Radial Turbulent Transport Research Articles

An extensive analysis of SOL properties in high-δ plasmas in ASDEX Upgrade

A set of dedicated H-mode discharges with constant heating power combining Neutral Beam Injection and Electron Cyclotron Resonance Heating have been executed at the ASDEX Upgrade tokamak using a high triangularity magnetic geometry in order to investigate the impact of filamentary transport to divertor and non-divertor components. The evolution of upstream scrape-off layer (SOL) profiles have been correlated with dedicated separatrix quantities, mostly with the turbulence control parameter αt (Eich and Manz 2021 Nucl. Fusion 61 086016) describing the turbulence level at the separatrix. With increasing αt , a broadening of the upstream density profiles in the near-SOL together with the formation of a density shoulder in the far-SOL have been observed. This phenomenon is associated with an enhanced filamentary transport dominating the radial turbulent transport in the far-SOL and confirmed by means of the cooling water calorimetry on non-divertor components. The probe measurements conducted with the ball-pen probe-head mounted on the midplane manipulator and a retarding-field analyzer close to the limiter surface indicate that the key mechanism increasing the radial filamentary transport to the first wall is an increase of the particle flux Γr,fil , caused primarily by the packing fraction fPF,fil and the filament density ne,fil . At the same time, the electron temperature Te and ion temperature Ti measured close to the limiter surface show only small variations above αt > 0.5. Both the filamentary heat flux and the gross erosion derived from the first wall probe measurements reach a magnitude that should be considered in the design of future fusion reactors.

Turbulence spreading effects on the ELM size and SOL width

BOUT++ turbulence simulations were performed to investigate the impact of turbulence spreading on the edge localized mode (ELM) size and divertor heat flux width $({\lambda _q})$ broadening in small ELM regimes. This study is motivated by EAST experiments. BOUT++ linear simulations of a pedestal radial electric field (Er) scan show that the dominant toroidal number mode (n) shifts from high-n to low-n, with a narrow mode spectrum, and the maximum linear growth rate increases as the pedestal Er well deepens. The nonlinear simulations show that as the net E × B pedestal flow increases, the pressure fluctuation level and its inward penetration beyond the top of the pedestal both increase. This leads to a transition from small ELMs to large ELMs. Both inward and outward turbulence spreading are sensitive to the scrape-off-layer (SOL) plasma profiles. The inward turbulence spreading increases for the steep SOL profiles, leading to increasing pedestal energy loss in the small ELM regime. The SOL width $({\lambda _q})$ is significantly broadened progressing from the ELM-free to small ELM regime, due to the onset of strong radial turbulent transport. The extent of the SOL width $({\lambda _q})$ broadening depends strongly on outward turbulence spreading. The fluctuation energy intensity flux ${\varGamma _\varepsilon }$ at the separatrix can be enhanced by increasing either pedestal Er flow shear or local SOL pressure gradient. The ${\lambda _q}$ is broadened as the fluctuation energy intensity flux ${\varGamma _\varepsilon }$ at the last close flux surface (LCFS) increases. Local SOL E × B flow shear will restrain outward turbulence spreading and the associated heat flux width broadening. Operating in H-mode with small ELMs has the potential to solve two critical problems: reducing the ELM size and broadening the SOL width.

A reduced-model (nSOLT) simulation of neutral recycling effects on plasma turbulence in the divertor region of MAST-U

