Radial Correlation Length Research Articles

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.

Liquid 4He: Contributions to First Principles Theory. II. Quantized Vortices and the λ Transition

Quantized vortices in liquid 4He at finite temperatures are treated by first principles theory that extends results presented in paper I of this two-part set. Then the possible role of thermally excited quantized vortices in accounting for the λ transition is studied. This study indicates that vortices are probably not the dominant mechanism responsible for the λ transition, but that they may account for some minor effects near Tλ. A model that identifies critical fluctuations with quantized isothermal fourth sound waves is developed and used to derive formulas for specific heat in He II and He I. Logarithmic divergence of the constant volume specific heat is found. Numerical calculations using those formulas produce close agreement with experimental data. A formula for the radial distribution function near Tλ in He II and He I is derived and numerically evaluated. A formula for the correlation length is derived and numerically evaluated and physical characteristics of the correlation length are discussed. Numerical calculations based on that formula for correlation length are compared with experimental results. Long-range order in the liquid exhibited in the radial distribution function and correlation length is shown not to involve a Bose-Einstein condensate in this theory. The isothermal compressibility is found by integration of the radial distribution function and the result shows that isothermal compressibility is unchanged by critical fluctuations of isothermal fourth sound.

Experimental investigations of turbulent structure propagation across a [formula omitted]-velocity shear

The influence of an externally generated E × B shear flow on the propagation of structures in drift-wave turbulence is investigated in a linear laboratory plasma device. Spatiotemporal studies of the dynamics of turbulent structures reveal that structures have a radial component of propagation, thereby contributing mainly to the fluctuation induced particle flux and leading to intermittent density fluctuations in the edge plasma. A radially localized radial E × B -velocity shear layer is generated by a biased emissive filament. The shear layer modifies the phase between density and potential fluctuations, which results in a reduction of transport driven by electrostatic turbulence. A shear decorrelation of the structures, i.e. a decrease of their radial correlation length, is not observed.

Modifications of turbulence and turbulent transport associated with a bias-induced confinement transition in the Large Plasma Device

Azimuthal flow is driven in the edge of the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] through biasing a section of the vacuum vessel relative to the plasma source cathode. As the applied bias exceeds a threshold, a transition in radial particle confinement is observed, evidenced by a dramatic steepening in the density profile, similar to the L- to H-mode transition in toroidal confinement devices. The threshold behavior and dynamic behavior of radial transport is related to flow penetration and the degree of spatial overlap between the flow shear and density gradient profiles. An investigation of the changes in turbulence and turbulent particle transport associated with the confinement transition is presented. Two-dimensional cross-correlation measurements show that the spatial coherence of edge turbulence in LAPD changes significantly with biasing. The azimuthal correlation in the turbulence increases dramatically, while the radial correlation length is little altered. Turbulent amplitude is reduced at the transition, particularly in electric field fluctuations, but the dominant change observed is in the cross-phase between density and electric field fluctuations. The changes in cross-phase lead to a suppression and then apparent reversal of turbulent particle flux as the threshold is exceeded.

Statistical analysis of the turbulent Reynolds stress and its link to the shear flow generation in a cylindrical laboratory plasma device

The statistical properties of the turbulent Reynolds stress arising from collisional drift turbulence in a magnetized plasma column are studied and a physical picture of turbulent driven shear flow generation is discussed. The Reynolds stress peaks near the maximal density gradient region, and is governed by the turbulence amplitude and cross-phase between the turbulent radial and azimuthal velocity fields. The amplitude probability distribution function (PDF) of the turbulent Reynolds stress is non-Gaussian and positively skewed at the density gradient maximum. The turbulent ion-saturation (Isat) current PDF shows that the region where the bursty Isat events are born coincides with the positively skewed non-Gaussian Reynolds stress PDF, which suggests that the bursts of particle transport appear to be associated with bursts of momentum transport as well. At the shear layer the density fluctuation radial correlation length has a strong minimum (∼4–6mm∼0.5Cs∕Ωci, where Cs is the ion acoustic speed and Ωci is the ion gyrofrequency), while the azimuthal turbulence correlation length is nearly constant across the shear layer. The results link the behavior of the Reynolds stress, its statistical properties, generation of bursty radially going azimuthal momentum transport events, and the formation of the large-scale shear layer.

Global stability analysis of ITG modes in the presence of a field-aligned ion flow

The linear stability analysis of the ITG modes in a plasma slab with an equilibrium ion flow has been carried out by solving the relevant eigenvalue equation for the complex electrostatic fluctuation amplitude , by retaining the electric, the diamagnetic and the gravitational-like drifts. For sufficiently broad Ti profiles, a novel regime with two-branch distributions of unstable eigenvalues has been found, which seems to be characterized by a broad radial correlation length. The plasma density profile and a macroscopic ion flow aligned to the magnetic field govern the relative importance of the two unstable sets of eigenfunctions.

