Turbulent Pinch Research Articles

Illustrating the physics of core tungsten (W) transport in a long-pulse steady-state H-mode discharge on EAST

The behavior of core tungsten (W) in a pure radio-frequency-heated long-pulse steady-state H-mode discharge in the Experimental Advanced Superconducting Tokamak (EAST) with an ITER-like divertor (ILD) is analyzed using experimental diagnostic data and modeled using a combination of drift-kinetic neoclassical and gyro-fluid turbulent software. In the steady state, the experimental core line-averaged W concentration (C W) is about 2 × 10−5, which is evaluated using the intensity of the W unresolved transition array (W-UTA) spectral structure in the region of 45–70 Å (which is composed of W 27+–W 45+ line emissions) through spectroscopy in the extreme ultraviolet region. W produces a peak of the radiated power density profile around a normalized radius of ρ ∼ 0.3. Therefore, W does not centrally accumulate in the experiment. A time slice of the steady-state is modeled, which accounts for both the neoclassical and turbulent transport components of W based on the self-consistent background plasma profiles simulated by TGYRO (Candy et al 2009 Phys. Plasmas 16 060704). It is found that turbulent transport dominates over neoclassical transport for W. In addition, the turbulent diffusion coefficient is large enough to offset the sum of the neoclassical and turbulent pinch (convection) velocities, so that the W density profile for a zero particle flux is not strongly peaked. By combining TGLF (Staebler et al 2017 Nucl. Fusion 57 066046) and NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010; 2012 Plasma Phys. Control. Fusion 54 015015) for the W transport coefficient with the impurity transport code STRAHL (Dux 2006 STRAHL User Manual), the experimental C W and the information radiated by W can be reproduced closely. In addition, the effect of toroidal rotation on the W transport is also clarified.

Understanding core tungsten (W) transport and control in an improved high-performance fully non-inductive discharge on EAST

The behavior of heavy/high-Z impurity tungsten (W) in an improved high-performance fully non-inductive discharge on EAST with ITER-like divertor (ILD) is analyzed. It is found that W could be well controlled. The causes of no W accumulation are clarified by analyzing the background plasma parameters and modeling the W transport. It turns out that the electron temperature (T e) and its gradient are usually high while the toroidal rotation and density peaking of the bulk plasma are small. In this condition, the modeled W turbulent diffusion coefficient is big enough to offset the total turbulent and neoclassical pinch, so that W density profile for zero particle flux will not be very peaked. Combining NEO and TGLF for the W transport coefficient and the impurity transport code STRAHL, not only the core W density profile is predicted but also the radiated information mainly produced by W in the experiment can be closely reconstructed. At last, the physics of controlling W accumulation by electron cyclotron resonance heating (ECRH) is illustrated considering the effects of changed T e by ECRH on ionization balance and transport of W. It shows that the change of ionization and recombination balance by changed T e is not enough to explain the experimental observation of W behavior, which should be attributed to the changed W transport. By comparing the W transport coefficients in two kinds of plasmas with different T e profiles, it is shown that high T e and its gradient play a key role to generate large turbulent diffusion through increasing the growth rate of linear instability so that W accumulation is prevented.

Turbulent transport of the W ions in tokamak plasmas: properties derived from a test particle approach

A detailed analysis of a special type of turbulent pinch mechanism for tungsten (W) ions is presented. It is based on the numerical simulation of ion trajectories in a complex test-particle model that contains realistic representations of the turbulence and of the confining magnetic field, plasma rotation, ion collisions, the polarization drift and the parallel stochastic acceleration. The origin of the pinch is a special type of order generated by an average poloidal velocity V p superposed on the E × B stochastic drift. It consists of a pair of radial symmetric drifts, the hidden drifts (HDs), that exactly compensate. The polarization drift and the parallel acceleration drive radial pinch velocities V x by destroying the perfect anti-symmetry of the HDs. These phenomena that were found in simplified models are theoretically validated here in a realistic model of W ion transport. The main conclusion of the paper is that this turbulent mechanism can be experimentally relevant for a large domain of parameters, which cover both existing plasmas and ITER conditions, and it can be responsible for an important amount of the W ion accumulation.

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.

