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DOE OSTI2020

Theory of the tertiary instability and the Dimits shift within a scalar model

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry--Horton system has been proposed by St-Onge [J. Plasma Phys. {\bf 83}, 905830504 (2017)] as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$, where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U''$. Then, depending on $U''$, the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $U'$. Our analytic predictions are in agreement with direct numerical simulations of the modified Terry--Horton system.

fusion plasmas↗

DOE OSTI2020

Theory of the tertiary instability and the Dimits shift within a scalar model

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in a magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry–Horton system has been proposed by St-Onge ( J. Plasma Phys. , vol. 83, 2017, 905830504) as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$ , where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U'' \doteq {\rm d}^2 U/{\rm d} x^2 $ . Then, depending on $U''$ , the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $| {\rm d} U / {\rm d} x |$ . Our analytic predictions are in agreement with direct numerical simulations of the modified Terry–Horton system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Physics of Edge-Core Coupling by Inward Turbulence Propagation

The dynamics of edge-core coupling is critically important to the optimization of magnetically confined fusion plasmas. Since early proposals, there has been persistent speculation that inward propagation of turbulence from the boundary is a possible means to energize the edge-core coupling region. However, the detailed mechanism of this process has remained a mystery until recent experiments observed that regular, intense gradient relaxation events generated blob-void pairs very close to the last closed flux surface. Blobs ($\tilde{n}$ >0) propagate outward and detach from the bulk plasma, while voids ($\tilde{n}$ <0) propagate inward, and so stir the core plasma. Here, in this work, we demonstrate that this heretofore ignored process of void emission can drive a broad turbulent layer of width ∼100 𝜌 𝑠 , for typical parameters. The mechanism is the Cherenkov emission of drift waves from inward-propagating voids. The model shows promise to resolve several questions surrounding the shortfall problem and the strong turbulence in the edge-core coupling region.

drift waves↗

DOE OSTI2026

Quantitative analysis of zonal flow influence on turbulent plasmas driven by trapped electrons

The role of zonal flow (ZF) in the turbulence saturation of trapped electron modes (TEM) in magnetically confined plasmas is revisited. Here, in this study, we examine ZF excitation and saturation mechanisms in TEM turbulence using detailed free-energy transfer diagnostics from nonlinear gyrokinetic simulations. When the ion channel becomes subdominant, electrons shift to transferring energy to the zonal component, which results in zonal flows always playing a significant though subdominant role, in the case of the temperature gradient driven TEM. The velocity-space structure of energy transfer reveals that trapped electrons directly couple to ZF. Regarding the saturation physics, the zonal flow advection, drift-wave–drift-wave interactions, and stable modes at the pump waves are compared. When ZF saturation is weak, drift-wave–drift-wave interactions play a larger role in maintaining turbulence saturation. The findings elucidate the roles of nonzonal to zonal flow coupling, stable modes, and nonzonal wave-wave interactions, and provide a basis for improving reduced models of turbulent transport.

Song, Jiheon [Hanyang University, Seoul (Korea, Re↗

DOE OSTI2024

Langmuir turbulence in suspended kelp farms

This study investigates the influence of suspended kelp farms on ocean mixed layer hydrodynamics in the presence of currents and waves. We use the large eddy simulation method, where the wave effect is incorporated by solving the wave-averaged equations. Distinct Langmuir circulation patterns are generated within various suspended farm configurations, including horizontally uniform kelp blocks and spaced kelp rows. Intensified turbulence arises from the farm-generated Langmuir circulation, as opposed to the standard Langmuir turbulence observed without a farm. The creation of Langmuir circulation within the farm is attributed to two primary factors depending on farm configuration: (i) enhanced vertical shear due to kelp frond area density variability, and (ii) enhanced lateral shear due to canopy discontinuity at lateral edges of spaced rows. Both enhanced vertical and lateral shear of streamwise velocity, representing the lateral and vertical vorticity components, respectively, can be tilted into downstream vorticity to create Langmuir circulation. This vorticity tilting is driven by the Craik–Leibovich vortex force associated with the Stokes drift of surface gravity waves. In addition to the farm-generated Langmuir turbulence, canopy shear layer turbulence is created at the farm bottom edge due to drag discontinuity. The intensity of different types of turbulence depends on both kelp frond area density and the geometric configuration of the farm. The farm-generated turbulence has substantial consequences for nutrient supply and kelp growth. These findings also underscore the significance of the presence of obstacle structures in modifying ocean mixed layer characteristics.

