Toroidal Flow Research Articles

Nonlinear evolution of weakly coupled double tearing modes with equilibrium sheared toroidal flow

Abstract The nonlinear evolution of weakly coupled DTMs with and without sheared toroidal flow is systematically investigated with the three-dimensional, toroidal-geometry, and nonlinear MHD code CLT. Due to the explosive growth of the weakly coupled DTMs, the pressure crashes are much more severe than those caused by the strongly coupled DTMs. The weakly coupled DTMs can easily be decoupled by sheared toroidal flow, and then the mutually driven term between the two tearing modes becomes periodically positive and negative, leading to periodic growth. The interaction slows the rotation between the two tearing modes when the phase difference is close to 180 degrees. When the islands are sufficiently large, the interaction can overcome the decoupling effect of the shear flow, and the two tearing modes then lock with each other. Due to the different coupling effects of the two tearing modes, the threshold island width or perturbed magnetic field for mode-locking increases with increasing separation. The coupling effect between the two tearing modes is also related to the resistivity. If the resistivity is high, the coupling effect between the two tearing modes can be huge. A stronger shear flow is needed to decouple them, and even a small island can lead to mode-locking in high-resistivity plasma.

MHD stability analysis against pressure and current-driven modes in the SMall Aspect Ratio Tokamak

Abstract Linear magnetohydrodynamic (MHD) simulations for the SMall Aspect Ratio Tokamak (SMART) have been carried out for the first time, for both positive (PT) and negative triangularity (NT) shaped plasmas using the MARS-F code. The MHD stability of projected SMART plasmas against internal kinks, infernal modes and edge peeling-ballooning modes have been analyzed for a wide range of realistic equilibria. A stabilization of internal kinks and infernal modes is observed when increasing the safety factor profile and reducing plasma beta. PT shaped plasmas are more stable against both internal kinks and infernal modes than their counterpart NT shaped plasmas. Toroidal flows have little impact on the MHD stability of the internal kinks, but they have a strong stabilizing effect on infernal modes, which can be further mitigated in NT shaped plasmas. The MHD stability of peeling-ballooning modes is reduced in NT shaped plasmas, as observed in conventional tokamaks.

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Toroidal mean flow and complex temperature distribution in a thermoacoustic core

Increasing the capacity of thermoacoustic machines (engines or refrigerators) requires increasing the diameter of the regenerator, which may result in non-uniform temperature distributions inside the regenerator. In the current study, the temperature is measured at different radial and axial locations inside the regenerator of a thermoacoustic refrigerator with a diameter of 148 mm. The working gas is a mixture of helium and Argon at a static pressure of 40 bar. Non-uniform radial temperature distributions are observed at different axial positions. Also, the predicted axial temperature distributions by a 1-D linear model (DeltaEC) do not agree with the measured temperature distributions. We suspect that the non-uniform radial temperature distribution generates a steady flow through the regenerator which increases the radial temperature non-uniformity and results in non-linear axial temperature distribution. Given the measured temperature distribution, the presence of a toroidal steady flow inside the regenerator is suspected. To confirm this hypothesis, the regenerator is divided into three segments connected in parallel in the DeltaEC model. Mean flows are added in each segment of the regenerator to simulate the presence of toroidal flow in the regenerator. The predicted temperature distributions from this modified DeltaEC model agree with the measured temperature distributions.

J-TEXT achievements in turbulence and transport in support of future device/reactor

Following the reconstruction of the TEXT tokamak at Huazhong University of Science and Technology in China, renamed as J-TEXT, a plethora of experimental and theoretical investigations has been conducted to elucidate the intricacies of turbulent transport within the tokamak configuration. These endeavors encompass not only the J-TEXT device’s experimental advancements but also delve into critical issues pertinent to the optimization of future fusion devices and reactors. The research includes topics on the suppression of turbulence, flow drive and damping, density limit, non-local transport, intrinsic toroidal flow, turbulence and flow with magnetic islands, turbulent transport in the stochastic layer, and turbulence and zonal flow with energetic particles or helium ash. Several important achievements have been made in the last few years, which will be further elaborated upon in this comprehensive review.