The 2D scrape-off-layer turbulence code (nSOLT), which includes 1D kinetic neutral–plasma interactions, is applied to study effects of neutral recycling on plasma turbulence for parameters illustrative of the MAST-U divertor region. Neutral recycling is modeled by injecting a fraction of the parallel plasma flux to the divertor back into the simulation domain as a source of Franck–Condon-distributed neutrals. Stationary sources, concentrated at the magnetic separatrix, model plasma streaming into the divertor region from the upstream scrape-off-layer and sustain plasma turbulence absent neutral recycling. Starting from one such no-neutrals equilibrium, we initiate recycling in a numerical experiment designed to diagnose and identify the effects of various neutral–plasma interactions on the divertor plasma, divertor turbulence, and plasma exhaust. The onset of recycling triggers an initial burst of enhanced cross field plasma transport that is quelled by ionization cooling and charge–exchange (CX) friction, with growing neutral pressure, leading to a quiescent, turbulence-free state. Diagnosis of this transient burst reveals that (1) the sudden increase in plasma density due to ionization dominates the onset of the burst, (2) electron cooling due to ionization increases collisionality and disconnects blob filaments from the sheath, and (3) CX friction drives tripole polarization of a blob that can dominate the curvature-driven dipole polarization, leading to the stagnation of blob propagation and reduced radial turbulent transport. It is shown that CX friction is negligible compared to sheath physics in determining equilibrium mean flow shearing rates, for parameters considered herein (specifically a short connection length to the divertor target), while it can significantly reduce interchange-instability growth rates.

Edge turbulence transport during ELM suppression with n = 4 resonant magnetic perturbation on EAST

The edge turbulence characteristics and the induced radial transport have been investigated in edge localized mode (ELM) suppression by using the 4 resonant magnetic perturbation coils on EAST, with 3.6 and the electron collisionality 0.5. During ELM suppression, the edge turbulence is enhanced dramatically, as measured by the reciprocating probe and the poloidal correlation reflectometry. In the near SOL, the low frequency turbulence (<30 kHz) has a large fluctuation level and propagates along the ion diamagnetic drift direction with a speed of 0.35 km s−1 in the plasma frame; an electromagnetic mode around 120 kHz with a small (∼0.15 cm−1) appears when the ELM is suppressed; weak broadband turbulence between 40–120 kHz propagates in the electron diamagnetic drift direction with a velocity of 3.4 km s−1 in the plasma frame. During the ELM suppression, the radial turbulent particle flux, calculated in both the time and frequency domains, is much higher (can be up to five times) than that in the inter-ELM phase. Furthermore, the low frequency turbulence (<30 kHz) dominates the cross-field particle transport. The 120 kHz electromagnetic mode also contributes to outward particle flux, which is relatively small. A set of CGYRO simulations are performed to illustrate the nature of the 120 kHz electromagnetic mode and the low frequency turbulence, suggesting that the former is the micro-tearing mode and the latter is the ion temperature gradient mode. The bispectral analysis suggests a strong three-wave coupling between the low frequency and high frequency turbulence (>250 kHz), which could be beneficial to form the observed turbulent transport. The estimated upstream cross-field particle flux is consistent with the total particle flux deposited on divertor targets, demonstrating that the enhanced radial turbulent particle transport is an important mechanism for particle exhaust in ELM suppression.

Analysis of the momentum recovery in the wake of aligned axial-flow hydrokinetic turbines

Large-Eddy Simulations are reported, dealing with an axial-flow hydrokinetic turbine operating in the wake of an upstream one. Computations were conducted on a cylindrical grid consisting of 3.8 × 109 points, using an Immersed-Boundary methodology. The performance of the downstream turbine was negatively affected by the wake of the upstream one and substantially dependent on its distance. Results demonstrated a faster wake development, compared to the case of the same turbine operating in isolated conditions within a uniform flow, due to the faster instability of the tip vortices, induced by the perturbation of the inflow conditions by the wake of the upstream turbine. In contrast with the turbine performance, the process of wake recovery was found rather insensitive to the distance from the upstream turbine. In comparison with the case of the isolated turbine, the role of radial turbulent transport just downstream of the instability of the tip vortices was found especially important in accelerating the process of wake recovery at the outer radii, providing a significant contribution together with radial advection. Further downstream, the contribution by turbulent transport was verified reinforced also within the wake core, where instead momentum replenishment by radial advection was rather limited.

Evidence on the effects of main-chamber neutrals on density shoulder broadening

Evidence that density shoulder broadening is dependent on high main-chamber neutral density is presented. Shoulder broadening does not occur when the sources for main-chamber neutrals are minimized using divertor baffles and wide gaps to the first wall (∼3× the density decay length). Removing the baffles or reducing the gap to the inner wall both act to increase the density shoulder amplitude in otherwise identical TCV discharges. Radial turbulent transport is correlated with shoulder amplitude.

