Poloidal Correlation Lengths Research Articles

Parametric dependence of microwave beam broadening by plasma density turbulence

High-power microwave beams used for heating and current drive in magnetically confined fusion plasmas can be broadened significantly by plasma turbulence, negatively impacting the efficiency of the machine. The dependence of this beam broadening on plasma and beam parameters is not yet fully understood, particularly where the dependence on one parameter is not separable from the dependence on the other parameters, meaning the dependence must be expressed via functions of linear combinations of parameters, rather than functions of single parameters. The aim of this work is to develop an empirical model for how the broadening depends on plasma and beam parameters, allowing for the easy estimation of beam broadening by turbulence without the need for computationally expensive full-wave simulations. In this paper, a microwave beam is simulated propagating through a turbulent layer of plasma using the 2D full-wave cold plasma code EMIT-2D. The dependence of beam broadening on background plasma density, fluctuation amplitude, turbulence correlation lengths in the radial and poloidal direction, thickness of the turbulence layer, and microwave beam waist are considered. The parameter scans are conducted in pairwise combinations of the parameters in order to determine the separability of the dependencies. We find that the dependence on the radial and poloidal correlation lengths are not separable from each other, and neither are the dependences on the fluctuation level and the background density, but all other dependencies are separable. Ignoring this inseparability in the correlation lengths will usually result in an over-prediction of the broadening in tokamak plasmas. An empirical formula for the beam broadening based on the turbulence and beam parameters is found for fusion-relevant scenarios, making prediction of the effect possible in microseconds, instead of the hours required for full-wave simulation. This could then be of use for integrated modelling of heating and current drive systems.

Divertor leg filaments in NSTX-U

This paper presents the first observation of divertor localized turbulence in the NSTX-Upgrade spherical tokamak. Previous work in NSTX discharges (Maqueda et al 2010 Nucl. Fusion 50 075002) described fluctuations on the divertor target due to blobs generated on the low field side midplane. In the region that shows disconnection from upstream turbulence (private flux region and proximity of the strike point), divertor-localized fluctuations are observed via imaging of C III and D-α emission in diverted L-mode discharges and are characterized in this paper. Field-aligned filaments connected to the divertor target plate are radially localized at the separatrix on the outer divertor leg and in the private flux region on the inner divertor leg. These are limited to the region below the X-point with fluctuation levels up to 10%–20%. The filaments have comparable poloidal and radial correlation lengths (10–100 ion gyroradii ) and parallel correlation lengths of several meters. Toroidal mode numbers are in the range of 10–30 and 2–10 for outer and inner leg filaments. The poloidal motion of outer leg filaments has the same direction and comparable magnitude to advection due to drift calculated by the multi-fluid edge transport code UEDGE with inclusion of cross field drifts. Disconnection between inner and outer leg filaments as well as the absence of correlation with upstream turbulence support the hypothesis of X-point disconnection for divertor leg filaments. Simulations with the ArbiTER linear eigenvalue solver and a resistive-balooning model were performed with a simulation grid limited to the divertor legs. Instabilities localized to the bad curvature side of the divertor legs were observed, in qualitative agreement with the experiment.

Evolution of magnetic Kubo number of stochastic magnetic fields during the edge pedestal collapse simulation

Using a statistical correlation analysis, we compute the evolution of the magnetic Kubo number during an edge pedestal collapse in nonlinear reduced magnetohydrodynamic simulations. The Kubo number is found not to exceed the unity in spite of performing the simulation with a highly unstable initial pressure profile in the ideal ballooning mode. During the edge pedestal collapse, the Kubo number is within the values of 0.2 and 0.6 suggesting that the quasilinear diffusion model is sufficient to explain the energy loss mechanism during the pedestal collapse. Temporal evolution of poloidal correlation lengths of pressure fluctuations resembles with that of the Chirikov parameter and the Kubo number, while radial correlation lengths of the pressure fluctuations are strongly correlated with the radial width of the magnetic stochastic layer.

