Impurity Seeding in ASDEX Upgrade Tokamak Modeled by COREDIV Code

Contrib. Plasma Phys. 56, No. 6-8, 772 777 (2016) / DOI 10.1002/ctpp.201610008 Impurity Seeding in ASDEX Upgrade Tokamak Modeled by COREDIV Code K. Gała zka 1, I. Ivanova-Stanik 1, M. Bernert 2, A. Czarnecka 1, A. Kallenbach 2, R. Zagórski 1, and the ASDEX Upgrade Team 1 Institute of Plasma Physics and Laser Microfusion, ul. Hery 23, 01-497 Warsaw, Poland 2 Max-Planck-Institut für Plasmaphysik, Boltzmannstrasse 2, D-85748 Garching, Germany Received 20 September 2015, revised 07 December 2015, accepted 19 December 2015 Published online 08 July 2016 Key words Tokamak, integrated modelling, core plasma, edge plasma, ASDEX Upgrade, impurity seeding, impurity transport. The self-consistent COREDIV code is used to simulate discharges in a tokamak plasma, especially the influence of impurities during nitrogen and argon seeding on the key plasma parameters. The calculations are performed with and without taking into account the W prompt redeposition in the divertor area and are compared to the experimental results acquired on ASDEX Upgrade tokamak (shots #29254 and #29257). For both impurities the modeling shows a better agreement with the experiment in the case without prompt redeposition. It is attributed to higher average tungsten concentration, which on the other hand seriously exceeds the experimental value. By turning the prompt redeposition process on, the W concentration is lowered, what, in turn, results in underestimation of the radiative power losses. By analyzing the influence of the transport coefficients on the radiative power loss and average W concentration it is concluded that the way to compromise the opposing tendencies is to include the edge-localized mode flushing mechanism into the code, which dominates the experimental particle and energy balance. Also performing the calculations with both anomalous and neoclassical diffusion transport mechanisms included is suggested. 1 Introduction and physical model For a controllable and safe operation of a future nuclear fusion power plant based on a tokamak magnetic field configuration (ITER, DEMO) impurity seeding is the most feasible mechanism of power exhaust which also provides a solution for limiting the heat load delivered to the divertor plate [1, 2]. In the all-tungsten ASDEX Upgrade (AUG) tokamak several experiments with seeding were performed to study these phenomena [3, 4]. Similarly as in our previous work [5] the aim was to reproduce the experimental plasma parameters with the use of the COREDIV code [6], but this time the calculations were extended to an Ar-seeded discharge. COREDIV solves 1D radial transport equations with semi-empirical transport coefficients for densities and temperatures, modified to describe the transport barrier of plasma and impurities in the core region. In the scrapeoff layer (SOL) 2D multi-fluid transport equations developed by Braginskii and rate equations are solved for all ionization states of impurities. The balance between the core and the SOL regions is done self-consistently by imposing appropriate continuity boundary conditions at the separatrix. Details of the model can be found elsewhere [5, 6]. In the presented simulations the main focus was to study the steady state plasma parameters and the activity of edge localized modes (ELMs) was neglected (time-averaged effective transport coefficients are used). Since tungsten has a huge impact on radiative heat exhaust as an impurity [5,7] and AUG has all plasma facing elements made of W, improving the model for accurate accounting of W production is of great importance. Here a simple W prompt redeposition model is employed. It follows a simple modification of the tungsten sputtering This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Corresponding author. E-mail: krzysztof.galazka@ifpilm.pl, Phone: +48 (22) 638 1460

Contrib. Plasma Phys. 56, No. 6-8 (2016) / 773 yield at the divertor plate Y according to Y = (1 f prompt ) Y, where the probability that a particle is redeposited within the first gyro-orbit is given by: f prompt = 1 1+(λ ion /ρ W +) 2, (1) where λ ion is the ionization length calculated from ionization frequency and average thermal velocity and ρ W + is the gyro-radius of a singly-ionized W in perpendicular magnetic field [8, 9]. Modeling results for both cases, with and without prompt redeposition, were compared against the experimental data. 2 Results and discussion As a reference point for modeling two discharges performed on AUG were taken: #29254 with N seeding and #29257 with Ar seeding [3]. Time evolution of both discharges is presented in Fig. 1. In case of N seeding the time plot can be divided in 3 stages according to 3 levels of seeded impurity gas puff: without seeding (2.3-2.5 s), with lower seeding level (3.7-4.0 s) and with higher seeding level (4.6-4.8 s). Similarly, in case of Ar-seeded discharge 2 stages are present: without seeding (2.5-2.7 s) and with seeding (3.5-3.8 s). At this reference time periods plasma parameters were stable enough to be averaged and compared to the calculated values. Fig. 1 