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Divertor power spreading in DEMO reactor by impurity seeding
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Divertor power spreading in DEMO reactor by impurity seeding ˛ Roman Zagórski ∗ , Krzysztof Gałazka, Irena Ivanova-Stanik Institute of Plasma Physics and Laser Microfusion, Hery Str. 23, 01-497 Warsaw, Poland
h i g h l i g h t s • The COREDIV code has been used to simulate DEMO inductive discharges with different impurity seeding (Ne, Ar, Kr) and different sputtering models (with and w/o prompt re-deposition process).
• It has been shown that only for Ar and Kr seeding it is possible to achieve H-mode plasma operation with acceptable level of the power to the tungsten target plates.
• For neon seeding, such regime of operation seems not to be possible. • Prompt re-deposition model extends the DEMO operation window.
a r t i c l e
i n f o
Article history: Received 29 July 2015 Received in revised form 29 February 2016 Accepted 14 March 2016 Available online xxx Keywords: Numerical modeling Edge plasma Impurity seeding Fusion reactor
a b s t r a c t Numerical simulation with COREDIV code of DEMO H-mode discharges (tungsten divertor and wall) are performed considering the influence of seeding impurities with different atomic numbers: Ne, Ar and Kr on the DEMO scenarios. The approach is based on integrated numerical modeling using the COREDIV code, which self-consistently solves radial transport equations in the core region and 2D multi-fluid transport in the SOL. In this paper we focus on investigations how the operational domain of DEMO can be influenced by seeding gasses. Simulations with the updated prompt re-deposition model implemented in the code show that only for Ar and Kr, for high enough radial diffusion in the SOL, it is possible to achieve H-mode plasma operation (power to the SOL> L-H transition threshold power) with acceptable level of the power to the target plates. For neon seeding such regime of operation seems not to be possible. © 2016 EURATOM. Published by Elsevier B.V. All rights reserved.
1. Introduction The operating point of a future DEMO fusion reactor will be optimized to fulfill the following criteria: (1) maximize the fusion power output, (2) allow for an H-mode operation through keeping the power flux to scrape-off layer (SOL) considerably higher than H-L transition threshold and (3) minimize the heat load to divertor plates [1]. One of the ways to manage the plasma performance and power exhaust to realize these requirements is by controlling the impurity content in the plasma. From our earlier simulations [2], it comes out that the level of the power going to the scrape-off layer (SOL) depends strongly on the tungsten radiation in the core, the latter being quite significant. It is expected that by increasing the seeding level, the radiation in the SOL region is increased leading to the decrease of the power to
∗ Corresponding author. E-mail address: [email protected] (R. Zagórski).
the plate and tungsten production. But, smaller tungsten concentration in the core results in the reduction of the tungsten radiation and increase of the power to the SOL, which in turn, increases the tungsten production. In order to account properly on this strongly nonlinear behavior, only integrated approach can to be used taking into account the coupling between the core and edge regions. In this paper, numerical simulations with COREDIV code [3] of DEMO discharges with tungsten as armor material (divertor and wall) for H-mode scenarios are presented. Calculations are performed for inductive DEMO 2012 steady-state configuration [4] and focus on two especially important issues related to DEMO operation: finding an appropriate kind and amount of seeded impurity to mitigate the heat load to the divertor to an acceptable level (5–10 MW/m2 ) [5], [6] and replacing the intrinsic W impurity in the core which by high line radiation might lead to radiative collapse [7]. In existing devices (JET, ASDEX-Upgrade) a beneficial influence of nitrogen puffing on lowering the L-H threshold, improvement in the pedestal stability and reduction of the divertor heat load was observed [8]. This results were reproduced by numerical modeling
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Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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by COREDIV code [9], which brought some insight in the JET operational domain [10]. COREDIV was applied also to DEMO scenarios to study various impurities (Ne, Ar, Ni) and the main conclusion was that for DEMO an element with atomic number Z ≥ 18 would be suitable [2], [3]. Referring to a recent publication on an optimal impurity mix for DEMO [1] we would like to present here a systematic study on Kr seeding and compare it to Ar and Ne impurities analyzed before. Additionally, the calculations included a simple model for prompt re-deposition processes for W on the divertor plate, as described below. 