Poloidal Flow Research Articles

3-D effects on viscosity and generation of toroidal and poloidal flows in LHD

Three-dimensional effects on plasma flows have been experimentally studied in the large helical device with 3D configurations. Spontaneous toroidal flow without net driving force using the combination of perpendicular neutral beam injection (NBI) heating and balanced tangential NBI heating has been investigated with two magnetic configurations. Co- and counter-directed spontaneous flows have been observed depending on the collisionality. Toroidal flow shear changes the sign at 0.4<reff<0.6 between co- and counter-flowing plasmas, where reff is a averaged minor radius. The detailed flow structures have been also examined at the edge region with stochastic magnetic field. A poloidal flow driven by the positive radial electric field has been observed at the open field region just outside of the plasma boundary. At the stochastic region, a shear of poloidal flow has been observed, while no shear of toroidal flow has been observed. The toroidal flow shear changes only in the nested magnetic flux surface region. A difference of density fluctuation property has been observed between co- and counter-flowing plasmas, where toroidal flow shears are formed.

Parallel transport studies of high-Z impurities in the core of Alcator C-Mod plasmas

Measurements of poloidal variation, ñz/⟨nz⟩, in high-Z impurity density have been made using photodiode arrays sensitive to vacuum ultraviolet and soft x-ray emission in Alcator C-Mod plasmas. In/out asymmetries in the range of −0.2<nz,cos/⟨nz⟩<0.3 are observed for r/a<0.8, and accumulation on both the high-field side, nz,cos<0, and low-field side, nz,cos>0, of a flux surface is found to be well described by a combination of centrifugal, poloidal electric field, and ion-impurity friction effects. Up/down asymmetries, −0.05<nz,sin/⟨nz⟩<0.10, are observed over 0.5<r/a<0.9 with nz,sin>0 corresponding to accumulation opposite the ion ∇B drift direction. Measurements of the up/down asymmetry of molybdenum are found to disagree with predictions from recent neoclassical theory in the trace limit, nzZ2/ni≪1. Non-trace levels of impurities are expected to modify the main-ion poloidal flow and thus change friction-driven impurity density asymmetries and impurity poloidal rotation, vθ,z. Artificially modifying main-ion flow in parallel transport simulations is shown to impact both ñz/⟨nz⟩ and vθ,z, but simultaneous agreement between measured and predicted up/down and in/out asymmetry as well as impurity poloidal rotation is not possible for these C-Mod data. This link between poloidal flow and poloidal impurity density variation outlines a more stringent test for parallel neoclassical transport theory than has previously been performed. Measurement and computational techniques specific to the study of poloidal impurity asymmetry physics are discussed as well.

Poloidal flow damping inside transport barriers in a tokamak

The poloidal flow in a tokamak is damped by collisions. Thus, the poloidal damping can be described by the neoclassical theory. The effective poloidal Mach number, Mp, can be of the order of one or higher inside transport barriers in a tokamak. It is found that the poloidal damping rate decreases exponentially as the effective poloidal Mach number increases. The poloidal damping rate is reduced by one order of magnitude in the presence of sonic Mp. We also found that the ion plasma viscosity becomes negligible compared with the electron plasma viscosity when Mp>1.5. In this case, the poloidal flow is damped by electron collisions rather than ion collisions.

Kinetic effects on a tokamak pedestal ion flow, ion heat transport and bootstrap current

We consider the effects of a finite radial electric field on ion orbits in a subsonic pedestal. Using a procedure that makes a clear distinction between a transit average and a flux surface average we are able to solve the kinetic equation to retain the modifications due to finite drift orbit departures from flux surfaces. Our approach properly determines the velocity space localized, as well as the nonlocal, portion of the ion distribution function in the banana and plateau regimes in the small aspect ratio limit. The rapid variation of the poloidal ion flow coefficient and the electrostatic potential in the total energy modify previous banana regime evaluations of the ion flow, the bootstrap current, and the radial ion heat flux in a subsonic pedestal. In the plateau regime, the rapid variation of the poloidal flow coefficient alters earlier results for the ion flow and bootstrap current, while leaving the ion heat flux unchanged since the rapid poloidal variation of the total energy was properly retained.

The excitation of geodesic acoustic mode flows by a resonant magnetic field and by resonant heating

Toroidal magnetohydrodynamic (MHD) simulations demonstrate that sheared poloidal flows in tokamaks can be generated by the resonant excitation of the geodesic acoustic mode (GAM). Poloidal flows are generated by two resonant excitation methods: oscillating currents in an external coil and an oscillating heat source. The coil current and the heat source oscillate in time at the local GAM frequency. The sheared poloidal flow generated by the excitation of the GAM may be useful for the suppression of plasma instabilities.

