Fluctuations and anomalous transport in tokamaks

Testing image-velocimetry methods for turbulence diagnostics

Two image-based velocity-inference techniques, cross-correlation time-delay estimation (CCTDE) and dynamic time warping (DTW), were tested. These techniques are conventionally used in the study of plasma dynamics, but they can be applied to any data where features propagate across the image field-of-view. Differences between the techniques were investigated, which showed that the shortcomings of each technique are complemented well by the strengths of the other. Thus, the techniques should be used in conjunction with each other for optimal velocimetry. For ease of use, an example workflow that applies the results in this paper to experimental measurements is provided for both techniques. The findings were based on a thorough analysis of the uncertainties for both techniques. Specifically, the accuracy and precision associated with inferred velocity fields were systematically tested using synthetic data. Novel findings are presented that strongly improve the performance of both techniques, some of which are as follows: CCTDE was able to operate accurately under most conditions with an inference frequency as short as 1 per 32 frames, as opposed to the typical 1 per ≥256 frames used in the literature; an underlying pattern in CCTDE accuracy depending on the magnitude of the underlying velocity was found; spurious velocities due to the barber pole illusion can now be predicted prior to CCTDE velocimetry through a simple analysis; DTW was more robust against the barber pole illusion than CCTDE; DTW performance with sheared flows was tested; DTW was able to reliably infer accurate flow fields from data with as low as 8 × 8 spatial channels; and however, if the flow direction was unknown prior to DTW analysis, DTW could not reliably infer any velocities.

Database study of turbulent electron temperature fluctuation measurements at ASDEX Upgrade

In this work, an automated method for the analysis of data from the correlation electron cyclotron emission (CECE) diagnostic is applied to discharges in the ASDEX Upgrade (AUG) tokamak. This recently developed, automated method provides an efficient means of accurately analysing large quantities of experimental turbulence data, enabling the development of the largest database of CECE measurements of tokamak plasmas to-date. The turbulence database provides the opportunity to search for large-scale trends in experimental data to improve our understanding of transport-relevant plasma turbulence. The results of physics-based investigations utilizing this turbulence database will be reported on separately from this work.

Theory of coupled resistive drift and resistive drift ballooning instabilities in fusion plasma

Drift wave instabilities (DWI) associated with the two-fluid dynamics seems to be responsible for anomalous transport in modern day tokamaks. Ballooning instabilities tend to exchange flux tubes of different pressure, resulting in convective transport. The micro-level turbulence (drift wave) is coupled with the macro-level (ballooning mode) dynamics in fusion experiments. The co-existence of DWI and drift ballooning instabilities (DBI) is discussed in this work using a four-field plasma model. The formulation preserves both the microscopic and macroscopic dynamics of plasma. To demonstrate the coupling, a new dispersion relation is derived to analyze stability of the coupled modes in a non-uniform magnetized plasma. Linear stability of coupled drift-ballooning and drift-acoustic modes have been explored. The two-fluid effect (micro-level influence) through diamagnetic drift frequency for electrons and curvature drift frequency on unstable modes are demonstrated.

Ion temperature and rotation fluctuation measurements with ultra-fast charge exchange recombination spectroscopy (UF-CHERS) in the DIII-D tokamak

An upgraded detector and several optimizations have significantly improved the Ultra-Fast Charge Exchange Recombination Spectroscopy (UF-CHERS) diagnostic sensitivity to ion temperature and parallel velocity fluctuations at turbulence relevant spatio-temporal scales. Normalized broadband ion temperature and parallel velocity fluctuations down to x̃x∼1% (x = T_i, v_∥) and up to ∼450 kHz have been measured in a variety of plasmas. The multi-field nature of the CHERS technique also allows measurements of the cross-phase angles of the fluctuating fields. UF-CHERS is optimized to observe emissions from the electron exchange reaction between intrinsic C⁶⁺ and hydrogenic neutral beam injected particles near 529 nm. UF-CHERS consists of two chords separated by ∼1 cm radially, less than the turbulence correlation length in DIII-D plasmas, which enables correlated measurements to suppress incoherent electronic and photon noise. The optical components of the spectrometer include a volume-phase-holographic grating with >90% transmission between 528 and 530 nm and f/2 200-mm lenses, selected to maximize the optical efficiency and photon flux. Diffracted light from each chord is collected in eight spectral bins, each with a bandwidth of ∼0.25 nm, and detected and amplified by chilled avalanche photodiodes and custom high-gain, wide bandwidth low-noise preamplifiers to achieve the optimal signal-to-noise ratio. The resulting signals are digitized at 1 MHz, 10³-10⁴× faster than the conventional CHERS diagnostics. Spatial coverage is achieved by repositioning a motorized fiber tray between plasmas. UF-CHERS measurements will advance the understanding of turbulent ion transport and contribute to the validation of transport models and simulations.

