Turbulent Particle Flux Research Articles

Characterization of the poloidal asymmetries in the ISTTOK edge plasma

Edge plasma in/out and up/down asymmetries have been directly investigated on ISTTOK with a probe system that simultaneously samples the plasma at four poloidal angles. An experimental investigation of the asymmetries is presented as a function of the direction of plasma current and toroidal magnetic field. The edge plasma parameters show significant in/out asymmetries in both equilibrium and fluctuating parameters. Asymmetries favoring the outboard side are observed in density, turbulent particle flux and diffusion coefficient independently of the toroidal magnetic field and plasma current directions, suggesting a ballooning-like transport. This interpretation is supported by the characteristics of the fluctuations as they are found to be more intermittent on the outboard side. In addition, smaller up/down asymmetries reversing with the reversal of the toroidal magnetic field direction and favoring the ion ∇B drift direction are found. Significant poloidal asymmetries were also measured in the parallel flow that can be attributed mainly to Pfirsch–Schluter flows.

Latest investigations on fluctuations, ELM filaments and turbulent transport in the SOL of ASDEX Upgrade

This paper presents turbulence investigations in the scrape-off layer (SOL) of ASDEX Upgrade in ohmic, L-mode and H-mode discharges using electrostatic and electromagnetic probes. Detailed studies are performed on small scale turbulence and on ELM filaments. Simultaneous measurements of floating and plasma potential fluctuations revealed significant differences between these quantities. Large errors can occur when the electric field is extracted from floating potential measurements, even in ohmic discharges. Turbulence studies in ohmic plasmas show the existence of density holes inside the separatrix and blobs outside. Close to the separatrix a reversal of the poloidal blob propagation velocity occurs. Investigations on the Reynolds stress in the scrape-off layer (SOL) show its importance for the momentum transport in L-mode while its impact for momentum transport during ELMs in H-mode is rather small. In the far SOL the electron density and temperature were measured during type-I ELMy H-mode at ASDEX Upgrade resolving ELM filaments. Strong density peaks and temperatures of several 10 eV were detected during the ELM events. Additional investigations on the ions in ELM filaments by a retarding field analyser indicate ion temperatures of 50–80 eV. ELMs also expel current concentrated in filaments into the SOL. Furthermore, discharges with small ELMs were studied. In N2 seeded discharges the type-I ELM frequency rises and the ELM duration decreases. For discharges with small type-II ELMs the mean turbulent radial particle flux is increased over the mean particle flux in type-I ELM discharges at otherwise similar plasma parameters.

A Quasi-Coherent Electrostatic Mode in ECRH Plasmas on TJ-II

A new type of instability mode, related to suprathermal electrons, was found in extremely low-density plasmas, (ne = (0.2-0.5) ×10 19 m −3 ) with electron cyclotron resonance heating and current drive (ECRH/ECCD) in the TJ-II heliac. The quasi-monochromatic density and plasma potential oscillations in the frequency range 20-120kHz tend to have several “branches” with constant frequency shift between them. The typical amplitude of the mode induced potential oscillations was estimated to be Δϕ EM ∼20V. The mode branches have an individual and finite radial extent, odd low poloidal structure (m ≤5) and angular phase velocity of poloidal rotation of about 8 ×10 4 rad/s in the ion diamagnetic drift direction. The contribution of the mode to the turbulent particle flux ΓE×B for the observed wave vectors kθ < 3cm −1 was found to be small in comparison with the contribution from broadband turbulence. c

Plasma flow and transport on the tokamak ISTTOK boundary plasma

The ISTTOK boundary plasma velocity near the outer midplane is measured on the parallel and perpendicular directions in four different configurations by reversing independently the toroidal magnetic field and the plasma current directions. The parallel flow is found to not depend significantly on both the toroidal magnetic field and plasma current directions, being always directed towards the nearest limiter in the scrape-off layer. On the contrary, the perpendicular flow is found to follow the Er×B drift direction. The poloidal velocity has also been derived from the correlation of floating potential signals measured on poloidally separated probes and a good agreement with the value derived with the Gundestrup probe is found. Finally, the dynamical interplay between parallel momentum and turbulent particle flux has been investigated and a clear dynamical coupling between these quantities is found in the region inside the limiter.

