Edge Turbulence Research Articles

High-Frequency Nongyrokinetic Turbulence at Tokamak Edge Parameters

First of a kind 6D-Vlasov computer simulations of high frequency ion Bernstein wave turbulence for parameters relevant to the tokamak edge show transport comparable to sub-Larmor-frequency gyrokinetic turbulence. The customary restriction of magnetized plasma turbulence studies to the gyrokinetic approximation may not be based on physics but only on a practical constraint due to computational cost. Deciphering turbulent transport is crucial since edge turbulence significantly influences the confinement properties of magnetically confined plasmas. Despite the high computational costs, performing 6D kinetic simulations is essential for understanding the limitations of our current models. Published by the American Physical Society 2024

Impurity convection reversal caused by edge localized turbulence for generating a stationary edge radiative layer in the HL-2A tokamak

Abstract Effect of impurity on edge turbulence was investigated on the HL-2A tokamak by using Neon supersonic molecular beam injection (SMBI). For the first time, a stationary radiative layer accompanied by edge localized turbulence lasting more than 100ms is observed at the edge region ρ=0.7-0.9. This duration is much longer than the SMBI pulse length (1.2ms), indicating that the impurity diffusion is on the whole cancelled out by the impurity convection without spreading of the localized turbulence during this period. This implies that the impurity convection is reversed from positive to negative impurity density gradient region. This reversal could be explained by the parallel impurity compression mechanism. The observed turbulence is a broadband electrostatic turbulence (25-70 kHz) propagating in the electron diamagnetic drift direction with normalized poloidal wavenumber of 0.1≤ kθρs≤0.4. It has been found that the excitation of the edge localized turbulence strongly depends on the local collisionality. This feature is qualitatively predicted by the spectral multiscale gyrokinetic turbulence simulation, which suggests that the turbulence could be a dissipative trapped electron mode (DTEM). This experiment demonstrates that mutual interaction between externally injected impurity ions and edge turbulence can generate a stationary edge radiative layer and avoid impurity core accumulation. These results could provide a potential approach for the formation of a stable impurity radiative layer by impurity injection in tokamaks.

Plasma edge and scrape-off layer turbulence in gyrokinetic simulations of negative triangularity plasmas

Abstract Gyrokinetic simulations in the long-wavelength or drift-kinetic limit are carried out of DIII-D inner-wall-limited (IWL) plasmas to investigate the effect of triangularity on edge and scrape-off layer (SOL) turbulence. The effect of neutral interactions and triangularity on plasma blobs is explored due to the impact blobs can have in setting the SOL width or introducing impurities through interactions with plasma-facing components. Seeded blob simulations with neutrals in shaped SOL scenarios demonstrate that increasing elongation, triangularity, or Shafranov shift decreases radial blob velocities, but neutral interactions have a minor effect. Fully turbulent simulations of DIII-D IWL plasmas include both open- and closed-field-line regions. The negative triangularity (NT) simulation has lower average core Te , lower normalized Te fluctuations, and lower fluxes, but a greater number of coherent structures (blobs) identified with increased size and velocity, on average. Density and electron temperature profiles are within a factor of 2 of experimental values. The increased trapped electron particle fraction in NT simulations is consistent with previous studies.

Density fluctuation statistics and turbulence spreading at the edge of L-mode plasmas

Abstract Long wavelength density fluctuations (kρ_i < 1) are studied using Beam Emission Spectroscopy (BES) at the edge of DIII-D L-mode plasmas (ρ = 0.88-1.1) in scenarios with ECH power ramp (P_ECH up to 1.5 MW), NBI power ramp (P_NBI up to 2.5 MW) and injected torque scan (-1 < T_inj < 0.6 Nm). We find that broadband turbulent density fluctuations (f ~ 20-120 kHz) have a non-Gaussian distribution. Skewness of δn/n changes sign from negative at ρ < 0.95-0.97 to positive at ρ > 0.97, indicating the prevalence of density ‘voids’ at inner radii and density ‘blobs’ at outer radii and outside of the separatrix. Turbulence intensity flux ⟨v ̃_r n ̃^2〉 is calculated to characterize turbulence spreading at the plasma edge. During ECH/NBI power ramps and at counter-I_p injected torque ⟨v ̃_r n ̃^2〉 is directed inward inside the separatrix which is evidence of inward spreading of turbulence intensity from the edge gradient region caused by the inner propagation of density ‘voids’. Significantly weaker ⟨v ̃_r n ̃^2〉 observed with co-I_p torque. Correlation between co-I_p torque, turbulence intensity δn/n at ρ=0.97 and increased SOL heat flux decay length λ_q is found in the torque scan scenario, showing that edge turbulence plays a material role in determining the SOL conditions and heat flux width.

