Edge Turbulence Research Articles

Electric Field and Poloidal Rotation in the Turbulent Edge Plasma of the T-10 Tokamak

The dynamics of turbulent edge plasma in the T-10 tokamak is simulated numerically by solving reduced nonlinear MHD equations of Braginskii’s two-fluid hydrodynamics. It is shown that the poloidal plasma velocity is determined by the combined effect of two forces: the turbulent Reynolds force FR and the Stringer–Winsor geodesic force FSW, which is associated with the geodesic acoustic mode of the total plasma pressure $$\left\langle {p{\text{sin}}\theta } \right\rangle $$ . It follows from the simulation results that the FR and FSW forces are directed oppositely and partially balance one another. It is shown that, as the electron temperature increases, the resulting balance of these forces changes in such a way that the amplitude of the poloidal ion flow velocity and, accordingly, the electrostatic potential $${{\phi }_{0}}(r,t)$$ decrease. As the plasma density increases, the “driving forces” of turbulence (the dn0/dr and dp0/dr gradients) also increase, while dissipation due to the longitudinal current decreases, which results in an increase in the amplitude of turbulent fluctuations and the Reynolds force FR. On one hand, the force FSW increases with increasing plasma density due to an increase in the pressure $$\left\langle {p{\text{sin}}\theta } \right\rangle $$ ; however, on the other hand, it decreases in view of the factor 1/n0. As a result, the net force driving poloidal rotation increases, which leads to the growth of the plasma potential. Both under electron-cyclotron resonance heating and in regimes with evolving plasma density, the results of numerical simulations qualitatively agree with experimental data on the electrostatic potential of the T-10 plasma.

A universal mechanism for plasma blob formation

The formation of a density blob in the boundary region of a tokamak plasma is widely believed to be due to the presence of poloidal velocity shear that differentially breaks off a radially elongated streamer structure. However, blobs have also been experimentally detected in the absence of poloidal velocity shear. We ascribe the formation of such blobs to the differential stretching of the streamer arising from a radial velocity shear and thereby present a unified picture of the breaking mechanism that takes into account both the processes in a synergistic manner. Our universal condition for blob formation is validated from detailed numerical simulations of the edge turbulence in a typical L-mode scenario.

Mode rotation control in a tokamak with a feedback-driven biased electrode.

Rotation of the plasma and MHD modes in tokamaks has been shown to stabilize resistive wall and tearing modes as well as improve confinement through suppression of edge turbulence. In this work, we control mode rotation with a biased electrode inserted into the plasma of the High Beta Tokamak-Extended Pulse's facility in conjunction with its active GPU (Graphical Processing Unit) feedback system. We first characterize a negative linear relationship between the electrode voltage and mode rotation. Using this relationship, we design, simulate, and implement a proof-of-concept, GPU-based active-control system, which shows consistent success in controlling mode rotation in both feedforward and feedback operation. Controllability is limited by operating conditions, the electrode's voltage range, and by the electrode's proximity to the vessel's walls. The final control system has a 15 μs cycle time, but the addition of various signal filters results in a full cycle latency of 200 μs.

The deteriorating effect of plasma density fluctuations on microwave beam quality

Turbulent plasma edge density fluctuations can broaden a traversing microwave beam degrading its quality. This can be a problem for scenarios relying on a high spatial localization of the deposition of injected microwave power, like controlling MHD instabilities. Here we present numerical estimations of the scattering of a microwave beam by density fluctuations over a large parameter range, including extrapolations to ITER. Two codes are used, the full-wave code IPF-FDMC and the wave kinetic equation solver WKBeam. A successful comparison between beam broadening obtained from DIII-D experiments and corresponding full-wave simulations is shown.

