Toroidal Flow Research Articles

Dynamic responses of the Earth’s outer core to assimilation of observed geomagnetic secular variation

Assimilation of surface geomagnetic observations and geodynamo models has advanced very quickly in recent years. However, compared to advanced data assimilation systems in meteorology, geomagnetic data assimilation (GDAS) is still in an early stage. Among many challenges ranging from data to models is the disparity between the short observation records and the long time scales of the core dynamics. To better utilize available observational information, we have made an effort in this study to directly assimilate the Gauss coefficients of both the core field and its secular variation (SV) obtained via global geomagnetic field modeling, aiming at understanding the dynamical responses of the core fluid to these additional observational constraints. Our studies show that the SV assimilation helps significantly to shorten the dynamo model spin-up process. The flow beneath the core-mantle boundary (CMB) responds significantly to the observed field and its SV. The strongest responses occur in the relatively small scale flow (of the degrees L≈30 in spherical harmonic expansions). This part of the flow includes the axisymmetric toroidal flow (of order m=0) and non-axisymmetric poloidal flow with m≥5. These responses can be used to better understand the core flow and, in particular, to improve accuracies of predicting geomagnetic variability in the future.

Seismic anisotropy beneath the Juan de Fuca plate system: Evidence for heterogeneous mantle flow

Here we use SKS shear wave splitting observations from ocean-bottom seismometer data to infer patterns of mantle deformation beneath the Juan de Fuca plate and its adjoining boundaries. Our results indicate that the asthenosphere beneath the Juan de Fuca plate responds largely to absolute plate motion with an anisotropic layer developing rapidly near the ridge and persisting into the subduction zone. Geographically restricted deviations from this pattern indicate the presence of secondary processes. At discrete plate boundaries, such as the Blanco transform fault, seismic anisotropy is attributed to relative plate motion within a narrow zone (<50 km). Beneath the deforming southern Gorda plate region—a diffuse plate boundary—splitting observations similarly suggest deformation dominated by relative motion between the rigid Juan de Fuca and Pacific plates but distributed over a broad zone (∼200 km). Our results are inconsistent with toroidal flow around the southern edge of the subducting slab due to rollback, as suggested by onshore studies. Instead, reorganization of upper mantle flow associated with plate fragmentation seems to dominate the anisotropic signature of southern Cascadia.

Collisionality dependence of edge rotation and in–out impurity asymmetries in ASDEX Upgrade H-mode plasmas

The poloidal and toroidal impurity flows in the edge transport barrier of H-mode plasmas have been studied over a wide range of pedestal top ion collisionalities. A comparison of the edge poloidal rotation measurements to neoclassical predictions shows good agreement in all cases. The measured edge impurity toroidal rotation is observed to change sign from co-current to counter-current with decreasing collisionality. The switch occurs at the same collisionality at which neoclassical theory predicts the main ion poloidal rotation to change from the electron to the ion diamagnetic direction. The behaviour of these two species, when used to calculate the main ion toroidal rotation via the radial force balance equation, leads to fairly constant co-current main ion toroidal rotation. Hence, at low collisionality, due to a reduced frictional coupling, the main ion-impurity differential rotation can be quite large. The behaviour of impurity ion flows on a flux surface has also been investigated in detail and it was found that the measurements are consistent with the continuity equation only if the poloidally asymmetric impurity density distribution is taken into account. The asymmetry is found to be the result of the interplay of all forces in the parallel momentum balance, with the friction force providing the dominant drive. Close to the separatrix the poloidal centrifugal force, which is usually neglected, also gives an additional contribution to the impurity density asymmetry. Within the experimental uncertainties the ion temperature and the electrostatic potential are simultaneous flux functions, despite the presence of a poloidally asymmetric impurity density profile.

Tokamak Plasma Flows Induced by Local RF Forces**supported by National Natural Science Foundation of China (Nos. 11405218, 11325524, 11375235 and 11261140327), in part by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB111002, 2013GB112001 and 2013GB112010), and the Program of Fusion Reactor Physics and Digital Tokamak with the CAS “One-Three-Five” Strategic Planning

The tokamak plasma flows induced by the local radio frequency (RF) forces in the core region are analyzed. The effective components of local RF forces are composed of the momentum absorption term and the resonant parallel momentum transport term (i.e. the parallel component of the resonant ponderomotive forces). Different momentum balance relations are employed to calculate the plasma flows depending on different assumptions of momentum transport. With the RF fields solved from RF simulation codes, the toroidal and poloidal flows by these forces under the lower hybrid current drive and the mode conversion ion cyclotron resonance heating on EAST-like plasmas are evaluated.