Bo, Tong (ORCID:0000000260300561)↗

DOE OSTI2021

Integrating CVMix into GOTM (v6.0): a consistent framework for testing, comparing, and applying ocean mixing schemes

Abstract. The General Ocean Turbulence Model (GOTM) is a one-dimensional water column model, including a set of state-of-the-art turbulence closure models, and has widely been used in various applications in the ocean modeling community. Here, we extend GOTM to include a set of newly developed ocean surface vertical mixing parameterizations of Langmuir turbulence via coupling with the Community Vertical Mixing Project (CVMix). A Stokes drift module is also implemented in GOTM to provide the necessary ocean surface waves information to the Langmuir turbulence parameterizations, as well as to facilitate future development and evaluation of new Langmuir turbulence parameterizations. In addition, a streamlined workflow with Python and Jupyter notebooks is also described, enabled by the newly developed and more flexible configuration capability of GOTM. The newly implemented Langmuir turbulence parameterizations are evaluated against theoretical scalings and available observations in four test cases, including an idealized wind-driven entrainment case and three realistic cases at Ocean Station Papa, the northern North Sea, and the central Baltic Sea, and compared with the existing general length scale scheme in GOTM. The results are consistent with previous studies. This development extends the capability of GOTM towards including the effects of ocean surface waves and provides useful toolsets for the ocean modeling community to further study the effects of Langmuir turbulence in a broader scope.

58 GEOSCIENCES↗

DOE OSTI2024

Turbulence link to L-mode, I-mode, and H-mode confinement in the DIII-D tokamak

Understanding the physics of low-confinement (L-), improved-confinement (I-), and high-confinement (H-) modes is critical for fusion reactors. The finding herein reports observations of two types of turbulence coexisting near the L-mode edge, one magnetohydrodynamic (MHD)-like and another micro-tearing mode (MTM)-like, linked to the H-mode and I-mode confinement in the DIII-D tokamak. Ion-scale magnetic and density turbulence is measured using a Faraday-effect radial-interferometer-polarimeter and beam-emission-spectroscopy (BES). Broadband turbulence spectra of up to ~600 kHz are observed in two discharges where transitions between L-mode, I-mode, and H-mode occurs. Turbulence is found to be inversely correlated with confinement, meaning lower turbulence power at higher confinement. Distinctively, the high-frequency (HF, >~100 kHz) magnetic turbulence power changes by the most (55%) during transitions primarily involving energy confinement change, whereas the low-frequency (LF, <~100 kHz) magnetic and density turbulence power changes by the most (80%) during transitions primarily involving particle confinement change. The LF turbulence amplitude oscillates with and leads to deuterium-alpha emission oscillations before an H-mode. These results imply that HF turbulence mainly affects energy confinement whereas LF turbulence can affect particle confinement. The magnetic and density turbulence exhibits coherence up to 0.6 and cross-phase magnitude close to π/2 in most cases, suggesting they have a common origin in both the LF and HF ranges. BES suggests that LF turbulence resides at the edge (ρ = 0.95) and HF turbulence can be at the outer core (ρ = 0.8) or edge (ρ = 0.95). Comparisons of measurements, theory, and gyrokinetic simulations suggest that HF turbulence is MTM-like in all cases, whereas LF turbulence is more consistent with MHD-like modes and the exact instability might change during transitions—except that a drift-wave origin is possible in a low collisionality H-mode. These results suggest that the H-mode involves suppressed MHD-like turbulence, whereas the I-mode mitigates MTM-like turbulence along with largely unchanged MHD-like turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Reversal of Simple Hydrogenic Isotope Scaling Laws in Tokamak Edge Turbulence

