Density Fluctuation Level Research Articles

Recent results on turbulence and MHD activity achieved by reflectometry

Over the last years, owing to hardware progress and the development of new methods, reflectometry has become a common diagnostic on plasma fusion devices. This paper presents some results obtained with reflectometry on transport, turbulence and magnetohydrodynamic (MHD). The emphasis is put on some new results from Tore-Supra. Combining the density profile and fluctuation measurement, it was shown on Tore-Supra that the particle pinch inside the q = 1 surface is close to the neoclassical value in ohmic plasma, while the observed small diffusion is in agreement with a very low level of density fluctuations inside the q = 1 surface. In β scaling experiments, no change in the fluctuation levels was found on Tore-Supra, in agreement with the observation of weak confinement degradation with increasing β. Zonal flows have been detected by Doppler reflectometry in ASDEX-U and with correlation reflectometry in T-10. On Tore-Supra, a fast decrease in the density fluctuation level at high poloidal wavenumbers was measured with Doppler reflectometry, suggesting a minor role of electron temperature gradient driven modes. Various forms of Alfvén eigenmodes (toroidal Alfvén eigenmodes, Alfvén cascades and possibly beta Alfvén eigenmodes) have been detected with reflectometry in TFTR, JET and Tore-Supra. The density fluctuations induced by the mode were found to be higher on the high-field side.

Reflectometry measurements during operation of the dynamic ergodic divertor at TEXTOR

The O-mode correlation reflectometer at TEXTOR is used for the investigation of the propagation and the properties of the turbulence at the plasma edge. The multi-horn antenna set-up allows the investigation of the correlation properties of the turbulence and its rotation. Turbulence and plasma rotation for different plasma conditions are found to be in agreement and based on this comparison the radial electric field is estimated. In addition the density fluctuation level is estimated from the standard deviation of the phase of the reflected signal.The influence of a magnetic perturbation field, generated by the dynamic ergodic divertor (DED), on the turbulence and transport properties is studied and compared with plasmas without such a field perturbation. The strength and radial range of the perturbation field can be widely varied. Together with tangential neutral beam injection in co- and counter-current directions, the turbulent transport is investigated. The combination of neutral beam injection and the DED enables the modification of the plasma rotation profile. It can lead either to the generation of a locked mode or the formation of a transport barrier.

Quantitative density fluctuation measurements utilizing quadrature reflectometers on DIII-D

Fixed-frequency reflectometers utilizing quadrature phase detection are employed on DIII-D to study both coherent and turbulent density fluctuations. For coherent fluctuations, the reconstructed phase information successfully identifies MHD/coherent mode activity, e.g. tearing modes, compressional Alfvén eigenmodes, etc. For an m = 3/n = 2 tearing mode, a basic 1D phase screen model is applied to infer fluctuation levels, and the result is consistent with the beam emission spectroscopy (BES) measurement. For turbulent fluctuation studies, a 2D full-wave code (Valeo E.J., Kramer G.J. and Nazikian R. 2002 Plasma Phys. Control. Fusion 44 L1) is applied to interpret reflectometry data obtained in the H-mode edge pedestal region to deduce density fluctuation levels. The measurement is simulated using realistic geometry, plasma conditions and antenna patterns. Comparison of the fluctuation level deduced from the 2D code with BES measurement shows reasonable agreement.

Confinement transitions (H-mode) in JET inner wall limiter plasmas

Transitions in confinement with characteristics of H-mode are observed in JET inner wall limited plasmas in experiments performed at a magnetic field of 0.8 T and at a current of 0.9 MA, using up to 7 MW of auxiliary heating power. These transitions in confinement are short lived, with durations of up to 20 ms, but the overall stored energy increases by up to 5% and edge density by up to 20%. The termination of the period of good confinement correlates with the observation of a burst of magnetic fluctuations, similar to those associated with edge localized modes (ELMs).These transitions in confinement also correlate with a significant decrease in the density fluctuations measured by the microwave reflectometer and a small decrease in the magnetic fluctuations measured using ‘Mirnov’ probes, accompanied by a reduction of the D(alpha) emission. The comparison of the fluctuations in the limiter H-mode in JET with the divertor H-modes shows a similar behaviour, in particular the reduction of the fluctuation levels at high frequencies (f > 10 kHz) and an increase in the fluctuation levels at lower frequencies (f < 10 kHz). The strong electrostatic nature of the plasma edge turbulence is confirmed, where a reduction of up to ∼50% in the density fluctuation levels correlates with an increase of up to 50% in the confinement time during the transition to H-mode. However, the importance of instabilities with a dominant magnetic component (such as ELMs) is also highlighted, which cause significant increase in transport, including the loss of the good confinement phase in limiter H-modes.