Sensitivity analysis of airfoil aerodynamics during pitching motion at a Reynolds number of 1.35×105

Numerically reproducing wind tunnel experimental tests of flow behavior around a pitching airfoil is a challenge, especially under the occurrence of dynamic stall at relatively high angles of attack. This not only requires the application of advanced turbulence models, but also asks for examining the influence of the most relevant model parameters in detail. This contribution presents the results of an extensive computational study of the unsteady flow around a pitching NACA0012 airfoil at a Reynolds number of 1.35 × 105, as obtained by first performing 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations whereby the flow characteristics are simulated by the Transition SST turbulence model. The influence of a large number of parameters on the numerical results is investigated, namely the blockage ratio, computational grid resolution and y+ value, time step size, inlet freestream turbulence properties, airfoil trailing edge detailing and turbulence model. Integral aerodynamic force coefficients and detailed flow patterns are analyzed and compared with measurements from wind tunnel experiments presented in the literature. For the best-performing parameters, an adequate agreement with the experimental tests is obtained for the upstroke phase, while for the downstroke phase some differences appear. These differences are investigated in more detail by considering the results from a 2.5D Large Eddy Simulation (LES), which provides deep and complementary insights into the flow behavior during dynamic stall at the selected Reynolds number.

Millimeter-wave beam scattering by edge-plasma density fluctuations in TCV

In magnetically confined fusion devices, the use of millimeter waves (mmw) at the electron cyclotron (EC) frequencies ranges from plasma diagnostics to plasma heating, current drive and core confinement preservation. For large tokamaks such as ITER, numerical simulations and analytical estimates suggest that plasma edge turbulence could significantly broaden the EC-beam, possibly preventing tearing modes stabilization at the designed power levels. We report measurements of mmw-beam scattering by plasma turbulence in the TCV tokamak. A mmw-Gaussian beam is injected from the top of the device and the transmitted power is measured at the bottom. We show that the measured plasma density fluctuations in the upper part of the scrape-off layer (SOL) are the cause of fluctuations of the transmitted mmw-power. A full-wave model based on COMSOL multiphysics is presented and compared against the wave-kinetic-equation solver WKBeam in a TCV case. Using the SOL turbulence simulations from the GBS code, comparison between the scattering effect on the mmw-beam with both the full-wave simulations and the experiments are ongoing. We also present experimental observations of rapid changes in the transmitted power caused by ELMs in ELMy H-mode plasma.

LES/CMC modelling of ignition and flame propagation in a non-premixed methane jet

The Large Eddy Simulation (LES) / Conditional Moment Closure (CMC) model with detailed chemistry is used for modelling spark ignition and flame propagation in a turbulent methane jet in ambient air. Two centerline and one off-axis ignition locations are simulated. We focus on predicting the flame kernel formation, flame edge propagation and stabilization. The current LES/CMC computations capture the three stages reasonably well compared to available experimental data. Regarding the formation of flame kernel, it is found that the convection dominates the propagation of its downstream edge. The simulated initial downstream and radial flame propagation compare well with OH-PLIF images from the experiment. Additionally, when the spark is deposited at off-centerline locations, the flame first propagates downstream and then back upstream from the other side of the stoichiometric iso-surface. At the leading edge location, the chemical source term is larger than others in magnitude, indicating its role in the flame propagation. The time evolution of flame edge position and the final lift-off height are compared with measurements and generally good agreement is observed. The conditional quantities at the stabilization point reflect a balance between chemistry and micro-mixing. This investigation, which focused on model validation for various stages of spark ignition of a turbulent lifted jet flame through comparison with measurements, demonstrates that turbulent edge flame propagation in non-premixed systems can be reasonably well captured by LES/CMC.

Nonlinear gyrokinetic particle simulation of dissipative trapped electron mode

Electron turbulence induced by the trapped electron mode has been widely studied. The dissipative trapped electron mode (DTEM) is an important candidate for tokamak edge turbulence. Nonlinear gyrokinetic particle simulations based on edge parameters are carried out to investigate the collisional effects on the nonlinear transport of DTEM turbulence. It is found that the collisions can induce a low level radially inward electron transport for the DTEM turbulence, which is closely related to the phase difference between the radial turbulent motion and perturbed density fluctuation induced by collisional dissipation. We observe an inverse spectral cascade of the turbulence during the nonlinear DTEM saturation, which is caused by quasimode scattering induced by trapped electrons and important for determining the magnitude of turbulent transport. The nonlinear transport of DTEM is found to be inversely proportional to the collisional frequency by gyrokinetic simulation, which is consistent with the prediction of quasilinear theory.

