Transport Of Trace Impurities Research Articles

Quantification of the effect of uncertainty on impurity migration in PISCES-A simulated with GITR

A Bayesian inference strategy has been used to estimate uncertain inputs to global impurity transport code (GITR) modeling predictions of tungsten erosion and migration in the linear plasma device, PISCES-A. This allows quantification of GITR output uncertainty based on the uncertainties in measured PISCES-A plasma electron density and temperature profiles (n e, T e) used as inputs to GITR. The technique has been applied for comparison to dedicated experiments performed for high (4 × 1022 m−2 s−1) and low (5 × 1021 m−2 s−1) flux 250 eV He–plasma exposed tungsten (W) targets designed to assess the net and gross erosion of tungsten, and corresponding W impurity transport. The W target design and orientation, impurity collector, and diagnostics, have been designed to eliminate complexities associated with tokamak divertor plasma exposures (inclined target, mixed plasma species, re-erosion, etc) to benchmark results against the trace impurity transport model simulated by GITR. The simulated results of the erosion, migration, and re-deposition of W during the experiment from the GITR code coupled to materials response models are presented. Specifically, the modeled and experimental W I emission spectroscopy data for a 429.4 nm line and net erosion through the target and collector mass difference measurements are compared. The methodology provides predictions of observable quantities of interest with quantified uncertainty, allowing estimation of moments, together with the sensitivities to plasma temperature and density.

Trace impurity transport in multi-species plasmas with large particle fluxes

A burning fusion plasma has a large inwards flux of fuel and outwards flux of ash. Existing impurity transport theories do not account for a steady-state environment of such large fluxes. In this paper, we extend classical transport theory to account for a background of such fluxes. In a mainly two-ion species magnetized plasma, with oppositely directed density gradients maintained by oppositely directed sources of the two species, trace impurity ions are shown to align with the larger mass ions. This unexpected behavior is derived analytically and simulated numerically using the MITNS (Multiple-Ion Transport Numerical Solver) code. The result suggests a potential advantage of edge-fueled p-B11 fusion in extracting high-Z impurities, and possible applications in plasma-based separation methods.

Code/Code comparison of impurity transport in EMC3 and DIVIMP**Poster PB029.

Recently, the global impurity migration code WallDYN was coupled to the 3D edge transport code EMC3-Eirene in order to make WallDYN applicable to 3D, non-toroidally symmetric, geometries. As part of the coupling, a new impurity transport module was implemented, which, in contrast to the existing impurity module, takes the inertia of the impurity into account, making it more suitable for heavy impurities like W. This new ‘kinetic’ impurity transport module uses the same physics as the 2D trace impurity transport code DIVIMP and therefore, to check the correctness of the implementation, a code/code benchmark was performed comparing the transport of Be- and W-impurities in EMC3 and DIVIMP. The comparison was performed for toroidally symmetric plasma that could be handled both by EMC3 and DIVIMP. Both codes were setup such that they would treat the transport of the impurities as similar as possible. Then the re-distribution of Be and W launched from different positions around the poloidal circumference of the first wall was calculated in both codes. To compare the resulting material re-distribution data () and judge the significance of any differences, was used in WallDYN calculations that model the evolution of the first wall due to erosion, deposition, re-erosion and re-deposition. These WallDYN calculations, performed using the from EMC3 or DIVIMP, showed the same major erosion and deposition areas and it can therefore be concluded that the new kinetic impurity transport module is implemented correctly and now allows us to make DIVIMP-like transport calculations using EMC3 in 3D.

3D global impurity transport modeling with WallDYN and EMC3-Eirene

The global impurity migration code WallDYN was coupled to the 3D scrape off layer plasma solver EMC3-Eirene in order to make WallDYN applicable to 3D, non-toroidally symmetric, geometries. To make EMC3-Eirene suitable for migration studies its impurity transport module was extended to not just compute the impurity density in the plasma but also their deposition on the wall tiles. Originally EMC3 treats the impurity transport in the plasma as a diffusion convection problem thereby assuming immediate equilibration with the local background plasma in order to derive the local parallel convection velocity. While this is a reasonable approximation for light elements, it is not suitable for the treatment of heavy element which need significant time to equilibrate their velocity and temperature with the background plasma. Therefore EMC3-Eirene was augmented by a new kinetic impurity transport module that handles acceleration and thermalisation in a manner similar to what is implemented in the 2D trace impurity transport code DIVIMP. This paper will first describe the modification introduced in EMC3-Eirene and then show the differences between the impurity transport models and the new possibilities now available in WallDYN to interpret migration studies in non-toroidally symmetric geometries .

Self-consistent gyrokinetic modeling of neoclassical and turbulent impurity transport

Trace impurity transport is studied with the flux-driven gyrokinetic GYSELA code (Grandgirard et al 2016 Comput. Phys. Commun. 207 35). A reduced and linearized multi-species collision operator has been recently implemented, so that both neoclassical and turbulent transport channels can be treated self-consistently on an equal footing. In the Pfirsch–Schlüter regime that is probably relevant for tungsten, the standard expression for the neoclassical impurity flux is shown to be recovered from gyrokinetics with the employed collision operator. Purely neoclassical simulations of deuterium plasma with trace impurities of helium, carbon and tungsten lead to impurity diffusion coefficients, inward pinch velocities due to density peaking, and thermo-diffusion terms which quantitatively agree with neoclassical predictions and NEO simulations (Belli et al 2012 Plasma Phys. Control. Fusion 54 015015). The thermal screening factor appears to be less than predicted analytically in the Pfirsch–Schlüter regime, which can be detrimental to fusion performance. Finally, self-consistent nonlinear simulations have revealed that the tungsten impurity flux is not the sum of turbulent and neoclassical fluxes computed separately, as is usually assumed. The synergy partly results from the turbulence-driven in–out poloidal asymmetry of tungsten density. This result suggests the need for self-consistent simulations of impurity transport, i.e. including both turbulence and neoclassical physics, in view of quantitative predictions for ITER.