The role of nonadiabatic electrons in regulating the hydrogenic isotope-mass scaling of gyrokinetic turbulence in tokamak fusion plasmas is assessed in the transition from ion-dominated core transport regimes to electron-dominated edge transport regimes. We propose a new isotope-mass scaling law that describes the electron-to-ion mass-ratio dependence of turbulent ion and electron energy fluxes. Here, the massratio dependence arises from the nonadiabatic response associated with fast electron parallel motion and plays a key role in altering—and in the case of the DIII-D edge, favorably reversing—the naive gyro-Bohm scaling behavior. In the reversed regime hydrogen energy fluxes are larger than deuterium fluxes, which is the opposite of the naive prediction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Large Eddy Simulation of the Southern Ocean

The data set contains seven Large Eddy Simulations (LES) at the Southern Ocean Flux Site for studies of deep turbulent ocean boundary layers, with and without surface wave effects, and with both idealized and observed forcing by wind, surface buoyancy flux and Stokes drift profiles. There are 20 days of hourly statistics computed every half-hour of turbulence quantities; namely, the vertical fluxes of buoyancy (temperature) and momentum, buoyancy and velocity variances, and the turbulent kinetic energy, its production terms and its dissipation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Threshold Heat-Flux Reduction by Near-Resonant Energy Transfer

Near-resonant energy transfer to large-scale stable modes is shown to reduce transport above the linear critical gradient, contributing to the onset of transport at higher gradients. This is demonstrated for a threshold fluid theory of ion temperature gradient turbulence based on zonal-flow-catalyzed transfer. Furthermore, the heat flux is suppressed above the critical gradient by resonance in the triplet correlation time, a condition enforced by the wave numbers of the interaction of the unstable mode, zonal flow, and stable mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Nonlinear coupling of whistler waves to oblique electrostatic turbulence enabled by cold plasma

Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. Furthermore, this mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth's magnetosphere where cold background plasma of sufficient density is present.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

The diurnal cycle of entrainment and detrainment in LES of the Southern Ocean driven by observed surface fluxes and waves

Empirical rules for both entrainment and detrainment are developed from LES of the Southern Ocean boundary layer when the turbulence, stratification, and shear cannot be assumed to be in equilibrium with diurnal variability in surface flux and wave (Stokes drift) forcing. A major consequence is the failure of downgradient eddy viscosity, which becomes more serious with Stokes drift and is overcome by relating the angle between the stress and shear vectors to the orientations of Lagrangian shear to the surface and of local Eulerian shear over 5 m. Thus, the momentum flux can be parameterized as a stress magnitude and this empirical direction. In addition, the response of a deep boundary layer to sufficiently strong diurnal heating includes boundary layer collapse and the subsequent growth of a morning boundary layer, whose depth is empirically related to the time history of the forcing, as are both morning detrainment and afternoon entrainment into weak diurnal stratification. Below the boundary layer, detrainment rules give the maximum buoyancy flux and its depth, as well a specific stress direction. Another rule relates both afternoon and nighttime entrainment depth and buoyancy flux to surface layer turbulent kinetic energy production integrals. These empirical relationships are combined with rules for boundary layer transport to formulate two parameterizations; one based on eddy diffusivity and viscosity profiles and another on flux profiles of buoyancy and of stress magnitude. Evaluations against LES fluxes show the flux profiles to be more representative of the diurnal cycle, especially with Stokes drift.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Explaining the lack of power degradation of energy confinement in wide pedestal quiescent H-modes via transport modeling

Wide pedestal quiescent H (WPQH)-mode is an attractive scenario for future burning plasmas as they operate without ELMs. WPQH is characterized by formation of a wider and higher pedestal (than quiescent H-mode), and broadband fluctuations in the pedestal. Unlike conventional H-modes, where the energy confinement time reduces with increasing heating power, the WPQH plasmas reported in this paper do not show power degradation of the energy confinement. As the injected neutral beam power was increased, reduced core (ρ ≤ 0.45) transport calculated by transp, as well as increased core temperatures, pressure gradient and diamagnetic E × B shear rate were observed. The reduction in the heat transport and rapid decrease in the ion temperature gradient scale length suggest the formation of an ion internal transport barrier (ITB) that was accompanied by increased stored energy in the core. Quasilinear turbulent transport modeling using the trapped gyro Landau fluid (tglf) code was used to predict the ITB and its turbulence stability properties. By using profiles and equilibria produced by matching the transp transport fluxes with the tglf transport model within the tgyro transport solver, the energy confinement time captures the experimentally observed insensitivity to the increased PNBI. Linear stability analysis reveals that drift-wave instabilities in the core are stabilized by E × B shear, T i /T e ratio and Shafranov shift; the latter was found to have the strongest effect on the turbulence suppression at the highest heating level.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Coherent mode and turbulence measurements with a fast camera