A flux-balanced fluid model for collisional plasma edge turbulence: Model derivation and basic physical features

We propose a new reduced fluid model for the study of the drift wave–zonal flow dynamics in magnetically confined plasmas. Our model can be viewed as an extension of the classic Hasegawa-Wakatani (HW) model and is based on an improved treatment of the electron dynamics parallel to the field lines, to guarantee a balanced electron flux on the magnetic surfaces. Our flux-balanced HW (bHW) model contains the same drift-wave instability as previous HW models, but unlike these models, it converges exactly to the modified Hasegawa-Mima model in the collisionless limit. We rely on direct numerical simulations to illustrate some of the key features of the bHW model, such as the enhanced variability in the turbulent fluctuations and the existence of stronger and more turbulent zonal jets than the jets observed in other HW models, especially for high plasma resistivity. Our simulations also highlight the crucial role of the feedback of the third-order statistical moments in achieving a statistical equilibrium with strong zonal structures. Finally, we investigate the changes in the observed dynamics when more general dissipation effects are included and, in particular, when we include the reduced model for ion Landau damping originally proposed by Wakatani and Hasegawa.

Scaling trends of the critical E × B shear for edge harmonic oscillation onset in DIII-D quiescent H-mode plasmas

Quiescent H-mode (QH-mode) has been identified as an attractive stationary operational regime in tokamaks due to its lack of edge localized modes (ELMs), along with good particle and impurity control aided by the presence of magnetohydrodynamic modes such as the edge harmonic oscillation (EHO) or edge turbulence. Experiments on the DIII-D tokamak explore local access conditions for QH-mode through measurements of the critical edge rotational shear necessary for the transition from a QH-mode with a coherent EHO to a typical ELMy H-mode. The critical E × B shear and EHO frequency are predicted by a nonlinear phase-dynamics model relating the pressure and velocity perturbations in the edge pedestal region. The reduced theoretical model predicts a linear relationship between critical shearing rate and , where is the ion acoustic velocity, Lp the pressure gradient scale length, and the radial width of the mode. This scaling of the critical shearing rate agrees with the experimental trend, although the absolute magnitude of the shearing rate threshold is over-predicted by the model. Through a normalized predicted scaling, the model demonstrates the dynamic transition into and out of QH-mode qualitatively, within a single plasma discharge. The experimental comparison lends insight into improving the theoretical model by including more accurate geometry and toroidal mode number physics for more accurate quantitative predictions.

Two-fluid MHD regime of resistive drift-wave instability

Drift instabilities contribute to the formation of edge turbulence and zonal flows and thus the anomalous transport in tokamaks. Experiments often found micro-scale turbulence strongly coupled with large-scale magnetohydrodynamic (MHD) processes, whereas a general framework has been lacking that can cover both regimes, in particular, their coupling. In this paper, the linear resistive drift wave instability is investigated using a full 2-fluid MHD model, as well as its numerical implementation in the NIMROD code. Both analytical and numerical analyses reveal a macro-scale global drift wave eigenmode coupled with MHD dynamics and illustrate a non-monotonic dispersion relation with respect to both perpendicular and parallel wavenumbers. NIMROD results also reveal an edge-localized behavior in the radial mode structure as the azimuthal mode number increases, implying the dependence of the 2-fluid effects due to the inhomogeneous density profile. The edge-localization introduces a non-trivial dependence of the effective perpendicular wavenumber to the perpendicular mode number, which may explain the quantitative difference between the global dispersion relation and its local approximation from the conventional local theory.

Impact of safety factor and magnetic shear profiles on edge turbulence in circular limited geometry

The impact of magnetic configuration on edge turbulence properties in circular limiter geometry is investigated using TOKAM3X, a three‐dimensional (3D), first‐principle, fluid code for edge plasma. The theoretical spatial tilting of magnetic shear on turbulence fluctuations is recovered. Magnetic shear is found to generate or enhance poloidal high/low field sides (HFS/LFS) and up/down asymmetries. A simulation mimicking the impact of an X‐point on circular limiter geometry leads to the formation of two transport barriers that are stable in time, thus leading to the improvement of core particle confinement and to reduction of radial turbulent transport. The magnetic shear, which also strongly enhances the E × B shear, is responsible for the barrier formation.

