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Modest effects of deuterium line radiation trapping in MAST Upgrade tokamak Super-X and snowflake (SF) divertor plasmas are found using SOLPS-EIRENE and UEDGE code divertor plasma modeling (1, 2), and CRETIN code (3) radiation transport and collisional-radiative modeling. In MAST-U, both the Super-X and SF divertor plasmas are predicted to reach highly radiative (detached) regimes at lower upstream densities as compared to standard divertor configurations (1,2). Lyman series line radiation trapping in divertor increases deuterium ionization rate, reduces recombination and radiation volumetric rates. This may increase divertor detachment density threshold and diminish the advanced divertor geometry benefits (4-7). The CRETIN and UEDGE modeling of the detached Super-X and SF divertors shows that 1) divertor plasma properties are modified insignificantly ( $\le 10$ \%) when opacity effects are included; 2) however, deuterium Lyman radiation trapping is non-negligible and may be experimentally detectible. Divertor radiation trapping is likely to play an important role in future reactor-scale divertor tokamaks, including ITER (8). Model validation experiments are planned in MAST-U, as part of a comprehensive advanced divertor research program (9).
Plasma opacity $\tau=L / \lambda_{MFP}$, (where $L$ is spatial scale and $\lambda_{MFP}$ is a photon mean free path (MFP)) scales with $(L n_0)$, where $n_0$ is neutral (atomic) deuterium density.
In the SOLPS and UEDGE models of a 2.5-5 MW NBI-heated 1 MA H-mode plasmas, high $n_0 \le 10^{19}-10^{21} m^{-3}$ are found in detached regimes in Super-X and SF divertor configurations (1,2).
An expanded tightly baffled outer divertor leg plasma volume with a radial spatial scale of $L \sim 60$ cm is present in the Super-X divertor (1).
In the SF divertors, the primary and secondary strike points land on vertical targets in the divertor throat, leading to high recycling neutral fluxes and densities (2).
The impact of Lyman line radiation transport on divertor plasma parameters was studied with UEDGE and found to be weak.
A Lyman-$\alpha$ escape factor model in UEDGE (10) introduces corrections to ionization, recombination and electron heating rates calculated by CRETIN based on parametrized optical depth $r_{\tau} \sim \int n_0 \; dx$ (integration is to the nearest boundary), as shown in Fig. 1 (a-c) for the Super-X, SF-plus and SF-minus configurations.
In the Super-X configuration, it is the outer leg that is mostly affected, where the optical depths reach $r_{\tau} \le 1000$.
In the SF-plus and SF-minus, insignificant opacity is predicted in the strike point regions and between the X-points, with the optical depths up to 100.
At detached Super-X divertor conditions in MAST-U, radiation trapping changes neutral and plasma properties, however, these changes appear to be insignificant.
Fig. 1 (d) shows $T_e, n_e$ and $n_0$ changes on the divertor plate normalized to the no radiation trapping case properties.
Fig. 1 (e) shows $T_e$ profiles along the separatrix (along the connection length) between the X-point and the plate for different densities, with and without impurities (carbon), and with and without radiation trapping.
Divertor heat and particle fluxes and detachment trend are weakly affected as well.
Detailed continuum and line radiation transfer was studied with CRETIN, and the results demonstrate that whereas Lyman series line radiation absorption, scattering, and reemission take place, the impact on kinetic atomic rates and level populations is modest.
CRETIN was used with plasma and neutral backgrounds modeled by SOLPS and UEDGE for the Super-X configuration (1), and UEDGE for SF configurations (2).
A deuterium atom model with $n \le 20$ and sublevels was used.
In the SOLPS-EIRENE detached Super-X divertor model with 2.5 MW NBI heating, small Lyman-$\alpha$ optical depth $\tau_{\nu} = \int \kappa_{\nu} \rho dx \le 2$ (here $\kappa_{\nu}$ is absorption coefficient and $\rho$ is mass density) were observed in radial and poloidal directions.
In the SOLPS detached Super-X divertor model with 5 MW NBI heating, neutral densities in the outer leg were higher, hence the Lyman-$\alpha$ photon MFP was $\le 10$ cm, leading to some trapping in the Lyman-$\alpha$ line center with modest Lyman-$\alpha$ optical depth $\tau_{\nu} \le 10$ above the outer target plate.
In the UEDGE detached Super-X model with 2.5 MW NBI, higher recycling coefficients and no pumping, neutral densities were higher than in the SOLPS-EIRENE model, and the trapping was stronger ($\tau_{\nu} \le 1000$), leading to visible dips in Lyman series profiles.
In the SF-plus and SF-minus divertor models with detached strike points, the plasma, neutral and radiation fields were highly non-uniform because of the multiple dissimilar magnetic regions.
Lyman-$\alpha$ photon MFP was down to several cm in the strike point regions, resulting in weak line center trapping (optical depth between divertor throat sides (targets) $\tau_{\nu} \le 2$). In both Super-X and SF divertor simulations, the inclusion of radiation transport led to the increased $n\ge2$ atomic level populations (up to 20-100), and a modest reduction (30-50 \%) of Lyman series radiative flux on the divertor plates.
The detailed CRETIN radiation transfer calculations used three models for the line shape due to thermal Doppler broadening, Stark broadening due to plasma electron and ion microfields, and the Zeeman splitting due to magnetic field.
At MAST-U divertor conditions, radiation transfer was weakly affected, the differences in Lyman intensities and radiated power were less than 5-10 \% .
However, the Lyman line shapes were significantly altered: while Doppler broadening was less than 0.005 eV, and Zeeman splitting at mostly toroidal field $\sim 0.5$ T was small, Stark broadening at detached divertor densities $\le 10^{20} m^{-3}$ could be potentially measured with spectroscopic diagnostics.
In summary, if the present CRETIN and UEDGE predictions for the Super-X and SF divertors are validated in MAST-U experiments, detached plasma properties are not expected to be modified significantly as Lyman-$\alpha$ optical depths are modest. However, if neutral densities are increased, an increased opacity may lead to stronger non-linear plasma effects.
This work is supported by the US DOE under Contract DE-AC52-07NA27344 and the RCUK Energy Programme Grant Number EP/P012450/1 and EURATOM.
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| Affiliation | Lawrence Livermore National Laboratory |
|---|---|
| Country or International Organization | United States |