Study of Doppler reflectometry capability to determine the perpendicular velocity and the k-spectrum of the density fluctuations using a 2D full-wave code

The capability of Doppler reflectometry to determine the perpendicular velocity and the perpendicular wave-number spectrum of the density fluctuations has been studied using a two-dimensional full-wave code. The numerical results show that the perpendicular velocity of the density fluctuations can be obtained with high accuracy for broad ranges of antenna tilt angles, turbulence levels and radial correlation lengths of the density fluctuations. The diagnostic potential of Doppler reflectometry to determine the perpendicular wave-number spectrum of the density fluctuations depends on the reflectometer response at different probed wave numbers and different turbulence levels. A linear dependence between the scattered wave amplitude and the turbulence level has been found for low turbulence levels and short radial correlation lengths of the density fluctuations, whereas at high turbulence levels and/or large radial correlation lengths the relationship becomes non-linear. In addition, numerical results show that the reflectometer response depends only very slightly on the probed wave number.

Transport Dynamics and Multi-Scale Coupling of Turbulence in LHD

Spatiotemporal correlation of heat transport and micro- to meso- scale or macro-scale coupling of plasma turbulence are investigated in LHD plasmas, where fast propagation of a cold pulse and a non-local temperature rise are observed. Evidence of a timescale shorter than the diffusion time and a spatial scale longer than the micro-turbulence correlation length between core heat fluxes and edge temperature gradients is found. At the same time, an envelope of turbulent density fluctuations is also found to be modulated. Observation of low frequency (≤ 2 kHz) amplitude modulation of density fluctuation suggests the existence of meso- to macro-scale turbulent structures in the plasma, in which a non-local temperature rise takes place. Relationships between the turbulence with long radial correlation length and the edge-core coupling of heat transport are 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.

Gyrokinetic δf particle simulation of trapped electron mode driven turbulence

The linear instabilities and nonlinear transport driven by collisionless trapped electron modes (CTEM) are systematically investigated using three-dimensional gyrokinetic δf particle-in-cell simulations. Scalings with local plasma parameters are presented. Simulation results are compared with previous simulations and theoretical predictions. The magnetic shear is found to be linearly stabilizing, but nonlinearly the transport level increases with increasing magnetic shear. This is explained by the changes in radial eddy correlation lengths caused by toroidal coupling. The effect of zonal flows in suppressing the nonlinear CTEM transport is demonstrated to depend on electron temperature gradient and electron to ion temperature ratio. Zonal flow suppression is consistent with the rate of E×B shearing of the ambient turbulence and radial spectra broadening. Strong geodesic acoustic modes (GAM) are generated along with zonal flows.

Radial correlation length measurements on ASDEX Upgrade using correlation Doppler reflectometry

The technique of correlation Doppler reflectometry for providing radial correlation length L r measurements is explored in this paper. Experimental L r measurements are obtained using the recently installed dual channel Doppler reflectometer system on ASDEX Upgrade. The experimental measurements agree well with theory and with L r measured on other fusion devices using different diagnostic techniques. A strong link between L r and plasma confinement could be observed. From the L- to the H-mode, an increase in the absolute value of E r shear was detected at the same plasma edge region where a decrease in L r was measured. This observation is in agreement with theoretical models which predict that an increase in the absolute shear suppresses turbulent fluctuations in the plasma, leading to a reduction in L r . Furthermore, L r decreases from the plasma core to the edge and decreases with increasing plasma triangularity δ. The experimental results have been extensively modelled using a 2-dimensional finite difference time domain code. The simulations confirm that Doppler reflectometry provides robust radial correlation lengths of the turbulence with high resolution and suggests that L r is independent of the turbulence wavenumber k ⊥ and its fluctuation level.

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.

Comparison of Experimental Fluctuation and Turbulence Measurements with Theory and Simulation at DIII-D

Considerable research at DIII-D has been aimed at detailed comparisons of a variety of experimental fluctuation and turbulence measurements to turbulence simulations and theory. The goals of such comparisons are to improve the understanding of turbulence and transport as well as to test and provide feedback to the theory and simulations. Progress in this area will lead to confidence in the extrapolation of predictions to next-step fusion devices and, potentially, to improved control of transport. This paper summarizes some of the more recent and significant results of comparisons of experiment to theory and simulation that have been performed at DIII-D. These comparisons cover a range of plasma conditions (ohmic, L-mode, and impurity enhanced confinement), physical phenomena [transport, avalanches, zonal flows, and geodesic acoustic modes (GAMs)], and measurements (fluctuation levels, fluctuation spectra, radial correlation lengths, heat transport, and poloidal fluctuation velocity). Results reviewed here include comparisons between experimental turbulent radial correlation lengths and nonlinear turbulence simulations, measurements showing GAM activity (a type of zonal flow) similar to predictions, long-range or avalanche-type behavior with significant heat transport similar to that seen in nonlinear simulations, and reduction of turbulence with an enhancement of confinement during impurity injection similar to theory and simulation.