Review of plasma turbulence experiments

Understandings of turbulent plasma have been developed along with nuclear fusion research for more than a half century. Long international research has produced discoveries concerning turbulent plasma that allow us to notice the hidden nature and physics questions that could contribute to other scientific fields and the development of technologies. Guiding concepts have been established up to now that stimulate investigations on turbulent plasma. Research based on concepts concerning symmetry breaking and global linkage requires observing the entire field of plasma turbulence for an ultimate understanding of plasma. This article reviews the achievements as well as contemporary problems regarding turbulence experiments associated with strongly magnetized plasmas in the last and present century, and introduces forthcoming experimental issues, including new diagnostics and physics-oriented devices related to plasma turbulence.

Measurement of electron temperature fluctuations on J-TEXT via correlation ECE

The capabilities of the joint-Texas experimental tokamak correlation electron cyclotron emission (CECE) diagnostic have recently been extended with an upgrade. Four new yttrium iron garnet (YIG) filters from 4 GHz to 18 GHz with a bandwidth of 90 ∼ 230 MHz are added to the previous 4 channels. Optical optimization of the transmission line has improved the poloidal resolution, which allows k _θ < 3.08 cm^-1. The improvement of video amplifiers allows the frequency and amplitude gain to be adjusted discretely from 200 kHz to 1 MHz and from 200 to 1000, respectively, for different situations. A controller is designed to remotely adjust the center frequency of the YIG filters. Based on the CECE, the distribution and the effect of magnetohydrodynamic instabilities on electron temperature fluctuations have been observed. The experiment results show good performance of the upgraded CECE diagnostic.

Measurement of density fluctuation propagation direction via the far-forward collective scattering diagnostic based on polarimeter-interferometer

Previously, the 17-channel three-wave polarimeter-interferometer system (POLARIS) on the J-TEXT tokamak has been implemented to measure far-forward collective scattering (FFCS) from electron density fluctuations. Recently, this system has been exploited to measure the propagation direction of density fluctuation. After considering the refraction of the laser probe beam passing through plasma, the ray tracing result shows that the detector of POLARIS may receive asymmetric far-forward scattering beams. Thus, the heterodyne detection of FFCS is available to identify the propagation direction of density fluctuation by resolving the asymmetric scattering spectrum. Experimentally, the transform of the heterodyne scattering spectrum from symmetry to asymmetry has been observed, while the refraction effect becomes strong demonstrating the capacity of measuring the propagation direction of fluctuation. Furthermore, by changing the plasma potential through the use of an applied positive electrode biasing, the reverse of frequency shift for the heterodyne scattering spectrum is identified, confirming the validity of direction discrimination of density fluctuation.

Turbulent transport reduction induced by transition on radial electric field shear and curvature through amplitude and cross-phase in torus plasma

Spatiotemporal evolutions of radial electric field and turbulence are measured simultaneously in the H-mode transition, which is a prototypical example of turbulence structure formation in high-temperature plasmas. In the dynamical phase where transport barrier is established abruptly, the time-space-frequency-resolved turbulent particle flux is obtained. Here we report the validation of the mechanism of transport barrier formation quantitatively. It is found that the particle flux is suppressed predominantly by reducing density fluctuation amplitude and cross phase between density fluctuation and potential fluctuation. Both radial electric field shear and curvature are responsible for the amplitude suppression as was predicted by theory. Turbulence amplitude reduction immediately responds to the growth of the radial electric field non-uniformity and saturates, while cross phase continuously approaches zero.