Gyrokinetic study of the role of β on electron particle transport in tokamaks

Electromagnetic effects on the radial transport of electrons in the core of tokamak plasmas are studied by means of linear and nonlinear gyrokinetic simulations with the code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and by an analytical derivation. The impact of a finite β, that is, a finite ratio of the plasma pressure to the magnetic pressure, is considered on the fluctuations of the magnetic field through Ampére’s law, as well as on the geometrical modification of the vertical drift produced by the Shafranov shift in the magnetic equilibrium, which, for realistic descriptions, has to be included in both electrostatic and electromagnetic modeling. The condition of turbulent particle flux at the null, which allows the determination of stationary logarithmic density gradients when neoclassical transport and particle sources are negligible, is investigated for increasing values of β, in regimes of ion temperature gradient and trapped electron mode turbulence. The loss of adiabaticity of passing electrons produced by fluctuations in the magnetic vector potential produces an outward convection. When the magnetic equilibrium geometry is kept fixed, this induces a strong reduction of the stationary logarithmic density gradient with increasing β. This effect is partly compensated by the geometrical effect on the vertical drift. This compensation effect, however, is significantly weaker in nonlinear simulations as compared to quasilinear calculations. A detailed comparison between quasilinear and nonlinear results reveals that the predicted value of the logarithmic density gradient is highly sensitive on the assumptions on the wave number spectrum applied in the quasilinear model. The qualitative consistency of the theoretical predictions with the experimental results obtained so far on the dependence of density peaking on β is discussed by considering the additional impact, with increasing β, of a particle source delivered by neutral beam injection heating. (Some figures in this article are in color only in the electronic version.)

Poloidal asymmetries in the ISTTOK edge plasma

The ISTTOK edge plasma parameters show significant poloidal asymmetries in both equilibrium and fluctuating parameters. Asymmetries favoring the outboard side are observed in density, turbulent particle flux and diffusion coefficient independently of the toroidal magnetic field direction, suggesting a ballooning-like transport. This interpretation is supported by the characteristics of the fluctuations as they are found to be more intermittent on the outboard side. In addition, up/down asymmetries reversing with the reversal of the toroidal magnetic field direction are found. Significant poloidal asymmetries were also measured in the parallel flow that can be attributed mainly to Pfirsch–Schluter flows.

Internal measurements of Alfvén eigenmodes with heavy ion beam probing in toroidal plasmas**Dedicated to the 80th anniversary of L.I. Krupnik.

Energetic ion driven Alfvén eigenmodes (AEs) are believed to be an important element disturbing the transport in a future fusion reactor. The studies of the AE properties in modern toroidal devices have made crucial contributions to the reactor relevant physics. AEs are conventionally studied by magnetic probes (MPs), which provide the poloidal m and toroidal n mode numbers and their spectral characteristics. Heavy ion beam probing (HIBP) has become a new tool to study AEs with high spatial and frequency resolution. HIBP in the TJ-II heliac observes locally (∼1 cm) resolved AEs over the whole radial interval. The set of low-m (m < 8) modes, detected with the high-frequency resolution (<5 kHz), present different types of AEs. AEs are pronounced in the local density, electric potential and poloidal magnetic field oscillations, detected simultaneously by HIBP in the frequency range 50 kHz < fAE < 300 kHz. Various AE modes are visible in the neutral beam injector (NBI)-heated plasma for co-NBI (<450 kW), counter- (<450 kW) and balanced NBI (<900 kW) from the plasma centre to the edge. A high coherence between MP and HIBP data was found for specific AEs. When the density rises, AE frequency decreases, , and the cross-phase between the plasma density, poloidal magnetic field and potential remains constant. The amplitude of the AE potential oscillations δφAE ∼ 10 V was estimated. Poloidally resolved density and potential measurements may provide information about the AE poloidal wavelength and the AE contribution to the poloidal electric field Epol and the turbulent particle flux \U0001d6aaE×B. The typical range of Epol oscillations for AEs is . Depending on the δne and δEpol amplitudes and cross-phase, AEs may make a small or a significant contribution to the turbulent particle flux \U0001d6aaE×B for the observed wavenumbers kθ < 3 cm−1.