Analysis of equilibrium and turbulent fluxes across the separatrix in a gyrokinetic simulation

The SOL width is a parameter of paramount importance in modern tokamaks as it controls the power density deposited at the divertor plates, critical for plasma-facing material survivability. An understanding of the parameters controlling it has consequently long been sought [Connor et al. Nucl. Fusion 39(2), 169 (1999)]. Prior to Chang et al. [Nucl. Fusion 57(11), 116023 (2017)], studies of the tokamak edge have been mostly confined to reduced fluid models and simplified geometries, leaving out important pieces of physics. Here, we analyze the results of a DIII-D simulation performed with the full-f gyrokinetic code XGC1 which includes both turbulence and neoclassical effects in realistic divertor geometry. More specifically, we calculate the particle and heat E × B fluxes along the separatrix, discriminating between equilibrium and turbulent contributions. We find that the density SOL width is impacted almost exclusively by the turbulent electron flux. In this simulation, the level of edge turbulence is regulated by a mechanism that we are only beginning to understand: ∇B-drifts and ion X-point losses at the top and bottom of the machine, along with ion banana orbits at the low field side, result in a complex poloidal potential structure at the separatrix which is the cause of the E × B drift pattern that we observe. Turbulence is being suppressed by the shear flows that this potential generates. At the same time, turbulence, along with increased edge collisionality and electron inertia, can influence the shape of the potential structure by making the electrons non-adiabatic. Moreover, being the only means through which the electrons can lose confinement, it needs to be in a balance with the original direct ion orbit losses to maintain charge neutrality.

Effect of magnetic shear on edge turbulence in SOL-like open field line configuration in QUEST

Intensity fluctuations are investigated using the fast camera imaging technique in the slab annular plasma as a function of magnetic shear and connection length in the spherical tokamak QUEST. Note that here QUEST is operated as a simple magnetized torus with a tight aspect ratio. Slab annular plasmas feature open magnetic field lines and can mimic the tokamak edge-scrape off layer (SOL)-like plasma attributes reasonably well. Three magnetic shear regimes are realized using three poloidal magnetic field (PF) coil pairs. A whole range of connection lengths (∼∞ ≥ Lc ≥ 5.5 m) is scanned by varying the PF strength for a given toroidal field for each magnetic shear regime. For the first time a systematic study of the effect of magnetic shear and field line pitch together on edge-SOL-like plasma fluctuations is being reported. Slab plasmas with intermediate magnetic shear are observed to be more susceptible to generate distinct blobs when Lc is reduced by increasing the PF strength. A distinct coherent mode appears only at the lowest magnetic shear slab featuring a deep potential well. Such mode is not apparent at other magnetic shear cases even at the same Lc. Finally, with a combination of PF coil pairs, both the features of intermediate and low magnetic shear slabs are shown to be realizable simultaneously. Significantly stronger blobs are observed with such combination of PF mirror ratios in the presence of a coherent mode. This study may provide better insight into the effect of magnetic configuration in the tokamak edge and SOL turbulence and can help in searching for better tools to control cross-field convective intermittent transport in tokamaks.

GDB: A global 3D two-fluid model of plasma turbulence and transport in the tokamak edge

The global drift-ballooning (GDB) code is developed to study tokamak edge low frequency turbulence and transport, and their relationship to global profile evolution. The code employs a 3D electromagnetic fluid model that does not discriminate between equilibrium and perturbative contributions, capturing arbitrary amplitude fluctuations. Primitive plasma variables, including the E×B flow profiles, are evolved self-consistently in both closed-flux surfaces and the scrape-off-layer (SOL). A suite of numerical techniques described here handle the linear and non-linear components of the model efficiently so as to support realistic discharge parameters (such as realistic deuterium mass ratio mi∕me≈60) and yield good scaling on high performance computing (HPC) systems. GDB resolves turbulence slower than the ion gyrofrequency in simulations that capture the millisecond-scale evolution of global plasma profiles.

On the phase velocity in between weak and strong plasma edge turbulence

The influence of strong fluctuation levels on the phase velocity is studied just inside the last closed flux surface in the edge of magnetized confined plasmas by means of gyrofluid simulations. Linear features as growth rates and dispersion can be suppressed by small-scale vorticity generated by nonlinear self-sustainment. Measurements of the phase velocity by different diagnostic techniques could still provide finite values, which are not a result of linear instabilities, but are due to the nonlinear redistribution of spectral energy.