A self‐consistent mean‐field model for turbulent particle and heat transport in 2D interchange‐dominated electrostatic ExB turbulence in a sheath‐limited scrape‐off layer

AbstractIn this paper, a self‐consistent model for the average radial turbulent transport of heat and particles in 2D anisothermal interchange‐dominated electrostatic ExB drift turbulence in sheath‐limited scrape‐off layers is presented. Diffusion models are used for the turbulent particle and heat fluxes, in which the transport coefficients scale with the square root of the turbulent kinetic energy (). The interchange drive proves to be the main source of turbulent kinetic energy, while the sheath term provides the main sink. These observations are qualitatively the same as for the isothermal case studied earlier. An analytical relation for the interchange term is derived, showing that the turbulent ExB thermal energy flux is the direct driver for through the interchange source. A series decomposition of the sheath term in the equation shows it includes a sink contribution that was also present in the isothermal case, but also a new source due to the sheath‐driven conducting‐wall (SCW) instability caused by electron temperature fluctuations. Using a simple regression model to close the total sheath term, a closed model for the turbulent transport is obtained. The interchange drive due to the ExB energy flux leads to a self‐saturation mechanism in the model, where the gradients and turbulence intensity increase until a sufficient transport level is reached to carry the power and particles across the field lines to find a balance with the sheath sink. An implementation of this model in a 1D mean‐field code approximates the profiles of the turbulence simulations with remarkable accuracy in part of the parameter space, while the error increases in parameter regimes where the relative importance of the SCW term is varied.

Momentum recovery downstream of an axial-flow hydrokinetic turbine

Large-Eddy Simulation is adopted to reproduce the wake of an axial-flow hydrokinetic turbine. The process of momentum recovery is correlated with the destabilization of the wake system, starting wake contraction and radial flows from the free-stream towards the wake core. All terms of the momentum balance equation are analyzed. The radial advection dominates the momentum recovery at the outer radii (in the vicinity of the radial boundary of the wake), just downstream of the instability of the system of tip vortices. Further downstream the reduction of the mean radial gradients makes advection less significant and the radial turbulent transport becomes the main source of momentum replenishment at inner radii, near the wake axis. The details of the process of momentum recovery and its correlation with the instability of the wake system, revealed by the present high-fidelity eddy-resolving computations, provide new insight on the development of the wake of axial-flow hydrokinetic turbines.

Edge turbulence characteristics and transport during the ELM mitigation with n = 1 resonant magnetic perturbation on EAST

The edge localized mode (ELM) has been mitigated by n = 1 resonant magnetic perturbation (RMP) in EAST tokamak. The turbulence characteristics and transport during the ELM mitigation have been measured by a series of diagnostics. The edge coherent mode (ECM) with a frequency about 25 kHz almost disappears when ELM is mitigated. The scrape-off layer (SOL) radial turbulent transport is measured by a four-tip Langmuir probe mounted on the manipulator at the outer midplane, exhibiting a strong enhancement of outward particle during the ELM mitigation in the SOL region (3–25 mm outside the LCFS). This enhanced outward radial transport is mainly driven by the low frequency turbulence (< 50 kHz), and is compared with the particle flux deposited on divertor targets quantitatively, revealing a good agreement with each other. It is suggested that a new channel for particle exhaust induced by the low frequency turbulence is beneficial to maintain the ELM mitigation by RMP.

Turbulent pinch in whole-plasma simulations of a dipole-confined plasma.

Whole-plasma simulations of turbulent transport and upgradient plasma pinch are presented in a dipole magnetic geometry relevant to the Levitated Dipole Experiment (LDX). The self-consistent evolution of an inward particle pinch and the establishment of centrally peaked plasma profiles in a dipole field are explored from whole-plasma simulations using a flux-tube averaged fluid model. The nonlinear evolution of global drift-interchange modes leads to the development of large-scale turbulent convection. Global convective cells are shown to play an important role in radial turbulent transport that causes centrally peaked profiles in a dipole magnetic field. The simulations show that the system self-consistently evolves towards a nonlinear saturated state in which the plasma pressure and density profiles are marginally stable to both drift-interchange and entropy modes.