Energy exchange dynamics across L–H transitions in NSTX

We studied the energy exchange dynamics across the low-to-high-confinement (L–H) transition in NSTX discharges using the gas-puff imaging (GPI) diagnostic. The investigation focused on the energy exchange between flows and turbulence to help clarify the mechanism of the L–H transition. We applied this study to three types of heating schemes, including a total of 17 shots from the NSTX 2010 campaign run. Results show that the edge fluctuation characteristics (fluctuation levels, radial and poloidal correlation lengths) measured using GPI do not vary just prior to the H-mode transition, but change after the transition. Using a velocimetry approach (orthogonal-dynamics programming), velocity fields of a cm GPI view during the L–H transition were obtained with good spatial (∼1 cm) and temporal (∼2.5 μs) resolutions. Analysis using these velocity fields shows that the production term is systematically negative just prior to the L–H transition, indicating a transfer from mean flows to turbulence, which is inconsistent with the predator–prey paradigm. Moreover, the inferred absolute value of the production term is two orders of magnitude too small to explain the observed rapid L–H transition. These discrepancies are further reinforced by consideration of the ratio between the kinetic energy in the mean flow to the thermal free energy, which is estimated to be much less than 1, suggesting again that the turbulence depletion mechanism may not play an important role in the transition to the H-mode. Although the Reynolds work therefore appears to be too small to directly deplete the turbulent free energy reservoir, order-of-magnitude analysis shows that the Reynolds stress may still make a non-negligible contribution to the observed poloidal flows.

Comparison of 3D flux-driven scrape-off layer turbulence simulations with gas-puff imaging of Alcator C-Mod inner-wall limited discharges

We carry out a quantitative comparison between gas-puff imaging (GPI) turbulence measurements in Alcator C-Mod inner-wall limited discharges (Zweben et al 2009 Phys. Plasmas 18 082505) and 3D flux-driven drift-reduced Braginskii turbulence simulations of scrape-off layer dynamics. The comparison is carried out for a series of inner-wall limited discharges where the magnetic field and the density are varied. The comparison between GPI data and non-linear simulations yields overall good agreement for several observables, such as the Dα emission levels and intermittency, the radial and poloidal correlation lengths and propagation velocities, and the power and frequency spectral density.

Comparison of fluctuations properties measured by Langmuir and ball-pen probes in the ISTTOK boundary plasma

In this work, the fluctuations properties measured by Langmuir and ball-pen probes are compared, aiming at investigating the influence of temperature fluctuations on Langmuir probe measurements, including the cross-field turbulent particle flux. With this aim, a 5-pin probe was designed to estimate the radial particle transport due to fluctuations simultaneously using Langmuir and ball-pen probes. A considerable difference is observed in the amplitude of the floating potential fluctuations measured by the two types of probes, but not in statistical properties such as skewness. The turbulent particle flux was found to be roughly four times larger when measured with Langmuir probes. However, quantities such as the phase velocity of the fluctuations or the poloidal correlation lengths are not significantly different, as floating potential fluctuations measured by both types of probes are highly correlated and roughly in phase. Finally, it is suggested that ball-pen and emissive probes may underestimate the amplitude of the plasma potential fluctuations and therefore probe measurements must be carefully validated.

Progress in characterization of the pedestal stability and turbulence during the edge-localized-mode cycle on National Spherical Torus Experiment

Progress in characterizing the edge stability and properties of the microinstabilities responsible for enhanced transport in the pedestal region is reported. The stability of the pedestal is characterized in high performance discharges on National Spherical Torus Experiment. These high performance plasmas are found to be ideal kink-peeling and ideal infinite-n ballooning unstable prior to the onset of edge-localized modes (ELM). The spatial structure of turbulence present during an ELM cycle in the pedestal region indicates poloidal spatial scales propagating in the ion diamagnetic drift direction at the pedestal top, and radial spatial scales . These propagating spatial scales are found to be poloidally elongated and consistent with ion-scale microturbulence. Both global and local gyrokinetic simulations have been performed to identify the microturbulence structure. The local gyrokinetic analysis indicates the presence of a linearly unstable hybrid kinetic ballooning mode and trapped electron mode with spatial scale and propagation direction consistent with experimental observations. In the global gyrokinetic analysis, the nonlinearly saturated potential fluctuations show radial and poloidal correlation lengths in agreement with experimental density fluctuation correlation length measurements.