This study employs a fast camera with frame rates up to 900,000 fps to measure the transfer of energy across spatial scales in helicon source plasmas and during flux rope mergers and the measurement of azimuthal mode structures in helicon plasmas. By extracting pixel-scale dispersion relations and power spectral density (PSD) measurements, we measure the details of turbulent wave modes and energy distribution across a broad range of spatial scales within the plasma. We confirm the presence of drift waves in helicon plasmas, as well as the existence of strong dissipation regions in the PSD at electron skin depth scales for both helicon and flux rope merger experiments. This approach overcomes many limitations of conventional probes, providing high spatial and temporal resolution, without perturbing the plasma.

Instruments & Instrumentation↗

DOE OSTI2020

Comparison of edge turbulence characteristics between DIII-D and C-Mod simulations with XGC1

The physical processes taking place at the separatrix and scrape-off layer regions are crucial for the operation of tokamaks as they govern the interaction of hot plasma with the vessel walls. Numerical modeling of the edge with state-of-the-art codes attempts to elucidate the complex interactions between neoclassical drifts, turbulence, poloidal and parallel flows that control the physical set-up of the SOL region. Here, we present post-processing analysis of simulation results from the gyrokinetic code XGC1, comparing and contrasting edge turbulence characteristics from a simulation of the DIII-D tokamak against a simulation of the Alcator C-Mod tokamak. We find that the equilibrium ExB flux across the separatrix has a similar poloidal pattern in both discharges which can be explained by rB-drifts and trapped ion excursions. Furthermore, collisionality is noted to play a major role in the way that it prevents local charge accumulations from having more global effects in the C-Mod case. In both cases, turbulent electron heat flux is observed to be higher than the ion one and is possibly related to the need of electrons to maintain quasineutrality through the only channel available to them for exiting the confinement. By Fourier analysis, we identify turbulent frequencies and growth rates of the dominant mode in both simulations. In the case of C-Mod, these numbers point to the presence of a drift wave. In the DIII-D case, further linear simulations with the Gene code reveal a trapped electron mode. Furthermore, using a blob detection and tracking tool, we present the amplitude and size distributions of the blobs from both simulations. The amplitude distributions are in qualitative agreement with experimental observations while the size distributions are consistent with the fact that most of the blobs are not connecting to the divertor plates and suggest that they are generated by the shearing of the turbulent modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Spectral transition of multiscale turbulence in the tokamak pedestal

The transition in the turbulence spectrum from ion-scale dominated regimes to multiscale transport regimes that couple ion and electron scales is studied with gyrokinetic simulations of turbulent transport. The simulations are based on DIII-D high-confinement mode (H-mode) plasma parameters in the tokamak pedestal. The transition is initiated by varying the ion temperature gradient. To our knowledge, no full multiscale simulations of pedestal-like transport have been done previously. The experimental parameters lie in a bifurcation region between the two regimes. At long wavelengths, a complex, ion-direction hybrid mode is the dominant linearly unstable drift wave, while an electron temperature gradient-driven mode is unstable at short wavelengths. In the transition from the multiscale branch to the ion-scale branch, the magnitude of the ion-scale poloidal wavenumber spectrum of the nonlinear turbulent energy flux increases and the magnitude of the high-wavenumber spectrum decreases. Here, the decrease in the electron-scale transport is due to nonlinear mixing with ion-scale fluctuations and the ion-scale-driven zonal flows. A shift in the total energy associated with the fluctuating electrostatic potential intensity from dominantly drift kinetic energy in the multiscale regime to dominantly potential intensity in the ion-scale regime is well-correlated with the trend in the total energy flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Energy transport analysis of NSTX plasmas with the TGLF turbulent and NEO neoclassical transport models

