Poloidal Flow Research Articles

Effects of ion diamagnetic drift on the m⁄n = 1 high-order harmonic modes in rotating tokamak plasmas

The effects of ion diamagnetic drift on the high-order harmonic modes in rotating tokamak plasmas are numerically investigated by using a cylindrical reduced magnetohydrodynamic model. It is found that the ion diamagnetic drift has a stabilizing effect on the high-order tearing modes in the small ion diamagnetic drift regime and can excite the high-order Kelvin–Helmholtz (KH) instability in the large ion diamagnetic drift regime. The effects of ion diamagnetic drift flow on the tearing modes are different from those of the poloidal shear flow. Moreover, the combined effect of the two flows on tearing modes and KH modes depends on their relative direction. The eigenmode structures of the tearing modes and KH modes under the influence of ion diamagnetic drift flow are also presented. Finally, the numerical results are verified reasonably by the scalings on resistivity.

Observation of the L-H confinement bifurcation triggered by a turbulence-driven shear flow in a tokamak plasma.

Comprehensive 2D turbulence and eddy flow velocity measurements on DIII-D demonstrate a rapidly increasing turbulence-driven shear flow that develops ∼100 μs prior to the low-confinement (L mode) to high-confinement (H mode) transition and appears to trigger it. These changes are localized to a narrow layer 1-2cm inside the magnetic boundary. Increasing heating power increases the Reynolds stress, the energy transfer from turbulence to the poloidal flow, and the edge flow shearing rate that then exceeds the decorrelation rate, suppressing turbulence and triggering the transition.

Publisher's Note: “Momentum transport in the vicinity of q min in reverse shear tokamaks due to ion temperature gradient turbulence” [Phys. Plasmas 21, 012302 (2014)

Publisher's Note: “Momentum transport in the vicinity of <i>q</i> <i>min</i> in reverse shear tokamaks due to ion temperature gradient turbulence” [Phys. Plasmas 21, 012302 (2014)

Pronounced zonation of seismic anisotropy in the Western Hellenic subduction zone and its geodynamic significance

Many subduction zones exhibit significant retrograde motion of their arc and trench. The observation of fast shear-wave velocities parallel to the trench in such settings has been inferred to represent trench-parallel mantle flow beneath a retreating slab. Here, we investigate this process by measuring seismic anisotropy in the shallow Aegean mantle. We carry out shear-wave splitting analysis on a dense array of seismometers across the Western Hellenic Subduction Zone, and find a pronounced zonation of anisotropy at the scale of the subduction zone. Fast SKS splitting directions subparallel to the trench-retreat direction dominate the region nearest to the trench. Fast splitting directions abruptly transition to trench-parallel above the corner of the mantle wedge, and rotate back to trench-normal over the back-arc. We argue that the trench-normal anisotropy near the trench is explained by entrainment of an asthenospheric layer beneath the shallow-dipping portion of the slab. Toward the volcanic arc this signature is overprinted by trench-parallel anisotropy in the mantle wedge, likely caused by a layer of strained serpentine immediately above the slab. Arcward steepening of the slab and horizontal divergence of mantle flow due to rollback may generate an additional component of sub-slab trench-parallel anisotropy in this region. Poloidal flow above the retreating slab is likely the dominant source of back-arc trench-normal anisotropy. We hypothesize that trench-normal anisotropy associated with significant entrainment of the asthenospheric mantle near the trench may be widespread but only observable at shallow-dipping subduction zones where stations nearest the trench do not overlie the mantle wedge.

Momentum transport in the vicinity of qmin in reverse shear tokamaks due to ion temperature gradient turbulence

We present an analytic study of momentum transport of tokamak plasmas in the vicinity of minimum safety factor (q) position in reversed magnetic shear configuration. Slab ion temperature gradient modes with an equilibrium flow profile are considered in this study. Quasi-linear calculations of momentum flux clearly show the novel effects of q-curvature on the generation of intrinsic rotation and mean poloidal flow without invoking reflectional symmetry breaking of parallel wavenumber (k∥). This q-curvature effect originates from the inherent asymmetry in k∥ populations with respect to a rational surface due to the quadratic proportionality of k∥ when q-curvature is taken into account. Discussions are made of possible implications of q-curvature induced plasma flows on internal transport barrier formation in reversed shear tokamaks.