Temporal variation of density fluctuation and transport in reversed shear plasmas on JT-60U

Further transport reduction is induced by a pellet or electron cyclotron (EC) wave injection after the formation of an internal transport barrier in JT-60U reversed shear plasmas. After pellet injection, the O-mode reflectometer signal drastically decreases, indicating reduction in the electron density fluctuation level. The ion thermal diffusivity decreases by one order of magnitude and reaches the neoclassical level. The effective particle diffusivity also decreases by one order of magnitude, but the electron thermal diffusivity remains constant. After EC wave injection, when no reduction of the O-mode reflectometer signal is observed, the electron thermal diffusivity decreases by a factor of ∼2–3, while decreases in the ion thermal diffusivity and the effective particle diffusivity are small. These results indicate that the ion heat transport and particle transport were coupled with the measured density fluctuation, but electron heat transport was decoupled. Ion heat and particle transport and electron heat transport were dominated by different types of fluctuation.

A simulation method for the calculation of chemical potentials in small, inhomogeneous, and dense systems

We present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.

Turbulence in the inner solar wind determined from frequency fluctuations of the downlink signals from the ULYSSES and GALILEO spacecraft

The results of several sets of measurements of the frequency of radio signals during coronal-sounding experiments carried out from 1991 to 2000 using the ULYSSES and GALILEO spacecraft are presented and analyzed. The S-band signals (carrier frequency f = 2295 MHz) were received at the three 70-m widely spaced ground stations of the NASA Deep Space Network. As a rule, the frequency-fluctuation spectra at frequencies above 1 mHz are power-laws. At small heliocentric distances, R < 10R ⊙ (R ⊙ is the solar radius), the spectral index is close to zero; this corresponds to a spectral index for the one-dimensional turbulence spectrum p 1 = 1. The index of the frequency-fluctuation spectra in the region of the supersonic solar wind at distances R > 30 R ⊙ is between 0.5 and 0.7 (p 1 = 1.5–1.7). The results demonstrate a substantial difference between the turbulence regimes in these regions: in the region of the established solar wind, the power-law spectra are determined by nonlinear cascade processes that pump energy from the outer turbulence scale to the small-scale part of the spectrum, whereas such cascade processes are absent in the solar wind acceleration region. Near the solar minimum, the change in the turbulence regime of the fast, high-latitude solar wind occurs at greater distances than for the slow, low-latitude solar wind. Spectra with a sharp cutoff at high frequencies have been detected for the first time. Such spectra are observed only at R < 10 R ⊙ and at sufficiently low levels of the electron density fluctuations. The measured cutoff frequencies are between 10 and 30 mHz; the cutoff frequency tends to increase with heliocentric distance. The variance of the plasma-density fluctuations has been estimated for the slow, low-latitude solar wind. These estimates suggest that the relative fluctuation level at distances 7 R ⊙ < R < 30 R ⊙ does not depend on heliocentric distance. The cross correlation of the frequency fluctuations recorded at widely spaced ground stations increases with the index of the frequency-fluctuation spectrum. At distances R ≈ 10 R ⊙, the rate of temporal changes in irregularities on the scale of several thousand kilometers is less than or comparable to the solar wind velocity.

