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# 28th IAEA Fusion Energy Conference (FEC 2020)

10-15 May 2021
Nice, France
Europe/Vienna timezone
The Conference will be held virtually from 10-15 May 2021

## SOLPS studies of hydrogen radiation trapping in tokamak divertor plasmas and its influence on detachment threshold

12 May 2021, 14:00
4h 45m
Nice, France

#### Nice, France

Regular Poster Magnetic Fusion Theory and Modelling

### Speaker

Dr Andrey Pshenov (NRC "Kurchatov Institute")

### Description

Transition to the detached (or partially detached) divertor plasma regime is currently considered mandatory to keep peak heat loads to the divertor targets in an ITER-scale tokamak-reactor below the limit of $10–15\ \mathrm{MW/m^2}$ [1]. Reaching detachment implies low divertor plasma temperature $T_e \sim 1\ \mathrm{eV}$, high density $n_{e} \sim 10^{21}\ \mathrm{m^{-3}}$ and high radiation loss from the divertor volume. In the case of high heating power $P_{\mathrm{heat}}$, impurity seeding becomes mandatory to provide the desired level of power dissipation inside the divertor. Edge transport codes used to interpret the experimental data and study various aspects of the detachment physics typically presume that the edge plasma is transparent for both impurity and hydrogen radiation. Whereas this assumption holds for the seeded impurity, unless some exotic scenarios like the liquid metal divertor or solid target melting during transient events are considered, it is apparently violated for the hydrogen isotopes. As detachment approaches, the divertor plasma gradually becomes opaque to the Lyman lines of the hydrogen isotopes and radiation transport becomes an important part of the problem influencing both power and particle balance inside the divertor volume [2].
We have revived the radiation transport block embedded into the SOLPS4.3 code package [3], tested it against the RADTRANSP code [4] and applied it to study the influence of the Lyman alpha ($Ly-\alpha$) radiation absorption on the transition to the detached divertor plasma regime in a DIII-D-scale tokamak [5]. It was demonstrated that the $Ly-\alpha$ photon absorption results in a noticeable (~30%) increase in the separatrix plasma density nesep required to reach the detachment in pure deuterium plasma. This result is illustrated in Fig. 1, where dependence of the total plasma flux to the outer divertor target plate on $n_{e}^{\mathrm{sep}}$ is plotted for three different assumptions on radiation transport: i) plasma transparent to the $Ly-\alpha$ radiation (labeled “transparent”); ii) plasma completely opaque to the $Ly-\alpha$ radiation (labeled “opaque”); and iii) detailed radiation transport modeling (labeled “CRM”). Transition from increase to decrease of the plasma flux to the target with increasing density, the so-called “rollover”, marks the transition to the detached regime.

Previous studies demonstrated virtually no influence of the radiation opacity on the detachment threshold in tokamaks with carbon plasma-facing components (PFCs) and attributed this finding to an almost exact compensation of the photon-assisted ionization with increasing recombination [3]. On the contrary, we have shown that the main reason behind the observed lack of opacity influence on the detachment threshold is increasing chemical erosion of the carbon PFC, resulting in compensation of the hydrogen radiation loss suppression by increased impurity radiation. Moreover, this compensation does no longer occur naturally in nowadays full-metal devices with impurity seeding, where the impurity concentration $c_{z}$ is a controllable parameter. The opacity in such devices results in an increase of $n_{e}^{sep}$ / $c_{z}$ detachment thresholds.
In the present contribution, these results are extended to allow for $Ly-\beta$ and $Ly-\gamma$ photon transport since these lines exhibit a noticeable degree of opaqueness in the recent experiments on JET [6]. Whereas Stark broadening is relatively unimportant for $Ly-\alpha$ it influences the $Ly-\beta$ and $Ly-\gamma$ transport substantially [7]. Hence, we have implemented Stark broadening in the radiation transport module of the SOLPS4.3 code package. We have also supplemented this module with a previously neglected photon reflection model further increasing the fraction of photons absorbed by the edge plasma. Both Stark broadening and reflection implementations are tested against the RADTRANSP code, yielding excellent agreement. Example of such test can be found in Fig. 2 where the spatial distribution of the fractional abundances of different excited states (with principal quantum number from 2 to 6) through a 2 meter long slab with fixed background plasma parameters ($n_e = 10^{20}\ \mathrm{m^{-3}}$, $T_e = 5\ \mathrm{eV}$ and $n_{D} = 10^{18}\ \mathrm{m^{-3}}$) obtained by both codes are compared.

The resulting model is applied to study the radiation transport influence on the detachment process in a DIII-D scale tokamak, highlighting the influence of $Ly-\beta$ and $Ly-\gamma$ opacities as well as the importance of allowing for Stark broadening and photon reflection. Finally, the results are compared with simplified simulations utilizing the escape factor approach aiming to verify the promising experimental findings from JET, which indicate that the influence of the opacity can be roughly captured by introducing the escape factors dependent on the plasma temperature in the vicinity of the target surface exclusively [6].

References
[1] Pitts R A, Bonnin X, Escourbiac F, et al. 2019 Physics basis for the first ITER tungsten divertor Nucl. Mater. Energy 20 100696
[2] Terry J L, Lipschultz B, Pigarov A Y, et al., 1998 Volume recombination and opacity in Alcator C-Mod divertor plasmas Phys. Plasmas 5 1759–66
[3] Kotov V, Reiter D, Kukushkin A S, et al. 2006 Radiation absorption effects in B2-EIRENE divertor modelling Contrib. to Plasma Phys. 46 635–42
[4] Marenkov E, Krasheninnikov S and Pshenov A 2018 Multi-level model of radiation transport in inhomogeneous plasma Contrib. to Plasma Phys. 58 570–7
[5] Pshenov A A, Kukushkin A S, Marenkov E D and Krasheninnikov S I 2019 On the role of hydrogen radiation absorption in divertor plasma detachment Nucl. Fusion 59 106025
[6] Lomanowski B, Groth M, Coffey I H, et al. 2020 Interpretation of Lyman opacity measurements in JET with the ITER-like wall using a particle balance approach Plasma Phys. Control. Fusion in press https://doi.org/10.1088/1361-6587/ab7432
[7] Rosato J, Reiter D, Kotov V, et al. 2010 Progress on Radiative Transfer Modelling in Optically Thick Divertor Plasmas Contrib. to Plasma Phys. 50 398–403

Country or International Organization Russia NRC "Kurchatov Institute"

### Primary authors

Dr Andrey Pshenov (NRC "Kurchatov Institute") Andrei Kukushkin (NRC "Kurchatov Institute")

### Presentation Materials

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