Time traces of two discharges used for COREDIV modeling with N-seeding, shot #29254 (left) and Ar-seeding, shot #29257 (right) as presented in [3]: a) and d) heating power and radiative power losses, b) and e) gas puff rates and N concentration from density measurements by charge exchange spectroscopy, c) and f) average effective charge, H 98 factor and the ratio of electron to Greenwald densities. The dashed areas indicate averaging limits. Calculations assumed experimental external heating power, which in both cases was rounded up to 14 MW, as well as average electron density, calculated from the experimental Greenwald density ratio, which was in all cases close to 8 10 19 m 3. The value of the confinement quality factor, H 98, changed from 0.85 for both discharges before seeding up to 1.2 and 1.0 for N-seeded and Ar-seeded discharge, respectively. Therefore the first step was to investigate the influence of its change on plasma parameters. 2.1 Confinement and dilution The experimental data presented in Fig. 1 show that during the steady state stages for both discharges the H 98 factor (IPB98(y, 2)) is constant. Its value increases when the seeding gas flux is started. Improvement of the confinement due to impurity seeding is a known fact [10]. As in COREDIV the H 98 is a directly controlled, fixed

774 K. Gała zka: COREDIV simulations of impurity seeding in AUG input parameter at first we checked how does it influence the radiation fraction, f rad, tungsten concentration, c W, and electron temperature on the divertor plate, Te plate. Figures 2 a), b) and c) show that almost no change in these parameters according to different H 98 was observed. In Fig. 2 d) T e profiles for simulations with different H 98 are presented along with the fitted experimental data for shot #29254 before and after N-seeding. As can be seen, there is an influence of the change of H 98 on the plasma profiles. Improvement of the confinement leads to a general increase of the temperature profile. Simulation shows also that increased impurity concentration c N has a similar effect due to dilution of plasma. In the experimental results both of these effects are responsible for a shift of T e profile for the seeded stage. Higher T e values in the central region suggest that despite no intentional impurity seeding there might be a substantial amount of unintentional impurities leading to the higher profile peaking in the unseeded case. It is justified to expect some amount of light impurities like C, O or B with concentrations as high as 0.5% [7]. For further calculations the value H 98 =1.1was used. Fig. 2 Left - the influence of H 98 factor on the plasma parameters as a function of N seeding: a) radiation fraction f rad,b) tungsten concentration (c W) and c) temperature of the target (Te plate ). Right - d) comparison of T e profiles for different H 98 factors and impurity concentration levels c N with experimental data for shot #29254. 2.2 Prompt redeposition modeling vs. experimental data The key global plasma parameters for unseeded and seeded discharges are presented in Fig. 3. As mentioned, three levels of seeding are investigated for N and two for Ar. In general, the gas puff level for the experimental data points was chosen to match the measured values of impurity concentration, c N/Ar, and the average effective charge, Z eff, shown in parts c), g) and b), f) of Fig. 3, respectively. Except for the case of low seeding in N-seeded discharge, it can be seen that a reasonable agreement between the experimental data and the results of modeling without prompt redeposition phenomenon could be established also for the radiative power losses: total Prad tot, the core contribution Prad core SOL and the SOL contribution Prad. For the case of high seeding in N-seeded discharge calculations show that the observed radiation levels would require significantly higher c N than measured. In this case uncertainties of c N and Z eff are slightly larger, mostly due to lack of stability of average electron density and H 98 factor (see Fig. 2 c). Nevertheless, this fact confirms that there should be some amount of other than N impurities making up for the experimental Z eff and radiative power losses [7]. A small discrepancy between the experiment and simulation for the unseeded stages of both discharges is due to neglecting the light impurities like O and B - in our calculations only a constant gas puff of C (1.5 10 20 at/s) is included to make up for the initial Z eff value. In the case of low seeding in N-seeded discharge the simulated Prad SOL and Prad tot seem to be underestimated. However, referring to the measurements of Prad tot reported in Fig. 6 in [3] the experimental values acquired by deconvolution of foil bolometers measurements prior and during N seeding are 5.2 MW and 10.7 MW, respectively, which is much closer to the calculations without prompt redeposition. If these values are closer to reality than the ones from the time traces, also the Prad SOL value would be in a better agreement with calculation. For the high seeding level the difference between the cases with prompt redeposition on and off vanishes due to low temperature in the divertor area, leading to a negligibly small f prompt values (c.f. [11]). In the case of Ar-seeding the discrepancies between the measured and simulated values of radiation losses in the

