Edge Turbulence Research Articles

Recent progress towards a physics-based understanding of the H-mode transition

Results from recent experiment and numerical simulation point towards a picture of the L-H transition in which edge shear flows interacting with edge turbulence create the conditions needed to produce a non-zero turbulent Reynolds stress at and just inside the LCFS during L-mode discharges. This stress acts to reinforce the shear flow at this location and the flow drive gets stronger as heating is increased. The L-H transition ensues when the rate of work done by this stress is strong enough to drive the shear flow to large values, which then grows at the expense of the turbulence intensity. The drop in turbulence intensity momentarily reduces the heat flux across the magnetic flux surface, which then allows the edge plasma pressure gradient to build. A sufficiently strong ion pressure gradient then locks in the H-mode state. These results are in general agreement with previously published reduced 0D and 1D predator prey models. An extended predator–prey model including separate ion and electron heat channels yields a non-monotonic power threshold dependence on plasma density provided that the fraction of heat deposited on the ions increases with plasma density. Possible mechanisms to explain other macroscopic transition threshold criteria are identified. A number of open questions and unexplained observations are identified, and must be addressed and resolved in order to build a physics-based model that can yield predictions of the macroscopic conditions needed for accessing H-mode.

Non-Ideal Ballooning Mode Instability with Real Electron Inertia

Impacts of electron inertia with an electron skin depth (ESD) longer than the realistic value used in early numerical studies on non-ideal ballooning modes (NIBMs) are numerically investigated by a linearized 3-field reduced MHD model. In this paper, 4 different ESDs,are used for an resistivity dependence study of the growth rate of NIBMs, where de s the real ESD and d*e = 10 corresponds to an order of ESD used in a numerical study on collisionless ballooning mode (CBM) reported in [Kleva and Guzdar Phys. Plasmas 6, 116 (1999)]. In the case with the real ESD d*e = de, a transition from resistive ballooning mode (RBM) to CBM occurs in the edge relevant resistivity regime, while the electron inertia effect is overestimated and the growth rate is almost independent of resistivity in the cases with d∗e =√10de and 10de. These results indicate that the real ESD is one of key factors for the edge stability and turbulence analysis.

Spark ignition of a turbulent shear-less fuel–air mixing layer

A planar methane–air mixing layer with equal velocity in the two streams has been used to examine the ignition probability and the non-premixed edge flame speed following spark ignition. The mixing layer has approximately homogeneous turbulent intensity and lengthscale. Mean local mixture fraction has also been measured for the whole flow field. The ignition and subsequent flame propagation were visualized with a high-speed camera and the flame’s edges in the upstream, downstream and cross-stream directions have been identified. The average rate of flame evolution in these directions allowed an estimation of the average absolute flame speed. Ignition probability contour of the mixing layer takes a V-shape, which matches the shape of the lean and rich flammability limits with a little discrepancy in the rich side. By subtracting the uniform mean velocity resulted in estimates of the mean relative edge flame speed. This quantity was approximately 2.5SL, where SL is the laminar burning velocity of stoichiometric methane–air premixed flames. The results are consistent with DNS of turbulent edge flames.

Three dimensional measurements of Geodesic Acoustic Mode with correlation Doppler reflectometers

Correlation Doppler reflectometers have been newly developed in the HL-2A Tokamak. Owing to the flexibility of the diagnostic arrangements, the multi-channel systems allow us to study, simultaneously, the radial properties of edge turbulence and its long-range correlation in both the poloidal and toroidal direction. With these reflectometers, three-dimensional spatial structure of Geodesic Acoustic Mode (GAM) is surveyed, including the symmetric feature of Er fluctuations in both poloidal and toroidal directions, and the radial propagation of GAMs. The bi-coherence analysis for the Er fluctuations suggests that the three-wave nonlinear interaction could be the mechanism for the generation of GAM. The temporal evolution of GAM during the plasma density modulation experiments has been studied. The results show that the collisional damping plays a role in suppressing the GAM magnitudes, and hence, weakening the regulating effects of GAM on ambient turbulence. Three dimensional correlation Doppler measurements of GAM activity demonstrate that the newly developed correlation Doppler reflectometers in HL-2A are powerful tools for edge turbulence studies with high reliability.A shorter version of this contribution is due to be published in PoS at: ``1st EPS conference on Plasma Diagnostics''.