Edge localized mode control with an edge resonant magnetic perturbation

A low amplitude (δbr∕BT=1 part in 5000) edge resonant magnetic field perturbation with toroidal mode number n=3 and poloidal mode numbers between 8 and 15 has been used to suppress most large type I edge localized modes (ELMs) without degrading core plasma confinement. ELMs have been suppressed for periods of up to 8.6 energy confinement times when the edge safety factor q95 is between 3.5 and 4. The large ELMs are replaced by packets of events (possibly type II ELMs) with small amplitude, narrow radial extent, and a higher level of magnetic field and density fluctuations, creating a duty cycle with long “active” intervals of high transport and short “quiet” intervals of low transport. The increased transport associated with these events is less impulsive and slows the recovery of the pedestal profiles to the values reached just before the large ELMs without the n=3 perturbation. Changing the toroidal phase of the perturbation by 60° with respect to the best ELM suppression case reduces the ELM amplitude and frequency by factors of 2–3 in the divertor, produces a more stochastic response in the H-mode pedestal profiles, and displays similar increases in small scale events, although significant numbers of large ELMs survive. In contrast to the best ELM suppression case where the type I ELMs are also suppressed on the outboard midplane, the midplane recycling increases until individual ELMs are no longer discernable. The ELM response depends on the toroidal phase of the applied perturbation because intrinsic error fields make the target plasma nonaxisymmetric, and suggests that at least some of the variation in ELM behavior in a single device or among different devices is due to differences in the intrinsic error fields in these devices. These results indicate that ELMs can be suppressed by small edge resonant magnetic field perturbations. Extrapolation to next-step burning plasma devices will require extending the regime of operation to lower collisionality and understanding the physical mechanism responsible for the ELM suppression.

Measurement of Turbulence Decorrelation during Transport Barrier Evolution in a High-Temperature Fusion Plasma

A low power polychromatic beam of microwaves is used to diagnose the behavior of turbulent fluctuations in the core of the JT-60U tokamak during the evolution of the internal transport barrier. A continuous reduction in the size of turbulent structures is observed concomitant with the reduction of the density scale length during the evolution of the internal transport barrier. The density correlation length decreases to the order of the ion gyroradius, in contrast with the much longer scale lengths observed earlier in the discharge, while the density fluctuation level remain similar to the level before transport barrier formation.

Electron cyclotron emission as a density fluctuation diagnostic

A new technique for measuring density fluctuations using a high-resolution heterodyne electron cyclotron emission (ECE) radiometer has been developed. Although ECE radiometry is typically used for electron temperature measurements, the unique viewing geometry of this system’s quasioptical antenna has been found to make the detected emission extremely sensitive to refractive effects under certain conditions. This sensitivity gives the diagnostic the ability to measure very low levels of density fluctuations in the core of Alcator C-Mod tokamak. The refractive effects have been modeled using ray-tracing methods, allowing estimates of the density fluctuation magnitude and spatial localization.

Density fluctuation measurement at edge and internal transport barriers in JT-60U

A new analytical method using a combination of the O-mode reflectometer and a time-dependent two-dimensional full-wave simulation code has been developed for the quantitative evaluation of density fluctuations in JT-60U. Two statistical parameters of the reflectometer signals, fluctuation index (F) and elongation factor (χ), are introduced as measures of the fluctuation amplitude (γ) and the width of the poloidal wave number spectrum (kθ0). This method is applied to the edge transport barrier (ETB) and internal transport barrier (ITB). At the transition to the ELM free H-mode phase, analysis suggests that the density fluctuation level reduced from 1.9–3.2% to 0.29–0.44%, while the value of kθ0 changed from 1.6–2.0 to 0.77–0.81 cm−1 in the ETB region. On the other hand, the amplitude of the density fluctuation was evaluated as 1.0–2.0% at the ITB region, even after the formation of the box type ITB. Instead, when a pellet was injected into the plasma with a box type ITB as an external perturbation, a remarkable change in the frequency spectrum was observed. Analysis suggests a reduction in the density fluctuation level to 0.4–0.6% after the pellet injection.

The small amplitude of density turbulence in the inner solar wind

Abstract. Very Long Baseline Interferometer (VLBI) observations were made of radio sources close to the Sun, whose lines of sight pass through the inner solar wind (impact parameters 16-26 RE). Power spectra were analyzed of the interferometer phase fluctuations due to the solar wind plasma. These power spectra provide information on the level of plasma density fluctuations on spatial scales of roughly one hundred to several thousand kilometers. By specifying an outer scale to the turbulence spectrum, we can estimate the root-mean-square (rms) amplitude of the density fluctuations. The data indicate that the rms fluctuation in density is only about 10% of the mean density. This value is low, and consistent with extrapolated estimates from more distant parts of the solar wind. Physical speculations based on this result are presented.

