updated code to RE beams in both DIII-D and ITER, a zoo of AE modes triggered by trapped REs due to precessional drift-kinetic resonances is computed while scanning the RE energy. At fixed RE energy, multiple unstable roots are also excited. These AE modes possess radially different eigenmode structures, ranging from global modes to core-localized ones. The computed mode frequency is in the Alfvén frequency range, increasing with the assumed RE energy in a staircase fashion and quantitatively matching the experimental measurement (in DIII-D). At the (more relevant) high-frequency range (above 1 MHz), the modeled eigenmodes are identified as compressional AEs (CAEs) in DIII-D and a mixture of CAE and shear Alfvén waves in ITER.

Alfvén eigenmodes↗
DOE OSTI2021

Alfvénic modes excited by the kink instability in PHASMA

Magnetic flux ropes have been successfully created with plasma guns in the newly commissioned PHAse Space MApping (PHASMA) experiment. The flux ropes exhibit the expected m = 1 kink instability. The observed threshold current for the onset of this kink instability is half of the Kruskal–Shafranov current limit, consistent with predictions for the non-line tied boundary condition of PHASMA. The helicity, paramagnetism, and growth rate of the observed magnetic fluctuations are also consistent with kink instability predictions. The observed fluctuation frequency appears to be a superposition of a real frequency due to a Doppler shift of the kink mode arising from plasma flow (~2kHz) and a contribution from a wave mode (~5 kHz). The dispersion of the wave mode is consistent with an Alfvén wave. Distinct from most previ-ous laboratory studies of flux ropes, the working gas in PHASMA is argon. Thus, the ion cyclotron frequency in PHASMA is quite low and the frequency of the Alfvénic mode plateaus at ~0.5 of the ion gyro frequency with increasing background magnetic field strength.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Stability optimization of energetic particle driven modes in nuclear fusion devices: the FAR3d gyro-fluid code

The development of reduced models provide efficient methods that can be used to perform short term experimental data analysis or narrow down the parametric range of more sophisticated numerical approaches. Reduced models are derived by simplifying the physics description with the goal of retaining only the essential ingredients required to reproduce the phenomena under study. This is the role of the gyro-fluid code FAR3d, dedicated to analyze the linear and nonlinear stability of Alfvén Eigenmodes (AE), Energetic Particle Modes (EPM) and magnetic-hydrodynamic modes as pressure gradient driven mode (PGDM) and current driven modes (CDM) in nuclear fusion devices. Such analysis is valuable for improving the plasma heating efficiency and confinement; this can enhance the overall device performance. The present review is dedicated to a description of the most important contributions of the FAR3d code in the field of energetic particles (EP) and AE/EPM stability. FAR3d is used to model and characterize the AE/EPM activity measured in fusion devices as LHD, JET, DIII-D, EAST, TJ-II and Heliotron J. In addition, the computational efficiency of FAR3d facilitates performing massive parametric studies leading to the identification of optimization trends with respect to the AE/EPM stability. This can aid in identifying operational regimes where AE/EPM activity is avoided or minimized. This technique is applied to the analysis of optimized configurations with respect to the thermal plasma parameters, magnetic field configuration, external actuators and the effect of multiple EP populations. In addition, the AE/EPM saturation phase is analyzed, taking into account both steady-state phases and bursting activity observed in LHD and DIII-D devices. The nonlinear calculations provide: the induced EP transport, the generation of zonal structures as well as the energy transfer towards the thermal plasma and between different toroidal/helical families. Finally, FAR3d is used to forecast the AE/EPM stability in operational scenarios of future devices as ITER, CFETR, JT60SA and CFQS as well as possible approaches to optimization with respect to variations in the most important plasma parameters.

Alfv én Eigenmodes↗