Transport theory in the collisional boundary layer regime for finite aspect ratio tokamaks with broken symmetry

Transport theory in the collisional boundary layer regime for tokamaks with broken symmetry is extended to include the effects of the finite aspect ratio and finite plasma β. Here, β is the ratio of the plasma thermal pressure to the magnetic field pressure. Transport fluxes are calculated on the perturbed magnetic surface where plasma pressure is constant. The extension of the theory to finite aspect ratio tokamaks is made possible because the perturbed particle distribution that contributes to the transport fluxes in the collisional boundary layer regime is localized in the pitch angle space. Invoking the flux-force relation, the transport fluxes can be used for modeling toroidal plasma flow in tokamaks.

THE SUN’S PHOTOSPHERIC CONVECTION SPECTRUM

Spectra of the cellular photospheric flows are determined from full-disk Doppler velocity observations acquired by the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO) spacecraft. Three different analysis methods are used to separately determine spectral coefficients representing the poloidal flows, the toroidal flows, and the radial flows. The amplitudes of these spectral coefficients are constrained by simulated data analyzed with the same procedures as the HMI data. We find that the total velocity spectrum rises smoothly to a peak at a wavenumber of about 120 (wavelength of about 35 Mm), which is typical of supergranules. The spectrum levels off out to wavenumbers of about 400, and then rises again to a peak at a wavenumber of about 3500 (wavelength of about 1200 km), which is typical of granules. The velocity spectrum is dominated by the poloidal flow component (horizontal flows with divergence but no curl) at wavenumbers above 30. The toroidal flow component (horizontal flows with curl but no divergence) dominates at wavenumbers less than 30. The radial flow velocity is only about 3\% of the total flow velocity at the lowest wavenumbers, but increases in strength to become about 50\% at wavenumbers near 4000. The spectrum compares well with the spectrum of giant cell flows at the lowest wavenumbers and with the spectrum of granulation from a 3D radiative-hydrodynamic simulation at the highest wavenumbers.

Vlasov tokamak equilibria with sheared toroidal flow and anisotropic pressure

By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e., the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions, these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.

Stabilization of resistive wall modes in tokamaks by drift kinetic effects combined with magnetic feedback

The synergetic effects of drift kinetic resonances, the resistive layer dissipation, the magnetic feedback, and the toroidal plasma flow on the stability of the resistive wall mode are numerically investigated using a full toroidal resistive magnetohydrodynamic-kinetic hybrid stability code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503). It is found that the plasma resistivity, coupled with the favourable average curvature effect, can enlarge the stable domain predicted by the drift kinetic model. A synergy between the precessional drift resonance damping, the magnetic feedback and the plasma flow helps open two stability windows. The width of the inner stability window increases with the feedback gain, but decreases with the flow speed. In addition, optimization of the toroidal phase difference of the feedback gains between the upper and lower active coils can lead to a full suppression of the mode.

A two‐way interaction between the Hainan plume and the Manila subduction zone

AbstractThe interaction between mantle plumes and subducting slabs is well accepted, but the influence of slabs on plumes has more often been portrayed than the reverse. Here we present three‐dimensional upper mantle laboratory models in which a compositional plume rises underneath a subducting plate. Slab/plume buoyancy flux ratios ranged between 7 and 18. The models exhibit a two‐way interaction. While the plume conduit increasingly tilts away from the trench as a result of slab rollback‐induced toroidal mantle flow, the slab subduction rate decreases as a function of the amount of plume buoyancy opposing that of the slab, which gets subducted beneath the slab. We propose that our models apply to the Hainan/Manila system and explain the recently imaged tilt of the Hainan plume by the Manila slab‐induced mantle return flow. The Hainan plume could lessen the Manila subduction rate from 8 Ma into the future.