Generation of plate tectonics with two-phase grain-damage and pinning: Source–sink model and toroidal flow

The grain-damage and pinning mechanism of Bercovici and Ricard (2012) for lithospheric shear-localization is employed in two-dimensional flow calculations to test its ability to generate toroidal (strike-slip) motion and influence plate evolution. This mechanism posits that damage to the interface between phases in a polycrystalline material like peridotite (composed primarily of olivine and pyroxene) increases the number of small Zener pinning surfaces, which then constrain mineral grains to ever smaller sizes, regardless of creep mechanism. This effect allows a self-softening feedback in which damage and grain-reduction can co-exist with a grain-size dependent diffusion creep rheology; moreover, grain growth and weak-zone healing are greatly impeded by Zener pinning thereby leading to long-lived relic weak zones. The fluid dynamical calculations employ source–sink driven flow as a proxy for convective poloidal flow (upwelling/downwelling and divergent/convergent motion), and the coupling of this flow with non-linear rheological mechanisms excites toroidal or strike-slip motion. The numerical experiments show that pure dislocation-creep rheology, and grain-damage without Zener pinning (as occurs in a single-phase assemblages) permit only weak localization and toroidal flow; however, the full grain-damage with pinning readily allows focussed localization and intense, plate-like toroidal motion and strike-slip deformation. Rapid plate motion changes are also tested with abrupt rotations of the source–sink field after a plate-like configuration is developed; the post-rotation flow and material property fields retain memory of the original configuration for extensive periods, leading to suboptimally aligned plate boundaries (e.g., strike-slip margins non-parallel to plate motion), oblique subduction, and highly localized, weak and long lived acute plate-boundary junctions such as at what is observed at the Aleutian–Kurile intersection. The grain-damage and pinning theory therefore readily satisfies key plate-tectonic metrics of localized toroidal motion and plate-boundary inheritance, and thus provides a predictive theory for the generation of plate tectonics on Earth and other planets.

Global migration of 13C impurities in high-density L-mode plasmas in ASDEX Upgrade

We have studied the migration of 13C in ASDEX Upgrade after a global impurity injection experiment in 2011. The main chamber was observed to be the largest deposition region for carbon: almost 35% of the injected atoms end up there. Moreover, gaps between wall tiles account for surface densities which are comparable to those on the plasma-facing surfaces. SOLPS modeling of the experiment produced a set of background plasmas and poloidal flow profiles for simulating the transport of 13C with ASCOT; a match with measured deposition, however, required using an imposed flow profile. ASCOT reproduced the observed localized deposition at the outer midplane but work is needed to explain the measured deposition at the inner side of the torus and at the top of the vessel.

Transport and drift-driven plasma flow components in the Alcator C-Mod boundary plasma

Boundary layer flows in the Alcator C-Mod tokamak are systematically examined as magnetic topology (upper versus lower-null) and plasma density are changed. Utilizing a unique set of scanning Langmuir–Mach probes, including one on the high-field side (HFS) midplane, the poloidal variation of plasma flow components in the parallel, diamagnetic and radial directions are resolved in detail. It is found that the plasma flow pattern can be decomposed into two principal parts: (1) a drift-driven component, which lies within a magnetic flux surface and is divergence-free and (2) a transport-driven component, which gives rise to near-sonic parallel flows on the HFS scrape-off layer (SOL). Toroidal rotation, Pfirsch–Schlüter and transport-driven contributions are unambiguously identified. Transport-driven parallel flows are found to dominate the HFS particle fluxes; the total poloidal-directed flow accounts for ∼1/3 to all of the ion flux arriving on the inner divertor. As a result, heat convection is found to be an important player in this region, consistent with the observation of divertor asymmetries that depend on the direction of B × ∇B relative to the active x-point. In contrast, the poloidal projection of parallel flow in the low-field SOL largely cancels with Er × B flow; toroidal rotation is the dominant plasma motion there. The magnitude of the transport-driven poloidal flow is found to be quantitatively consistent with fluctuation-induced radial particle fluxes on the low-field side (LFS), identifying this as the primary drive mechanism. Fluctuation-induced fluxes on the HFS are found to be essentially zero, excluding turbulent inward transport as the mechanism that closes the circulation loop in this region.

Observation of Direct Ion Heating in Double-Pulsing CHI in Helicity Injected Spherical Torus Plasmas

Anomalous ion heating has been observed for the first time during flux/current amplification by doublepulsing coaxial helicity injection (CHI) in the helicity injected spherical torus (HIST) device. Doppler ion temperature increases significantly near the separatrix on the inboard side during the second CHI pulse, whereas electron temperature remains constant. The experimental results indicate that selective ion heating may be associated with viscous damping of poloidal flows driven by the CHI pulse.