Dependence of the turbulent particle flux on hydrogen isotopes induced by collisionality

The impact of the change of the mass of hydrogen isotopes on the turbulent particle flux is studied. The trapped electron component of the turbulent particle convection induced by collisionality, which is outward in ion temperature gradient turbulence, increases with decreasing thermal velocity of the isotope. Thereby, the lighter is the isotope, the stronger is the turbulent pinch, and the larger is the predicted density gradient at the null of the particle flux. The passing particle component of the flux increases with decreasing mass of the isotope and can also affect the predicted density gradient. This effect is however subdominant for usual core plasma parameters. The analytical results are confirmed by means of both quasi-linear and nonlinear gyrokinetic simulations, and an estimate of the difference in local density gradient produced by this effect as a function of collisionality has been obtained for typical plasma parameters at mid-radius. Analysis of currently available experimental data from the JET and the ASDEX Upgrade tokamaks does not show any clear and general evidence of inconsistency with this theoretically predicted effect outside the errorbars and also allows the identification of cases providing weak evidence of qualitative consistency.

Main-Ion Intrinsic Toroidal Rotation Profile Driven by Residual Stress Torque from Ion Temperature Gradient Turbulence in the DIII-D Tokamak.

Intrinsic toroidal rotation of the deuterium main ions in the core of the DIII-D tokamak is observed to transition from flat to hollow, forming an off-axis peak, above a threshold level of direct electron heating. Nonlinear gyrokinetic simulations show that the residual stress associated with electrostatic ion temperature gradient turbulence possesses the correct radial location and stress structure to cause the observed hollow rotation profile. Residual stress momentum flux in the gyrokinetic simulations is balanced by turbulent momentum diffusion, with negligible contributions from turbulent pinch. The prediction of the velocity profile by integrating the momentum balance equation produces a rotation profile that qualitatively and quantitatively agrees with the measured main-ion profile, demonstrating that fluctuation-induced residual stress can drive the observed intrinsic velocity profile.

Turbulent fluctuations during pellet injection into a dipole confined plasma torus

We report measurements of the turbulent evolution of the plasma density profile following the fast injection of lithium pellets into the Levitated Dipole Experiment (LDX) [Boxer et al., Nat. Phys. 6, 207 (2010)]. As the pellet passes through the plasma, it provides a significant internal particle source and allows investigation of density profile evolution, turbulent relaxation, and turbulent fluctuations. The total electron number within the dipole plasma torus increases by more than a factor of three, and the central density increases by more than a factor of five. During these large changes in density, the shape of the density profile is nearly “stationary” such that the gradient of the particle number within tubes of equal magnetic flux vanishes. In comparison to the usual case, when the particle source is neutral gas at the plasma edge, the internal source from the pellet causes the toroidal phase velocity of the fluctuations to reverse and changes the average particle flux at the plasma edge. An edge particle source creates an inward turbulent pinch, but an internal particle source increases the outward turbulent particle flux. Statistical properties of the turbulence are measured by multiple microwave interferometers and by an array of probes at the edge. The spatial structures of the largest amplitude modes have long radial and toroidal wavelengths. Estimates of the local and toroidally averaged turbulent particle flux show intermittency and a non-Gaussian probability distribution function. The measured fluctuations, both before and during pellet injection, have frequency and wavenumber dispersion consistent with theoretical expectations for interchange and entropy modes excited within a dipole plasma torus having warm electrons and cool ions.

Turbulent momentum pinch of diamagnetic flows in a tokamak

The diamagnetic flow due to the radial pressure and temperature gradients and the E × B flow due to the radial electric field induce different turbulent momentum fluxes in a tokamak. As a result, when the diamagnetic and E × B flows cancel giving zero net toroidal rotation, there will still be finite momentum transport. This may be particularly important near the plasma–wall boundary where a strong pressure drop is established and the two types of flows are similar in size and opposite in direction. The different momentum fluxes in this region can give significant intrinsic rotation peaking in the core with scaling and values similar to those observed in high confinement mode plasmas.

Kinetic theory of the turbulent energy pinch in tokamak plasmas

The turbulent energy fluxes, including up-gradient ‘energy pinch’ effects, are derived using the nonlinear bounce-kinetic equation for trapped electrons and the nonlinear gyrokinetic equation for ions in toroidal geometry. The quasi-universal type of inward turbulent equipartition (TEP) energy pinch is recovered for both ions and trapped electrons, with different field dependence coefficients due to toroidal effects. A contribution from the density gradient to an outward convective energy flux is also obtained. The direction of the total energy convection is primarily determined by the competition between the TEP energy pinch and the outward density gradient driven energy convection. The magnetic shear dependence of the electron energy pinch is discussed. The energy pinches can provide possible explanations for some puzzling experimental observations.