Measurement of the internal magnetic fluctuation by the transport of runaways on J-TEXT

The measurement of internal magnetic fluctuation is important for the study of transport in tokamak plasmas. The runaway electron transport induced by the sawtooth crash can be used to obtain the internal magnetic fluctuation. Inversed sawtooth-like activities on hard x-ray (HXR) fluxes following sawtooth activities were observed after the application of electrode biasing on J-TEXT tokamak. The runaway diffusion coefficient D_r is deduced to be about 30 m²/s according to the time delay of HXR flux peaks to the sawtooth crashes. The averaged value of normalized magnetic fluctuation in the discharges with electrode biasing was increased to the order of 1 × 10^-4.

Experimental Identification of Electric Field Excitation Mechanisms in a Structural Transition of Tokamak Plasmas

Self-regulation between structure and turbulence, which is a fundamental process in the complex system, has been widely regarded as one of the central issues in modern physics. A typical example of that in magnetically confined plasmas is the Low confinement mode to High confinement mode (L-H) transition, which is intensely studied for more than thirty years since it provides a confinement improvement necessary for the realization of the fusion reactor. An essential issue in the L-H transition physics is the mechanism of the abrupt "radial" electric field generation in toroidal plasmas. To date, several models for the L-H transition have been proposed but the systematic experimental validation is still challenging. Here we report the systematic and quantitative model validations of the radial electric field excitation mechanism for the first time, using a data set of the turbulence and the radial electric field having a high spatiotemporal resolution. Examining time derivative of Poisson's equation, the sum of the loss-cone loss current and the neoclassical bulk viscosity current is found to behave as the experimentally observed radial current that excites the radial electric field within a few factors of magnitude.

A prototype diagnostics system to detect ultraviolet emission for plasma turbulence

A system to detect ultraviolet emissions from plasma is developed for multi-point measurement, the target of which is the imaging of turbulence with a high temporal resolution. A fluorescent glass, which converts ultraviolet emissions to visible light with a wavelength of approximately 540 nm, is utilized in the system. Following the conversion, the fluorescent light is transferred with fibre optics, and is converted to electric signals in a location that is sufficiently distant from an electrically noisy environment around the plasma device. This paper describes a prototype system of this diagnostic method and discusses the spectral analysis obtained using a low-aspect-ratio reversed field pinch RELAX.

Modification of tokamak edge plasma turbulence and transport by biasing and resonant helical magnetic field

In this paper, both Resonant Helical magnetic Field (RHF) and limiter biasing have been applied to the tokamak. We have investigated their effects on the turbulence and transport of the particles at the edge of the plasma. The biased limiter voltage has been fixed at 200 V and RHF has L = 2 and L = 3. Also, the effects of the time order of the application of RHF and biasing to the tokamak have been explored. The experiment has been performed under three conditions. At first, the biasing and RHF were applied at t = 15 ms and at t = 20 ms. In the next step, RHF and biasing were applied at t = 15 ms and t = 20 ms, respectively. Finally, both of them were turned on at t = 15 ms until the end of the shot. For this purpose, the ion saturation current (I(sat)) and the floating potential (V(f)) have been measured by the Langmuir probe at r/a = 0.9. Moreover, the power spectra of I(sat) and floating potential gradient (∇V(f)), the coherency, the phase between them, and the particle diffusion coefficient have been calculated. The density fluctuations of the particles have been measured by the Rake probe and they have been analyzed with the Probability Distribution Function (PDF) technique. Also the particle diffusion coefficient has been determined by the Fick's law. The results show that, when RHF and biasing were applied at the same time to the plasma (during flatness region of plasma current), the radial particle density gradient, the radial particle flux, and the particle diffusion coefficient decrease about 50%, 60%, and 55%, respectively, compared to the other conditions. For more precision, the average values of the particle flux and the particle density gradient were calculated in the work. When the time is less than 15 ms, the average values of the particle flux and the particle density gradient are identical under all conditions, but in the other time interval they change. They reduce with the simultaneous application of biasing and RHF. The same results obtain from the histogram of the particle flux and the gradient of the particle density and the particle diffusion coefficient. Consequently, the simultaneous application of biasing and RHF is more effective for the plasma confinement.