Study of the L–I–H transition with a new dual gas puff imaging system in the EAST superconducting tokamak

The intermediate oscillatory phase during the L–H transition, termed the I-phase, is studied in the EAST superconducting tokamak using a newly developed dual gas puff imaging (GPI) system near the L–H transition power threshold. The experimental observations suggest that the oscillatory behaviour appearing at the L–H transition could be induced by the synergistic effect of the two components of the sheared m, n = 0 E × B flow, i.e. the turbulence-driven zonal flow (ZF) and the equilibrium flow. The latter arises from the equilibrium, and is, to leading order, balanced by the ion diamagnetic term in the radial force balance equation. A slow increase in the poloidal flow and its shear at the plasma edge are observed tens of milliseconds prior to the I-phase. During the I-phase, the turbulence recovery appears to originate from the vicinity of the separatrix with clear wave fronts propagating both outwards into the far scrape-off layer (SOL) and inwards into the core plasma. The turbulence Reynolds stress is directly measured using the GPI system during the I-phase, providing direct evidence of kinetic energy transfer from turbulence to ZFs at the plasma edge. The GPI observations strongly suggest that the SOL transport physics and the evolution of pressure gradient near the separatrix play an important role in the L–I–H transition dynamics. To highlight these new physics, the previous predator–prey model is extended to include a new equation for the SOL physics. The model successfully reproduces the L–I–H transition process with several features comparing favourably with GPI observations.

Rotation and density asymmetries in the presence of large poloidal impurity flows in the edge pedestal

Novel flow rotation measurements based on charge exchange recombination spectroscopy at the inboard midplane of the ASDEX Upgrade tokamak reveal the existence of an asymmetric flow structure at the H-mode edge, which is shown to arise due to a poloidal impurity density asymmetry. A quantitative evaluation of the impurity density at the inboard side demonstrates that the impurities redistribute along the flux surface, resulting in a poloidal dependency of the impurity density. The poloidal and toroidal impurity flows measured at the high-field side (HFS) and low-field side (LFS) are compared to theoretical predictions based on the parallel momentum balance, which includes friction, inertia, pressure and electric force. Both a fluid and a kinetic approach are used, showing good agreement with each other. The measured impurity flow structure is described by the model quantitatively when a finite poloidal main ion flow of ∼2 km s−1 arises, which is in keeping with the standard neoclassical prediction. The interplay of all terms, in particular the inclusion of the impurity inertia term, is important in reproducing the observed flow structure and results in an impurity accumulation at the HFS. The existence of a poloidal impurity density asymmetry in the edge transport barrier slightly reduces the drift parameter v/D, however, the experimental value is consistent with standard neoclassical theory. This demonstrates that despite the asymmetry in the impurity density, the impurity particle transport is at the neoclassical level.

Conversion of poloidal flows into toroidal flows by phase space structures in trapped ion resonance driven turbulence

A theory to describe the conversion of poloidal momentum into toroidal momentum by phase space structures in trapped ion resonance driven turbulence is presented. In trapped ion resonance driven turbulence, phase space structures are expected to form and can contribute to transport by exerting dynamical friction. Toroidal momentum flux by dynamical friction is calculated. It is shown that dynamical friction exerted on trapped ion granulations can mediate momentum transfer between poloidal and toroidal flows. The conversion coefficient is calculated as measurable, which can be validated in current devices.

Relating the L–H power threshold scaling to edge turbulence dynamics

Understanding the physics of the L–H transition power threshold scaling dependencies on toroidal field and density is critical to operating and optimizing the performance of ITER. Measurements of long-wavelength (k⊥ρI < 1) turbulent eddy dynamics, characteristics, flows, and flow shear in the near edge region of DIIID plasmas have been obtained during an ion gyroradius scan (varying toroidal field and current) and density scan in a favourable geometry (ion ∇B drifts towards the X-point), in order to determine the underlying mechanisms that influence the macroscopic L–H power threshold scaling relations. It is found that the normalized integrated long wavelength density fluctuation amplitudes (ñ/n) in the pedestal increases with ρ* approaching the L–H transition. The turbulence poloidal flow spectrum evolves from geodesic acoustic mode dominant at lower power to low-frequency zonal flow (LFZF) dominant near the L–H transition, and the effective shearing rate correspondingly increases. An inferred Reynolds stress, , from BES velocimetry (inferring velocity field from imaging) measurements is found to significantly increase near the L–H transition. At lower electron density, a clear increase of the LFZF is observed prior to the L–H transition, which is not evident at higher density. Taken together, these results are qualitatively consistent with the electron density and toroidal field scaling of the L–H transition power threshold.

Unraveling Quasiperiodic Relaxations of Transport Barriers with Gyrokinetic Simulations of Tokamak Plasmas

The generation and dynamics of transport barriers governed by sheared poloidal flows are analyzed in flux-driven 5D gyrokinetic simulations of ion temperature gradient driven turbulence in tokamak plasmas. The transport barrier is triggered by a vorticity source that polarizes the system. The chosen source captures characteristic features of some experimental scenarios, namely, the generation of a sheared electric field coupled to anisotropic heating. For sufficiently large shearing rates, turbulent transport is suppressed and a transport barrier builds up, in agreement with the common understanding of transport barriers. The vorticity source also governs a secondary instability--driven by the temperature anisotropy (T(∥)≠T(⊥)). Turbulence and its associated zonal flows are generated in the vicinity of the barrier, destroying the latter due to the screening of the polarization source by the zonal flows. These barrier relaxations occur quasiperiodically, and generically result from the decoupling between the dynamics of the barrier generation, triggered by the source driven sheared flow, and that of the crash, triggered by the secondary instability. This result underlines that barriers triggered by sheared flows are prone to relaxations whenever secondary instabilities come into play.