Edge and SOL turbulence and blob variations over a large database in NSTX

This paper describes the range of variations in edge and SOL turbulence observed using a gas puff imaging (GPI) diagnostic in NSTX discharges. The database consists of 140 shots including Ohmic, L-mode, and H-mode plasmas measured during steady-state conditions (e.g. without ELMs). Turbulence quantities were evaluated using both cross-correlation analysis and blob tracking. Relative fluctuation levels varied from –1.0, correlation times were –40 μs, correlation lengths were –10 cm, and turbulence velocities were km s−1 and km s−1 outwards. These variations were evaluated with respect to both the global and local edge plasma parameters, and compared with simplified theoretical models.

Simulation as a tool to improve wave heating in fusion plasmas

Firstly, a brief overview will be given on different models that are able to describe the behaviour of wave propagation as a function of specific frequency ranges. Each range corresponds to different heating systems, namely, 20–100 MHz for the ion cyclotron resonant heating, 2–20 GHz for lower-hybrid heating or current drive, and 100–250 GHz for electron cyclotron resonant heating or current drive systems. The specification of every system will be explained in detail, including the typical set of equations and the assumptions needed to describe the properties of these heating or current drive systems, as well as their specific domains of validity. In these descriptions, special attention will be paid to the boundary conditions. A review of specific physical problems associated with the wave heating systems will also be provided. The review will detail the role of simulation in answering questions that arise from experiments on magnetized plasma devices devoted to fusion. A few examples that will be covered are the impact of edge turbulence on wave propagation and its consequences on heating system performance, the effects of fast particles and ponderomotive effects, among others. A study that is more focused on radio-frequency sheath effects will also be discussed. It shows that such simulations require very sophisticated tools to gain a partial understanding of the observations undertaken in dedicated experiments. To conclude this review, an overview will be given about the requirements and progress necessary to obtain relevant predictive simulation tools able to describe the wave heating systems used in fusion devices.

Alcator C-Mod: research in support of ITER and steps beyond

This paper presents an overview of recent highlights from research on Alcator C-Mod. Significant progress has been made across all research areas over the last two years, with particular emphasis on divertor physics and power handling, plasma–material interaction studies, edge localized mode-suppressed pedestal dynamics, core transport and turbulence, and RF heating and current drive utilizing ion cyclotron and lower hybrid tools. Specific results of particular relevance to ITER include: inner wall SOL transport studies that have led, together with results from other experiments, to the change of the detailed shape of the inner wall in ITER; runaway electron studies showing that the critical electric field required for runaway generation is much higher than predicted from collisional theory; core tungsten impurity transport studies reveal that tungsten accumulation is naturally avoided in typical C-Mod conditions.

Overview of the RFX-mod contribution to the international Fusion Science Program

The RFX-mod device is operated both as a reversed field pinch (RFP), where advanced regimes featuring helical shape develop, and as a tokamak. Due to its flexibility, RFX-mod is contributing to the solution of key issues in the roadmap to ITER and DEMO, including MHD instability control, internal transport barriers, edge transport and turbulence, isotopic effect, high density limit and three-dimensional (3D) non-linear MHD modelling. This paper reports recent advancements in the understanding of the self-organized helical states, featuring a strong electron transport barrier, in the RFP configuration; the physical mechanism driving the residual transport at the barrier has been investigated. Following the first experiments with deuterium as the filling gas, new results concerning the isotope effect in the RFP are discussed. Studies on the high density limit show that in the RFP it is related to a toroidal particle accumulation due to the onset of a convective cell. In the tokamak configuration, q(a) regimes down to q(a) = 1.2 have been pioneered, with (2,1) tearing mode (TM) mitigated and (2,1) resistive wall mode (RWM) stabilized: the control of such modes can be obtained both by poloidal and radial sensors. Progress has been made in the avoidance of disruptions due to the (2,1) TM by applying q(a) control, and on the general issue of error field control. The effect of externally applied 3D fields on plasma flow and edge turbulence, sawtooth control and runaway electron decorrelation has been analysed. The experimental program is supported by substantial theoretical activity: 3D non-linear visco-resistive MHD and non-local transport modelling have been advanced; RWMs have been studied by a toroidal MHD kinetic hybrid stability code.