Modelling toroidal rotation damping in ITER due to external 3D fields

The linear and quasi-linear plasma response to the n = 3 and n = 4 (n is the toroidal mode number) resonant magnetic perturbation (RMP) fields, produced by the in-vessel edge localized mode control coils, is numerically studied for an ITER 15 MA H-mode baseline scenario. Both single fluid and fluid-kinetic hybrid models are used. The inclusion of drift kinetic effects does not strongly alter the plasma response compared to the fluid approximation for this ITER plasma. The full toroidal drift kinetic model is also used to compute the neoclassical toroidal viscous (NTV) torque, yielding results close to that of an analytic model based on geometric simplifications. The computed NTV torque from low-n RMP fields is generally smaller than the resonant electromagnetic torque for this ITER plasma. The linear response computations show a weak core kink response, contrary to a strong kink response often computed for plasmas from present day tokamak devices. Initial value quasi-linear simulations, including various torque models, show a localized damping of the plasma toroidal flow near the edge, as a result of the applied RMP fields. This localized rotation damping can be weak or strong depending on whether a weakly unstable edge localized peeling mode is present. No qualitative difference is found between the n = 3 and n = 4 RMP field configurations, in both the linear and non-linear response results.

Resistive Interchange Modes Destabilized by Helically Trapped Energetic Ions in a Helical Plasma

A new bursting m=1/n=1 instability (m,n: poloidal and toroidal mode numbers) with rapid frequency chirping down has been observed for the first time in a helical plasma with intense perpendicular neutral beam injection. This is destabilized in the plasma peripheral region by resonant interaction between helically trapped energetic ions and the resistive interchange mode. A large radial electric field is induced near the edge due to enhanced radial transport of the trapped energetic ions by the mode, and leads to clear change in toroidal plasma flow, suppression of microturbulence, and triggering an improvement of bulk plasma confinement.

Modelling and analytic studies of sheared flow effects on tearing modes

The effects of flow shear on the stability of a (2,1) tearing mode are examined using numerical and analytic studies on a number of model systems. For a cylindrical reduced magnetohydrodynamic (MHD) model, linear computations using the CUTIE code show that sheared axial flows have a destabilizing effect, while sheared poloidal flows tend to reduce the growth rate of the mode. These effects are independent of the direction of the flow. For helical flows the sign of the shear in the flow matters. This symmetry breaking is also seen in the nonlinear regime where the island saturation level is found to depend on the sign of the flows. In the absence of flow, the CUTIE simulations show that the linear mode is more stable in a two fluid as compared to a single fluid model. However, in the presence of sheared axial flows a negative sheared flow is more destabilizing while a positive sheared flow is more stabilizing, compared to the single fluid model. In contrast to the cylindrical model, simulations in a toroidal model, using the MHD code NEAR, always show a stabilizing effect in the presence of a sheared toroidal flow. This is understood analytically in terms of a flow induced ‘Shafranov’ like shift in the profiles of the equilibrium current that results in a stabilizing change in Δ′ and the saturated island size.

Capture of the Canary mantle plume material by the Gibraltar arc mantle wedge during slab rollback

Abstract Recent evidence suggests that a portion of the Canary plume travelled northeastwards below the lithosphere of the Atlas Mountains in North Africa towards the Alboran domain and was captured ∼10 Ma ago by the Gibraltar subduction system in the Western Mediterranean. The capture would have been associated with the mantle return flow induced by the westward-retreating slab that would have dragged and trapped a portion of the plume material in the mantle wedge of the Gibraltar subduction zone. Such material eventually contaminated the subduction related volcanism in the Alboran region. In this work, we use scaled analogue models of slab–plume interaction to investigate the plausibility of the plume capture. An upper-mantle-scaled model combines a narrow (400 km) edge-fixed subduction plate with a laterally offset compositional plume. The subduction dominated by slab rollback and toroidal mantle flow is seen to increasingly impact on the plume dynamics as the area of influence of the toroidal flow cells at the surface is up to 500 × 1350 km2. While the plume head initially spreads axisymmetrically, it starts being distorted parallel to the plate in the direction of the trench as the slab trench approaches the plume edge at a separation distance of about 500 km, before getting dragged towards mantle wedge. When applied to the Canary plume–Gibraltar subduction system, our model supports the observationally based conceptual model that mantle plume material may have been dragged towards the mantle wedge by slab rollback-induced toroidal mantle flow. Using a scaling argument for the spreading of a gravity current within a channel, we also show that more than 1500 km of plume propagation in the sublithospheric Atlas corridor is dynamically plausible.