Validation study of RWM stability in DIII-D high-βN plasmas

Abstract The n = 1 (n is the toroidal mode number) resistive wall mode (RWM) stability is numerically investigated for two DIII-D high-β N discharges 176440 and 172461, utilizing the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) and MARS-K (Liu et al 2008 Phys. Plasmas 15 112503) codes. Systematic validation efforts are attempted, for the first time, for discharges with very slow or vanishing toroidal flow for a large fraction of the plasma volume. While gaining physics insights in accessing stable operation regime at β N exceeding the Troyon no-wall limit in these slow-rotation experiments, the predictive capability of fluid and non-perturbative magnetohydrodynamic-kinetic hybrid models for the RWM is further confirmed. The MARS-F fluid model, with a strong but numerically tunable viscosity mimicking ion Landau damping of parallel sound waves, finds complete stabilization of the n = 1 RWM in the considered DIII-D plasmas under the experimental flow conditions. Similarly, either full stabilization (for discharge 176440) or marginal stability (for discharge 172461) of the mode is computed by the MARS-K hybrid model, which is first-principle based without free model parameters. In particular, all drift kinetic resonances, including those of thermal and energetic particles, are found to synergistically act to marginally stabilize the RWM in discharge 172461. These MARS-F/K modeling results explain the experimentally observed stable operational regime in DIII-D, as far as the RWM stability is concerned. Extensive numerical sensitivity studies, with respect to the plasma toroidal flow speed as well as the radial location of the resistive wall, are also carried out to further support the validation study.

Off-target gradient-driven flows in 3D simulations of ADITYA-Upgrade tokamak scrape-off layer plasma transport

Coupled plasma-neutral transport simulations are performed on ADITYA-Upgrade tokamak scrape-off layer (SOL) plasma, where flows in the core and SOL were measured to reverse signs with density variation. The simulations performed using the EMC3-Eirene plasma-neutral code combination incorporate the toroidally continuous high-field-side belt limiter placed in a moderate circular tokamak equilibrium. The development of mutually counter-propagating toroidal plasma flows in the top and bottom regions of both the SOL and core is recovered for relatively high upstream density cases with high input power (300 kW and 3 m2 s−1). The origin of the flows is traced to the poloidal density variation introduced by high recycling on the inboard localized belt limiter. The results are compared with similar observations, for example, in Doppler-shifted passive charge exchange line emission on the ADITYA-Upgrade (ADITYA-U) tokamak, highlighting the role played by residual stress in the total Reynolds stress. The external stimuli, such as a localized gas puff, are discussed as potential drivers of flow, via residual stress, based on the existing resonant model of the tokamak plasma rotation.

Resistive wall mode and fishbone mode in ITER steady state scenario: roles of fusion-born alphas and plasma flow

Drift-kinetic effects of fusion-born alpha particles on the n= 1 (n is the toroidal mode number) resistive wall mode (RWM) is numerically investigated for a recent design of the ITER 10 MA steady state plasma scenario, utilizing a magneto-hydrodynamic (MHD)-kinetic hybrid toroidal model. While the fluid theory predicts unstable RWM as the normalized plasma pressure β N exceeds the no-wall Troyon limit and with the mode growth rate monotonically increasing with β N, inclusion of the drift-kinetic contribution of trapped alphas qualitatively modifies the behavior by stabilizing the mode at high β N. In fact, a complete stabilization of the n= 1 RWM up to the ideal-wall Troyon limit is found. On the other hand, another unstable branch—the alpha-driven n = 1 fishbone mode (FB)—is identified in the high-β N regime, with the mode frequency matching that of the toroidal precession frequency of trapped alphas. Fast plasma toroidal flow however helps mitigate the FB instability. Kinetic stabilization of the RWM and flow stabilization of the (alpha-triggered) FB result in an enhancement of β N from the design value of 3.22–3.52 for the ITER scenario considered, while still maintaining stable plasma operation against the aforementioned MHD instabilities.

FLIPEC, an ideal MHD free-boundary axisymmetric equilibrium solver in the presence of macroscopic flows

The most relevant features of FLIPEC (Free fLow Iterative Plasma Equilibrium Code) are presented. This new code iteratively calculates free-boundary, axisymmetric ideal MHD equilibria with arbitrary poloidal and toroidal plasma flows. FLIPEC is a mature code that has emerged from a complete overhaul of a previous version (F-Torija Daza 2022 et al Nucl. Fusion 62 126044). It uses a (inverse) curvilinear coordinate representation for the Grad–Shafranov–Bernoulli equation system, which allows FLIPEC to extend its free-boundary capabilities to arbitrary plasma shapes and removes many limitations with regards to the distance between plasma and external coils. Run-time stabilization of vertical modes has also been implemented by means of artificial feedback coils. Finally, active targeting schemes have also been included. These capabilities are illustrated on two very different cases: the ITER tokamak baseline configuration and a NSTX spherical tokamak equilibrium.