Combined hydrogen and lithium beam emission spectroscopy observation system for Korea Superconducting Tokamak Advanced Research.

A novel beam emission spectroscopy observation system was designed, built, and installed onto the Korea Superconducting Tokamak Advanced Research tokamak. The system is designed in a way to be capable of measuring beam emission either from a heating deuterium or from a diagnostic lithium beam. The two beams have somewhat complementary capabilities: edge density profile and turbulence measurement with the lithium beam and two dimensional turbulence measurement with the heating beam. Two detectors can be used in parallel: a CMOS camera provides overview of the scene and lithium beam light intensity distribution at maximum few hundred Hz frame rate, while a 4 × 16 pixel avalanche photo-diode (APD) camera gives 500 kHz bandwidth data from a 4 cm × 16 cm region. The optics use direct imaging through lenses and mirrors from the observation window to the detectors, thus avoid the use of costly and inflexible fiber guides. Remotely controlled mechanisms allow adjustment of the APD camera's measurement location on a shot-to-shot basis, while temperature stabilized filter holders provide selection of either the Doppler shifted deuterium alpha or lithium resonance line. The capabilities of the system are illustrated by measurements of basic plasma turbulence properties.

Nonlinear transfer in heated L-modes approaching the L–H transition threshold in Alcator C-Mod

Nonlinear transfer processes between large-scale edge flows and the ambient broadband fluctuations have been shown to play a significant role in the dynamics of edge turbulence, including spreading power from coherent modes and suppressing turbulence at the formation of edge transport barriers. In order to predict thresholds of confinement regimes, both the transition dynamics and the parametric dependence of the nonlinear energy transfer must be studied. Since the expected flow damping terms depend on ion collision rates and local safety factors, recent experiments aimed also to explore the nonlinear drive at various values of the plasma current, density and amount of auxiliary heating. Nonlinear interactions between zonal flows and turbulence in L-mode are estimated using bispectral as well as time-resolved methods based on gas-puff-imaging in Alcator C-Mod [].

Plasma flows and fluctuations with magnetic islands in the edge plasmas of J-TEXT tokamak

The first comprehensive measurements of plasma flows and fluctuations nearby static magnetic islands driven by resonant magnetic perturbations are presented. These experiments were performed using multiple Langmuir probe arrays on the edge plasmas of the J-TEXT tokamak. Controlled variations of the island size and location are explored. This study aims to understand the interaction between turbulence and magnetic islands, and to elucidate magnetic island effects on edge turbulence and flow intensity profiles, edge electric fields, and thus confinement regime transitions. Turbulence and low frequency flows (LFFs) all drop inside the magnetic island, but increase at its boundary, as island width increases. The geodesic acoustic mode is damped in most of the edge area with magnetic islands. The sign of the radial electric field changes from negative to positive within the islands. The gradient of turbulent stresses vanishes at the island center, and becomes steeper at the boundaries of the islands. The particle transport induced by the turbulence is reduced inside the magnetic islands. The magnetic island effects on flows and turbulence can lead to an increase in LFFs and enhance Reynolds stresses near the last closed flux surface (LCFS). A stronger radial electric field layer can be formed near the LCFS when magnetic islands are present. The results suggest that magnetic islands can be used as a tool to enhance edge turbulence and flows, edge electric fields, and thus to trigger confinement regime transitions.

Mechanisms and dynamics of the external transport barrier formation in non-linear plasma edge simulations

L-H transition features are reproduced using three-dimensional first-principles plasma edge turbulence simulations. A transport barrier is observed to form spontaneously above a threshold of the input power. The physical mechanism relies on the coupling between the equilibrium pressure gradient and the poloidal flow, through both the radial force balance and the neoclassical friction. Accounting for the actual radial profile and time evolution of the latter is key to the barrier formation. It is found that neoclassical friction acts as an energy source for the flow, which largely overcomes the sink due to the turbulent Reynolds stress during the whole barrier lifetime. Importantly, experimentally reported dynamical features are recovered during the formation and lifetime of the barrier. This includes dithering of the radial electric field, which is reminiscent of experimentally observed limit-cycle oscillations and quasi-periodic relaxation oscillations showing similarities with type-III ELMs. These rich dynamics emerge from interplay between turbulence, turbulence-driven flows and the equilibrium flow governed by force balance.