Effect of resonant magnetic perturbation on boundary plasma turbulence and transport on J-TEXT tokamak

The effect of resonant magnetic perturbation (RMP) on boundary turbulence and transport in J-TEXT plasma is experimentally investigated. Edge plasma fluctuations in discharges with and without the (m/n = 3/1) RMP currents are diagnosed by using Langmuir probe arrays. It was found that fluctuations in the edge and scrape-off layer (SOL) regions decrease with the application of a 6 kA RMP. The broadband turbulence at the radial location of which has a characteristic frequency of 40–150 kHz was strongly suppressed when applying RMP, as was the radial turbulent particle flux and blob transport in the near-SOL region. These experimental findings make RMP a promising method of suppressing and controlling turbulence and particle transport in a plasma boundary.

Mean flow generation by an intermittently unstable boundary layer over a sloping wall

Direct numerical simulations (DNS) of the flow in various rotating annular confinements have been conducted to investigate the effects of wall inclination on secondary fluid motions due to an unstable boundary layer. The inner wall resembles a truncated cone (frustum) whose apex half-angle is varied from$18^{\circ }$to$0^{\circ }$(straight cylinder). The large inner radius$r_{1}$, the mean rotation rate$\unicode[STIX]{x1D6FA}_{0}$and the kinematic viscosity$\unicode[STIX]{x1D708}$were kept constant resulting in the constant Ekman number$E=\unicode[STIX]{x1D708}/(\unicode[STIX]{x1D6FA}_{0}r_{1}^{2})=4\times 10^{-5}$. Flows were excited by time-harmonic modulation of the inner wall’s rotation rate (so-called longitudinal libration) by prescribing the amplitude$\unicode[STIX]{x1D700}\unicode[STIX]{x1D6FA}_{0}$and the forcing frequency$\unicode[STIX]{x1D714}=\unicode[STIX]{x1D6FA}_{0}$. By steepening the inner wall and hence reducing the effect of the local Coriolis force in the boundary layer three different flow regimes can be realized: a rotation-dominated, a libration-dominated and an intermediate regime. In the present study we focus on the libration-dominated regime. For small libration amplitudes (here$\unicode[STIX]{x1D700}=0.2$), a laminar Ekman–Stokes boundary layer (ESBL) is realized at the librating wall. With the aid of laminar boundary layer theory and DNS we show that the ESBL exhibits an oscillatory mass flux along the librating wall (Ekman property) and an oscillatory azimuthal velocity, which resembles a radially damped wave (Stokes property). For large libration amplitudes (here$\unicode[STIX]{x1D700}=0.8$), the DNS results exhibit an intermittently unstable ESBL, which turns centrifugally unstable during the prograde (faster) part of a libration period. This instability is due to the Stokes property and gives rise to Görtler vortices, which are found to be tilted with respect to the azimuth when the librating wall is at a finite angle relative to the axis of rotation. We show that this tilt is related to the Ekman property of the ESBL. This suggests that linear and nonlinear dynamics are equally important for this intermittent instability. Our DNS results indicate further that the Görtler vortices propagate into the fluid bulk where they generate an azimuthal mean flow. This mean flow is notably different from the mean flow driven in the case of the stable ESBL. A diagnostic analysis of the Reynolds-averaged Navier–Stokes (RANS) equations in the unstable flow regime hints at a competition between the radial and axial turbulent transport terms which act as generating and destructing agents for the azimuthal mean flow, respectively. We show that the balance of both terms depends on the wall inclination, that is, on the wall-tangential component of the Coriolis force.

Impact of safety factor and magnetic shear profiles on edge turbulence in circular limited geometry

The impact of magnetic configuration on edge turbulence properties in circular limiter geometry is investigated using TOKAM3X, a three‐dimensional (3D), first‐principle, fluid code for edge plasma. The theoretical spatial tilting of magnetic shear on turbulence fluctuations is recovered. Magnetic shear is found to generate or enhance poloidal high/low field sides (HFS/LFS) and up/down asymmetries. A simulation mimicking the impact of an X‐point on circular limiter geometry leads to the formation of two transport barriers that are stable in time, thus leading to the improvement of core particle confinement and to reduction of radial turbulent transport. The magnetic shear, which also strongly enhances the E × B shear, is responsible for the barrier formation.