Velocimetry of edge turbulence during the dithering L–H transition with dynamic programming based time-delay estimation technique in the EAST superconducting tokamak

A dual gas puff imaging (GPI) system has been successfully assembled on the Experimental Advanced Superconducting Tokamak (EAST) and applied for the study of the dithering L–H transition in the 2012 spring campaign. A new method i.e., the dynamic programming based time-delay estimation technique, has been applied to the 64 × 64 pixels GPI video images to yield time-dependent two-dimensional velocity fields at the plasma edge on EAST. Local poloidal flow velocities up to ∼−3 km s−1 (in the electron diamagnetic direction) and radial flow velocities up to ∼−2 km s−1 (inward) are found inside the separatrix during a dithering burst. The radial and poloidal cross-correlation length, flow velocity and auto-correlation time inside the separatrix increase preceding the dithering burst and decrease following the dithering burst. These observations provide strong evidence for the shear flows playing an important role during the dithering L–H transition.

Phase mixing and nonlinearity in geodesic acoustic modes

Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.

Structure beneath the Alboran from geodynamic flow models and seismic anisotropy

Upper mantle heterogeneity beneath the Alboran Sea (western Mediterranean) as inferred from seismology has been associated with a range of subduction and lithospheric delamination scenarios. However, better constraints on the deep dynamics of the region are needed to determine the cause and consequence of complex surface tectonics. Here, we use an improved set of shear wave splitting observations and a suite of mantle flow models to test a range of suggested structures. We find that the observed seismic anisotropy is best reproduced by mantle flow models that include a continuous, deeply extending slab beneath the Alboran which elongates along the Iberian margin from Granada to Gibraltar and curves southward toward the High Atlas. Other models with detached slabs, slabs with spatial gaps, or drip‐like features produce results inconsistent with the splitting observations. SW‐directed shear flow, when combined with sublithospheric deflection in response to a dense sinker, generates NNW‐splitting orientations most similar to the patterns observed along Gibraltar. Slab viscosities of ∼250 times that of the upper mantle are preferred because they provide a balance between the poloidal flow induced by any sinker and toroidal flow induced by stiff slabs. The best match to anisotropy across the Atlas is a model with a stiff continental keel in northwestern Africa which deflects flow northward. Our results show that quantitative predictions of seismic anisotropy are useful in distinguishing the spatial and depth extent of regional density structures which may otherwise be ambiguous.

Fluctuations and intermittent poloidal transport in a simple toroidal plasma

In a simple magnetized toroidal plasma, fluctuation induced poloidal flux is found to be significant in magnitude. The probability distribution function of the fluctuation induced poloidal flux is observed to be strongly non-Gaussian in nature; however, in some cases, the distribution shows good agreement with the analytical form [Carreras et al., Phys. Plasmas 3, 2664 (1996)], assuming a coupling between the near Gaussian density and poloidal velocity fluctuations. The observed non-Gaussian nature of the fluctuation induced poloidal flux and other plasma parameters such as density and fluctuating poloidal velocity in this device is due to intermittent and bursty nature of poloidal transport. In the simple magnetized torus used here, such an intermittent fluctuation induced poloidal flux is found to play a crucial role in generating the poloidal flow.

Analytic Equilibria of High-Beta Tokamaks with Toroidal and Poloidal Flows and Pressure Anisotropy Associated with Parallel Heat Flux

Analytic solutions for a reduced set of magnetohydrodynamic equilibrium equations for high-beta tokamaks with toroidal and poloidal flow velocities comparable to the poloidal sound velocity as well as with pressure anisotropy associated with parallel heat flux are presented. The equations for the parallel heat flux are closed with a fluid closure model. Equilibrium profiles including anisotropic ion and electron pressures are self-consistently obtained and their properties are analytically examined. The solution indicates a qualitatively different behavior in the region around the poloidal sound velocity from those for adiabatic pressure [A. Ito and N. Nakajima: Plasma Phys. Control. Fusion 51 (2009) 035007] and the Chew–Goldberger–Low (CGL) double adiabatic pressure for ions since the parallel heat flux modifies the characteristics of sound waves.