Contrib. Plasma Phys. 56, No. 6-8 (2016) / 775 case of Ar-seeded discharge with no prompt redeposition are smaller than for N. The reason is a higher Z: the influence of Ar radiation is more pronounced than of the low Z unintentional impurities. Moreover, it radiates partially in the core and has less impact on SOL radiation, as visible in Fig. 3 e). Fig. 3 Results of COREDIV modeling (horizontally-connected points) together with experimental data (vertically-connected points) for the selected time averages: 3 seeding levels are considered in the case of N-seeded discharge (#29254) and 2 for Ar-seeded discharge (#29257). The calculations were performed without (prompt-off, open symbols) and with (prompt-on, filled symbols) W prompt redeposition model. As the prompt redeposition process affects the sputtering yield of W it is expected that the largest influence of turning the prompt redeposition process on will be seen in the W concentration c W. Indeed, at low seeding levels for both impurities c W is much different: the production of W in the divertor is lower and the saturation of the c W (Γ puff ) dependency is shifted to the higher gas puff when the prompt redeposition is taken into account. It must be noted that the only source of W in the code is by sputtering on the divertor plate, no production from limiters is assumed. This approach is justified if the conditions close to the wall are moderate in terms of electron temperature and density and do not lead to a significant wall erosion. Therefore an overall better agreement for the model without prompt redeposition can be explained by allowing the divertor W source to account also for the wall-sputtered material, if present in AUG. Unfortunately, neither of the models matches the experimental c W, which show much smaller values, especially for the seeded cases. Moreover, as it was previously found that W is responsible for the major part of radiation in the core [5, 7], a change in c W dramatically affects the Prad core value causing underestimation of the radiated power. This issue will be discussed in a dedicated section. 2.3 W concentration issue Assuming that the measurements of c W are reliable (in this case they are performed by spectroscopy of line radiation and confirmed by the quasicontinuum radiation) COREDIV overestimates the c W value. However, a simple limitation of W production (for example by prompt redeposition) leads to underestimation of radiation losses, as mentioned before. It will be seen in Tab. 1 that increased impurity diffusion coefficient in the SOL, Dr SOL, leads to a decrease in c W while maintaining the same Prad tot. It indicates that the transport phenomena play an important role and they can be the key to improving the agreement between the experimental data and calculations. For instance, from the recent modeling results for JT-60SA tokamak with W wall [12] it was found that c W is diminished and Prad tot grows even higher at a sufficiently large gas puff (Ne) when the transport model in the core includes also the neoclassical diffusion (in present calculations the anomalous diffusion was assumed

776 K. Gała zka: COREDIV simulations of impurity seeding in AUG the dominant transport mechanism in the core). Here the main issue to improve is modeling of the ELM flushing. Now it is not included in the code and introducing a time dependent pedestal would seriously affect the particle and energy balance, especially for W. As ELM effects dominate the experiment results, the penetration of W into the core plasma will be hampered. This issue presents a challenge and a direction of evolution of the code in the future. Fig. 4 W flux to divertor plate for the case of N-seeded and Ar-seeded discharge a) and b), respectively. The simulated W 0 flux for each seeding stage can be read out from the intersection of the calculated dependencies with the vertical lines. c) - electron temperature profiles on the target calculated without prompt redeposition process. In c) the first two cases were chosen to match closely the experimental seeded stages (in case of N - lower seeding) and to have the same total radiated power (Prad). tot The last case (N, Prad tot = 6.3 MW) can be regarded as without seeding. Figure 4 presents the total simulated W influx from the divertor for N and Ar together with temperature profiles on the divertor plate. W flux is higher in the case of Ar seeding, which agrees with the experimental data for the average neutral W influx close to the outer strikepoint [3]. Although the direct comparison to the experimental fluxes is impossible, the ratio of W 0 flux before and during the seeding stage (low seeding in case of N) can be compared to the experiment. The measured values of the ratio are 0.6 for N and 0.5 for Ar seeding. The values of the ratio calculated for the modeling without prompt redeposition model almost reproduce