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 ion ∇B drift direction on density fluctuation poloidal flow and flow shear

The divertor magnetic geometry has a significant effect on the poloidal velocity and resulting velocity shear of turbulent density fluctuations in the outer region of L-mode tokamak plasmas, as determined via two-dimensional measurements of density fluctuations with beam emission spectroscopy on DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. Plasmas with similar parameters, except that in one case the ion ∇B drift points towards the divertor X point (lower-single-null, LSN), and in the other case, the ion ∇B drift points away from the divertor X point (upper-single-null, USN), are compared. Inside r∕a=0.9, the turbulence characteristics (density fluctuation amplitude, flow direction, correlation lengths) are similar in both cases, while near r∕a=0.92, a dramatic reversal of the poloidal velocity of turbulent eddies relative to the core flow direction is observed in plasmas with the ion ∇B drift pointing towards the divertor X point. No such velocity reversal is observed in plasmas with the ion ∇B drift pointing away from the divertor X point. This poloidal velocity reversal results in a significantly larger local shear in the poloidal velocity of density fluctuations in plasmas with the ion ∇B drift pointing towards the divertor X point. Additionally, these plasmas locally exhibit significant dispersion with two distinct and counterpropagating turbulence modes. Likewise, the radial correlation length of the density fluctuations is reduced in these plasmas, consistent with biorthogonal decomposition measurements of dominant turbulence structures. The naturally occurring density fluctuation poloidal velocity shear in these LSN plasmas may facilitate the L-H transition that occurs at an input power of roughly one-half to one-third that of corresponding plasmas with the ion ∇B drift pointing away from the X point.

Upgrade of the X-mode reflectometry diagnostic for radial correlation measurements in the Joint European Torus

The recent upgrades and the potential of the X-mode reflectometry diagnostic on the Joint European Torus (JET), dedicated to measurement of the turbulence radial correlation length, are presented in this article. The reflectometer system now consists of four independent heterodyne instruments working at different probing frequencies, which in principle enables analysis of the density fluctuations at four distinct radial regions in the plasma. A VERSA Module Eurocard-based computer connected to the JET database computer system is used to control all of the diagnostic in particular the frequency of the tunable sources and frequency of the fast acquisition boards. The diagnostic is fully operated by remote control. A study of the effects of type-I edge localized modes observed at JET illustrates its potential. The main limitation comes from the low quality of the transmission lines, which leads to a strong attenuation of the signal and makes the measurements difficult especially in the plasma core. To reach higher performances, new low attenuation corrugated circular waveguides (with an expected gain of 20 dB) will be installed in the summer of 2004 during the JET shutdown.

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.

Observation of radial propagation of electrostatic fluctuations in the Saskatchewan torus-modified tokamak

Radial propagation of electrostatic fluctuations in the edge region of the Saskatchewan torus-modified [W. Zhang et al., Phys. Fluids B 4, 3277 (1992)] tokamak has been measured using Langmuir probes. The propagation characteristics of the density fluctuations are analyzed by two point correlation techniques. A finite radial propagation speed is measured and is found to be a large fraction of the poloidal propagation speed. The speed of propagation is inversely proportional to the toroidal magnetic field, suggesting that the origin of these fluctuations could be drift wave type turbulence. The radial correlation length of turbulence is found to decrease with increasing magnetic field. The power averaged wave number shows an increase with increasing magnetic field, suggesting a decrease in the correlation lengths.

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.

The Influence of Stochastic Layers of Magnetic Field Lines on Transport Barrier Formation in a Stellarator System

The results of local measurements of RF discharge plasma parameters in the process of internal transport barriers (ITB) formation in the vicinity of rational magnetic surfaces in the Uragan-3M torsatron are presented. The following phenomena were observed in the process of ITB formation: widening of the radial density distribution, formation of plateaus on radial density and electron temperature distributions, formation of regions with high shear of poloidal plasma rotation velocity and radial electric field in the vicinity of stochastic layers of magnetic field lines, decrease of density fluctuations and their radial correlation length, decorrelation of density fluctuations, and increase of the bootstrap current.