Numerical simulation of drift-resistive ballooning turbulence in the presence of the GA mode in the plasma edge tokamak

Drift-resistive ballooning turbulence is simulated numerically based on a quasi-three-dimensional computer code for solving nonlinear two-fluid MHD equations in the scrape-off layer plasma in a tokamak. It is shown that, when the toroidal geometry of the magnetic field is taken into account, additional (geodesic) flux terms associated with the first poloidal harmonic (∼sinθ) arise in the averaged equations for the momentum, density, and energy. Calculations show that the most important of these terms is the geodesic momentum flux (the Stringer-Windsor effect), which lowers the poloidal rotation velocity. It is also shown that accounting for the toroidal field geometry introduces experimentally observed, special low-frequency MHD harmonics—GA modes—in the Fourier spectra. GA modes are generated by the Reynolds turbulent force and also by the gradient of the poloidally nonuniform turbulent heat flux. Turbulent particle and heat fluxes are obtained as functions of the poloidal coordinate and are found to show that, in a tokamak, there is a “ballooning effect” associated with their maximum in the weak magnetic field region. The dependence of the density, temperature, and pressure on the poloidal coordinate is presented, as well as the dependence of turbulent fluxes on the toroidal magnetic field.

Self‐Similarity of Fluctuation Particle Fluxes in the Plasma Edge of the Stellarator L‐2M

AbstractResults are presented of statistical studies of probability density of fluctuations of plasma density, floating potential, and turbulent particle fluxes measured by a Langmuir probe in the edge plasma of the L‐2M stellarator. Empirical probability densities differ from Gaussian distributions. The empirical probability density distributions have heavy tails decreasing as x–α –1 and are leptokurtic. Fractional stable distributions were successfully applied to describing such distributions. It is shown that fractional stable distributions give good fit to the distri‐butions of increments of fluctuation amplitudes of physical variables under study. The distribution parameters are statistically estimated from measured time sequences (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Shear flow and drift wave turbulence dynamics in a cylindrical plasma device

The experimental observations of the dynamics of the coupled drift wave turbulence (DWT)/sheared zonal flow (ZF) system in a cylindrical plasma device using a combination of Langmuir probe and fast-framing imaging measurements are reported. The results show the presence of an azimuthal ZF that exhibits low frequency (∼250 Hz) fluctuations. The envelope of the higher frequency (above 5 kHz) floating potential fluctuations associated with the DWT, the density gradient, and the turbulent radial particle flux are all modulated out of phase with the strength of the ZF. The divergence of the turbulent Reynolds stress is also modulated at the same slow time scale in a phase-coherent manner consistent with a turbulent-driven shear flow sustained against the collisional and viscous damping. The radial turbulence correlation length and cross-field particle transport are reduced during periods of strong flow shear. The results are qualitatively consistent with theoretical expectations for coupled DWT-ZF dynamics.

Spectral and statistical analysis of fluctuations in the SOL and diverted plasmas of the Uragan-3M torsatron

In the l = 3/m = 9 Uragan-3M (U3-M) torsatron (R0 = 1 m, ā ≈ 0.12 m, ι(ā)/2π ∼ 0.3) with an open helical divertor and a plasma produced and heated by RF fields (ω ≲ ωci), studies of low frequency (5–100 kHz) density and potential fluctuations in the SOL plasma and in the diverted plasma flows (DPFs), have been carried out. It is shown, that in the SOL to more (less) distantly located points relative to the last closed magnetic surface, higher (lower) frequency fluctuations are inherent. Such a spectral splitting in two sub-ranges occurs in the DPFs too. A peculiarity of the spatial distribution of DPF fluctuation spectra is that lower frequency fluctuations dominate on the ion toroidal B × ∇B drift side. During L-H-like transition in U-3M simultaneously with strong Er shear formation, a suppression of lower frequency fluctuations and a decrease of local radial turbulent particle flux take place. Results are presented of investigation of plasma density fluctuations in SOL with the use of probability distribution function (PDF) analysis. Evaluations of skewness and kurtosis of fluctuations have been made. The analysis of Is fluctuations in DPF have been carried out in a similar way.

