STRAHL modeling of iron impurity transport with on- and off-axis heating during the first divertor campaign on Wendelstein 7-X

Abstract

Impurity transport characterization and ultimately impurity control is critical to the future prospects of magnetic confinement fusion energy. In particular for an optimized stellarator like Wendelstein 7-X the characterization of impurity transport is vital for identifying potential advanced scenarios where ideally both screening near the edge and core flushing of impurities can be realized. The experimental characterization of impurity transport in W7-X can be used to validate neoclassical simulations and to compare with turbulent transport predictions.

Overall across the entire ECRH on- to off-axis dataset as either more ECRH power is moved off-axis or less total ECRH power is deposited both the $\frac{T_{i}}{T_{e}}$ and the $\tau_I$ increases. As ECRH was moved off-axis there was an increase in the $\frac{T_{i}}{T_{e}}$ ratio for $\rho$ $\leq$ 0.6 due to the strong electron temperature variation in the core, $\rho$ $\leq$ 0.4, with changes of as much as $\sim$ 1.5 keV. This strong core electron temperature flattening had a marginal effect on the observed iron impurity transport time with $\tau_I$ enhanced by at most 27\% as core T$_e$ was decreased. On the other hand even though the purely on-axis ECRH power scan from 4.9 to 2.8 MW reduced the core T$_e$ a nearly identical amount as the 4.9 MW on- to off-axis dataset, the resulting global transport time enhancement was substantially larger for the on-axis power scan. The combination of the similar $\sim$ 900 eV drop in core T$_e$ during the 4.9 MW on- to off-axis dataset, the larger enhancement in the global transport time for the on-axis power scan, and the significant variation in the $\frac{T_{i}}{T_{e}}$ ratio outside $\rho$ $\geq$ 0.6 for the on-axis power scan all indicate that the kinetic profiles' magnitude/shape outside mid-radius has a greater impact on the observed iron impurity transport than core T$_e$ variations.

To better characterize these observational results a least squares minimization was performed to infer the anomalous transport profiles that most accurately produces the measured iron line emission using the transport code STRAHL. These experimentally observed iron spectral signals could only be well-matched when the anomalous diffusion channel was included within the least squares inference with this transport channel clearly dominating all other channels. The fact that an ordinary, charge-independent anomalous diffusion was necessary to match the iron line emission in combination with the dominance of the anomalous diffusive channel strongly suggests that turbulent transport is the main transport mechanism during these W7-X plasma discharges in accordance with gyrokinetic simulations performed by \citep[García-Regaña et al.][]{garcia-regana_2021}. Although the inferred anomalous diffusion profiles are still consistent with the concomitant increase of global transport time ($\tau_I$) and the ion-to-electron temperature ratio ($\frac{T_{i}}{T_{e}}$), the inferred profiles are only distinguishable in the on-axis ECRH power comparison when the total uncertainties are considered.

Finally to give confidence to the aforementioned inferred anomalous diffusion profiles numerous sensitivity studies were performed on the least squares minimization routine using both synthetic and experimentally derived data. The synthetic sensitivity tests demonstrated that for the inferred anomalous diffusion profile the 1-sigma T$_e$ profile shifts had minimal impact on the inferred accuracy, the LBO injection timing \& temporal shape had the largest influences on the profile accuracy, and the STRAHL edge parameterization also induced a large variation. These results from the synthetic sensitivity tests used to determine the accuracy of the least squares fits and to estimate the uncertainty in the anomalous diffusion profile were corroborated by the variational tests performed on experimental data.