Blob-hole correlation model for edge turbulence and comparisons with NSTX gas puff imaging data

Gas puff imaging (GPI) observations made in NSTX (Zweben et al 2017 Phys. Plasmas 24 102509) have revealed two‐point spatial correlations of edge and scrape-off layer (SOL) turbulence in the plane perpendicular to the magnetic field. A common feature is the occurrence of dipole-like patterns with significant regions of negative correlation. In this paper, we explore the possibility that these dipole patterns may be due to blob-hole pairs. Statistical methods are applied to determine the two-point spatial correlation that results from a model of blob-hole pair formation. It is shown that the model produces dipole correlation patterns that are qualitatively similar to the GPI data in several respects. Effects of the reference location (confined surfaces or SOL), a superimposed random background, hole velocity and lifetime, and background sheared flows are explored and discussed with respect to experimental observations. Additional analysis of the experimental GPI dataset is performed to further test this blob-hole correlation model. A time delay two‐point spatial correlation study did not reveal inward propagation of the negative correlation structures that were postulated to correspond to holes in the data nor did it suggest that the negative correlation structures are due to neutral shadowing. However, tracking of the highest and lowest values (extrema) of the normalized GPI fluctuations shows strong evidence for mean inward propagation of minima and outward propagation of maxima, in qualitative agreement with theoretical expectations. Other properties of the experimentally observed extrema are discussed.

Inflow Turbulence and Leading Edge Roughness Effects on Laminar-Turbulent Transition on NACA 63-418 Airfoil

The surface imperfections and the inflow turbulence in real operational conditions can cause significant deviations from the predicted wind turbine aerodynamic performance and energy yield. In this study, particular emphasis was placed on the effect of these parameters on the laminar-turbulent transition on wind turbine blades. For this purpose, the DAN-AERO wind tunnel measurements, with high frequency microphones flush mounted on the both suction and pressure sides of the NACA 63-418 airfoil profile, were used. Typical operating condition Reynolds numbers, turbulence grid and boundary layer control devices on the surface were implemented. The results indicate a high dependency of the transition process on these parameters. The analyses show that the critical height of the leading edge roughness (LER) is to be met in order to have a bypass transition to turbulent flow at the angle of attacks, where the stagnation point is upstream of the LER location. The transition location moves closer to the leading edge with increasing Reynolds number when the roughness height is smaller than the critical height. Inflow turbulence is observed to have a larger effect on the transition location than the predicted numerical results.

A fast low-to-high confinement mode bifurcation dynamics in the boundary-plasma gyrokinetic code XGC1

A fast edge turbulence suppression event has been simulated in the electrostatic version of the gyrokinetic particle-in-cell code XGC1 in a realistic diverted tokamak edge geometry under neutral particle recycling. The results show that the sequence of turbulent Reynolds stress followed by neoclassical ion orbit-loss driven together conspire to form the sustaining radial electric field shear and to quench turbulent transport just inside the last closed magnetic flux surface. The main suppression action is located in a thin radial layer around ψN≃0.96–0.98, where ψN is the normalized poloidal flux, with the time scale ∼0.1 ms.

2D scrape-off layer turbulence measurement using Deuterium beam emission spectroscopy on KSTAR

Intermittent events in the scrape-off layer (SOL) of magnetically confined plasmas, often called blobs and holes, contribute significantly to the particle and heat loss across the magnetic field lines. In this article, the results of the scrape-off layer and edge turbulence measurements are presented with the two-dimensional Deuterium Beam Emission Spectroscopy system (DBES) at KSTAR (Korea Superconducting Tokamak Advanced Research). The properties of blobs and holes are determined in an L-mode and an H-mode shot with statistical tools and conditional averaging. These results show the capabilities and limitations of the SOL turbulence measurement of a 2D BES system. The results from the BES study were compared with the analysis of probe measurements. It was found that while probes offer a better signal-to-noise ratio and can measure blobs down to 3 mm size, BES can monitor the two-dimensional dynamics of larger events continuously during full discharges, and the measurement is not limited to the SOL on KSTAR.