Using a local gyrokinetic code to study global ion temperature gradient modes in tokamaks

In this paper the global eigenmode structures of linear ion temperature gradient (ITG) modes in tokamak plasmas are obtained using a novel technique which combines results from the local gyrokinetic code GS2 with analytical theory to reconstruct global properties. Local gyrokinetic calculations are performed for a range of radial flux surfaces, x, and ballooning phase angles, p, to map out the local complex mode frequency, Ω0(x, p) = ω0(x, p) + iγ0(x, p) for a single toroidal mode number, n. Taylor expanding Ω0 about a reference surface at x = 0, and employing the Fourier-ballooning representation leads to a second order ODE for the amplitude envelope, A(p), which describes how the local results are combined to form the global mode. The equilibrium profiles impact on the variation of Ω0(x, p) and hence influence the global mode structure. The simulations presented here are based upon a global extension to the CYCLONE base case and employ the circular Miller equilibrium model. In an equilibrium with radially varying profiles of a/LT and a/Ln, peaked at x = 0, and with all other equilibrium profiles held constant, including ηi = Ln/LT, Ω0(x, p) is found to have a stationary point. The reconstructed global mode sits at the outboard mid-plane of the tokamak, with global growth rate, γ ∼ Max[γ0]. Including the radial variation of other equilibrium profiles like safety factor and magnetic shear, leads to a mode that peaks away from the outboard mid-plane, with a reduced global growth rate. Finally, the influence of toroidal flow shear has also been investigated through the introduction of a Doppler shift, , where Ωϕ is the equilibrium toroidal flow, and a prime denotes the radial derivative. The equilibrium profile variations introduce an asymmetry into the global growth rate spectrum with respect to the sign of , such that the maximum growth rate is achieved with non-zero shearing, consistent with recent global gyrokinetic calculations.

Theory and simulation of quasilinear transport from external magnetic field perturbations in a DIII-D plasma

The linear response profiles for the 3D perturbed magnetic fields, currents, ion velocities, plasma density, pressures, and electric potential from low-n external resonant magnetic field perturbations (RMPs) are obtained from the collisional two-fluid M3D-C1 code [N. M. Ferraro and S. C. Jardin, J. Comput. Phys. 228, 7742 (2009)]. A newly developed post-processing RMPtran code computes the resulting quasilinear E×B and magnetic (J×B) radial transport flows with respect to the unperturbed flux surfaces in all channels. RMPtran simulations focus on ion (center of mass) particle and transient non-ambipolar current flows, as well as the toroidal angular momentum flow. The paper attempts to delineate the RMP transport mechanisms that might be responsible for the RMP density pump-out seen in DIII-D [M. A. Mahdavi and J. L. Luxon, Fusion Sci. Technol. 48, 2 (2005)]. Experimentally, the starting high toroidal rotation does not brake to a significantly lower rotation after the pump-out suggesting that convective and E×B transport mechanisms dominate. The direct J×B torque from the transient non-ambipolar radial current expected to accelerate plasma rotation is shown to cancel much of the Maxwell stress J×B torque expected to brake the plasma rotation. The dominant E×B Reynolds stress accelerates rotation at the top of the pedestal while braking rotation further down the pedestal.

Investigation of toroidal flow effects on L-H transition in tokamak plasma based on bifurcation model

The impacts of toroidal flow on the L-H transition phenomenon in tokamak plasmas based on bifurcation concept are investigated. A set of pressure and density transport equations with both neoclassical and anomalous effects included is considered. The anomalous transport suppression mechanism considered is only from a flow shear, which is calculated based on a force balance equation with both pressure gradient and toroidal velocity components included. The toroidal velocity can be calculated using four different models. The first model is an empirical model in which the velocity is dependent on a local ion temperature. The second model is based on neoclassical toroidal viscosity theory in which the velocity is driven by ion temperature gradient. In the third model, the velocity is dependent on current density flow in plasma. The fourth model is essentially the third model including effect of an intrinsically generated bootstrap current. It is found that inclusion of toroidal velocity can substantially increase the plasma pressure and density, mainly due to an increase of the pedestal width. It is also found that the pedestal for pressure tends to form first. After the pedestal forms, it expands inwards with the characteristic of super-diffusive nature in initial state and become subdiffusive nature in final state before reaching steady state. The expansion speed depends sensitively on the strength of flow shear effect. It is also found that the time required plasma to reach steady state after the L-H transition is much longer than that for L-H transition.

Are geomagnetic data consistent with stably stratified flow at the core–mantle boundary?