Investigation on the effect of pressure on turbulent transports of the IR-T1 Tokamak plasma

Investigation on the effects of limiter biasing and applying external electric fields (positive and negative voltage of 200 V) under various pressures of 1.9, 2.3 and 2.7 Torr on the IR-T1 Tokamak plasma parameters such as plasma current, loop voltage, radial electric field, poloidal electric field and Reynolds stress and turbulent transports, was done in this work. The results show that the ramp time of the plasma current decreased and the change rate of loop voltage raised by increasing plasma pressure. The power of radial electric field is more than the power of poloidal electric field. According to the applied positive voltage to the plasma, it is observed that the Reynolds stress of IR-T1 Tokamak plasma has experienced a more significant reduction at the pressure of 2.3 Torr than other pressures. The results Also show that the applying positive voltage of 200 V to the IR-T1 Tokamak plasma at the pressure of 2.3 Torr (compared to other pressures) has more effect on increases and decreases the poloidal and radial turbulent transport, respectively.

Turbulent transport and entrainment in jets and plumes: A DNS study

We present a new DNS data set for a statistically axisymmetric turbulent jet, plume and forced plume in a domain of size $40 r_0 \times 40 r_0 \times 60 r_0$, where $r_0$ is the source diameter. The data set provides evidence of the validity of the Priestley and Ball entrainment model in unstratified environments (excluding the region near the source), which is corroborated further by the Wang and Law and Ezzamel \emph{et al.} experimental data sets, the latter being corrected for a small but influential co-flow that affected the statistics. We show that the turbulence in the core region of the jet and the plume are practically indistinguishable, although the invariants of the anisotropy tensor reveal a significant change in the turbulence near the plume edge. The DNS data indicates that the turbulent Prandtl number is about 0.7 for both jets and plumes. For plumes, this value is a result of the difference in the ratio of the radial turbulent transport of radial momentum and buoyancy. For jets however, the value originates from a different spread of the buoyancy and velocity profiles, in spite of the fact that the ratio of radial turbulent transport terms is approximately unity. The DNS data does not show any evidence of similarity drift associated with gradual variations in the ratio of buoyancy profile to velocity profile widths.

Quasi-symmetry and the nature of radial turbulent transport in quasi-poloidal stellarators

Quasi-symmetric configurations have a better neoclassical confinement compared to that of standard stellarators. The reduction of the neoclassical viscosity along the direction of quasi-symmetry should facilitate the self-generation of zonal flows and, consequently, the mitigation of turbulent fluctuations and the ensuing radial transport. Therefore, it is expected that quasi-symmetries should also result in better confinement properties regarding radial turbulent transport. In this paper we show that, at least for quasi-poloidal configurations, the influence of quasi-symmetry on radial transport exceeds the expected reduction of fluctuation levels and associated effective transport coefficients, and that the intimate nature of transport itself is affected. In particular, radial turbulent transport becomes increasingly subdiffusive as the degree of quasi-symmetry becomes larger. This behavior is somewhat reminiscent of what has been previously reported in tokamaks with strong radially sheared zonal flows.

Electrostatic particle-in-cell simulation of heat flux mitigation using magnetic fields

The particle-in-cell (PIC) method was used to simulate heat flux mitigation experiments with partially ionised argon. The experiments demonstrate the possibility of reducing heat flux towards a target using magnetic fields. Modelling using the PIC method is able to reproduce the heat flux mitigation qualitatively. This is driven by modified electron transport. Electrons are magnetised and react directly to the external magnetic field. In addition, an increase of radial turbulent transport is also needed to explain the experimental observations in the model. Close to the target an increase of electron density is created. Due to quasi-neutrality, ions follow the electrons. Charge exchange collisions couple the dynamics of the neutrals to the ions and reduce the flow velocity of neutrals by radial momentum transport and subsequent losses. By this, the dominant heat-transport channel by neutrals gets reduced and a reduction of the heat deposition, similar to the experiment, is observed. Using the simulation a diagnostic module for optical emission is developed and its results are compared with spectroscopic measurements and photos from the experiment. The results of this study are in good agreement with the experiment. Experimental observations such as a shrank bright emission region close to the nozzle exit, an additional emission in front of the target and an overall change in colour to red are reproduced by the simulation.

