Poloidal Flow Research Articles

Two-dimensional turbulence cross-correlation functions in the edge of NSTX

The 2D radial vs. poloidal cross-correlation functions of edge plasma turbulence were measured near the outer midplane using a gas puff imaging (GPI) diagnostic on NSTX. These correlation functions were evaluated at radii r = 0 cm, ±3 cm, and ±6 cm from the separatrix and poloidal locations p = 0 cm and ±7.5 cm from the GPI poloidal center line for 20 different shots. The ellipticity ε and tilt angle φ of the positive cross-correlation regions and the minimum negative cross-correlation “cmin” and total negative over positive values “neg/pos” were evaluated for each of these cases. The average results over this dataset were ε = 2.2 ± 0.9, φ = 87° ± 34° (i.e., poloidally oriented), cmin = −0.30 ± 0.15, and neg/pos = 0.25 ± 0.24. Thus, there was a significant variation in these correlation results within this database, with dependences on the location within the image, the magnetic geometry, and the plasma parameters. Possible causes for this variation are discussed, including the misalignment of the GPI view with the local B field line, the magnetic shear of field lines at the edge, the poloidal flow shear of the turbulence, blob-hole correlations, and the neutral density 'shadowing' effect in GPI.

Poloidal radiation asymmetries during disruption mitigation by massive gas injection on the DIII-D tokamak

A comparison of radiated power poloidal peaking during disruption mitigation using massive gas injection at multiple poloidal positions on the DIII-D tokamak is presented. The two injectors are located poloidally above and below the low field side midplane and toroidally located within the quadrants to either side of the fast bolometry diagnostic used to measure the radiated power. Differing quantities of injected neon are compared. A strong dependence of impurity poloidal flows upon the injector location is observed. Injection from the upper half of the vessel results in strong poloidal flows over the top of the plasma to the high field side midplane, while lower injection exhibits far less pronounced poloidal flow that is oriented in the opposite direction. The poloidal location of both pre-thermal quench and thermal quench emissivity peaking shows a strong dependence upon the injector location, although the poloidal flow in the upper injection case results in a much broader distribution. The wall radiative heat flux mimics the emissivity, but the distribution is smoothed with lower poloidal peaking due to geometric effects. Thermal quench MHD appears to have little effect upon the poloidal phase of maximum emissivity in experiment or modeling, which can be attributed to the slower parallel transport of impurities along field lines in the poloidal versus toroidal direction. Poloidal peaking factors of ≤1.6 and ≤2.2 were observed for upper and lower injection, respectively. Under very conservative assumptions, the observed poloidal peaking factor will bring ITER near the melting limit for first wall stainless steel. However, further modeling is required to determine if those conservative assumptions are warranted.

Radial impurity flux measuring method with plasma heating in general geometry

Devising a means to measure the radial impurity flux across the pedestal could be used to reduce impurity accumulation, if not prevent it while providing natural fueling, and thus improving fusion performance in tokamaks. We employ a novel solution procedure that takes advantage of the poloidal flow measurement to obtain the radial impurity flux directly from available diagnostics, such as charge exchange recombination spectroscopy and Thomson scattering. In the absence of our procedure, a computationally demanding kinetic calculation of the full bulk ion response would be required at finite aspect ratio for the flux surface shape of interest. The more general form of the model considered here permits large toroidal impurity flow on the order of the impurity thermal speed. Moreover, it allows plasma heating techniques to be employed to actively modify the poloidal variation of the potential to adjust the location of impurity accumulation and thereby alter the radial impurity flux.

Generation of zonal flows by coupled electrostatic drift and ion-acoustic waves

Generation of sheared zonal flow by low-frequency coupled electrostatic drift and ion-acoustic waves is presented. Primary waves of different (small, intermediate, and large) scales are considered, and the appropriate system of equations consisting of generalized Hasegawa-Mima equation for the electrostatic potential (involving both vector and scalar nonlinearities) and equation of parallel to magnetic field ions motion is obtained. It is shown that along with the mean poloidal flow with strong variation in minor radius mean sheared toroidal flow can also be generated. According to laboratory plasma experiments, main attention to large scale drift-ion-acoustic wave is given. Peculiarities of the Korteweg-de Vries type scalar nonlinearity due to the electrons temperature non-homogeneity in the formation of zonal flow by large-scale turbulence are widely discussed. Namely, it is observed that such type of flows need no generation condition and can be spontaneously excited.