Recent first principles calculations of the Earth's outer core thermal and electrical conductivities have raised their values by a factor of three. This has significant implications for geodynamo operation, in particular, forcing the development of a stably stratified layer at the core–mantle boundary (CMB). This study seeks to test the hypothesis of a stably stratified layer in the uppermost core by analysing geomagnetic observations made by the CHAMP satellite. An inversion method is utilized that jointly solves for the time-dependent main field and the core surface flow, where we assume the temporal variability of the main field, its secular variation (SV), to be entirely due to advective motion within the liquid outer core. The results show that a large-scale pure toroidal flow, consistent with a stably stratified layer atop the outer core, is not compatible with the observed magnetic field during the CHAMP era. However, allowing just a small amount of poloidal flow leads to a model fitting the observations satisfactorily. As this poloidal flow component is large scale, within a predominantly toroidal, essentially tangentially geostrophic flow, it is compatible with a stably stratified upper outer core. Further, our assumption of little or no diffusive SV may not hold, and a small amount of SV generated locally by diffusion might lead to a large-scale pure toroidal flow providing an acceptable fit to the data.

Study of mass transport in autogenous GTA welding of dissimilar metals

The transport processes associated with mixing of two dissimilar alloys in a gas-tungsten arc weld pool are investigated numerically and experimentally. The numerical model includes the electromagnetic, velocity, temperature, and concentration fields. The model is solved fully coupled using the finite element software COMSOL Multiphysics®. The simulation shows that at early times surface tension drives a toroidal vortex flow around the circumference of the weld pool. At these times, the distribution of metals in the weld pool is not uniform since the fluid flow within the melt is not fully developed. At later times, the weld pool expands and deepens, and a secondary flow develops that circulates the flow along the bottom of the weld pool and then back along its edges where it is coupled with a toroidal vortex. This flow causes the melt to quickly become homogeneous. The numerical predictions of the concentration distribution were verified by comparison with experimental results obtained from electron dispersive spectroscopy (EDS). The predicted weld-pool geometry was also in reasonable agreement with the experimental result. In examining the surface tension effects, it was found that, except at early times, the temperature driven Marangoni forces dominate the surfactant driven effects (sulfur). However, the surfactant still has an important role because it modifies the temperature sensitivity of the surface tension.

ECOM: A fast and accurate solver for toroidal axisymmetric MHD equilibria

We present ECOM (Equilibrium solver via COnformal Mapping), a fast and accurate fixed boundary solver for toroidally axisymmetric magnetohydrodynamic equilibria with or without a toroidal flow. ECOM combines conformal mapping and Fourier and integral equation methods on the unit disk to achieve exponential convergence for the poloidal flux function as well as its first and second partial derivatives. As a consequence of its high order accuracy, for dense grids and elongations comparable to or smaller than the elongation of ITER, ECOM computes key quantities such as the safety factor and the magnetic shear with higher accuracy than the finite element based code CHEASE (Lütjens et al., 1996) at equal run time. ECOM has been developed to provide equilibrium quantities and details of the flux contour geometry as inputs to stability, wave propagation and transport codes.

Spontaneous toroidal flow generation due to negative effective momentum diffusivity

Spontaneous structure formation, and in particular, zonal flows, is observed in a broad range of natural and engineered systems, often arising dynamically as the saturated state of a linear instability. Flows in tokamaks are known to self-organise on small scales, but large scale toroidal flows also arise even when externally applied torques are zero. This has previously been interpreted as the result of small externally imposed breaking of a symmetry. However, we show that for large enough field line pitch, a robust spontaneous symmetry breaking occurs, leading to the generation of strong toroidal flow structures; parameters are typical of Spherical Tokamak discharges with reversed shear profiles. The short wavelength dynamics are qualitatively similar to the growth of poloidal flow structures, and toroidal flow gradients nonlinearly saturate at levels where the shearing rate is comparable to linear growth rate. On long wavelengths, we measure Prandtl numbers of around zero for these systems, in conjunction with the formation of structured toroidal flows, and we show that this is consistent with a model of momentum transport where fluxes act to reinforce small flow gradients: the effective momentum diffusivity is negative. Toroidal flow structures are largely unaffected by collisional damping, so this may allow toroidal bulk flows of order the ion thermal velocity to be maintained with zero momentum input. This phenomenon also provides a mechanism for the generation of localised meso-scale structures like transport barriers.