Analytic expression for poloidal flow velocity in the banana regime

The poloidal flow velocity in the banana regime is calculated by improving the l = 1 approximation for the Fokker-Planck collision operator [M. Taguchi, Plasma Phys. Controlled Fusion 30, 1897 (1988)]. The obtained analytic expression for this flow, which can be used for general axisymmetric toroidal plasmas, agrees quite well with the recently calculated numerical results by Parker and Catto [Plasma Phys. Controlled Fusion 54, 085011 (2012)] in the full range of aspect ratio.

Nonlinear stability of magnetic islands in a rotating helical plasma

Coexistence of the forced magnetic reconnection by a resonant magnetic perturbation (RMP) and the curvature-driven tearing mode is investigated in a helical (stellarator) plasma rotated by helical trapped particle-induced neoclassical flows. A set of Rutherford-type equations of rotating magnetic islands and a poloidal flow evolution equation is revisited. Using the model, analytical expressions of criteria of spontaneous shrinkage (self-healing) of magnetic islands and sudden growth of locked magnetic islands (penetration of RMP) are obtained, where nonlinear saturation states of islands show bifurcation structures and hysteresis characteristics. Considering radial profile of poloidal flows across magnetic islands, it is found that the self-healing is driven by neoclassical viscosity even in the absence of micro-turbulence-induced anomalous viscosity. Effects of unfavorable curvature in stellarators are found to modify the critical values. The scalings of criteria are consistent with low-β experiments in the large helical device.

Leidenfrost levitated liquid tori

Levitating a liquid over a vapor film was limited to droplets. Here we show that on curved substrates a larger quantity of fluid can be suspended. This opens a new possibility for exploring free-liquid-surface phenomena without any contact with a solid. In one of the simplest possible situations, a large fluid torus is levitated over a circular trough. A poloidal flow inside the ring generates a wave on its inner side, making it polygonal. This wave is described by a solitonic model which balances surface tension and the pressure depletion due to the distortion of the poloidal flow.

Local and global Fokker–Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal

In transport barriers, particularly H-mode edge pedestals, radial scale lengths can become comparable to the ion orbit width, causing neoclassical physics to become radially nonlocal. In this work, the resulting changes to neoclassical flow and current are examined both analytically and numerically. Steep density gradients are considered, with scale lengths comparable to the poloidal ion gyroradius, together with strong radial electric fields sufficient to electrostatically confine the ions. Attention is restricted to relatively weak ion temperature gradients (but permitting arbitrary electron temperature gradients), since in this limit a δf (small departures from a Maxwellian distribution) rather than full-f approach is justified. This assumption is in fact consistent with measured inter-ELM H-Mode edge pedestal density and ion temperature profiles in many present experiments, and is expected to be increasingly valid in future lower collisionality experiments. In the numerical analysis, the distribution function and Rosenbluth potentials are solved for simultaneously, allowing use of the exact field term in the linearized Fokker–Planck–Landau collision operator. In the pedestal, the parallel and poloidal flows are found to deviate strongly from the best available conventional neoclassical prediction, with large poloidal variation of a different form than in the local theory. These predicted effects may be observable experimentally. In the local limit, the Sauter bootstrap current formulae appear accurate at low collisionality, but they can overestimate the bootstrap current in the plateau regime. In the pedestal ordering, ion contributions to the bootstrap and Pfirsch–Schlüter currents are also modified.

Magnetohydrodynamic simulations of edge poloidal flows

Edge poloidal flows exceeding the poloidal sound speed lead to the formation of a pedestal structure (Guazzotto and Betti 2011 Phys. Rev. Lett. 107 125002). This result is based on the existence of ‘transonic’ equilibria, in which the edge region of the plasma flows supersonically with respect to the poloidal sound speed (i.e. the sound speed reduced by a factor Bθ/B), while the plasma core is rotating with subsonic poloidal velocities. The ideal-MHD equilibrium force balance shows that radial discontinuities must be present at equilibrium in the presence of transonic flows. The formation of the transonic discontinuity was proven with time-dependent simulations. In this work, we prove that the transonic discontinuity can be formed with poloidal velocities no larger than a few tens of km s−1. Such relatively slow velocities are supersonic at the bottom of the pedestal where the temperature is a few tens of eVs. We also show how realistic toroidal velocity profiles can be obtained in transonic equilibria if the appropriate choice is made for the input free functions.

An electromagnetic theory of turbulence driven poloidal rotation

An electromagnetic theory of turbulence driven poloidal rotation is developed with particular emphasis on understanding poloidal rotation in finite-β plasmas. A relation linking the flux of polarization charge to the divergence of the total turbulent stress is derived for electromagnetic gyrokinetic modes. This relation is subsequently utilized to derive a constraint on the net electromagnetic turbulent stress exerted on the poloidal flow. Various limiting cases of this constraint are considered, where it is found that electromagnetic contributions to the turbulent stress may either enhance or reduce the net turbulent stress depending upon the branch of turbulence excited.