Single velocity-component modeling of leading edge turbulence interaction noise.

A computational aeroacoustics approach is used to predict leading edge turbulence interaction noise for real airfoils. One-component (transverse), two-component (transverse and streamwise), and three-component (transverse, streamwise, and spanwise) synthesized turbulence disturbances are modeled instead of harmonic transverse gusts, to which previous computational studies of leading edge noise have often been confined. The effects of the inclusion of streamwise and spanwise disturbances on the noise are assessed. It is shown that accurate noise predictions can be made by modeling only transverse disturbances which reduces the computational expense of simulations. The accuracy of using only transverse disturbances is assessed for symmetric and cambered airfoils, and also for airfoils at non-zero angle of attack.

Nonlinear parallel momentum transport in strong electrostatic turbulence

Most existing theoretical studies of momentum transport focus on calculating the Reynolds stress based on quasilinear theory, without considering the nonlinear momentum flux- ⟨ṽrñũ∥⟩. However, a recent experiment on TORPEX found that the nonlinear toroidal momentum flux induced by blobs makes a significant contribution as compared to the Reynolds stress [Labit et al., Phys. Plasmas 18, 032308 (2011)]. In this work, the nonlinear parallel momentum flux in strong electrostatic turbulence is calculated by using a three dimensional Hasegawa-Mima equation, which is relevant for tokamak edge turbulence. It is shown that the nonlinear diffusivity is smaller than the quasilinear diffusivity from Reynolds stress. However, the leading order nonlinear residual stress can be comparable to the quasilinear residual stress, and so may be important to intrinsic rotation in tokamak edge plasmas. A key difference from the quasilinear residual stress is that parallel fluctuation spectrum asymmetry is not required for nonlinear residual stress.

Improved confinement in high-density H-modes via modification of the plasma boundary with lower hybrid wavesa)

Injecting Lower Hybrid Range of Frequency (LHRF) waves into Alcator C-Mod's high-density H-mode plasmas has led to enhanced global energy confinement by increasing pedestal temperature and pressure gradients, decreasing the separatrix density, modifying the pedestal radial electric field and rotation, and decreasing edge turbulence. These experiments indicate that edge LHRF can be used as an actuator to increase energy confinement via modification of boundary quantities. H98-factor increases of up to ∼35% (e.g., H98 from 0.75 to 1.0) are seen when moderate amounts of LH power (PLH/Ptot ∼ 0.15) are applied to H-modes of densities n¯e ∼ 3 × 1020 m−3, corresponding to values ∼0.5 of the Greenwald density. However, the magnitude of the improvement is reduced if the confinement quality of the target H-mode plasma is already good (i.e., H98target ∼ 1). Ray-tracing modeling and accessibility calculations for the LH waves indicate that they do not penetrate to the core. The LHRF power appears to be deposited in p...

Multi-scale self-organisation of edge plasma turbulent transport in 3D global simulations

The 3D global edge turbulence code TOKAM3X is used to study the properties of edge particle turbulent transport in circular limited plasmas, including both closed and open flux surfaces. Turbulence is driven by an incoming particle flux from the core plasma and no scale separation between the equilibrium and the fluctuations is assumed. Simulations show the existence of a complex self-organization of turbulence transport coupling scales ranging from a few Larmor radii up to the machine scale. Particle transport is largely dominated by small scale turbulence with fluctuations forming quasi field-aligned filaments. Radial particle transport is intermittent and associated with the propagation of coherent structures on long distances via avalanches. Long range correlations are also found in the poloidal and toroidal direction. The statistical properties of fluctuations vary with the radial and poloidal directions, with larger fluctuation levels and intermittency found in the outboard scrape-off layer (SOL). Radial turbulent transport is strongly ballooned, with 90% of the flux at the separatrix flowing through the low-field side. One of the main consequences is the existence of quasi-sonic asymmetric parallel flows driving a net rotation of the plasma. Simulations also show the spontaneous onset of an intermittent E × B rotation characterized by a larger shear at the separatrix. Strong correlation is found between the turbulent particle flux and the E × B flow shear in a phenomenology reminiscent of H-mode physics. The poloidal position of the limiter is a key player in the observed dynamics.