Modal stability analysis of toroidal pipe flow approaching zero curvature

The present study investigates the modal stability of the steady incompressible flow inside a toroidal pipe for values of the curvature $\delta$ (ratio between pipe and torus radii) approaching zero, i.e. the limit of a straight pipe. The global neutral stability curve for $10^{-7} \leq \delta \leq ~10^{-2}$ is traced using a continuation algorithm. Two different families of unstable eigenmodes are identified. For curvatures below $1.5 \times 10^{-6}$ , the critical Reynolds number ${{Re}}_{cr}$ is proportional to $\delta ^{-1/2}$ . Hence, the critical Dean number is constant, ${{De}}_{cr} = 2\,{{Re}}_{cr}\,\sqrt {\delta } \approx 113$ . This behaviour confirms that the Hagen–Poiseuille flow is stable to infinitesimal perturbations for any Reynolds number and suggests that a continuous transition from the curved to the straight pipe takes place as far as it regards the stability properties. For low values of the curvature, an approximate self-similar solution for the steady base flow can be obtained at a fixed Dean number. Exploiting the proposed semi-analytic scaling in the stability analysis provides satisfactory results.

Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas

We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad–Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.

Suppression of radial motion in translated field-reversed configuration plasma via global gyro-effect

Abstract The radial motion of a field-reversed configuration (FRC) during translation at supersonic/Alfvénic speed was effectively suppressed by the global gyro-effect induced by toroidal flow. In magnetohydrodynamic approximation, an FRC is inherently unstable against radial motions such as tilt and wobble. Surprisingly, the magnetic structure of the FRC remained intact even during translation at speeds exceeding the ion sonic and Alfvén speeds, despite the presence of radial motions. Optical observations were conducted on the radial motion and toroidal flow of translated FRCs under various electric boundary conditions at the device end. The implementation of end-shorting led to an increased toroidal flow rate, consequently reducing the radial displacement of the FRC during translation. This control of toroidal flow from the device’s end not only suppressed radial motion but also facilitated head-on collisions in the formation of FRCs by the collisional merging technique. The findings emphasize the significance of toroidal flow control in preserving the integrity of FRC’s simply connected geometry and enhancing its formation performance.

Large-volume and swift magmatic response to Late Cenozoic segmentation of the subducted Neotethyan oceanic slab: evidence from the Galatian Volcanic Province, northwestern Turkey

ABSTRACT The Miocene Galatian Volcanic Province (GVP) is one of the largest volcanic provinces in central-western Anatolia, with an extent of ~ 8,900 km2. The volcanic activity is extended from 22.5 to 7.5 Ma. The volcanic compositions straddle the alkaline-subalkaline fields, from basic to acid compositions and mostly transitional to sodic affinity. Major oxides show good correlation with SiO2 indicating prolonged effects of fractional crystallization. Primitive mantle-normalized multi-element patterns indicate overall similarities among the different samples of the three geographic sectors, sharing strong negative anomalies in Nb–Ta–Ti, strong positive peaks at Cs and K, coupled with a common, albeit not always present, positive anomaly at Pb. Mineral-melt geothermobarometric estimates indicates ~1070–1235°C and ~7–19 kbar for melting conditions of basaltic compositions and ~1000–1150°C and ~3–12 kbar for andesitic-dacitic rocks. The absence of correlation between radiogenic isotopes and SiO2 and MgO is here interpreted as consequence of assimilation-fractional-crystalization processes involving lower continental crust as contaminant. The GVP parental magmas are generated from ~2% to 10% partial melting of a lherzolitic mantle with high spinel/garnet ratio based on intra-REE fractionation constraints. The subduction-related metasomatism inferred for the GVP mantle sources based on their chemistry is interpreted to be linked to the northward subduction of the northern branch of the Neo-Tethys slab. Successive slab retreat resulted in extension for the critical stress distribution through the Cyprus slab, favouring magma propagation for the GVP volcanic region. The eventual break-off of the slab after the continent-continent collision of Arabian and Eurasian plates could have caused a toroidal mantle flow, favouring the widely distributed 15–16 Ma alkaline magmatism in the eastern GVP, associated with passive hot asthenospheric upwelling imaged by teleseismic P-wave tomography.