Edge turbulence measurements in electron-heated Helically Symmetric Experiment plasmas

This paper presents edge measurements utilizing Langmuir probes to characterize plasma turbulence in the Helically Symmetric Experiment (HSX) [F. S. B. Anderson et al., Fusion Technol. 27, 273 (1995)]. Normalized density and potential fluctuations exhibit strong intensities but are comparable to mixing length estimates using measured correlation lengths. The correlation lengths are isotropic with respect to radial and poloidal directions and follow local (gyro-Bohm) drift wave expectations. These observations are common to measurements in both the optimized quasihelically symmetric (QHS) configuration, as well as a configuration where the symmetry is degraded intentionally. The resulting turbulent particle flux in higher density QHS discharges is in good quantitative agreement with transport analysis using three-dimensional neutral gas simulations. The measured turbulence characteristics are compared to a quasilinear trapped electron mode (TEM) drift wave model [H. Nordman, J. Weiland, and A. Jarmén, Nucl. Fusion 30, 983 (1990)] that has been used to predict the anomalous transport in HSX. While quantitative differences exist (factors of 2–3), there is a general consistency between the turbulence measurements and the TEM drift wave model.

Development of an in situ underwater particle image velocimetry (UWPIV) system

A low‐cost self‐contained underwater particle image velocimetry (UWPIV) system has been developed to measure small‐scale turbulent flow structures in situ. The UWPIV employs a compact continuous‐wave laser and an optical scanner to deliver a light sheet that illuminates naturally occurring particles. Particle images are taken by a CCD camera along with an ultra‐compact PC. The nontethered and compact design can be fit in two small underwater housings with all components powered by batteries: an ideal design for a variety of in situ deployments. The system has been field‐tested in the coastal zone of Lake Michigan. Turbulent flow structures of the wave‐current bottom boundary layer are measured right above the nearshore lakebed, which is densely covered by quagga mussels (Dreissena bugensis). Vertical profiles of mean velocity, Reynolds stresses, dissipation rate of the turbulent kinetic energy, turbulent viscosity, plankton particle concentration, and the turbulent flux of particles are presented and discussed.

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.

Direct determination of highly size-resolved turbulent particle fluxes with the disjunct eddy covariance method and a 12 – stage electrical low pressure impactor

Abstract. During summer 2007, turbulent vertical particle mass and number fluxes were measured for a period of 98 days near the city centre of Münster in north-west Germany. For this purpose, a valve controlled disjunct eddy covariance system was mounted at 65 m a.g.l. on a military radio tower. The concentration values for 11 size bins with aerodynamic diameters (D50) from 0.03 to 10 μm were measured with an electrical low pressure impactor. After comparison with other fluxes obtained from 10 Hz measurements with the classical eddy covariance method, the loss of information concerning high frequent parts of the flux could be stated as negligible. The results offer an extended insight in the turbulent atmospheric exchange of aerosol particles by highly size-resolved particle fluxes covering 11 size bins and show that the city of Münster acts as a relevant source for aerosol particles. Significant differences occur between the fluxes of the various particle size classes. While the total particle number flux shows a pattern which is strictly correlated to the diurnal course of the turbulence regime and the traffic intensity, the total mass flux exhibits a single minimum in the evening hours when coarse particles start to deposit. As a result, a mean mass deposition of about 10 mg m−2 per day was found above the urban test site, covering the aerosol size range from 40 nm to 2.0 μm. By contrast, the half-hourly total number fluxes accumulated over the lower ELPI stages range from −4.29×107 to +1.44×108 particles m−2 s−1 and are clearly dominated by the sub-micron particle fraction of the impactor stages with diameters between 40 nm and 320 nm. The averaged number fluxes of particles with diameters between 2.0 and 6.4 μm show lower turbulent dynamics during daytime and partially remarkably high negative fluxes with mean deposition velocities of 2×10−3 m s−1 that appear temporary during noontime and in the evening hours.