The formation of an radial edge electric field due to finite ion orbit width effects is the possible root cause of the H-mode edge

Abstract Full orbit-following simulations of thermal ions show that finite ion-orbit width effects create charge separation near the last closed flux surface (LCFS) which generates a localized radial electric field. Experimentally, edge electric fields are observed in H-mode plasmas and they are necessary for the edge turbulence suppression via the E × B flow shear mechanism. Confined trapped (and to a lesser extent co-passing) ions near the plasma edge form a positive charge distribution outside the LCFS, while thermal electrons are tied more tightly to field lines owing to their small mass and are poorly confined outside the LCFS, hence charge neutrality is violated outside the LCFS. A large number of reported observations from spherical and conventional tokamaks support the results from the simulations although the simulations were not performed fully self consistently. The results suggest ways to lower the H-mode power threshold and optimize the H-mode plasma edge.

Counteracting sawtooth crash effects via fluctuation-induced inward transport in HL-2A NBI plasma

The Langmuir probe observed an increase in density and floating potential fluctuations after the sawtooth crash at the edge of HL-2A neutral beam injection heated plasma. This process initiates fluctuating-induced radial inward particle transport once the plasma enters a period with strong sawtooth crash. The inward transport comprises broad-band fluctuations with varying scales, which occur uniquely in the immediate aftermath of the sawtooth crash-driven outflow, signifying a transient phenomenon confined to that specific interval. These results demonstrate that the sawtooth crash can significantly impact edge turbulence by modifying electrostatic fluctuations. This modification changes the direction of electric fluctuation-induced particle transport, thereby reducing the influence of the intense sawtooth crash-driven outflow. Furthermore, the observations support the existence of a damping mechanism for the outflow during the formation of inward flux after the sawtooth crash, which may be associated with the recovery process of sawtooth cycle.

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.

From L-mode to the L–H transition, experiments on ASDEX upgrade and related gyrokinetic simulations

This work combines experimental observations from the ASDEX Upgrade tokamak with related gyrokinetic simulations of the turbulence moving from L-mode toward, and beyond, the L–H transition. Dedicated experiments have been performed with slow steps of increasing electron cyclotron heating power. Gyrokinetic simulations of the edge turbulence of these plasmas highlight the key roles of the non-linear electromagnetic effects and the external flow shear (E × B shear), both related to the evolution of the plasma pressure profile with increasing heating power. The increase in the plasma βe destabilizes turbulence at low toroidal mode numbers, that, in turn, is strongly suppressed by the external flow shear. This allows the plasma pressure profiles to evolve without a sharp rise in the turbulent fluxes. When all the experimentally measured plasma parameters are consistently included as inputs of the local gyrokinetic simulations, both the experimental electron and ion heat fluxes are quantitatively reproduced on the whole L-mode phase of the selected discharge. Simulations carried out with edge parameters of an ELM-free H-mode phase still show the importance of the mechanisms discussed earlier while also indicating possible limitations of the local approach.

Experimental evidence for the drift wave nature of the weakly coherent mode in ASDEX Upgrade I-mode plasmas

The improved energy confinement mode (I-mode) is a potential candidate for future fusion power plants, as it combines ELM-free operation with good confinement. The unusual edge transport and turbulence in this regime is still not fully understood. This study analyzes the turbulent structure of the weakly coherent mode (WCM) in ASDEX Upgrade. Measurements from Doppler back-scattering and a thermal helium beam diagnostic are used to determine velocities of the background plasma and the WCM over multiple discharges. A phase velocity of the WCM of the order of 2–5 km s−1 in the electron diamagnetic drift direction is found, quantitatively close to a drift wave assuming negligible temperature fluctuations. A good agreement with a previously proposed mechanism behind the I-mode regime is observed. This marks the first experimental verification of a specific understanding of the WCM and the I-mode regime.