Progress toward a practical magnetic field diagnostic for low-field fusion plasmas based on dual mode correlation reflectometry

Previously, the proof of principle of measurement of magnetic field strength, |B| internal to a plasma by cross correlation of ordinary (O) and extraordinary (X) mode fluctuation reflectometer signals has been demonstrated in a linear plasma device. It was found that dual mode (O-X) reflectometry data could be interpreted by a one-dimensional numerical model to determine |B| in the vicinity of the reflectometer cutoff positions. Radial correlation properties of turbulence are also measured simultaneously with |B|. This technique is potentially well suited to measurement of |B| in low-field fusion devices (e.g., B&amp;lt;0.6 T) where standard magnetic field diagnostics are expected to be difficult to implement. However, transfer of this method to toroidal magnetic fusion devices presents a number of potential difficulties such as the effects of magnetic shear, steep density gradients, and limited time for cross correlations. In addition, recent simulations suggest that two-dimensional modeling may be required to interpret experimental data when density fluctuation levels are high. Dual mode correlation reflectometry experiments on the National Spherical Torus Experiment are presented, and progress toward the implementation of this technique as a practical diagnostic is discussed.

Intermittent Structures in the High Field Side Boundary of the HYBTOK-II Tokamak

The spatial and temporal characteristics of the turbulence in the inboard and outboard scrape-off layer (SOL) of tokamak HYBTOK-II have been studied using poloidal probe array. Bursty behaviour with intermittent bursts was observed for both outboard and inboard SOL. In the inboard (high field side), high level of density fluctuations has been observed. The fluctuations in the high field side and low field side are identical in statistics that is non-Gaussian one.

Comparing simulation of plasma turbulence with experiment. II. Gyrokinetic simulations

The direct quantitative correspondence between theoretical predictions and the measured plasma fluctuations and transport is tested by performing nonlinear gyrokinetic simulations with the GS2 code. This is a continuation of previous work with gyrofluid simulations [D. W. Ross et al., Phys. Plasmas 9, 177 (2002)], and the same L-mode reference discharge in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] is studied. The simulated turbulence is dominated by ion temperature gradient (ITG) modes, corrected by trapped-electron, passing-electron and impurity effects. The energy fluxes obtained in the gyrokinetic simulations are comparable to, even somewhat higher than, those of the earlier work, and the simulated ion thermal transport, corrected for E×B flow shear, exceeds the experimental value by more than a factor of 2. The simulation also overestimates the density fluctuation level. Varying the local temperature gradient shows a stiff response in the flux and an apparent up-shift from the linear mode threshold [A. M. Dimits et al., Phys. Plasmas 7, 969 (2000)]. This effect is insufficient, within the estimated error, to bring the results into conformity with the experiment.

Fluctuation reflectometry of azimuthally symmetric plasmas

The results of analytical solution of time-dependent two-dimensional full-wave equation are presented here for the case of fluctuation reflectometry. We consider a family of plasma density profiles with cylindrical symmetry, which allow for an integration of the microwave scattering equation.Based on the results of analytical modelling, Doppler reflectometry as a method of plasma velocity measurements is investigated. It is shown that the accuracy of Doppler shift measurements is sensitive to the spectral content of the broadband turbulence, as well as to the curvature of the plasma cut-off layer. Addressing the problem of fluctuation amplitude measurements, it is suggested that a power-related parameter of the microwave signal, called fluctuation index, is suitable to quantify the plasma turbulence level provided that the fluctuation spectrum is a priori estimated. As an illustration, we apply our model to estimate the density fluctuation level in the edge plasma of the JT-60U tokamak.

On the correlation between small scale density fluctuations and speed in the solar wind

The correlation between the level of small scale density fluctuations and the solar wind speed was recently found by Asai et al. (1998) from the tomography analysis of interplanetary scintillation measurements. The physical origin of this correlation is considered within an assumption that density fluctuations are generated locally by nonlinear interactions of Alfven waves. The radial evolution of density turbulence power spectrum is investigated as well as the speed dependence of the levels of Alfven waves and of density turbulence. It is shown that the combination of these two effects can result in sufficiently strong dependence of the fractional level of small scale density fluctuations on the solar wind speed. The fractional levels of density and of magnetic field fluctuations increase weakly with increasing of heliocentric distance due to the radial evolution of the turbulence power spectra. The results of the considered theoretical model are in a reasonably good agreement with the observational data of Asai et al. (1998) if invariance of the solar wind mass flux, but not the momentum flux, is assumed.