Turbulence and transport measurements with cold and emissive probes in ISTTOK

A probe array consisting of three emissive probes and one cold cylindrical probe was developed for edge plasma measurements in ISTTOK. Emissive probes are particularly suitable for turbulence studies as they are able to deliver a more accurate measure of the plasma potential by reducing the effect of temperature fluctuations. The probe array has the advantage of recording the density, the electric field and their fluctuations simultaneously. Radial plasma profiles were recorded with and without negative edge biasing by an emissive electrode. The statistical properties of the poloidal electric field and of the turbulent particle flux, measured with cold and emissive probes, were compared. Both the root mean square of the poloidal electric field and the fluctuation-induced particle flux were found to be significantly larger when measured with the emissive probes, indicating that temperature fluctuations are important for the measurement of the particle flux. The probability distribution of the particle flux was also found to be more peaked and asymmetric when measured with the emissive probes.

Toroidally non-uniform formation of the edge-transport-barrier by low-to-high confinement transition on the Compact Helical System

In the Compact Helical System, the radial structure of the edge-transport-barrier (ETB) and the characteristics of electrostatic fluctuations were measured for the first time at three toroidally separated locations (the upper side of the vertically elongated section and the outboard and inboard sides in the horizontally elongated section) by using triple Langmuir probes. Electron density (ne) near the plasma edge increased noticeably across the low-to-high confinement (L–H) transition without a clear electron temperature rise. A rapid vertical expansion and outward shift of the formed particle ETB were observed just after the transition. Radial profiles of ne and radial electric field at the inboard of the torus evolved to a peculiar shape across the transition, suggesting the presence of a sizable magnetic island at the rational surface of ι/2π = 1 (ι/2π: rotational transform). Turbulent particle flux derived experimentally was clearly reduced at the upper and outboard locations just after transition, but enhanced at the inboard location. Total turbulent flux passing through a whole LCFS is inferred to be reduced.

Turbulent transport in the TCV SOL

From probe measurements in the far SOL of TCV it is demonstrated that while the particle density profile becomes increasingly broader with increasing line averaged density, the radial variation of the fluctuation statistics remains the same. Excellent agreement is found between the experimental measurements and an interchange turbulence simulation, revealing intermittent plasma transport dominated by radial motion of plasma filaments. On the basis of this favourable code–experiment agreement, it is concluded that no reliable parameterization exists for the turbulent particle flux in terms of effective diffusion and convection coefficients.

Improved Confinement and Related Physics Study in the Compact Helical System

Various types of transport barriers have been studied in the Compact Helical System. In addition to the neoclassical transport barrier, the edge transport barrier (H-mode) was studied using the high-power heating of two coinjection neutral beam injections. A density pedestal is formed after the transition that is indicated by the drop of Hα emission signal. The heating power threshold for the transition was investigated by varying the heating power. Its dependence on the density and the magnetic field is close to the H-mode scaling obtained in tokamaks. The dependence of the power threshold on the magnetic field configuration was also found. Local density fluctuation was measured with beam emission spectroscopy, which observed harmonic oscillations appearing after the density pedestal was formed. For L-mode plasma, long-distance coherence of the potential fluctuations were measured with two sets of heavy ion beam probes (HIBPs). Those coherent modes are supposed to be the geodesic acoustic mode part of zonal flow. Turbulent particle flux was also measured with HIBP, and its change with internal transport barrier formation is demonstrated.

Turbulent particle fluxes to perfectly absorbing surfaces: a numerical study

The motion of small absorbing surfaces is modeled by numerical simulations of turbulent flows with realistic Reynolds numbers. We obtain empirical models for the encounter rate of particles, and in particular the turbulent particle fluxes to given surfaces following the flow. Particular attention is given to the limit, where the particle separations are in the viscous limit, where the scale size of the absorbing surfaces are comparable to or smaller the Kolmogorov length scale. Spherical surfaces represent a special limiting case, but more general shapes are considered as well. The relevance of the problem to the feeding rate of small planktonic organisms in turbulent environments is pointed out in particular, but the results have wider applications. Based on analytical results, we obtain first an empirical expression for the particle flux to a reference spherical surface of interception. This result covers ranges in the universal as well as the viscous subrange. The analysis is then generalized to conical surfaces of interception. We demonstrate the applicability of the results for a wide range of radii, and opening angles of the cones, as well as for two values of turbulence Reynolds numbers. We present also analytical models that account for finite size of particles being transported by a turbulent flow. These latter effects are important for cases where the particles are comparable to the Kolmogorov length in size.