Characterization and parametric dependencies of low wavenumber pedestal turbulence in the National Spherical Torus Experiment

The spherical torus edge region is among the most challenging regimes for plasma turbulence simulations. Here, we measure the spatial and temporal properties of ion-scale turbulence in the steep gradient region of H-mode pedestals during edge localized mode-free, MHD quiescent periods in the National Spherical Torus Experiment. Poloidal correlation lengths are about 10 ρi, and decorrelation times are about 5 a/cs. Next, we introduce a model aggregation technique to identify parametric dependencies among turbulence quantities and transport-relevant plasma parameters. The parametric dependencies show the most agreement with transport driven by trapped-electron mode, kinetic ballooning mode, and microtearing mode turbulence, and the least agreement with ion temperature gradient turbulence. In addition, the parametric dependencies are consistent with turbulence regulation by flow shear and the empirical relationship between wider pedestals and larger turbulent structures.

Experimental signatures of critically balanced turbulence in MAST.

Beam emission spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field, and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as ν(*i)(-0.8 ± 0.1), where ν(*i) = ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding those of the drift waves by ∼ ν(*i)(-0.8).

Diagnostic performance of the beam emission spectroscopy system on the National Spherical Torus Experiment

The beam emission spectroscopy system on the National Spherical Torus Experiment measures localized density fluctuations on the ion gyroscale. Optical sightlines provide core to edge radial coverage, and the sightlines are aligned to typical pitch angles to maximize cross-field spatial resolution. Sightline images are 2-3 cm, and point spread function calculations indicate image distortion from pitch angle misalignment and atomic state finite lifetimes is minor with a 15% increase in the image size. New generation photodetectors achieve photon noise limited measurements at frequencies up to 400 kHz with refrigerant cooling at -20 °C. Measurements near the pedestal show broadband turbulence up to 100 kHz, and poloidal correlation lengths are about 10 cm. Plasma turbulence signals can be 2-3 orders of magnitude above photon noise and amplifier thermal noise.

2D properties of core turbulence on DIII-D and comparison to gyrokinetic simulations

Quantitative 2D characteristics of localized density fluctuations are presented over the range of 0.3<r/a<0.9 in L-mode plasmas on DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. Broadband density fluctuations increase in amplitude from ñ/n<0.5% in the deep core to ñ/n∼2.5% near the outer region. The observed Doppler-shift due to the E×B velocity matches well with the measured turbulence group and phase velocities (in toroidally rotating neutral beam heated plasmas). Turbulence decorrelation rates are found to be ∼200 kHz at the edge and to decrease toward the core (0.45<r/a<0.9) where they approach the E×B shearing rate (∼50 kHz). Radial and poloidal correlation lengths are found to scale with the ion gyroradius and exhibit an asymmetric poloidally elongated eddy structure. The ensemble-averaged turbulent eddy structure changes its tilt with respect to the radial-poloidal coordinates in the core, consistent with an E×B shear mechanism. The 2D spatial correlation and wavenumber spectra [S(kr,kθ)] are presented and compared to nonlinear flux-tube GYRO simulations at two radii, r/a=0.5 and r/a=0.75, showing reasonable overall agreement, but the GYRO spectrum exhibits a peak at finite kr for r/a=0.75 that is not observed experimentally; E×B shear may cause this discrepancy.

Comparison of scrape-off layer turbulence in Alcator C-Mod with three dimensional gyrofluid computations

This paper describes quantitative comparisons between turbulence measured in the scrape-off layer (SOL) of Alcator C-Mod [S. Scott, A. Bader, M. Bakhtiari et al., Nucl. Fusion 47, S598 (2007)] and three dimensional computations using electromagnetic gyrofluid equations in a two-dimensional tokamak geometry. These comparisons were made for the outer midplane SOL for a set of inner-wall limited, near-circular Ohmic plasmas. The B field and plasma density were varied to assess gyroradius and collisionality scaling. The poloidal and radial correlation lengths in the experiment and computation agreed to within a factor of 2 and did not vary significantly with either B or density. The radial and poloidal propagation speeds and the frequency spectra and poloidal k-spectra also agreed fairly well. However, the autocorrelation times and relative Da fluctuation levels were higher in the experiment by more than a factor of 2. Possible causes for these disagreements are discussed.