Comparing simulation of plasma turbulence with experiment

The direct quantitative correspondence between theoretical predictions and the measured plasma fluctuations and transport is tested by performing nonlinear gyro-Landau-fluid simulations with the GRYFFIN (or ITG) code [W. Dorland and G. W. Hammett, Phys. Fluids B 5, 812 (1993); M. A. Beer and G. W. Hammett, Phys. Plasmas 3, 4046 (1996)]. In an L-mode reference discharge in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)], which has relatively large fluctuations and transport, the turbulence is dominated by ion temperature gradient (ITG) modes. Trapped electron modes and impurity drift waves also play a role. Density fluctuations are measured by beam emission spectroscopy [R. J. Fonck, P. A. Duperrex, and S. F. Paul, Rev. Sci. Instrum. 61, 3487 (1990)]. Experimental fluxes and corresponding diffusivities are analyzed by the TRANSP code [R. J. Hawryluk, in Physics of Plasmas Close to Thermonuclear Conditions, edited by B. Coppi, G. G. Leotta, D. Pfirsch, R. Pozzoli, and E. Sindoni (Pergamon, Oxford, 1980), Vol. 1, p. 19]. The shape of the simulated wave number spectrum is close to the measured one. The simulated ion thermal transport, corrected for E×B low shear, exceeds the experimental value by a factor of 1.5 to 2.0. The simulation overestimates the density fluctuation level by an even larger factor. On the other hand, the simulation underestimates the electron thermal transport, which may be accounted for by modes that are not accessible to the simulation or to the BES measurement.

Three‐dimensional structuring characteristics of high‐latitude plasma patches

A three‐dimensional nonlinear study of the turbulence and sheared flow, generated by the gradient drift instability with ion inertial effects in the high‐latitude plasma patches, is presented. Numerical simulations demonstrate quasi‐two‐dimensional turbulence with irregularities aligned along the magnetic field direction. Power spectra of the velocities in the plane transverse to the magnetic field and the density irregularities display anisotropy in the turbulence. Secondary Kelvin‐Helmholtz instability of the gradient drift elongated vortices tends to isotropize the spectra. Ion‐neutral collisions determine the level of the shear flow and therefore the saturation level of density and potential fluctuations. The irregularities penetrate through the entire patch due to the nonlinear development of the instability and do not remain localized on the edges of the plasma patch. The computed spectra and spatial structures, observed by DE 2 satellite in the midnight‐noon direction, are in good agreement. The inertial terms unify the gradient drift and Kelvin‐Helmholtz instabilities, the sources of small‐scale structures generated in the polar cap plasma patches, and give rise to irregularity characteristics which are in a good agreement with general features of the observed structures.

Radial electrostatic flux inferred from core measurements of potential and density fluctuations

Broadband potential fluctuations and electrostatic fluctuation induced particle flux have been measured in the core of a medium size tokamak plasma for the first time. Density fluctuations and wave numbers were simultaneously measured. Measurements indicate that radial electrostatic fluctuation induced particle flux in the core region, at the normalized radii of 0.17&amp;lt;ρ&amp;lt;0.38, due to modes with wave numbers less than 4 cm−1 is small in magnitude, is likely directed inward, and cannot account for particle flux predicted by the continuity equation and particle source codes. Estimates of electrostatic energy flux are also significantly less than values predicted via power balance analysis. Asymmetries in coherent density and potential fluctuation levels on closed flux surfaces are evident. Relative fluctuation levels ñ/n and φ̃ tend to increase with radius, and the fluctuations are Boltzmann-like in the region 0.17⩽ρ⩽0.38. The direction of mode propagation is in the electron diamagnetic drift direction. Corresponding phase velocities, vph∼3.5×105 cm/s, are similar to drift wave velocities.