Quasi-coherent Fluctuations Research Articles

Various edge low-frequency fluctuations during transition to a detached divertor in Experimental Advanced Superconducting Tokamak

Various edge low-frequency fluctuations with distinct characteristics exist in different detached divertor states. Three edge low-frequency fluctuations ( 10 kHz), namely low-frequency quasi-coherent fluctuation (LFCF), low-frequency broadband frequency fluctuation (LFBF), and low-n X-point mode (LNXM) on Experimental Advanced Superconducting Tokamak (EAST), are systematically assessed. The basic features of these fluctuations, such as spectral width, location, mode number, propagating direction, and particle transport capacities, are examined. LFCF occurs when the inner strike point is energy detached or nearly energy detached with 8–15 eV ( is the electron temperature of the inner strike point), and a large electron temperature gap between the inner and outer strike points 25 eV ( is the electron temperature gap between the inner and outer strike points) is essential for the occurrence of LFCF. By contrast, LFBF occurs when the inner strike point is energy detached with 8 eV, while the outer strike point is nearly energy detached or attached. The of LFBF is generally lower than that of LFCF, which is 25 eV. LNXM is related only to the radiative divertor with impurity seeding and considered to be excited by the geodesic acoustic mode proposed in earlier work (Sun 2021 Nucl. Fusion 61 014002; Diallo 2020 28th IAEA Fusion Energy Conf.), or the coupling of impurity radiation condensation instability and drift waves proposed in a previous work (Ye 2021 Nucl. Fusion 61 116032). In addition, the possible physical mechanisms of LFBF and LFCF are proposed, with LFBF being the purely growing rippling mode and LFCF being the mode formed by the coupling of the rippling mode to the drift waves. Related research may be beneficial to better clarify the various low-frequency fluctuations that occur during different divertor states.

Spectral and correlation analysis of microturbulences in the spherical Globus-M/M2 tokamaks

Results of the studies on turbulences carried out on the Globus-M2 and Globus-M tokamaks are presented. The main focus was on the analysis of the data obtained using Doppler backscattering method (DBS). The developed codes for the analysis of DBS signals allowed to study the effects of turbulences on the operational mode of the tokamak. A description of the data processing codes is also included. The analysis performed indicates the suppression of turbulence and the formation of a velocity shear during the L-H transition. It was also successfully used to study density fluctuations during and between edge localized modes (ELMs). Spectral and correlation analysis also led to the discovery of limit-cycle oscillations (LCO) and quasi coherent fluctuations (QCFs) during the I-phase.

Observation of quasi-coherent fluctuations in the Globus-M spherical tokamak

The first results of studies of quasi-coherent fluctuations (QCFs) in the spherical Globus-M tokamak are presented. QCFs were observed as oscillations of the Doppler backscattering (DBS) amplitude. These oscillations were not detected in the spectra of the complex signal of the quadrature detector, the shift of which determines the plasma rotation velocity. The multi-frequency DBS scheme allowed us to determine the region of existence of the QCFs (ρ = 0.6–0.7). Bicoherence analysis of the backscattered power demonstrates a nonlinear interaction between broadband turbulence and QCFs. The detected QC fluctuations were interpreted as relatively long-wave oscillations that influence the backscattering on shorter-wave oscillations.

High resolution density pedestal measurements during edge localized modes by short-pulse reflectometry in the TCV tokamak

This publication presents high spatio-temporal resolution (mm µs−1) density profile measurements of the pedestal top during type I, III, and small edge localized mode (ELM) H-mode plasmas in the tokamak à configuration variable (TCV). These measurements were performed using a novel short-pulse reflectometer. Average inter-ELM density profiles are obtained via conditional averaging using the D trace as ELM indicator. Changes to the pedestal density profile gradients prior to type-III ELMs reveal unique pedestal dynamics leading to the ELM crash which can provide important experimental data for validation of non-linear MHD ELM simulations. The small-ELM scenario is found to feature a ∼25–35 kHz quasi-coherent density fluctuation near the separatrix 0.993–1.05 not observed during a similar type-I ELM discharge. This oscillation is also found in low-field-side magnetic pick-up probes displaying a ballooning character and n = +1 toroidal mode number. This oscillation could help explain the markedly different pedestal dynamics observed in the small-ELM regime.