Observation of a critical gradient threshold for electron temperature fluctuations in the DIII-D Tokamak

A critical gradient threshold has been observed for the first time in a systematic, controlled experiment for a locally measured turbulent quantity in the core of a confined high-temperature plasma. In an experiment in the DIII-D tokamak where L(T(e))(-1) = |∇T(e)|/T(e) and toroidal rotation were varied, long wavelength (k(θ)ρ(s) ≲ 0.4) electron temperature fluctuations exhibit a threshold in L(T(e))(-1): below, they change little; above, they steadily increase. The increase in δT(e)/T(e) is concurrent with increased electron heat flux and transport stiffness. Observations were insensitive to rotation. Accumulated evidence strongly enforces the identification of the experimentally observed threshold with ∇T(e)-driven trapped electron mode turbulence.

Supersonic helium beam diagnostic for fluctuation measurements of electron temperature and density at the Tokamak TEXTOR

A supersonic helium beam diagnostic, based on the line-ratio technique for high resolution electron density and temperature measurements in the plasma edge (r/a > 0.9) was designed, built, and optimised at TEXTOR (Torus Experiment for Technology Oriented Research). The supersonic injection system, based on the Campargue skimmer-nozzle concept, was developed and optimised in order to provide both a high neutral helium beam density of n(0) = 1.5 × 10(18) m(-3) and a low beam divergence of ±1° simultaneously, achieving a poloidal resolution of Δ(poloidal) = 9 mm. The setup utilises a newly developed dead volume free piezo valve for operation in a high magnetic field environment of up to 2 T with a maximum repetition rate of 80 Hz. Gas injections are realised for a duration of 120 ms at a repetition rate of 2 Hz (duty cycle 1/3). In combination with a high sensitivity detection system, consisting of three 32 multi-channel photomultipliers (PMTs), measurements of edge electron temperature and density with a radial resolution of Δ(radial) = 2 mm and a maximum temporal resolution of Δt ≃ 2 μs (470 kHz) are possible for the first time. The diagnostic setup at TEXTOR is presented. The newly developed injection system and its theoretical bases are discussed. The applicability of the stationary collisional-radiative model as basis of the line-ratio technique is shown. Finally, an example of a fluctuation analysis demonstrating the unique high temporal and spatial resolution capabilities of this new diagnostic is presented.

Beam emission spectroscopy turbulence imaging system for the MAST spherical tokamak

A new beam emission spectroscopy turbulence imaging system has recently been installed onto the MAST spherical tokamak. The system utilises a high-throughput, direct coupled imaging optics, and a single large interference filter for collection of the Doppler shifted D(α) emission from the ~2 MW heating beam of ~70 keV injection energy. The collected light is imaged onto a 2D array detector with 8 × 4 avalanche photodiode sensors which is incorporated into a custom camera unit to perform simultaneous 14-bit digitization at 2 MHz of all 32 channels. The array is imaged at the beam to achieve a spatial resolution of ~2 cm in the radial (horizontal) and poloidal (vertical) directions, which is sufficient for detection of the ion-scale plasma turbulence. At the typical photon fluxes of ~10(11) s(-1) the achieved signal-to-noise ratio of ~300 at the 0.5 MHz analogue bandwidth is sufficient for detection of relative density fluctuations at the level of a few 0.1%. The system is to be utilised for the study of the characteristics of the broadband, ion-scale turbulence, in particular its interaction with flow shear, as well as coherent fluctuations due to various types of MHD activity.

Beam emission spectroscopy for density turbulence measurements on the MAST spherical tokamak

Beam emission spectroscopy (BES) of the energetic deuterium (D(0)) heating beams can provide a means of characterizing the density turbulence in tokamak plasmas. First such measurements have been performed on the MAST spherical tokamak using a trial BES system, which shares the collection optics of the charge-exchange recombination spectroscopy system. This system, with eight spatial channels covering the outer part of the plasma cross section, uses avalanche photodiode detectors with custom preamplifiers to provide measurements at 1 MHz bandwidth with a spatial resolution of 4 cm. Simulations of the measurement, including the beam absorption and excitation, line-of-sight integration of the emission spectrum, and the characteristics of the detection system have been benchmarked against the measured absolute intensity of the Doppler shifted Dalpha fluorescence from the 50 keV beam. This gives confidence in predictions of the performance of a two-dimensional imaging BES system planned for MAST. Correlation techniques have also provided information on the characteristics of the density turbulence at the periphery of L-mode plasmas as well as density perturbations due to coherent magnetohydrodynamic activity at the edge of H-mode plasmas. Precursor oscillations of the density in the pedestal region to edge-localized modes occurring during H-mode plasmas with a single-null diverted magnetic configuration are also observable in the raw signals from the trial BES system.