Effects of resonant magnetic perturbations on turbulence and flows in the edge of HL-2A plasmas

The influence of resonant magnetic perturbations (RMPs) on the dynamics of turbulence and flows at the edge of the HL-2A tokamak is analyzed utilizing transfer entropy technique. The results have shown that the RMP damps the poloidal flows as well as the E × B shearing rate, whereas enhances the toroidal flows and leads to a broadened particle spectrum with increased small scale turbulence transport. The causality analysis indicates that the regulation impact of poloidal flow on turbulent fluctuations and particle flux is weakened, while that of the toroidal rotation on the latter is strengthened by the RMP field. The impact of the changes in poloidal flow dominates over that of the modified toroidal flow on turbulent transport in the edge. The magnetic perturbation and the flows generally show predator–prey oscillations, where the causal effect between the former and the toroidal flow transits to a synchronization relation in the presence of RMP. In addition, the RMP field will weaken the causal effect on poloidal Reynolds stress while strengthening the parallel-radial component simultaneously. The present findings provide a possible explanation on the effects of external fields on the edge transport, which is suggested to be dominated by the complex interactions among external perturbations, flows, and ambient microturbulence.

Local-S shear wave splitting along the length of the Alaska–Aleutian subduction zone

SUMMARY The Alaska–Aleutian subduction zone represents an ideal location to study dynamics within a mantle wedge. The subduction system spans several thousand kilometres, is characterized by a slab edge, and has ample seismicity. Additionally, the majority of islands along the arc house broad-band seismic instruments. We examine shear wave splitting of local-S phases originating along the length of the subduction zone. We have dense measurement spacing in two regions, the central Aleutians and beneath Alaska. Beneath Alaska, we observe a rotation in fast splitting directions near the edge of the subducting slab. Fast directions change from roughly trench perpendicular away from the slab edge to trench parallel near the boundary. This is indicative of toroidal flow around the edge of the subducting Alaska slab. In the central Aleutians, local-S splitting is primarily oriented parallel to, or oblique to, the strike of the trench. The local-S measurements, however, exhibit a depth dependence where deeper events show more consistently trench-parallel directions indicating prevalent trench-parallel mantle flow. Our local-S shear wave splitting results suggest trench-parallel orientation are likely present along much of the subduction zone excited by the slab edge, but that additional complexities exist along strike.

Deciphering the crustal anisotropy and mantle flow beneath the Indo-Burma ranges from the harmonic decomposition of the receiver functions

The hyper-oblique indentation of the Indian plate beneath the Burmese sliver gives rise to the Indo-Burma Ranges (IBR) in the eastern part of the Indian subcontinent. This geological formation encompasses one of the enigmatic hotspots and includes the densely populated regions of India and Myanmar. Harmonic Decomposition (HD) of the receiver functions, derived from the Multi-Taper Correlation (MTC) technique, is used to model seismic anisotropy and morphological crustal deformation caused by subduction underneath IBR. We used teleseismic earthquake data from eleven broadband seismic stations installed within the IBR and its foredeep region. The findings indicate that the attitude of the fast symmetry axis or dipping direction of the interface is influenced by the trend of regional geological features and absolute plate motion, with the IBR exhibiting NNE-SSW and N-S directions and the Himalayan region showing NE-SW and E-W directions. Our results reveal that the coupling of the Indian plate with the Burmese and Eurasian plates induces lithospheric fabrics that align perpendicular to the coupling direction, resulting in anisotropy in the brittle upper crust. Directional analysis of the HD model for the interfaces at the middle or lower crust reveals the strike of the fast symmetry axis in the NNE-SSW direction, which suggests the alignment of minerals and partial melt in the direction of the major shear stress. The interface across the Moho reflects four-lobed periodicity, that is, 90o ambiguity in the strike direction of the fast symmetry axis, varying from the E-W to the N-S directions. The ambiguity indicates the possibility of the 2D-induced entrained mantle flow along the subducting Indian plate and the 3D toroidal flow parallel to the trend of the IBR.