Experimental study of core and edge fluctuations by reflectometry on EAST tokamak

An eight-channel poloidal correlation reflectometer (PCR) with O-mode polarization has been installed in the EAST tokamak to measure the fluctuations from core to edge. The PCR launches eight different frequency microwaves (20.4, 24.8, 33, 40, 42.4, 48, 52.6, 57.2 GHz) into the plasma from the low field side and two poloidally separated antennae are used to receive the reflected waves. As a result, the diagnostic can measure fluctuations in eight (radial)× two (poloidal) spatial positions. The diagnostic has been applied to study the core and edge pedestal fluctuations during an inter-ELM phase in H-mode plasma. This inter-ELM phase can be divided into two stages. In the first stage, a low frequency (<50 kHz) broadband fluctuation dominates in the pedestal gradient region. In the second stage, this fluctuation is strongly suppressed and quasi-coherent fluctuations (QCFs) appear. The QCF’s amplitude increases with the pedestal density gradient, implying density gradient driven instabilities. But the core fluctuations inside the pedestal show no evident changes during the inter-ELM phase.

Observation of quasi-coherent density fluctuation in scrape-off layer enhancing boundary transport in high- hybrid plasmas on DIII-D

We report the observation of a quasi-coherent fluctuation (QCF) by the Doppler backscattering system in the scrape-off layer (SOL) region of the DIII-D tokamak. This QCF is observed in high power, high performance hybrid plasmas with near double-null divertor shape during the electron cyclotron heating period. This mode is correlated with a steepened SOL density profile, and leads to significantly elevated particle and heat fluxes between edge localized modes. The SOL QCF is a long-wavelength ion-scale fluctuation (–0.4 and ), and propagates in the ion diamagnetic direction in the plasma frame. Its radial expanse is about 1.5–2 cm, well beyond the typical width of heat flux λ q on DIII-D. Also, the SOL QCF does not show any clear dependence on the effective SOL collisionality, and thus may raise issues on the control of plasma-material interactions in low collisionality plasmas in which the blob-induced transport is reduced. A linear simulation using BOUT++ with a five-field reduced model is performed and compared with experimental observations. In simulation results, an interchange-like density perturbation can be driven by the SOL density gradient, and its peak location and the radial width of the density perturbation are in agreement with the experimental observations.

Full-Wave Modeling of Doppler Backscattering from Filaments

It is recognized that the filaments have a significant effect on the anomalous energy and particle transport in the tokamak periphery. They are actively investigated using various diagnostics in this regard. Recently studies of filaments using the Doppler backscattering method have been performed in the Globus-M and the ASDEX-Upgrade tokamaks. Backscattering from filaments manifests itself as a burst of quasi-coherent fluctuations of the signals of detectors. Such signals are easy to describe in the Born approximation using the diagnostic weighting function. However, the filaments in tokamaks differ noticeably in their size and intensity. With an increase in the amplitude of the filaments, it is necessary to consider the transition from linear scattering to nonlinear one and further up to the transition from backscattering to reflection from a moving filament. This problem can be solved only using a full wave code. Our simulation was carried out using the finite-difference time-domain code IPF-FD3D in slab geometry. We did not resort to using well-known non-linear MHD codes to determine filament parameters. In the simulation artificial filament-like perturbations were used, the parameters of which varied over a wide range. Modeling Doppler backscattering signal was focused on the identification of the influence of the amplitude of the filament and its size on the shape and the size of the Doppler backscattering output signal. The results obtained largely explain the similarity of the IQ detector data registered in different tokamaks.

Observation of spatiotemporal structures of temperature fluctuations by using of a statistical phase detection method in a linear magnetized plasma

In this paper, we evaluated electron temperature fluctuations by using a conditional sampling and a statistical phase detection method. These methods allow us to reconstruct probe I − V characteristics at each time delay; that is, we can extract electron temperature and ion saturation current fluctuations in high temporal resolution without complex electronic circuits. Our method was applied to two quasi-coherent fluctuations observed in a linear magnetized plasma device, PANTA. We observed spatiotemporal structures of electron temperature and ion saturation current fluctuations. The results revealed the amplitudes and phase relation between electron temperature and density fluctuations.

Study of turbulence intermittency in linear magnetized plasma

The intermittent behavior of a quasi-coherent density fluctuation is observed in a laboratory plasma. The quasi-coherent fluctuation is localized but intermittent events are observed in the whole region of plasma. Conditional averaging shows the intermittent events propagate from the central region of the magnetized plasma column to the peripheral region. Auto-correlation function of fluctuations and Hurst analysis reveal the intermittency is highly auto-correlated and the Hurst parameter reaches to 0.8, indicating the existence of self-similar behavior and long-range time correlation, and self-organized criticality dynamics might be the mechanism. Cross-bicoherence between different radii shows the nonlinear coupling between the quasi-coherent fluctuation and ambient turbulence, which will contribute to the generation of intermittency of turbulence.