A collective scattering system for measuring electron gyroscale fluctuations on the National Spherical Torus Experiment

A collective scattering system has been installed on the National Spherical Torus Experiment (NSTX) to measure electron gyroscale fluctuations in NSTX plasmas. The system measures fluctuations with k( perpendicular)rho(e) less, similar0.6 and k( perpendicular) less, similar20 cm(-1). Up to five distinct wavenumbers are measured simultaneously, and the large toroidal curvature of NSTX plasmas provides enhanced spatial localization. Steerable optics can position the scattering volume throughout the plasma from the magnetic axis to the outboard edge. Initial measurements indicate rich turbulent dynamics on the electron gyroscale. The system will be a valuable tool for investigating the connection between electron temperature gradient turbulence and electron thermal transport in NSTX plasmas.

Observation of reduced electron-temperature fluctuations in the core of H-mode plasmas

Core electron-temperature fluctuations [0.5%< or =T[over ]_(e)/T_(e)< or =2%, k_(theta)rho_(s)< or =0.3 in neutral-beam-heated low confinement-mode (L-mode) plasmas] are observed to decrease by at least a factor of 4 in standard and quiescent high-confinement-mode (H-mode and QH-mode) regimes in the DIII-D tokamak (r/a=0.7). These fluctuations are attributed to ion temperature gradient (ITG) modes stabilized by rotational shear at the H-mode transition. The simultaneous reduction in electron heat diffusivity (chi_(e)(QH)/chi_(e)(L)<0.25) suggests that T[over ]_(e) fluctuations can contribute significantly to L-mode electron heat transport.

Renormalization of tracer turbulence leading to fractional differential equations

For many years quasilinear renormalization has been applied to numerous problems in turbulent transport. This scheme relies on the localization hypothesis to derive a linear transport equation from a simplified stochastic description of the underlying microscopic dynamics. However, use of the localization hypothesis narrows the range of transport behaviors that can be captured by the renormalized equations. In this paper, we construct a renormalization procedure that manages to avoid the localization hypothesis completely and produces renormalized transport equations, expressed in terms of fractional differential operators, that exhibit much more of the transport phenomenology observed in nature. This technique provides a first step toward establishing a rigorous link between the microscopic physics of turbulence and the fractional transport models proposed phenomenologically for a wide variety of turbulent systems such as neutral fluids or plasmas.

Control of Hamiltonian chaos as a possible tool to control anomalous transport in fusion plasmas

It is shown that a relevant control of Hamiltonian chaos is possible through suitable small perturbations whose form can be explicitly computed. In particular, it is possible to control (reduce) the chaotic diffusion in the phase space of a Hamiltonian system with 1.5 degrees of freedom which models the diffusion of charged test particles in a turbulent electric field across the confining magnetic field in controlled thermonuclear fusion devices. Though still far from practical applications, this result suggests that some strategy to control turbulent transport in magnetized plasmas, in particular, tokamaks, is conceivable. The robustness of the control is investigated in terms of a departure from the optimum magnitude, of a varying cutoff at large wave vectors, and of random errors on the phases of the modes. In all three cases, there is a significant region of maximum efficiency in the vicinity of the optimum control term.

Adiabatic electron thermal pressure fluctuations in tokamak plasmas

Electron thermal pressure fluctuations measured in the edge plasma of the Texas Experimental Tokamak Upgrade are a fundamental component of plasma turbulence on both sides of the velocity shear layer. The ratio of specific heats, estimated from fluctuations in electron temperature and electron number density measured simultaneously at the same electrode, indicates that observed fluctuations are adiabatic. The observations are made by means of a novel Langmuir probe technique, the time domain triple-probe method, which concurrently measures multiple plasma properties at each of two electrodes with the temporal and the spatial resolution required to estimate thermodynamic properties in a turbulent plasma.

Signature of turbulent zonal flows observed in the DIII-D tokamak

The spectrum of turbulent density fluctuations at long poloidal wavelengths in the edge plasma of the DIII-D tokamak peaks at nonzero radial wave number. The associated electric-potential fluctuations cause sheared E x B flows primarily in the poloidal direction. These zonal flows have been predicted by theory and are believed to regulate the overall level of turbulence and anomalous transport. This study provides the first indirect experimental identification of zonal flows.