The effect of divertor particle sources on scrape-off-layer turbulence

Tokamak edge turbulence is crucial for the cross-field transport of particles and energy away from the separatrix. A better understanding of what affects the turbulence helps to control the heat flux to the divertor targets and the wall. One potentially important factor is the ion particle source in the divertor, as the neutral pathways and the ionisation source distributions are different depending on the divertor geometry, e.g. vertical- and horizontal-target configurations. Numerically, how to represent the sources and mimic the effects on the SOL in the simulations is still an open question. In this paper, we use a 3D turbulence code STORM, based on drift-reduced Braginskii equations, to study the effects of the divertor particle source distribution on turbulence in a simplified 3D slab geometry. The results show that it requires a large amount of divertor particle source to be peaked near the separatrix to alter the heat flux deposited on the target in attached conditions. This large non-uniform particle source can locally enhance the turbulence in the divertor volume, which redistributes the energy flux to the target and reduces the maximum amplitude. Meanwhile, the plasma profiles evaluated at the outboard midplane, such as the amplitudes and fluctuations of the density and temperature, are marginally changed. Another consequence of our results is that the prediction of the temperature difference between the outboard midplane and the target would be underestimated, if the calculation only considers the conductive heat flux and ignores this enhanced cross-field transport in the divertor.

Finite pedestal width formation from early L-H transition stage with a strong edge safety-factor dependence through the resistive ballooning mode

An approximate modeling of the low- to high-confinement (L-H) transition dynamics is given using the method, similar to that by Hinton et al. [Phys. Fluid B 5, 1281 (1993)], but considering more explicitly the L-mode edge turbulence which is here assumed to be dominated by the resistive ballooning mode (RBM) near the separatrix, while the ion temperature gradient (ITG) mode in the inner edge–core region. It is shown that the L-H transition can then be initiated from an inner edge near the ITG-RBM transition point with a finite width. Especially, this width is found to have a strong edge safety-factor or poloidal field dependence, similar to that shown by the EPED1 model. Meanwhile, unlike the pedestal width, the H-mode threshold power appears to be much less sensitive to the edge safety-factor, in qualitative agreement with the observed weak dependence of the threshold power on plasma current (IP). From an additional brief check, these dependences on IP are also found to be quite different from the behavior of other parameters (ion mass, toroidal field, plasma density, and effective Z-number) where the threshold power depends relatively strongly while the initial width depends somewhat weakly on most of them, except the effective Z-number.

The role of shear flow collapse and enhanced turbulence spreading in edge cooling approaching the density limit

Experimental studies of the dynamics of shear flow and turbulence spreading at the edge of tokamak plasmas are reported. Scans of line-averaged density and plasma current are carried out while approaching the Greenwald density limit on the J-TEXT tokamak. In all scans, when the Greenwald fraction fG=n¯/nG=n¯/(Ip/πa2) increases, a common feature of enhanced turbulence spreading and edge cooling is found. The result suggests that turbulence spreading is a good indicator of edge cooling, indeed better than turbulent particle transport is. The normalized turbulence spreading power increases significantly when the normalized E×B shearing rate decreases. This indicates that turbulence spreading becomes prominent when the shearing rate is weaker than the turbulence scattering rate. The asymmetry between positive/negative (blobs/holes) spreading events, turbulence spreading power and shear flow are discussed. These results elucidate the important effects of interaction between shear flow and turbulence spreading on plasma edge cooling.

Global fluid turbulence simulations in the scrape-off layer of a stellarator island divertor

Isothermal fluid turbulence simulations have been performed in the edge and scrape-off layer (SOL) of an analytic stellarator configuration with an island divertor, thereby providing numerical insight into edge turbulence in regions around islands in a stellarator. The steady-state transport follows the a curvature drive that is inverse to the major radius ( $1/R$ ) toward the outboard side, but large fluctuations are present throughout the island divertor region, with the average wavelength of similar size to the island width. The system exhibits a prominent $m=2$ , $n=5$ mode, where m is the poloidal mode number and n is the toroidal mode number, although other modes are present. The amplitude and radial extent of the density fluctuations are similar throughout the edge and SOL, but can decrease near island O-points. The fluctuations exhibit a predominantly positive skewness on the outboard midplane, indicating blob-like perturbations for the transport into the outer SOL. It is determined that a point on the separatrix is generally more correlated with regions outside of the SOL than a nearby reference point which does not lie on the separatrix.