The study of filaments by the Doppler backscattering method in the ‘Globus-M’ tokamak

Investigation of filamentary structures was performed on the spherical tokamak Globus-M by the Doppler backscattering (DBS) method. Filaments were detected in the H-mode regime both during the edge localized mode event and in the periods between them. They manifested themselves as bursts of quasi-coherent fluctuations (BQFs) of the output signals of the DBS quadrature detector. To confirm BQF appearing due to backscattering from a moving filament, special experiments were carried out with two DBS systems located at different poloidal angles. Using the new filament research method one could evaluate their velocity, mode number, and radial and poloidal positions. Using this technique, it was possible to estimate the size of the filaments. Experiments have shown that the filaments move predominantly in the direction of the electron diamagnetic drift with a velocity exceeding the velocity of background small-scale fluctuations. Filaments were recorded more frequently when the density gradient on the plasma periphery increased.

3D structure of density fluctuations in the T-10 tokamak and new approach for current profile estimation

The paper is focused on the new systematic measurements of the 3D spatial distributions of the amplitudes, the radial correlation lengths and the long-range correlations along the magnetic field lines for the different turbulence types. The density fluctuations were measured by the heterodyne correlation reflectometry (CR) using the plasma probing with ordinary mode. CR data was supported by recent experiments with the measurements of the perturbation properties using an heavy ion beam probe (HIBP). The new reflectometer antenna array in T-10 tokamak consists of sets of horns distributed at four places toroidally and poloidally over the torus. The experiments confirmed previously found strong poloidal asymmetry of the amplitude for the broadband (BB) and quasi-coherent (QC) fluctuations. It was found that amplitude of density fluctuations is uniform poloidally for the stochastic low frequency (SLF) fluctuations. The radial correlation were measured at four poloidal angles to reveal the poloidal dependence of the radial correlation length for the different fluctuation types. The significant decrease of the radial correlation lengths towards the high magnetic field side was observed for the QC and the SLF fluctuations. The long-range correlations along the field lines were measured by the reflectometers in two cross-sections separated by 1/4 of the torus. The reflectometers had the same probing frequency thus provide reflection from the same magnetic surface. The measurements were carried out at the low and the high field sides with two currents and two magnetic configurations with simultaneous reversal of the toroidal field and plasma current. The positions of the resonance radius were calculated also using 3D tracing of the magnetic field line and demonstrated good agreement with experiment ones. These results allow to propose the new approach for the current profile measurements in tokamaks.

Direct Observation of Nonlinear Coupling between Pedestal Modes Leading to the Onset of Edge Localized Modes.

Prior to eruptive events such as edge localized modes (ELMs), quasicoherent fluctuations, referred to as pedestal modes, are observed in the edge of fusion devices. We report on the investigations of nonlinear coupling between these modes during quasistationary inter-ELM phases leading to the ELM onset. Three dominant modes, with density and magnetic signatures, are identified as key players in the triggering mechanism of certain classes of ELMs. We demonstrate that one of these modes is amplified by the two others through three wave interactions. The amplified mode is radially shifted relative to the other two modes towards the last-closed flux surface as the ELM event approaches. Our results suggest that nonlinear coupling of pedestal modes, associated with radial distortions pushing out of the pedestal, is a possible mechanism for the triggering of low frequency ELMs relevant for future fusion devices.

Fast camera imaging of plasmas in Alcator C-Mod and W7-X

In this work we present an analysis of fast-camera imaging of Alcator C-Mod's divertor region and of the plasma cross section in the W7-X stellarator. In C-Mod, the dynamics of intermittent edge plasma filaments are imaged at 397,100 frames per second in an oblique view. An automatic pipeline was developed to reconstruct the filament motion in the R, Z plane of the divertor using EFIT field line projections. Next, we added our fast-framing camera to W7-X's diagnostic suite for the 2017 run campaign, the first with a divertor. It has a tangential view of the machine cross section, including part of a divertor module. The view is coupled to the camera via a coherent fiber bundle. The spatial resolution is 2–4 cm and the typical plasma brightness limits the fastest usable frame rate to 30k frames/s. We observe filaments in the plasma boundary that rotate around the magnetic axis during radiative collapse; filaments were observed in steady state in the limiter configuration of W7-X by Kocsis et al. [1]. We also observe for the first time a 1–2 kHz quasi-coherent fluctuation in divertor target emissions in the W7-X “standard” magnetic configuration. Finally, a rough analysis of edge gas fueling efficiency using fast camera data and S/XB coefficients finds that fueling is less efficient at densities higher than 4 × 1019 m−3.