Fluctuation driven transport and stationary profiles

Transport equations for particles and energy can be derived when the fluctuations conserve adiabatic invariants. The transport equations determine both stationary density and pressure profiles and the direction of the turbulence-driven fluxes which can be inward or outward. An inward turbulent pinch is predicted which creates stationary profiles and reverses direction depending on the density and temperature gradients. The transport fluxes are independent of the underlying drive that leads to plasma turbulence. For low frequency turbulence, the formulation remains correct when the collisional time scale is faster than the confinement time scale.

The pinch of cold ions from recycling in the tokamak edge pedestal

We apply the “natural fueling mechanism” [W. Wan, S. E. Parker, Y. Chen, and F. W. Perkins, Phys. Plasmas 17, 040701 (2010)] to the edge pedestal. The natural fueling mechanism is where cold ions naturally pinch radially inward for a heat-flux dominated plasma. It is shown from neoclassical-neutral transport coupled simulations that the recycling neutrals and the associated source ions are colder than the main ions in the edge pedestal. These recycling source ions will pinch radially inward due to microturbulence. Gyrokinetic turbulence simulations indicate that near the top of the pedestal, the pinch velocity of the recycling source ions is much higher than the main ion outgoing flow velocity. The turbulent pinch of the recycling source ions may play a role in the edge pedestal transport and dynamics. The cold ion temperature significantly enhances the pinch velocity of the recycling source ions near to the pedestal top. Neoclassical calculations show a cold ion pinch in the pedestal as well.

A simple model of intrinsic rotation in high confinement regime tokamak plasmas

A simple unified model of intrinsic rotation and momentum transport in high confinement regime (H-mode) tokamak plasmas is presented. Motivated by the common dynamics of the onset of intrinsic rotation and the L-H transition, this simple model combines E×B shear-driven residual stress in the pedestal with a turbulent equipartition pinch to yield rotation profiles. The residual stress is the primary mechanism for buildup of intrinsic rotation in the H-mode pedestal, while the pinch drives on-axis peaking of rotation profiles. Analytical estimates for pedestal flow velocities are given in terms of the pedestal width, the pedestal height, and various model parameters. The predicted scaling of the toroidal flow speed with pedestal width is found to be consistent with the International Tokamak Physics Activity database global scaling of the flow speed on-axis with the total plasma stored energy.

Turbulent inward pinch of plasma confined by a levitated dipole magnet

Turbulence usually makes plasmas more homogeneous. But in an unusual device for which the confining field is generated by a levitated half-tonne superconducting magnet, a study finds that turbulent fluctuations can actually increase the density of a plasma by driving diffusion against a density gradient.

Turbulent pinch in the non-homogeneous confining magnetic field

Two models of turbulent pinches due to the inhomogeneity of the confining magnetic field have been proposed: the curvature and the ratchet pinches. The first is the effect of compressibility of the density due to the divergence of the E × B drift and the second reflects the influence of the magnetic field inhomogeneity on the trajectories. The relation between these models is analyzed. The average velocity for the density advected by the stochastic E × B drift is determined for quasi linear and nonlinear turbulence. We show that the density pinch velocity is the sum of the ratchet and curvature pinches and that peaked density profiles can be obtained due to the ratchet effect in nonlinear turbulence in the presence of poloidal rotation.

Density profile behavior in T-10 experiments with gas puffing

Features of density profile behavior in T-10 experiments with gas puffing are discussed in this paper. It is shown that density peaking increases with the increase in collisionality in ohmic discharges and in discharges with electron cyclotron resonant heating. The observed regularity cannot be explained by neoclassical effects only. The existence of a turbulent pinch mechanism leading to a relative increase in the inward particle flux should be proposed. The stability of drift turbulence is discussed since these instabilities could be considered as a candidate mechanism explaining the anomalous transport.

Fluid simulations of turbulent impurity transport

Impurity transport in tokamak plasmas is studied with a fluid turbulence code, which has been upgraded to implement two ion species and electrons. The (fixed-flux) simulations are compared to the predictions of a quasilinear model. These simulations mostly agree with quasilinear estimates; they indicate that a turbulent impurity pinch exists. Moreover, this pinch is found to be dominated by curvature terms, as thermodiffusion pinches are found to decrease as 1∕Z and observed parallel velocity effects remain weak. The sign of the pinch is also investigated.