Two distinct regimes of turbulence in HL-2A tokamak plasmas

Two distinct regimes of turbulence are identified with Langmuir probe arrays in the edge plasmas of the HuanLiuqi (HL)-2A tokamak for the first time. The spatial and temporal coherent characteristics of the low frequency fluctuations (LFFs) of 20–100 kHz are found in significant contrast to the high frequency ambient turbulence (HFAT) of 100 kHz or higher. In the LFF regime, the deviations from the regular linear dispersion relations of the HFAT are observed. The poloidal and toroidal correlation lengths of the former are measured one order of magnitude longer than that of the latter. The ratio of the temporal scales of the fluctuations in the LFF and HFAT regimes is estimated to be of the same order as that for the spatial scales. The LFF may coexist with and differentiate from the geodesic acoustic modes. The bispectrum analysis of the data indicates that nonlinear three wave coupling between the LFF and HFAT is a possible creation mechanism for the former. The possible correlation of the results with the theory and simulation predictions on quasimodes is discussed.

Edge turbulence during the static dynamic ergodic divertor experiments in TEXTOR

The influence of the magnetic ergodization on edge turbulence and turbulence-induced transport has been investigated by Langmuir probes in TEXTOR under three different static DED configurations. Common features are observed. With DED, the edge equilibrium profiles are altered and the resultant positive Er is in agreement with modelling. In the ergodic zone, the potential fluctuations are strongly reduced and the local turbulent flux changes direction from radially outwards to inwards. In the same zone, the turbulence properties are profoundly modified by energy redistribution in frequency spectra, suppression of large-scale structures and reduction of the radial and poloidal correlation lengths for all frequencies. Meanwhile, the fluctuation poloidal phase velocity changes sign from the electron to ion diamagnetic drift, consistent with the change of the Er × B flow, whereas the slight radially outward propagation of fluctuations is hindered by the DED. In the laminar region, the turbulence correlation is found to react to the observed reduced flow shear. Before the DED the Reynolds stress displays a radial gradient at the plasma edge while during DED the profile is suppressed, suggesting a rearrangement by the DED on the flow momentum profile.

Structure and motion of edge turbulence in the National Spherical Torus Experiment and Alcator C-Mod

In this paper we compare the structure and motion of edge turbulence observed in L-mode vs. H-mode plasmas in the National Spherical Torus Experiment (NSTX) [M. Ono, M. G. Bell, R. E. Bell et al., Plasma Phys. Controlled Fusion 45, A335 (2003)]. The radial and poloidal correlation lengths are not significantly different between the L-mode and the H-mode in the cases examined. The poloidal velocity fluctuations are lower and the radial profiles of the poloidal turbulence velocity are somewhat flatter in the H-mode compared with the L-mode plasmas. These results are compared with similar measurements Alcator C-Mod [E. Marmar, B. Bai, R. L. Boivin et al., Nucl. Fusion 43, 1610 (2003)], and with theoretical models.

Two-dimensional density and density fluctuation diagnostic for the edge plasma in fusion devices

A technique is described for the two-dimensional measurement of electron density profile and fluctuations in edge regions of magnetically confined fusion plasmas. The method is based on existing lithium beam beam emission spectroscopy technique, two-dimensional resolution is achieved by electrostatically scanning the beam. If scanning is performed faster than the lifetime of the turbulent structures in the plasma, the diagnostic is capable of measuring the structure of electron density fluctuations as well. The beam strength of currently available beams makes the detection of single fluctuation events impossible, but the full two-dimensional spatial structure of correlations can still be determined. The article describes the technique and fast beam deflection tests up to 250kHz. The capabilities of such a diagnostic for fluctuation measurement are explored by simulating measurement signals. Measurement of both the two-dimensional density profile, fluctuation correlation function and poloidal flow velocity are demonstrated at the Wendelstein 7-AS stellarator. The shape of the density profile, the radial and poloidal correlation lengths and the flow velocity are in agreement with expectations and previous Langmuir probe measurement.