A new quasilinear model for turbulent momentum transport in tokamaks with flow shear and plasma shaping

In tokamak experiments, sufficiently strong E × B flow shear reduces turbulent transport, thereby improving the prospects for fusion power plants. It is therefore of great importance to efficiently explore parameter space to find where strong plasma flow can be achieved. To this end, we propose a new, physically motivated quasi-linear model for estimating momentum transport from turbulence in the presence of toroidal flow shear and plasma shaping. The method gives good estimates of momentum transport for up–down asymmetric geometries as well as low magnetic shear and tight aspect ratio. The results are benchmarked with high-fidelity nonlinear GENE simulations, demonstrating that it provides a fast and accurate estimate of momentum transport.

Perturbed Ion Temperature and Toroidal Flow Profile Measurements in Rotating Neoclassical Tearing Mode Magnetic Islands.

The perturbed ion temperature and toroidal flow were measured in rotating neoclassical tearing modes (NTM) in a tokamak for the first time. These toroidally and radially resolved profiles were obtained by impurity ion spectroscopy in a 2,1 NTM in DIII-D. In agreement with drift-kinetic simulations, the electron temperature profile is flat, while the ion temperature gradient is restored across the magnetic island O point in the presence of fast ions; the perturbed flow has minima in the O points and maxima at the X points. These measurements provide the first confirmation of the theoretically expected ion temperature and flow response to a magnetic island needed to predict the NTM onset threshold scaling for ITER and other future tokamaks.

Toroidal mantle flow beneath the NE termination of the Kuril–Kamchatka subduction zone from seismic anisotropy

SUMMARY This study presents the findings of a splitting analysis conducted on core-refracted teleseismic shear waves (SKS, SKKS and PKS, called together as XKS) and local shear waves, obtained from a dense seismological network spanning the Kamchatka Peninsula. The objective of the study is to examine the pattern of mantle flow beneath the study area through the investigation of seismic anisotropy. The peninsula is situated at the northeastern end of the Kuril–Kamchatka subduction zone, where the Kuril trench intersects with the western boundary of the Aleutian trench. The data set utilized in this study comprises waveform data from a dense network of seismic stations (99 broad-band and short-period stations for the local shear wave splitting analysis and 69 broad-band stations for the SKS splitting analysis). The seismograms were downloaded from publicly available data repositories including the IRIS Data Management Center and the GFZ Data Services (GEOFON program). The dense station coverage allows us to investigate the lateral variations in anisotropy, providing insights into the flow patterns within the mantle. The processing of the combined data sets of local shear wave and teleseismic XKS waves allowed us to partially decipher the source of anisotropy in the mantle. Small delay (splitting) times (∼0.35 s) observed from the local-S data suggest that anisotropy in the mantle wedge is relatively weak with lateral variations. Larger splitting times (∼1.1 s) observed for the XKS waves relative to local S suggest that the main part of splitting on the XKS waves occurs in the subslab mantle. On the other hand, the rotational pattern of seismic anisotropy observed by both the local S and XKS waves suggests the presence of a toroidal flow at the NE edge of the subducting slab, which affects both the mantle wedge and subslab mantle. For the regions away from the edge of the slab, the mantle flow seems to be governed mainly by the drag of the lithospheric plate over the underlying asthenosphere.

Mechanism analysis of secondary flow and mechanical energy loss in toroidal flow field

The imbalance between the radial pressure gradient and centrifugal force in curved pipe flow produces a secondary flow, resulting in a non-uniform distribution of streamwise velocity across the pipe cross section. These phenomena are believed to exhibit higher fluid resistance than straight pipes with similar flow rates, thereby motivating research into the mechanical energy losses in curved pipes. First, to ensure the accuracy and efficiency of the calculations, the results of various turbulence models were compared with direct numerical simulation to select the most appropriate turbulence model. Based on the momentum conservation equation, the mechanical influencing factors of secondary flow and streamwise velocity stratification in toroidal flow field were theoretically studied. Computational fluid dynamics method was employed to explore the spatiotemporal evolution characteristics of the mechanics and velocity distribution in transient flow fields to explain the formation mechanism of the secondary flow and the coupling relationship between the streamwise and radial directions. Then, the typical energy components of the toroidal flow field were analyzed using the energy equation, and the energy conservation and distribution characteristics were numerically studied. Furthermore, the influence of typical parameters (Reynolds number and curvature ratio) on the velocity distributions and mechanical properties as well as the percentage and distribution of various energy components were analyzed. Finally, the calculation results were statistically presented to quantify the variation of the energy components with typical parameters.