this values (0.61 for N and 0.52 for Ar). With prompt redeposition taken into account this ratio drops to 0.17 for N and 0.16 for Ar, which is much smaller than the experimental values. Also electron temperature profiles on the target calculated without prompt redeposition modeling agree reasonably well (c.f. Fig. 5 in [3]). It was possible to reproduce the broader Te plate peak for the Ar-seeded discharge. In both cases the maximum Te plate in the first 8 cm of the target is about 15 ev compared to about 30 ev in the unseeded case and corresponds well to the experimental data. 2.4 The influence of impurity radial diffusion To get a better insight into the interdependence of W concentration and radiative heat losses calculations with different radial impurity diffusion coefficients in the SOL, Dr SOL, were performed for the case with N seeding. The precise value of Dr SOL is unknown and in AUG is in the range of a few m 2 s 1 [9]. By assuming a constant Prad tot and changing DSOL r it was found that the share of the SOL radiation increases when increasing Dr SOL (see Table 1). This fact can be explained by the interdependence of transport and radiation in the SOL. Increased collisionality in the SOL leads to higher radiation losses which reduce the electron temperature. As lower temperature affects the transport, the mechanism can be considered as a negative feedback loop, leading to a dynamic equilibrium between the radiated energy and thermal energy influx due to particle flux. With increased Dr SOL the

Contrib. Plasma Phys. 56, No. 6-8 (2016) / 777 same total radiation level is achieved for a higher gas puff value. This corresponds to a higher Z eff and a lower average W concentration. It can be concluded that the transport phenomena in the SOL have a large impact on the global plasma state. Table 1 The shares of the core and the SOL radiation for different set values of radial diffusion coefficient for impurities in the SOL Dr SOL. The gas puff was adjusted to keep the total radiated power the same - here 10.5 MW. Also the resulting Z eff and c W values are presented. The calculations were performed with no prompt redeposition. D SOL r [m 2 s 1 ] 0.5 0.75 1.0 P tot rad [MW] 10.5 10.5 10.5 P core rad [MW] 7.85 6.5 5.3 P SOL rad [MW] 2.65 4.0 5.2 Z eff 2.4 2.6 2.8 c W [%] 0.031 0.024 0.019 Γ N [ 10 22 el/s] 1.56 2.44 3.27 3 Conclusions The COREDIV code has been used to simulate nitrogen- and argon-seeded discharges in ASDEX Upgrade tokamak. The influence of incorporating W prompt redeposition process into the model was investigated. The calculations without prompt redeposition show a better agreement with the main plasma parameters, however they tend to overestimate the W concentration when compared to the experimental data. The prompt redeposition process is indeed able to limit the W sputtering rate and lower the W concentration, but also seriously affects the radiative power losses. By analyzing the influence of transport coefficients like impurity diffusion coefficient in the SOL on the radiative power loss and average W concentration it was concluded that the way to improve the agreement between the experiment and simulation is to include an ELM mechanism into the code by a timedependent pedestal. Also performing the calculations with both anomalous and neoclassical diffusion transport mechanisms included is suggested. Performed calculations show that when interpreting the experimental data the availability of as many as possible plasma parameters is crucial for global fitting. Still, the space for improvement of the model remains open, especially the transport phenomena near the pedestal, which would better match the present experiments and strengthen the extrapolations to larger devices. Moreover, the benchmarking of COREDIV for ASDEX Upgrade tokamak for single impurity seeding paves the way to model multiple seeding impurity experiments, which are of high importance for radiative power exhaust in reactors. Acknowledgements This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This scientific work was partly supported by Polish Ministry of Science and Higher Education within the framework of the scientific financial resources in the year 2015 allocated for the realization of the international co-financed project. References [1] R. Wenninger et al., Nucl. Fusion 55, 063003 (2015). [2] H. Zohm et al., Nucl. Fusion 53, 073019 (2013). [3] A. Kallenbach et al., Plasma Phys. Control. Fusion 55, 124041 (2013). [4] G. Tardini et al., Plasma Phys. Control. Fusion 55, 015010 (2013). [5] R. Zagórski, R.Neu, and ASDEX Upgrade Team, Contrib. Plasma Phys. 52, 379 (2012). [6] R. Stankiewicz and R. Zagórski, Czech. J. Phys. 52, 32 (2002). [7] L. Casali et al., EPJ Web of Conferences 79, 01007 (2014). [8] G. Fussmann et al., Plasma Physics and Controlled Nuclear Fusion Research 1994 Vol. 2 (IAEA, Austria, 1995). [9] R. Dux, A. Janzer, and T. Pütterich, Nucl. Fusion 51, 053002 (2011). [10] R.L. Neu et. al., IEEE Trans. Plasma Sci. 42, 552 (2014). [11] R. Zagórski et al., submitted to Fusion Eng. Des. [12] K. Gała zka et al., to be submitted to J. Nucl Mater.