Effect of poloidal velocity shear on the edge fluctuations in the SINP tokamak

The fluctuations of potential, density and electron temperature have been measured in the edge of the SINP tokamak using Langmuir probes. A naturally occurring extended E × B velocity shear region has been found to exist near the limiter. The poloidal and radial correlation lengths decrease in this region, indicating a spatial decorrelation induced by the velocity shear. The phase angles of the fluctuating signals are also different in the shear region. The turbulent transport drops, causing a steepening of the density and temperature profiles, resembling the characteristics of the high confinement modes in tokamaks.

Measurements of poloidal rotation velocity using cross-correlation spectroscopy in the H-1 heliac

A correlation spectroscopy diagnostic [M.G. Shats and J. Howard, Fusion Eng. Des. 34–35, 271 (1997)] measures fluctuation spectra and local fluctuation intensities in a radiation-dominated plasma, such as the low-temperature plasma in the H-1 heliac (Te<50 eV, ne<2×1018 m−3). When the fluctuation coherence lengths in the poloidal and radial directions are shorter than the plasma radius, the cross-correlation function of the two crossed-sightline fluctuating intensities contains information about the fluctuations amplitude and their phase in the intersection volume. The optical setup on the H-1 heliac uses two nearly orthogonal views to image 20 optical fibers arranged into two linear arrays in the plasma poloidal cross section. A matrix of 10×10 cross-correlation functions is then analyzed to determine the poloidal phase velocity of the fluctuations, poloidal and radial correlation lengths, and the radial profiles of the fluctuations intensity. The results on the poloidal propagation velocity measured using the cross-correlation technique (time delay of the cross-correlation functions) are compared with the poloidal velocity measured using poloidally separated probes in the plasma. Both velocities are found to be in good agreement and also agree well with the E×B drift velocity in this plasma.

2D turbulence imaging in DIII-D via beam emission spectroscopy

Two-dimensional measurements of density fluctuations have been performed in DIII-D using the beam emission spectroscopy diagnostic. The 32 spatial channels are arranged to image a 5×6 cm2 (radial×poloidal) region in the plasma cross section, at a nominal 1 cm spatial resolution and separation. The typical decorrelation time, poloidal and radial correlation lengths, as well as a time-averaged flow field plot are obtained from spatial and temporal correlation analyses. A biorthogonal decomposition algorithm is applied to expand the data set into a set of modes that are orthogonal in time and in space, thus providing a simultaneous analysis of the space and time dependencies of fluctuation data.

A three-wave heterodyne correlation reflectometer developed in the T-10 tokamak

A three-wave heterodyne O-mode reflectometer was developed and tested in experiments on the T-10 tokamak. Three launched waves are obtained by frequency splitting due to amplitude modulation with a p-i-n diode. Source frequencies from 36 to 78 GHz were used in the experiments. The ability of the reflectometer to measure simultaneously density profile characteristics, such as the time evolution of the relative phase and the unambiguous time delay of the reflected wave together with small-scale density fluctuation characteristics such as the radial and poloidal correlation lengths, was demonstrated with T-10 experimental data. The reflectometer can provide important information about fine changes in the density profile during sawteeth and low-m magnetohydrodynamics oscillations. Poloidal correlation measurements make it possible to measure transverse turbulence velocities and velocity shear. It was shown that both types of correlation measurements enable one to distinguish different types of turbulence according to the values of their correlation lengths, and that probing the plasma from several poloidal directions simultaneously greatly enhances the potential of reflectometry for the investigation of turbulence physics. In particular, it was found that different turbulence types may be either poloidally symmetrical or have much higher amplitude on the low field side of the discharge. Probing with several poloidal directions also enables one to make toroidal correlation measurements over long distances at certain resonant q values after one or two turns of magnetic field line around the major tokamak axis. In fact, correlations near 40% were observed experimentally. Such measurements may give additional information about turbulence characteristics on the one hand and allow radial q profile measurements on the other hand. In addition, the capabilities of reflectometry may be enhanced with the application of a proposed holography approach.