Modelling of turbulent impurity transport in fusion edge plasmas using measured and calculated ionization cross sections

Turbulent transport of trace 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×B advection of the impurities by intermittent fluctuations and coherent filamentary structures (blobs) across the scrape-off-layer.

Analytic formulae for centrifugal effects on turbulent transport of trace impurities in tokamak plasmas

A local gyrokinetic description of the centrifugal effects on impurity transport in tokamak plasmas is presented, which extends previous models with the inclusion of the gradient of the background toroidal angular velocity in the equilibrium distribution. The equations are implemented in a gyrokinetic code. An analytical model is derived and formulae are proposed which allow the calculation of centrifugal effects on impurity transport in the limit where centrifugal effects are large only for heavy impurities in trace concentration, but are negligible for the bulk plasma. The analytic formulae are shown to be in quantitative agreement with the numerical results and are proposed for complementing present transport models.

Electromagnetic effects on trace impurity transport in tokamak plasmas

The impact of electromagnetic effects on the transport of light and heavy impurities in tokamak plasmas is investigated by means of an extensive set of linear gyrokinetic numerical calculations with the code GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and of analytical derivations with a fluid model. The impurity transport is studied by appropriately separating diffusive and convective contributions, and conditions of background microturbulence dominated by both ion temperature gradient (ITG) and trapped electron modes (TEMs) are analyzed. The dominant contribution from magnetic flutter transport turns out to be of pure convective type. However it remains small, below 10% with respect to the E×B transport. A significant impact on the impurity transport due to an increase in the plasma normalized pressure parameter β is observed in the case of ITG modes, while for TEM the overall effect remains weak. In realistic conditions of high β plasmas in the high confinement (H-) mode with dominant ITG turbulence, the impurity diffusivity is found to decrease with increasing β in qualitative agreement with recent observations in tokamaks. In contrast, in these conditions, the ratio of the total off-diagonal convective velocity to the diagonal diffusivity is not strongly affected by an increase in β, particularly at low impurity charge, due to a compensation between the different off-diagonal contributions.

Influence of the radio frequency ponderomotive force on anomalous impurity transport in tokamaks

Trace impurity transport in tokamaks is studied using an electrostatic, collisionless fluid model for ion-temperature-gradient and trapped-electron mode driven turbulence in the presence of radio frequency (rf) fields, and the results are compared with neoclassical predictions. It is shown that the inward impurity convective velocity (pinch) that is usually obtained can be reduced by the rf fields, in particular close to the wave resonance location where the rf ponderomotive force may be significant. However, the impurity diffusivity and convective velocity are usually similarly affected by the ponderomotive force, and hence the steady-state impurity density peaking factor −∇nz∕nz is only moderately affected by the rf fields.

A phenomenological interpretation of trace impurity transport

An interpretive theory of trace impurity transport in tokamaks is presented. It is based on an earlier phenomenological approach developed by the authors for describing tokamak plasma transport experiments. The present model is used to explain disparate phenomena observed in ALCATOR C and DITE in a unified phenomenological framework. Predictive numerical calculations are presented for DITE conditions. If experimentally confirmed, the model could be used to correlate plasma properties with trace impurity behaviour.

Anion Analysis of High Purity Water

The semiconductor, power and pharmaceutical industries all require ultra high purity water for process control. While the type of demineralizer system used and the specific contaminants of concern may differ, the problems associated with maintaining and monitoring process water quality are similar. The power industry has become increasingly concerned over the levels and transport of trace impurities in steam cycle systems as a result of corrosion problems experienced at supercritical generating units. On-line sodium analysis and continuous conductivity and acid conductivity measurements, used to monitor the high purity water in steam cycle systems, had not prevented the turbine and reheater corrosion in supercritical units. In order to identify the contaminants responsible, ion chromatographic (IC) techniques were developed for analysis of chloride, fluoride, sulfate, formate, acetate, and glycolate at the ppb and ppt levels (parts per billion and parts per trillion). In addition to a discussion of the 1C procedures developed, the paper provides a summary of sample collection and conditioning methods and identifies potential interferences. The paper also examines the relationships between conductivity (or its reciprocal, resistivity), acid conductivity and the level of ionic contamination and presents evidence demonstrating that specific analytical techniques such as 1C need to be used in conjunction with conductivity or resistivity monitoring of ultra pure water.

Trace impurity transport in doublet III beam heated plasma: Comparison of numerical simulations with decay time of titanium line emission in L- and H-mode discharges

Decay time τd of the line emissivity of Ti XX(259.3 Å) injected by a laser blow-off technique has a dependence on the electron density from the L-mode discharges to the H-mode discharges. Time behaviours of titanium line emissions are simulated with a numerical code using a density-dependent, anomalous diffusion coefficient DA and a neoclassical flow velocity in the impurity flux density. The DA of (4−5) ×1019/nc(m2/s) (the local electron density nc is in m−3) can well explain the density dependence of the experimental decay time.