Density peaking and turbulent pinch in DIII-D discharges

A study of density peaking and particle flow in low confinement (L-mode) DIII-D discharges [G. R. McKee, C. C. Petty, R. E. Waltz et al., Nucl. Fusion 41, 1235 (2001)], using global gyrokinetic simulations, is presented. It is found that under experimental conditions, in particular when realistic collisionality is included, a turbulent pinch driven by electron temperature and density gradients can occur.

Turbulent particle transport in Tore Supra

Steady state fully non-inductive current plasmas in Tore Supra offer an opportunity to study the turbulent particle pinch. The local parametric dependence of the particle pinch velocity allows us to discriminate between different theories. The existence of an anomalous pinch is unambiguously demonstrated. The results support the turbulent theories based on ion temperature gradient and trapped electron modes. An anomalous inward pinch related to the safety factor (q) profile is found to be dominant in the gradient region (normalized radius 0.3 ⩽ r/a ⩽ 0.6). In contrast, the direction of the anomalous pinch in the plasma core (r/a ⩽ 0.3) is more sensitive to the electron temperature (Te) profile.

Steady-state operation of tokamaks: key experiments, integrated modelling and technology developments on Tore Supra

Key technological and physics issues related to long pulse operation required for a reactor are now being addressed in Tore Supra. This paper focuses on the experimental results from conditions where all the plasma facing components (PFCs) are actively cooled. Full steady-state plasma quantities as well as stable PFC temperature during pulses exceeding 6 min are reported. Particle balance and D retention in the steady-state are analysed. Physics phenomena related to continuous operation are observed in non-inductively driven plasmas, namely (i) a regime characterized by large sinusoidal oscillations of the central electron temperature, governed by a predator–prey mechanism of non-linear coupling between heat transport and plasma current; (ii) a strong synergy effect between lower hybrid and electron cyclotron waves; (iii) a peaked density profile generated by turbulent inward pinch. Integrated modelling activity at Tore Supra is also reported.

Turbulent particle transport in magnetized fusion plasma

Understanding the mechanisms responsible for particle transport is of the utmost importance for magnetized fusion plasmas. A peaked density profile is attractive to improve the fusion rate, which is proportional to the square of the density, and to self-generate a large fraction of non-inductive current required for continuous operation.Experiments in various tokamak devices (ASDEX Upgrade, DIII-D, JET, TCV, TEXT, TFTR) indicate the existence of a turbulent particle pinch. Recently, such a turbulent pinch has been unambiguously identified in Tore Supra very long discharges, in the absence of both collisional particle pinch and central particle source, for more than 4 min (Hoang et al 2003 Phys. Rev. Lett. 90 155002). This turbulent pinch is predicted by a quasilinear theory of particle transport (Weiland J et al 1989 Nucl. Fusion 29 1810), and confirmed by non-linear turbulence simulations (Garbet et al 2003 Phys. Rev. Lett. 91 035001) and general considerations based on the conservation of motion invariants (Baker et al 2004 Phys. Plasmas 11 992). Experimentally, the particle pinch is found to be sensitive to the magnetic field gradient in many cases (Hoang et al 2004 Phys. Rev. Lett. 93 135003, Zabolotsky et al 2003 Plasma Phys. Control. Fusion 45 735, Weisen et al 2004 Plasma Phys. Control. Fusion 46 751, Baker et al 2000 Nucl. Fusion 40 1003), to the temperature profile (Hoang et al 2004 Phys. Rev. Lett. 93 135003, Angioni et al 2004 Nucl. Fusion 44 827) and also to the collisionality that changes the nature of the microturbulence (Angioni et al 2003 Phys. Rev. Lett. 90 205003, Garzotti et al 2003 Nucl. Fusion 43 1829, Weisen et al 2004 31st EPS Conf. on Plasma Phys. (London) vol 28G (ECA) P-1.146, Lopes Cardozo N J 1995 Plasma Phys. Control. Fusion 37 799). The consistency of some of the observed dependences with the theoretical predictions gives us a clearer understanding of the particle pinch in tokamaks, allowing us to predict more accurately the density profile in ITER.