Plasma flows in scrape-off layer of Aditya tokamak

The magnetized Mach probe is used to make measurement of plasma flows in the scrape-off layer of the Aditya tokamak [R. Jha et al., Plasma Phys. Controlled Fusion 51, 095010 (2009)]. This probe is further used to measure dependencies of Mach number on local plasma densities and radial distances of the probe in the scrape-off layer. The measured Mach number has contributions from E×B drift, Pfrisch-Schlüter, and transport driven flows. We have determined that the toroidal flow is towards the ion side of the limiter and the poloidal flow direction is towards the contact of the last closed flux surface with the limiter.

Spatio-temporal evolution of the L → I → H transition

We investigate the dynamics of the low(L) → high(H) transition using a time-dependent, one dimensional (in radius) model which self-consistently describes the time evolution of zonal flows (ZFs), mean flows (MFs), poloidal spin-up, and density and pressure profiles. The model represents the physics of ZF and MF competition, turbulence suppression via E×B shearing, and poloidal flows driven by turbulence. Numerical solutions of this model show that the L→H transition can occur via an intermediate phase (I-phase) which involves oscillations of profiles due to ZF and MF competition. The I-phase appears as a nonlinear transition wave originating at the edge boundary and propagates inward. Locally, I-phase exhibits the characteristics of a limit-cycle oscillation. All these observations are consistent with recent experimental results. We examine the trigger of the L→H transition, by defining a ratio of the rate of energy transfer from the turbulence to the zonal flow to the rate of energy input into the turbulence. When the ratio exceeds order unity, ZF shear gains energy, and a net decay of the turbulence is possible, thus triggering the L→H transition. Numerical calculations indicate that the L→H transition is triggered by this peak of the normalized ZF shearing. Zonal flows act as “reservoir,” in which to store increasing fluctuation energy without increasing transport, thus allowing the mean flow shear to increase and lock in the transition. A counterpart of the L → I→H transition, i.e., an L→H transition without I-phase, is obtained in a fast power ramp, for which I-phase is compressed into a single burst of ZF, which triggers the transition. Effects of neutral charge exchange on the L→H transition are studied by varying ZF damping and neoclassical viscosity. Results show that the predicted L→H transition power increases when either ZF damping or viscosity increase, suggesting a link between recycling, ZF damping, and the L→H threshold. Studies of fueling effects on the transition and pedestal structure with an emphasis on the particle pinch are reported.

Saturation of a toroidal Alfvén eigenmode due to enhanced damping of nonlinear sidebands

This paper examines nonlinear magneto-hydrodynamic effects on the energetic particle driven toroidal Alfvén eigenmode (TAE) for lower dissipation coefficients and with higher numerical resolution than in the previous simulations (Todo et al 2010 Nucl. Fusion 50 084016). The investigation is focused on a TAE mode with toroidal mode number n = 4. It is demonstrated that the mechanism of mode saturation involves generation of zonal (n = 0) and higher-n (n ⩾ 8) sidebands, and that the sidebands effectively increase the mode damping rate via continuum damping. The n = 0 sideband includes the zonal flow peaks at the TAE gap locations. It is also found that the n = 0 poloidal flow represents a balance between the nonlinear driving force from the n = 4 components and the equilibrium plasma response to the n = 0 fluctuations. The spatial profile of the n = 8 sideband peaks at the n = 8 Alfvén continuum, indicating enhanced dissipation due to continuum damping.

Plasma Equilibrium in Presence of the Poloidal Flow in Tokamaks

Main purposes of this contribution are analysis of dynamic equilibrium properties of a large aspect ratio and low beta tokamaks, in particular deriving a modified relation for the Shafranov shift in the presence of poloidal flow, and demonstrate it experimentally. Poloidal flow can produce modifications in the equilibrium properties. By increasing Alfvenic Mach number from zero, flow produce outward force, and plasma shifted in outward direction. If the poloidal Alfvenic Mach number equal to one, singularity will observe in the solution of generalized Grad-Shafranov equation. Also inversion of Shafranov shift in the transition of flow speed between sub-Alfvenic to super-Alfvenic speeds can be observed due to inward force produced by flow.

Model experiment for studying lane formation in binary complex plasmas

We present the first experimental realisation on lane formation in binary complex plasmas under gravity conditions. The amount of penetrating particles can be controlled. The experiment can be operated with stable conditions continuously, which allows to study steady state. The driving force is independent of time and position and the background density is homogeneous and isotropic. This provides an ideal model system for comparison with numerical experiments and observations in colloidal suspensions. The experiment setup is based on PK-3 Plus laboratory operated on the International Space Station. Gravitation is compensated by thermophoretic force and penetrating particles are controlled via a toroidal vortex with poloidal flow. The evolution of lane formation along the penetration direction is illustrated by lane order parameter.