Generation of a magnetic island by edge turbulence in tokamak plasmas

We investigate, through extensive 3D magneto-hydro-dynamics numerical simulations, the nonlinear excitation of a large scale magnetic island and its dynamical properties due to the presence of small-scale turbulence. Turbulence is induced by a steep pressure gradient in the edge region [B. D. Scott, Plasma Phys. Controlled Fusion 49, S25 (2007)], close to the separatrix in tokamaks where there is an X-point magnetic configuration. We find that quasi-resonant localized interchange modes at the plasma edge can beat together and produce extended modes that transfer energy to the lowest order resonant surface in an inner stable zone and induce a seed magnetic island. The island width displays high frequency fluctuations that are associated with the fluctuating nature of the energy transfer process from the turbulence, while its mean size is controlled by the magnetic energy content of the turbulence.

Report on recent results obtained in TCABR

Recent results of experimental work and theoretical modeling carried out in the TCABR tokamak are reported on characterization of MHD instabilities, improved diagnostics of rotation of the plasma column, excitation of Alven global modes, identification of GAMs, and the effect of rotation on their behavior. Detailed measurements of edge electrostatic perturbations and of magnetic island evolution and rotation indicate that the edge turbulence is substantially affected by the islands growth, leading to a strong modulation of the edge particle losses at the same frequency of the MHD activity. Measurements with spatial resolution also show that the growth of the MHD activity is due to nonlinear coupling of magnetic islands with different poloidal mode numbers, which increases the impurity influx. A new system of data acquisition and processing of the TCABR plasma rotation diagnostic was implemented. The system is based upon a single monochromator coupled with six photomultipliers tubes and allows one toroidal and two poloidal simultaneous rotation measurements. The excitation of Global Alfven Waves - GAW has been investigated, using a new type of radio frequency amplifier. The GAW resonances are searched either by a pre-programmed density variation, at fixed generator frequency, or through three RF frequency sweeps from 2 to 4.5 MHz, at stationary density. GAW resonances have been found and their somewhat new characteristics are presented. The investigation of the effect of poloidal and toroidal rotation on the characteristics of the geodesic acoustic mode has been investigated, both theoretically and experimentally. It is found that the assumption of isothermal flux surfaces gives rise to a third branch of this mode. Detailed predictions coupled with experimental measurements are currently being carried out to investigate this question.

Electron cyclotron resonance heating beam broadening in the edge turbulent plasma of fusion machines

Two analytical models for the ordinary mode propagating through a turbulent inhomogeneous edge plasma layer are developed based on the eikonal perturbation method and weak turbulence theory approach. Simple analytical expression for a diffusion-like angular beam width variation is obtained by both methods in the case of long scale density perturbations. The predictions for the spatial beam width are benchmarked against timeaveraged results coming from the 2D Maxwell's equations solver for different turbulence k-spectra and plasma conditions. The strong (more than twofold) increase of the microwave beam angular and spatial width after crossing the turbulent edge is predicted at realistic parameters for ECRH experiments at ITER.

Impact of magnetic perturbation coils on the edge radial electric field and turbulence in ASDEX Upgrade

The impact of applied magnetic perturbations (MPs) on tokamak edge parameters has been investigated in ASDEX Upgrade low collisionallity L-mode discharges using a flexible set of in-vessel saddle coils (capable of generating n = 0, 1, 2 and 4 toroidal modes) and an extensive set of high resolution edge diagnostics. Doppler reflectometry is used principally to probe the MP field penetration and structure via the radial electric field Er and density fluctuation δne behaviour. Different MP response behaviour are observed for the near scrape-off-layer, SOL, (where Er flattens) and in the confinement region (where the negative Er well reverses). The radial structure of Er and δne are particularly sensitive to the degree of MP resonance with the edge rational field-lines. Specifically, the edge turbulence is enhanced for strongly resonant MPs and reduced when non-resonant. The toroidal structure of the MP response has also been probed for various MP configurations by rotating the MP field toroidally and is found to be different for the edge and near SOL regions.