We study the impact of impurities on turbulence driven intrinsic rotation (via residual stress) in the context of the quasi-linear theory. A two-fluid formulation for main and impurity ions is employed to study ion temperature gradient modes in sheared slab geometry modified by the presence of impurities. An effective form of the parallel Reynolds stress is derived in the center of mass frame of a coupled main ion-impurity system. Analyses show that the contents and the radial profile of impurities have a strong influence on the residual stress. In particular, an impurity profile aligned with that of main ions is shown to cause a considerable reduction of the residual stress, which may lead to the reduction of turbulence driven intrinsic rotation.
Turbulent transport of trace impurities impurities in the edge and scrape-off-layer of tokamak fusion plasmas is modelled by three dimensional electromagnetic gyrofluid computations including evolution of plasma profile gradients. The source function of impurity ions is dynamically computed from pre-determined measured and calculated electron impact ionization cross section data. The simulations describe the generation and further passive turbulent E-cross-B advection of the impurities by intermittent fluctuations and coherent filamentary structures (blobs) across the scrape-off-layer.
Poloidal asymmetries in the impurity density can be generated by radio frequency heating in the core and by neoclassical effects in the edge of tokamak plasmas. In a pedestal case study, using global neoclassical simulations we find that finite orbit width effects can generate significant poloidal variation in the electrostatic potential, which varies on a small radial scale. Gyrokinetic modeling shows that these poloidal asymmetries can be strong enough to significantly modify turbulent impurity peaking. In the pedestal the ExB drift in the radial electric field can give a larger contribution…
A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ITG, TEM and ETG modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the non…
A process specific to the dynamics of the heavy impurities in turbulent tokamak plasmas is found and analysed. We show that the parallel stochastic acceleration is strongly coupled to the perpendicular transport and generates a radial pinch velocity. The interaction is produced with the hidden drifts, a quasi-coherent component of the motion that consists of a pair of average radial velocities in opposite directions. The parallel acceleration breaks this symmetry and yields a radial average velocity that can be in the inward or outward direction. The transport of the tungsten ions in three-dim…
By presenting linear and nonlinear gyrokinetic studies, based on a balanced neutral beam injection deuterium discharge from the DIII-D tokamak, we demonstrate that impurities alter the scaling of the transport on the charge and mass of the main species, and even more importantly, they can dramatically change the energy transport even in relatively small quantities. A poloidally varying equilibrium electrostatic potential can lead to a strong reduction or sign change of the impurity peaking factor due to the combined effect of the in-out impurity density asymmetry and the EXB drift of impuritie…
The turbulent transport of minority species/impurities is investigated in 2D drift-wave turbulence as well as in 3D toroidal drift-Alfven edge turbulence. The full effects of perpendicular and -- in 3D -- parallel advection are kept for the impurity species. Anomalous pinch effects are recovered and explained in terms of Turbulent EquiPartition (TEP)
Test particle transport determined by the Lorentz force in turbulent magnetized plasmas is studied. The time dependent diffusion coefficient, valid for the whole range of parameters, is obtained by developing the decorrelation trajectory method. The effects of Larmor gyration in the presence of trapping are analyzed and several transport regimes are evidenced.
Carbon and nitrogen impurity transport coefficients are determined from gas puff experiments carried out during repeat L-mode discharges on the Mega-Amp Spherical Tokamak (MAST) and compared against a previous analysis of helium impurity transport on MAST. The impurity density profiles are measured on the low-field side of the plasma, therefore this paper focuses on light impurities where the impact of poloidal asymmetries on impurity transport is predicted to be negligible. A weak screening of carbon and nitrogen is found in the plasma core, whereas the helium density profile is peaked over t…
Several new results in the physics of edge poloidal flows, turbulent stresses and momentum transport are reported. These are based on experiments on the HL-2A tokamak. Significant deviation from neoclassical prediction for mean poloidal flow in Ohmic and L mode discharges is deduced from direct measurements of the turbulent Reynolds stress. The deviation increases with heating power. The turbulent poloidal viscosity is synthesized from fluctuation data, and is found to be comparable to the turbulent particle diffusivity. The intrinsic poloidal torque is deduced from synthesis, for the first ti…
Laser blow-off injections of aluminum and tungsten have been performed on the DIII-D tokamak to investigate the variation of impurity transport in a set of dedicated ion and electron heating scans with a fixed value of the external torque. The particle transport is quantified via the Bayesian inference method, which, constrained by a combination of a charge exchange recombination spectroscopy, soft X-ray measurements, and VUV spectroscopy provides a detailed uncertainty quantification of the transport coefficients. Contrasting discharge phases with a dominant electron and ion heating reveal a …
A large diffusive turbulent contribution to the radial impurity transport in Wendelstein 7-X (W7-X) plasmas has been experimentally inferred during the first campaigns and numerically confirmed by means of gyrokinetic simulations with the code stella. In general, the absence of strong impurity accumulation during the initial W7-X campaigns is attributed to this diffusive term. In the present work the diffusive contribution is also calculated in other stellarator plasmas. In particular, the diffusion (D) and convection (V) coefficients of carbon and iron impurities produced by ion-temperature-g…