This work presents a study of plasma transport at low aspect ratio on the National Spherical Torus Experiment tokamak, where the turbulent and neoclassical energy fluxes calculated by the quasilinear Trapped Gyro Landau Fluid (TGLF) model and the multi species drift-kinetic Neoclassical solver (NEO) are validated against experimental data. The turbulent energy transport of two plasma discharges, one in the L-mode confinement regime and another in the H-mode regime, is dominated by electrostatic drift-wave instabilities, while the ion heat transport has a significant neoclassical contribution. The data analysis workflow is described in detail to understand how the variations of mapping and fitting of experimental data affect the power balance solution and subsequent flux-matching plasma profile predictions with the TGYRO solver. On average, the predicted plasma profiles are consistent with experimental data. However, the solutions are sensitive to various input parameters, including boundary conditions, and the electron-ion coupling. Linear gyrokinetic stability analysis demonstrates close agreement of the real frequencies of unstable modes between TGLF and CGYRO gyrokinetic simulations, but higher growth rates are predicted by TGLF, especially for the H-mode case. Estimates of the low-k modes' contributions to the total flux are consistent with linear stability analysis and the E × B suppression of turbulence in TGLF simulations with the SAT1 saturation model, while the SAT2 saturation model over-predicts the low-k modes' contribution in the H-mode case. Moreover, the results with SAT1 model are consistent with power balance analysis, which indicates only neoclassical ion energy fluxes inside ρ < 0.4 in the L-mode case and $\rho \unicode{x2A7D} 0.7$ in the H-mode case. The presence of multi-scale turbulence and ion-scale driven zonal flow mixing effects are also observed in TGLF scans of the electron turbulent heat flux over a range of temperature gradients and the electron-ion temperature ratio, which could explain the strong model sensitivity to variations of input parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Thermal confinement and transport in spherical tokamaks: a review

Here, we review the thermal plasma confinement and transport properties observed and predicted in low aspect ratio tokamaks, or spherical tokamaks (STs), which can depart significantly from those observed at higher aspect ratio. In particular, thermal energy confinement scalings show a strong, near linear dependence of energy confinement time on toroidal magnetic field, while the dependence on plasma current is more modest, the opposite of what is seen at higher aspect ratio. STs have revealed a very strong improvement in normalized confinement with decreasing collisionality, much stronger than at higher aspect ratio, which bodes well for an ST-based fusion pilot plant should this trend continue at an even lower collisionality than has already been accessed. These differences arise because of fundamental differences in transport in STs due to the more extreme toroidicity (i.e. reduced region of bad curvature), and to the relatively larger $E_r \times B$ shearing rates, both of which can suppress electrostatic drift wave instabilities at both ion and electron gyroradius scales. In addition, electromagnetic effects are much stronger in STs because they operate at high β T . Gyrokinetic (GK) studies, coupled with low- and high-k turbulence measurements, have shed light on the underlying physics controlling transport. At lower β T , both ion- and electron-scale electrostatic drift turbulence may be responsible for transport. At higher β T , microtearing, kinetic ballooning, and hybrid trapped electron/kinetic ballooning modes increasingly play a role, and they have a much stronger impact in the core of ST plasmas than at higher aspect ratio. Flow shear affects the balance between ion- and electron-scale modes. Non-linear GK simulations find regimes where the electron heat flux decreases with decreasing collisionality, consistent with the experimental global normalized confinement scaling. The ST is unique in that the relatively low toroidal magnetic field allows for localized measurements of electron-scale turbulence, and this coupled with turbulence measurements at ion-scales has facilitated detailed comparisons with GK simulations. These data have provided compelling evidence for the presence of ion temperature gradient and electron temperature gradient turbulence in some plasmas, and direct experimental support for the impact of experimental actuators like rotation shear, density gradient and magnetic shear on turbulence and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