Outer midplane scrape-off layer profiles and turbulence in simulations of Alcator C-Mod inner-wall limited discharges

A region of steep plasma gradients, the so-called “narrow-feature,” has been found in the near scrape-off layer (SOL) of inner-wall limited (IWL) discharges. Dedicated IWL discharges were carried out in Alcator C-Mod [Marmar et al., Nucl. Fusion 55, 104020 (2015)] to study this phenomenon, allowing detailed observations of the plasma profiles and fluctuations. Langmuir probe (LP) measurements show a clear two-decay length ne and Te profile structure at the outer midplane. The Gas-Puff Imaging (GPI) diagnostic shows large turbulent fluctuations across the last closed flux-surface, hence supporting the hypothesis that turbulent phenomena play a role in setting the profile steepness. Flux-driven non-linear turbulence simulations of two C-Mod discharges have been carried out, allowing a three-way comparison between LP, GPI, and simulation data. Observations and simulations correlate the steep gradient region characterizing the narrow feature with sheared poloidal flows and a deviation of the plasma potential from its floating value. The E × B shear rate exceeds the linear ballooning growth rate, indicating that the narrow feature could result from the effects of sheared flows, although causality could not be established. The fluctuation level in the narrow feature remains of order unity across the entire SOL, indicating that the transport reduction in the near-SOL cannot result from a simple quench rule.

Distorted magnetic island formation during slowing down to mode locking in helical plasmas

We report the first observation of the formation of a magnetic island before the occurrence of mode locking in helical plasma. New analysis and observation techniques applied to the ECE signal and poloidal flow in LHD experiments yield the following results. (i) A magnetic island structure is present, rotating at the end of the rotating phase. (ii) The rotation speed of the island is not uniform in space and time. The rotation of the island changes significantly at the end of the rotating phase, and the deformation increases until the mode is locked.

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.

Intrinsic rotation reversal, non-local transport, and turbulence transition in KSTAR L-mode plasmas

Experiments of electron cyclotron resonance heating (ECH) power scan in KSTAR tokamak clearly demonstrate that both the cutoff density for non-local heat transport (NLT) and the threshold density for intrinsic rotation reversal can be determined by the collisionality. We demonstrate that NLT can be affected by ECH, and the intrinsic rotation direction follows the changes of NLT. The cutoff density of NLT and threshold density for rotation reversal can be significantly increased by ECH. The poloidal flow of turbulence in core plasma is in the electron and the ion diamagnetic direction in ECH plasmas and high density OH plasma, respectively. The auto-power spectra of density fluctuation are almost the same in the outer region for both ECH and OH plasmas. On the other hand, the divergence in density fluctuation spectra at high frequency range between OH and ECH plasma is clearly observed in core region. The features of linear confinement and saturated confinement also appeared in ECH plasma, which is similar to the linear ohmic confinement (LOC) mode and saturate ohmic confinement (SOC) mode. All these observations in macroscopic parameters and micro fluctuations suggest a possible link between the macro phenomena and the structural changes in turbulence mode.

Collisional damping of the geodesic acoustic mode with poloidal rotation

The collisional damping of the geodesic acoustic mode is investigated by using the gyrokinetic equation with a poloidal rotation flow and a number-conserving Krook collision operator. A dispersion relation of the geodesic acoustic mode with poloidal rotation and collision terms is derived and solved both analytically and numerically. It is shown that poloidal rotation has a significant influence on the collisional damping rate of the geodesic acoustic mode within a certain collision rate and safety factor domain. The variation of the damping rate induced by poloidal rotation depends on the safety factor and collision rate. In addition, the effect of poloidal rotation on the geodesic acoustic mode would be weakened by the safety factor, especially when the safety factor is relatively large. The ratio of the collisional damping rate to the collisionless damping rate of the geodesic acoustic mode in the large safety factor domain is performed, and the critical collision rate is estimated. Besides, the physical mechanism of the results is briefly discussed.

Investigation of the interaction between competing types of nondiffusive transport in drift wave turbulence

Radial transport in turbulence dominated tokamak plasmas has been observed to deviate from classical diffusion in certain regimes relevant for magnetic confinement fusion. These situations at least include near-marginal turbulence, where radial transport becomes superdiffusive and mediated by elongated radial structures (or avalanches) and transport across radially sheared poloidal flows, where radial subdiffusion often ensues. In this paper, the interaction between very different physical ingredients responsible for these two types of nondiffusive dynamics (namely, turbulent profile relaxation close to a local threshold and the interaction with radially sheared zonal flows) is studied in detail in the context of a simple two-dimensional electrostatic plasma fluid turbulence model based on the dissipative trapped electron mode. It is shown that, depending on the relative relevance of each of these ingredients, which can be tuned in various ways, a variety of non-diffusive radial transport behaviors can be found in the system. The results also illustrate the fact that the classical diffusion paradigm is often insufficient to describe turbulent transport in systems with self-generated flows and turbulent profile relaxations.