The turbulent transport of impurity or minority species, as for example Tritium, is investigated in drift-Alfvén edge turbulence. The full effects of perpendicular and parallel convection are kept for the impurity species. The impurity density develops a granular structure with steep gradients and locally exceeds its initial values due to the compressibility of the flow. An approximate decomposition of the impurity flux into a diffusive part and an effective convective part (characterized by a pinch velocity) is performed and a net inward pinch effect is recovered. The pinch velocity is explai…
The quasilinear intrinsic parallel flow drive including parallel residual stress, kinetic stress, cross Maxwell stress and parallel turbulent acceleration by electromagnetic ion temperature gradient (ITG) turbulence is calculated analytically using electromagnetic gyrokinetic theory. Both the kinetic stress and cross Maxwell stress also enter the mean parallel flow velocity equation via their divergence, as for the usual residual stress. The turbulent acceleration driven by ion pressure gradient along the total magnetic field (including equilibrium magnetic field and fluctuating radial magneti…
The turbulence-induced quasi-linear particle flux of a highly-charged, collisional impurity species is calculated from the electrostatic gyrokinetic equation including collisions with the bulk ions and the impurities themselves. The equation is solved by an expansion in powers of the impurity charge number $Z$. In this formalism, the collision operator only affects the impurity flux through the dynamics of the impurities in the direction parallel to the magnetic field. At reactor-relevant collisionality, the parallel dynamics is dominated by the parallel electric field, and collisions have a m…
In the present study, turbulent impurity transport in Deuterium tokamak plasmas, driven by Ion Temperature Gradient (ITG) and Trapped Electron (TE) modes, has been investigated using fluid and gyrokinetic models. The impurity diffusivity ($D_Z$) and convective velocity ($V_Z$) are calculated, and from these the zero-flux peaking factor ($PF_0$) is derived. This quantity expresses the impurity density gradient at which the convective and diffusive transport of impurities are exactly balanced. The sign of $PF_0$ is of special interest, as it determines whether the impurities are subject to an in…
Impurity particle transport in an ion cyclotron resonance heated Alcator C-Mod discharge is studied with local gyrokinetic simulations and a theoretical model including the effect of poloidal asymmetries and elongation. In spite of the strong minority temperature anisotropy in the deep core region, the poloidal asymmetries are found to have a negligible effect on the turbulent impurity transport due to low magnetic shear in this region, in agreement with the experimental observations. According to the theoretical model, in outer core regions poloidal asymmetries may contribute to the reduction…
The turbulent transport of main ion and trace impurities in a tokamak device in the presence of steep electron density gradients has been studied. The parameters are chosen for trapped electron (TE) mode turbulence, driven primarily by steep electron density gradients relevant to H-mode physics, but with a transition to temperature gradient driven turbulence as the density gradient flattens. Results obtained through non-linear (NL) and quasilinear (QL) gyrokinetic simulations using the GENE code are compared with results obtained from a fluid model. Main ion and impurity transport is studied b…
Both the parallel residual stress and parallel turbulent acceleration driven by electrostatic collisionsless trapped electron mode (CTEM) turbulence are calculated analytically using gyrokinetic theory. Quasilinear results show that the parallel residual stress contributes an outward flux of co-current rotation for normal magnetic shear and turbulence intensity profile increasing outward. This may induce intrinsic counter-current rotation or flattening of the co-current rotation profile. The parallel turbulent acceleration driven by CTEM turbulence vanishes, due to the absence of a phase shift…
Turbulence driven zonal flows play an important role in fusion devices since they improve plasma confinement by limiting the level of anomalous transport. Current theories mostly focus on flow excitation but do not self-consistently describe the nearly stationary zonal flow turbulence equilibrium state. First-principles two-fluid turbulence studies are used to construct a Reynolds stress response functional from observations in turbulent states. This permits, for the first time, a reliable charting of zonal flow turbulence equilibria.
The turbulent transport of impurity particles in plasma edge turbulence is investigated. The impurities are modeled as a passive fluid advected by the electric and polarization drifts, while the ambient plasma turbulence is modeled using the two-dimensional Hasegawa--Wakatani paradigm for resistive drift-wave turbulence. The features of the turbulent transport of impurities are investigated by numerical simulations using a novel code that applies semi-Lagrangian pseudospectral schemes. The diffusive character of the turbulent transport of ideal impurities is demonstrated by relative-diffusion …
We present a fully Bayesian approach for the inference of radial profiles of impurity transport coefficients and compare its results to neoclassical, gyrofluid and gyrokinetic modeling. Using nested sampling, the Bayesian Impurity Transport InferencE (BITE) framework can handle complex parameter spaces with multiple possible solutions, offering great advantages in interpretative power and reliability with respect to previously demonstrated methods. BITE employs a forward model based on the pySTRAHL package, built on the success of the well-known STRAHL code [Dux, IPP Report, 2004], to simulate…
The theory of turbulent transport of parallel momentum and ion heat by the interaction of stochastic magnetic fields and turbulence is presented. Attention is focused on determining the kinetic stress and the compressive energy flux. A critical parameter is identified as the ratio of the turbulent scattering rate to the rate of parallel acoustic dispersion. For the parameter large, the kinetic stress takes the form of a viscous stress. For the parameter small, the quasilinear residual stress is recovered. In practice, the viscous stress is the relevant form, and the quasilinear limit is not ob…