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

AbstractThe equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

Edge sheared flows and the dynamics of blob-filaments

The edge and scrape-off layer (SOL) region of a tokamak plasma is considered, with emphasis on sheared flow generation and the dynamics of blob-filaments. Both numerical simulations and experimental data analysis are employed. The simulations use the fluid-based two-dimensional (2D) curvature-interchange model embedded in the SOLT code. A blob-tracking algorithm based on 2D time-resolved images from the gas puff imaging diagnostic has also been developed and applied to NSTX, Alcator C-Mod and simulation data. The algorithm is able to track the blob motion and changes in blob structure, such as elliptical deformations, that can be affected by sheared flows. Results of seeded blob simulations and quasi-steady turbulence simulations are compared with the experimental data to determine the role of plasma parameters on the blob tracks and to evaluate the exchange of momentum between the blobs and flows. The simulations are shown to reproduce many qualitative and quantitative features of the data including size, scale-length and direction of perpendicular (approximately poloidal) flows, the inferred Reynolds acceleration and residual stress, poloidal reversal of blob tracks, and blob trapping and/or ejection. Mechanisms related to blob motion, SOL currents and radial inhomogeneity are shown to be sufficient to explain the presence or absence of mean and oscillating zonal sheared flows in selected shots.

A new driving mechanism for backarc extension and backarc shortening through slab sinking induced toroidal and poloidal mantle flow: Results from dynamic subduction models with an overriding plate

AbstractWe present numerical subduction models to investigate overriding plate deformation at subduction zones. All models show forearc shortening, resulting predominantly from shear stresses at the subduction zone interface and opposite‐sense mantle shear stresses at the base of the forearc lithosphere. Models dominated by backarc extension show that it results from trench‐normal positive velocity gradients in the mantle below the overriding plate. Such gradients result from toroidal mantle flow induced by slab rollback, with velocities below the leading part of the backarc faster than the overriding plate velocity. The velocity gradients induce basal shear stresses that increase trenchward and cause trenchward overriding plate motion at a velocity (vOP⊥) whose spatial average is below the trench retreat velocity (vT⊥). The combination of basal shear stresses and average vOP⊥ &lt; vT⊥ causes trench‐normal deviatoric tension in the backarc and backarc extension. Models dominated by backarc shortening show that it results from a relatively immobile subduction hinge and trenchward overriding plate motion driven by poloidal mantle flow. The poloidal mantle flow is induced by downdip slab sinking and causes the average vOP⊥ &gt; vT⊥. This results in trench‐normal deviatoric compression and shortening in the leading part of the overriding plate as it collides with the subduction hinge. Ultimately, the geodynamic models demonstrate that backarc extension is favored for narrow slabs and near lateral slab edges and is driven by rollback induced toroidal mantle flow, while backarc shortening is favored for the center of wide slabs and is driven by poloidal mantle flow resulting from downdip slab motion.

Determination of structure tilting in magnetized plasmas—Time delay estimation in two dimensions

Time delay estimation (TDE) is a well-known technique to investigate poloidal flows in fusion plasmas. The present work is an extension of the earlier works of Bencze and Zoletnik [Phys. Plasmas 12, 052323 (2005)] and Tal et al. [Phys. Plasmas 18, 122304 (2011)]. From the prospective of the comparison of theory and experiment, it seems to be important to estimate the statistical properties of the TDE based on solid mathematical groundings. This paper provides analytic derivation of the variance of the TDE using a two-dimensional model for coherent turbulent structures in the plasma edge and also gives an explicit method for determination of the tilt angle of structures. As a demonstration, this method is then applied to the results of a quasi-2D Beam Emission Spectroscopy measurement performed at the TEXTOR tokamak.

Collisionality scaling of main-ion toroidal and poloidal rotation in low torque DIII-D plasmas

In tokamak plasmas with low levels of toroidal rotation, the radial electric field Er is a combination of pressure gradient and toroidal and poloidal rotation components, all having similar magnitudes. In order to assess the validity of neoclassical poloidal rotation theory for determining the poloidal rotation contribution to Er, Dα emission from neutral beam heated tokamak discharges in DIII-D (Luxon 2002 Nucl. Fusion 42 614) has been evaluated in a sequence of low torque (electron cyclotron resonance heating and balanced diagnostic neutral beam pulse) discharges to determine the local deuterium toroidal rotation velocity. By invoking the radial force balance relation the deuterium poloidal rotation can be inferred. It is found that the deuterium poloidal flow exceeds the neoclassical value in plasmas with collisionality , being more ion diamagnetic, and with a stronger dependence on collisionality than neoclassical theory predicts. At low toroidal rotation, the poloidal rotation contribution to the radial electric field and its shear is significant. The effect of anomalous levels of poloidal rotation on the radial electric field and cross-field heat transport is investigated for ITER parameters.