Quasi-coherent fluctuation measurement with the upgraded microwave imaging reflectometer in KSTAR

The microwave imaging reflectometer (MIR) is the leading diagnostic tool for study of density fluctuations in KSTAR. For last three years since 2014, major components such as the multi-frequency probe beam source, multi-channel detector array, signal processing electronic system, data acquisition system, and optical system have been gradually upgraded. In this paper, the detailed system upgrade with test results in the laboratory and/or plasma is given, and analysis results of a distinctive fluctuation structure referred to as the quasi-coherent mode (QCM) measured by the upgraded MIR system for an L-mode discharge are presented. Cross-coherence analysis with multiple channels shows that the QCM is localized in a core region and appears to be driven by electron temperature gradient for the discharge.

The observation of small ELM post-cursor mode in EAST

A ‘post-cursor’ quasi-coherent mode with frequency ∼50 kHz has been observed following the crash of small edge localized modes (ELMs) in the Experimental Advanced Superconducting Tokamak by using a reciprocating Langmuir probe system inserted at the outboard midplane. This mode with strong potential and magnetic perturbations propagates in the electron-diamagnetic drift direction in the laboratory frame. In addition, these quasi-coherent fluctuations appear to be modulated by a MHD mode with lower frequency (∼5 kHz). The bi-coherence analysis shows that the post-cursor mode and the MHD mode have nonlinear interaction through three-wave coupling. The understanding on post-cursor mode can enhance our knowledge of ELMs and pedestal physics, and give new insight into the ELM process itself.

Experimental studies of toroidal correlations of plasma density fluctuations along the magnetic field lines in the T-10 tokamak and first results of numerical modeling

The antenna system of reflectometry diagnostics at the T-10 tokamak allows to study long-range toroidal correlations of plasma density fluctuations along the magnetic field lines. The antenna systems are installed in two poloidal cross-sections of the vacuum chamber separated by a 90° angle in the toroidal direction. The experiments, which were conducted at the low field side, showed that the high level of toroidal correlations is observed only for quasi-coherent fluctuations. However, broadband and stochastic low frequency fluctuations are not correlated. Numerical modeling of the plasma turbulence structure in the T-10 tokamak was conducted to interpret the experimental results and take into account non-locality of reflectometry measurements. In the model used, it was assumed that the magnitudes of density fluctuations are constant along the magnetic field lines. The 2D full-wave Tamic-RTH code was used to model the reflectometry signals. High level of correlations for quasi-coherent fluctuations was obtained during the modeling, which agrees with the experimental observations. However, the performed modeling also predicts high level of correlations for broadband fluctuations, which contradicts the experimental data. The modeling showed that the effective reflection radius, from which the information on quasi-coherent plasma turbulence is obtained, is shifted outwards from the reflection radius by approximately 7 mm.

Influence of magnetic configuration on edge turbulence and transport in the H-1 Heliac

The role of the rotational transform (ι) profile on fluctuations and transport is investigated in the H-1 Heliac by means of dynamic (i.e. changing during a shot) and static (fixed during a shot) scans of rotational transform through a range of values where the electron density drops markedly and which correspond to having the point of located near in a region of magnetic well (such that the surface averaged magnetic field strength increases with radius). The gap is near the resonance, but as the resonance is not in the plasma for more than half the gap it is not clear that this is relevant. Although this drop is clearly driven by the variation of helical current, under particular circumstances, similar density changes occur spontaneously. Plasma currents are measured throughout the scan and are found to slightly affect the rotational transform profile, and reverse about the configuration of minimum confinement, while induced currents through a toroidal loop voltage in the dynamical scans are not found to be significant. The confinement and fluctuation properties are studied by means of 2D movable Langmuir probes. Large near edge-localised dithering quasi-coherent fluctuations at kHz develop in a strong density gradient region with low magnetic shear as ι is scanned up to a point where the density collapses in the outer region. This dithering corresponds to an m = 3 mode comprising of standing and propagating components. The net and fluctuation-induced transport components are measured near the plasma edge in a similar discharge, and it is found that fluctuation-induced transport driven by these low frequency coherent modes dominates the particle balance during the low density phase but is only a small component of the net flux when the density is higher.