Neoclassical flows in deuterium–helium plasma density pedestals

In tokamak transport barriers, the radial scale of profile variations can be comparable to a typical ion orbit width, which makes the coupling of the distribution function across flux surfaces important in the collisional dynamics. We use the radially global steady-state neoclassical code Perfect (Landreman et al 2014 Plasma Phys. Control. Fusion 56 045005) to calculate poloidal and toroidal flows, and radial fluxes, in the pedestal. In particular, we have studied the changes in these quantities as the plasma composition is changed from a deuterium bulk species with a helium impurity to a helium bulk with a deuterium impurity, under specific profile similarity assumptions. In the presence of sharp profile variations, the poloidally resolved radial fluxes are important for the total fluxes to be divergence-free, which leads to the appearance of poloidal return-flows. These flows exhibit a complex radial–poloidal structure that extends several orbit widths into the core and is sensitive to abrupt radial changes in the ion temperature gradient. We find that a sizable neoclassical toroidal angular momentum transport can arise in the radially global theory, in contrast to the local.

Pedestal radial flux measuring method to prevent impurity accumulation

The use of high-z wall materials attempts to shift the fusion challenge from heat handling to impurity removal. We demonstrate that not only the impurity density in-out asymmetry but also the poloidal flow has a major impact on the radial impurity flux direction. This realization provides the first method of measuring the flux from available diagnostics, without the need of a computationally demanding kinetic calculation of the full bulk ion response. Moreover, it affords insight into optimal tokamak operation to avoid impurity accumulation while allowing free fueling.

Measurement of N+ flows in the high-field side scrape-off layer of ASDEX upgrade with different degrees of inner divertor detachment

Toroidal and poloidal flows of injected N+ ions were measured in the high-field side (HFS) scrape-off layer (SOL) of ASDEX Upgrade by Doppler spectroscopy with different degrees of HFS divertor detachment. In high-recycling conditions, the results suggest reversed parallel N+ flow away from the inner divertor in the near SOL close to the separatrix, while the flow is towards the inner divertor throughout the SOL in detached conditions. The measured poloidal N+ flows were directed away from the HFS divertor in the near SOL for all density cases. Divertor plasma oscillations, characterized by momentary peaking of the HFS target ion flux and decrease of the HFS SOL density, were observed slightly before the roll-over of the ion saturation current to the HFS target and lead to an increase in the N+ flow towards the HFS divertor. SOLPS and ERO simulations of the experiment predict entrainment below 50% between the velocities of N+ and D+ ions, suggesting that N+ ions are quantitatively a limited proxy for measuring D+ flows. ERO simulations show significantly higher entrainment for higher ionization states, e.g., N2+ and N3+.

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604–614 (2004)] is presented for relevant scenarios.

Numerical study of Hall effects on counter-helicity spheromak merging by two-dimensional Hall-MHD simulations

Hall effects on counter-helicity spheromak merging were investigated by two-dimensional MHD and Hall-MHD simulations of merging two axisymmetric toroidal flux tubes. In Hall-MHD cases, the structure of the reconnection current sheet and reconnection outflow are modified from the MHD case due to the Hall effect. We compared two cases (called “case-O” and “case-I”) of counter-helicity merging, which are distinguished by the polarity of toroidal magnetic fluxes. Radial motion of the reconnection X-point is controlled by poloidal electron flow accompanying the toroidal flux of the merging two spheromaks, and this creates a large difference in the current sheet and flow structure between the two cases of the Hall-MHD regime. The radial shift of the reconnection X-point depending on the polarity of toroidal magnetic flux of the spheromaks breaks the symmetry between the two cases. It was also found that there widely exists separation of ion and electron flow which are affected by the modification of the current sheet structure due to the radial shift of the X-point in the downstream side of the merging, and its spatial scale of the distribution of the Hall electric field is larger than the ion skin depth.