How turbulence spreading improves power handling in quiescent high confinement fusion plasmas

Viable magnetic fusion devices necessitate combining good confinement with effective power flux handling. A major concern for ITER, and devices beyond, is the divertor heat load width, which sets peak boundary heat loads on the plasma-facing materials. Current estimates of the heat flux width are narrow for future reactors. Here, we demonstrate how pedestal turbulence can expand into, or entrain, the stable scrape-off-layer and so broaden the heat flux width beyond these neoclassical predictions. Employing combined theoretical, computational, and experimental approaches, we focus on quiescent high confinement discharges on the DIII-D tokamak, but the results are of broader significance. Our findings uncover common trends in the edge turbulence intensity flux, the pressure perturbation skewness, and the turbulence mixing length, which together determine the heat flux width. This research demonstrates the physics of scrape-off-layer broadening by turbulence and highlights the promise of a turbulent pedestal for successful core-edge integration in ITER and future fusion devices.

An improved TDE technique for derivation of 2D turbulence structures based on GPI data in toroidal plasma

This paper reports an improved time-delay estimation (TDE) technique for the derivation of turbulence structures based on gas-puff imaging data. The improved TDE technique, integrating an inverse timing search and hierarchical strategy, offers superior accuracy in calculating turbulent velocity field maps and analyzing blob dynamics, which has the power to obtain the radial profiles of equilibrium poloidal velocity, blob size and its radial velocity, even the fluctuation analysis, such as geodesic acoustic modes and quasi-coherent mode, etc. This improved technique could provide important 2D information for the study of edge turbulence and blob dynamics, advancing the understanding of edge turbulence physics in fusion plasmas.

A direct Monte Carlo approach for the modeling of neutrals at the plasma edge and its self-consistent coupling with the 2D fluid plasma edge turbulence model HESEL

This paper presents a novel coupling of a kinetic description of neutrals with a fluid description of a fusion plasma. The code, plasma interacting super-atoms and molecules (PISAM), employs a grid-free Cartesian geometry and a direct simulation Monte Carlo approach to solve the kinetic equations of deuterium atoms and molecules. The grid-free geometry and the parallel nature of the neutral dynamics, in the absence of neutral–neutral interactions, allow for an unlimited and work-efficient parallelization of PISAM that always ensures a balanced workload. The highly optimized Python implementation obtains good performance while securing easy accessibility to new users. The coupling of PISAM with the edge turbulence model HESEL is outlined with emphasis on the technical aspects of coupling Message Passing Interface-parallelized Python and C++ codes. Furthermore, the paper presents and analyzes simulation results from running the coupled HESEL-PISAM model. These results demonstrate the impact of radial neutral transport and plasma–neutral dynamics perpendicular to the magnetic field. Specifically, they illustrate how the inward flow of neutral kinetic energy and the inhibition of radial electric shear, resulting from poloidal momentum transfer between atoms and ions, can affect the energy containment time. By comparing the results of the HESEL-PISAM model with those obtained from coupling HESEL with a diffusive-fluid-neutral model, the capabilities of diffusion models in predicting neutral transport in the plasma edge and scrape-off layer are elucidated.

Self‐organization of plasma edge turbulence in interaction with recycling neutrals