Toward integrated multi-scale pedestal simulations including edge-localized-mode dynamics, evolution of edge-localized-mode cycles, and continuous fluctuations

The high-fidelity BOUT++ two-fluid code suite has demonstrated significant recent progress toward integrated multi-scale simulations of tokamak pedestal, including Edge-Localized-Mode (ELM) dynamics, evolution of ELM cycles, and continuous fluctuations, as observed in experiments. Nonlinear ELM simulations show three stages of an ELM event: (1) a linear growing phase; (2) a fast crash phase; and (3) a slow inward turbulence spreading phase lasting until the core heating flux balances the ELM energy loss and the ELM is terminated. A new coupling/splitting model has been developed to perform simulations of multi-scale ELM dynamics. Simulation tracks five ELM cycles for 10 000 Alfvén times for small ELMs. The temporal evolution of the pedestal pressure is similar to that of experimental measurements for the pedestal pressure profile collapses and recovers to a steep gradient during ELM cycles. To validate BOUT++ simulations against experimental data and develop physics understanding of the fluctuation characteristics for different tokamak operation regimes, both quasi-coherent fluctuations (QCFs) in ELMy H-modes and Weakly Coherent Modes in I-modes have been simulated using three dimensional 6-field 2-fluid electromagnetic model. The H-mode simulation results show that (1) QCFs are localized in the pedestal region having a predominant frequency at f≃300−400 kHz and poloidal wavenumber at kθ≃0.7 cm−1, and propagate in the electron diamagnetic direction in the laboratory frame. The overall signatures of simulation results for QCFs show good agreement with C-Mod and DIII-D measurements. (2) The pedestal profiles giving rise to QCFs are near the marginal instability threshold for ideal peeling-ballooning modes for both C-Mod and DIII-D, while the collisional electromagnetic drift-Alfvén wave appears to be dominant for DIII-D. (3) Particle diffusivity is either smaller than the heat diffusivity for DIII-D or similar to the heat diffusivity for C-Mod. Key I-mode simulation results are that (1) a strong instability exists at n≥20 for resistive ballooning mode and drift-Alfvén wave; (2) the frequency spectrum of nonlinear BOUT++ simulation features a peak around 300 kHz for the mode number n = 20, consistent with a reflectometer measurement at nearby position; (3) the calculated particle diffusivity is larger than the calculated heat diffusivity, which is consistent with a key feature of the I-mode pedestal with no particle barrier.

Observation of 20–400 kHz fluctuations in the U-3M torsatron

First observations of quasi-coherent fluctuations in the frequency range of 20–400 kHz in Alfvén-wave-heated plasmas of the U-3M torsatron are presented. The excitation conditions of these modes depend on the radio frequency antenna type and the plasma density, the appearance of the modes correlating with the presence of both suprathermal electrons and high-energy ions in the plasma, which supports our opinion that the modes are excited by energetic particles. Complicated evolution of the mode frequencies with abrupt changes at the instants of plasma confinement transitions is observed at the initial stage of each discharge. The frequencies become stable at the stage of the plasma current flattop. Raw estimates show that toroidicity-induced Alfvén eigenmodes could be responsible for the 150–400 kHz fluctuations. Low-frequency 20–70 kHz bursts are observed during plasma confinement transitions. The poloidal mode number of one of these bursts with the frequency of 20 kHz burst was determined to be m = 2. This mode rotated in the electron diamagnetic rotation direction with a frequency lower than the geodesic acoustic mode frequency and can be identified as a drift-sound-type mode.

Correlations between quasi-coherent fluctuations and the pedestal evolution during the inter-edge localized modes phase on DIII-Da)

Direct measurements of the pedestal recovery during an edge-localized mode cycle provide evidence that quasi-coherent fluctuations (QCFs) play a role in the inter-ELM pedestal dynamics. Using fast Thomson scattering measurements, the pedestal density and temperature evolutions are probed on sub-millisecond time scales to show a fast recovery of the density gradient compared to the temperature gradient. The temperature gradient appears to provide a drive for the onset of quasi-coherent fluctuations (as measured with the magnetic probe and the density diagnostics) localized in the pedestal. The amplitude evolution of these QCFs tracks the temperature gradient evolution including its saturation. Such correlation suggests that these QCFs play a key role in limiting the pedestal temperature gradient. The saturation of the QCFs coincides with the pressure gradient reaching the kinetic-ballooning mode (KBM) critical gradient as predicted by EPED1. Furthermore, linear microinstability analysis using GS2 indicates that the steep gradient is near the KBM threshold. Thus, the modeling and the observations together suggest that QCFs are consistent with dominant KBMs, although microtearing cannot be excluded as subdominant.