Interpretations of the impact of cross-field drifts on divertor flows in DIII-D with UEDGE

Simulations using the multi-fluid code UEDGE indicates that, in low confinement (L-mode) plasmas in DIII-D, poloidal projection of the ionization driven flows dominate poloidal particle flows in the divertor near the divertor plates, whereas E ×B drift flows dominate the radial particle flows. In contrast, in high confinement (H-mode) conditions E ×B drift flows dominate both poloidal and radial particle flows in the divertor in the vicinity of the strong gradient region near the separatrix. UEDGE indicates that the toroidal C2+ flow velocities in the divertor plasmas are mainly entrained within 30% to the background deuterium flow in both L- and H-mode plasmas in the plasma region where the CIII 465nm emission is measured. Therefore, UEDGE indicates that the Doppler Coherence Imaging Spectroscopy (CIS), measuring the toroidal velocity of the C2+ ions, can provide insight to the deuterium flows in the divertor. Parallel-to-B velocity dominates the toroidal divertor flow; direct drift impact being less than 1%. Toroidal divertor flow is predicted to reverse when the magnetic field is reversed. This is explained by the parallel-B flow towards the nearest divertor plate corresponding to opposite toroidal directions in opposite toroidal field configurations.

Eye formation in rotating convection

We consider rotating convection in a shallow, cylindrical domain. We examine the conditions under which the resulting vortex develops an eye at its core; that is, a region where the poloidal flow reverses and the angular momentum is low. For simplicity, we restrict ourselves to steady, axisymmetric flows in a Boussinesq fluid. Our numerical experiments show that, in such systems, an eye forms as a passive response to the development of a so-called eyewall, a conical annulus of intense, negative azimuthal vorticity that can form near the axis and separates the eye from the primary vortex. We also observe that the vorticity in the eyewall comes from the lower boundary layer, and relies on the fact the poloidal flow strips negative vorticity out of the boundary layer and carries it up into the fluid above as it turns upward near the axis. This process is effective only if the Reynolds number is sufficiently high for the advection of vorticity to dominate over diffusion. Finally we observe that, in the vicinity of the eye and the eyewall, the buoyancy and Coriolis forces are negligible, and so although these forces are crucial to driving and shaping the primary vortex, they play no direct role in eye formation in a Boussinesq fluid.

Influence of the poloidal equilibrium flow and flow shear on the tearing mode instabilities in tokamak plasmas

The effect of the poloidal equilibrium flow and flow shear on the tearing mode instabilities for tokamak plasmas is investigated. The vorticity equation is derived and approximately solved for large poloidal mode numbers (m). Asymptotic matching of the inner solution to the outer solution can approximately give the classical tearing mode stability index Δ′. For typical plasma parameters with positive flow shear, we notice that the poloidal mean flows have a beneficial effect on the classical tearing mode and vice versa. To study the modes with arbitrary poloidal mode numbers, we numerically solve the vorticity equation for delta prime (Δ′) for typical plasma parameters with positive flow shear at the rational surface and the resulting Δ′ with large m also decreases with increasing poloidal flow velocity, consistent with the approximate analytical large m results. Our numerical calculations indicate that the poloidal mean flow with positive flow shear has beneficial influence on the stabilization of classical tearing modes in tokamak plasmas.

Velocity shear, turbulent saturation, and steep plasma gradients in the scrape-off layer of inner-wall limited tokamaks

The narrow power decay-length (), recently found in the scrape-off layer (SOL) of inner-wall limited (IWL) discharges in tokamaks, is studied using 3D, flux-driven, global two-fluid turbulence simulations. The formation of the steep plasma profiles is found to arise due to radially sheared poloidal flows. A complex interaction between sheared flows and parallel plasma currents outflowing into the sheath regulates the turbulent saturation, determining the transport levels. We quantify the effects of sheared flows, obtaining theoretical estimates in agreement with our non-linear simulations. Analytical calculations suggest that the IWL is roughly equal to the turbulent correlation length.

Generation of electrostatic drift zonal flows under the action of mean sheared flows

Generation of large-scale zonal flows by the small-scale electrostatic drift wave turbulence in the magnetized plasma under the action of mean poloidal sheared flow is considered. Attention to large-scale (compared to the ion Larmor radius) drift structures is paid. To this end, the generalized Hasegawa-Mima equation containing both vector and scalar nonlinearities is derived, and the appropriate eigenvalue problem is solved numerically. Destabilizing role of the small amplitude mean shear flow and spatial inhomogeneity of electron temperature is shown.