Bias Effects on the Reynolds Stress Using the Multi-Purpose Probe in IR-T1 Tokamak

The effect of the positive bias on Reynolds stress (RS) and its effect on the radial turbulent transport at the edge plasma (r/a = 0.9) and scrape-off layer (SOL) region of plasma in tokamak are investigated. The radial and poloidal electric fields (Er, Ep) and ion saturation current (Is) are measured by multi-purpose probe (MPP). This probe is fabricated and constructed for the first time in the IR-T1 tokamak. The most advantage of this probe is that the variations of Er and Ep can be measured in different radii at the single shot. Thus the information of different radii can be compared with high precision. The bias voltage is fixed at Vbias = 200 V and it has been applied with the limiter bias that is fixed in r/a = 0.9. Moreover, the phase difference between radial and poloidal electric fields, and temporal evolution of the RS spectrum detected by MPP are calculated. RS magnitude on the edge (r/a = 0.9) is more than its value in the SOL (r/a = 1.02). With the applied bias 200 V, RS and the magnitude of the phase difference between Er and Ep are increased, while the radial turbulent transport is decreased simultaneously. Thus it can be concluded that RS affects radial turbulence. Temporal evolution of the RS spectrum shows that the frequency of RS is increased and reaches its highest value at r/a = 0.9 in the presence of bias.

Impact of rotating magnetic islands on density profile flattening and turbulent transport

The impact of rotating magnetic islands on background radial profiles in the presence of strong turbulent transport is analysed, with particular emphasis on island widths of the order of 6–10 ion Larmor radii. Only the case of ion temperature gradient (ITG) turbulence is considered. A significant reduction of fluctuations is found when island and turbulence co-rotate and the island width is of the order of the radial correlation length of turbulence. This reduction is not due to a flattening of ion temperature, suggesting an additional mechanism. A nonlinear transfer of energy from small to large scale structures might be responsible for the stabilization at a scale close to the radial correlation length of turbulence. It is shown that in the presence of intermediate magnetic islands rotating in the ion diamagnetic direction the density flattening survives the radial turbulent transport, representing a destabilizing effect for a magnetic island in terms of bootstrap current. However, this flattening is not necessarily due to an adiabatic response of trapped ions. Owing to the fast parallel motion of electrons, their temperature is always flattened. Finally, when the island width is large enough (island width greater than 18 ion Larmor radii), the standard profile flattening leading to a linear stabilization of turbulence dominates over the other mechanisms.

Multi-scale self-organisation of edge plasma turbulent transport in 3D global simulations

The 3D global edge turbulence code TOKAM3X is used to study the properties of edge particle turbulent transport in circular limited plasmas, including both closed and open flux surfaces. Turbulence is driven by an incoming particle flux from the core plasma and no scale separation between the equilibrium and the fluctuations is assumed. Simulations show the existence of a complex self-organization of turbulence transport coupling scales ranging from a few Larmor radii up to the machine scale. Particle transport is largely dominated by small scale turbulence with fluctuations forming quasi field-aligned filaments. Radial particle transport is intermittent and associated with the propagation of coherent structures on long distances via avalanches. Long range correlations are also found in the poloidal and toroidal direction. The statistical properties of fluctuations vary with the radial and poloidal directions, with larger fluctuation levels and intermittency found in the outboard scrape-off layer (SOL). Radial turbulent transport is strongly ballooned, with 90% of the flux at the separatrix flowing through the low-field side. One of the main consequences is the existence of quasi-sonic asymmetric parallel flows driving a net rotation of the plasma. Simulations also show the spontaneous onset of an intermittent E × B rotation characterized by a larger shear at the separatrix. Strong correlation is found between the turbulent particle flux and the E × B flow shear in a phenomenology reminiscent of H-mode physics. The poloidal position of the limiter is a key player in the observed dynamics.