AbstractExperimental results from several tokamaks suggest a strong impact of divertor density regimes on turbulent transport in the edge plasma. Reciprocally, the change in transverse transport and SOL width affects the access to density regimes, making it a fundamental topic for heat exhaust issue. Such phenomenology is highly nonlinear and can only be approached quantitatively using numerical simulations treating turbulence and neutrals recycling physics self‐consistently. In this study, the SOLEDGE3X edge multi‐fluid code is used to investigate the mutual interaction between edge plasma turbulence and neutrals recycling. A fluid neutrals model based on the assumption of a charge‐exchange‐dominated plasma‐neutral interaction has been implemented. Two simulations in circular geometry are compared: one without neutrals, where the particle flux is driven by a constant in flux from the core region, and the other one with neutrals recycling included in which the particle input to the system is self‐consistently injected by a gas puff from the midplane. The presence of the neutrals triggers three types of perturbations on the plasma: a local and non‐axisymmetric one driven by the gas puff, a global perturbation affecting both profiles and turbulence properties in the whole domain, and a local one in the vicinity of the limiter where recycling occurs. The largest effect of the inclusion of self‐consistent neutrals recycling is a large‐scale reorganization of the plasma profiles and turbulence properties due to the dissociation of particle and energy fluxes. These effects are expected to be more important at higher densities regimes or in diverted configuration.

Magnetic flutter effect on validated edge turbulence simulations

Small magnetic fluctuations ( B1/B0∼10−4 ) are intrinsically present in a magnetic confinement plasma due to turbulent currents. While the perpendicular transport of particles and heat is typically dominated by fluctuations of the electric field, the parallel stream of plasma is affected by fluttering magnetic field lines. In particular through electrons, this indirectly impacts the turbulence dynamics. Even in low beta conditions, we find that E × B turbulent transport can be reduced by more than a factor 2 when magnetic flutter is included in our validated edge turbulence simulations of L-mode ASDEX Upgrade. The primary reason for this is the stabilization of drift-Alfvén-waves, which reduces the phase shifts of density and temperature fluctuations with respect to potential fluctuations. This stabilization can be qualitatively explained by linear analytical theory and appreciably reinforced by the flutter nonlinearity. As a secondary effect, the steeper temperature gradients and thus higher η i increase the impact of the ion-temperature-gradient mode on overall turbulent transport. With increasing beta, the stabilizing effect on E × B turbulence increases, balancing the destabilization by induction, until direct electromagnetic perpendicular transport is triggered. We conclude that including flutter is crucial for predictive edge turbulence simulations.

Impact of microwave beam scattering by density fluctuations on the electron–cyclotron power deposition profile in tokamaks

Electron–cyclotron waves are a tool commonly used in tokamaks, in particular to drive current. Their ability to drive current in a very localized manner renders them an optimal tool for MHD mode mitigation. However, such applications require high accuracy and good control of the power deposition location to efficiently target the magnetic islands. It has been indirectly observed that the suprathermal electron distribution, resulting from the wave absorption, is broader than what is expected from experimentally-constrained forward drift-kinetic modeling. The present paper explores the possibility that beam scattering through the turbulent edge of the plasma may explain this observed discrepancy. In particular, full-wave studies exhibit three beam broadening regimes, from superdiffusive to diffusive, with an intermediate regime characterized by a Lorentzian beam profile with a slightly increased full-width at half maximum with respect to the quiet plasma case. In the tokamak à configuration variable, dedicated plasma scenarios have been developed to test this hypothesis. A realistic worst-case fluctuation scenario falls into this intermediate beam broadening regime. By comparing the experimental hard x-ray emission from suprathermal electron Bremmstrahlung with the emission calculated by coupling a full-wave model to a Fokker–Planck solver, it is shown that, in the tested cases, the beam broadening is not sufficient to explain the aforementioned discrepancy between simulation and experiment and that another mechanism must play the main role in broadening the suprathermal electron distribution.

Overview of recent turbulence studies across multiple confinement modes at the ASDEX Upgrade tokamak using the Correlation Electron Cyclotron Emission diagnostic

This work presents an overview of recent and ongoing experimental measurements of core and edge turbulence across multiple confinement regimes using the Correlation Electron Cyclotron Emission (CECE) diagnostic at the ASDEX Upgrade (AUG) tokamak. A common goal among these investigations is to identify how the properties of the turbulent electron temperature fluctuations measured by CECE influence and regulate the unique transport characteristics of each confinement regime, including L-mode, I-mode, ELMy H-mode, and ELM-free H-mode. Optics and signal processing methods to aid in the analysis and interpretation of experimental turbulence results are also presented. These methods, and particularly the down-sampling and ensemble averaging method, are relevant to a wide variety of fusion and non-fusion applications.