2. Model The simulations were performed by using COREDIV code which is based on an integrated approach coupling the radial transport in the core and the 2D multifluid description of the SOL. The interaction between seeded and intrinsic impurities as well as the effect of the impurities on the fusion power significantly affects the particles and energy flows in the plasma, therefore the self-consistent approach is essential for a correct evaluation of the average power to the divertor plate. As this work is a follow-up of our previous calculations the detailed description and parameters used can be found in Refs. [2,3] and only the main points of the model are reported here. In the core, the 1D radial transport equations for bulk ions, for each ionization state of impurity ions and for the electron and ion temperatures are solved. For auxiliary heating paraboliclike deposition profile is assumed and heating due to alpha power is calculated self-consistently taking into account the dilution effect due to helium transport. The energy losses are determined by Bremstrahlung and synchrotron radiation together with ionization and line radiation losses. The energy and particle transport are defined by the local transport model with prescribed profile of transport coefficients taking into account the barrier formation in the edge region and which reproduces a prescribed energy confinement law. In the present simulations, the radial impurity transport is described only by anomalous transport with only relatively small pinch term. That would correspond to the situation with the ECRH control of the central electron temperature leading to mitigation of W accumulation in the core. In the SOL, the 2D fluid equations are solved in the simplified slab geometry but taking into account plasma recycling in the divertor and sputtering processes due to all ions: D, T, He, Ne, (or Ar Kr) and W at the target plate. It is assumed that the seeding gasses are puffed at the side wall in the divertor region. We are looking for steady state solutions and the model provides, from a number of inputs like the heating power, the average density and the confinement enhancement factor H98 , the core temperature and density profiles, the effective ion charge Zeff , the radiated and fusion power, the W flux and concentration and the plasma parameters in the divertor/SOL region. The prompt re-deposition process in case of W plate was recently modeled with PIC and Monte Carlo methods [11,12], but here we use a relatively simple description taking into account only single ionization process. The fraction of the re-deposited W to all sputtered W atoms fprompt is given by fprompt =
1 + ion /W +
2 −1
,(1)
where ion is the ionization length calculated from ionization frequency and average thermal velocity and W + is the gyroradius of singly ionized W in magnetic field [13,14]. The resulting fprompt is incorporated into W sputtering yield Y as follows: Y = Y 1 − fprompt . The simulations are prepared for the European DEMO configuration with the following main parameters [4]: toroidal radius RT = 9m, minor plasma radius a = 2.49 m, plasma current
Ip = 16.79 MA, toroidal magnetic field BT = 6.5T, elongation ε = 1.56, volume averaged electron densityVOL = 0.933 × 1020 m−3 , separatrix density ne sep = 40%VOL , H-factor (IPB98(y,2)) H98 = 1.1 and auxiliary heating power Paux equal to 50 MW. 3. Results and discussion In the recent JET ILW experiments with nitrogen and neon seeding [15,16], high radiation in the SOL (>50% of total radiation) is observed. In order to reproduce by COREDIV this experimental situation it was necessary to increase the value of radial anomalous transport in the SOL, from our standard value of DSOL = 0.25 m2 /s to DSOL = 0.5 m2 /s. It has been also shown in the Kukushkin’s study for ITER [17] that the increase of the radial transport in the SOL results in the extension of the ITER operational space. 3.1. Influence of the radial (anomalous) transport in the SOL In this part, the influence of the radial transport in the SOL on the DEMO working space is investigated. We have done simulations for two different values of the radial diffusion in SOL DSOL = 0.25 m2 /s and 0.5 m2 /s which leads to the q values in the midplane of about 5 mm and 6 mm, respectively. Some global plasma parameters for two different seeding impurities: argon and krypton are presented in Fig. 1. The main effect of the increased transport is related to the improvement of the screening efficiency of the SOL, which has important consequences for the discharge parameters. First we note that better confinement of tungsten in the SOL, reduces W concentration in the core and correspondingly the W radiation. Alpha power (Q-factor) is weakly affected by the SOL transport, and is only slightly reduced due to dilution effect by seeding impurity. Therefore the power crossing separatrix (PSOL ) increases significantly for both impurities (Ar and Kr), but only for argon it stays always above the power threshold for the LH transition (PL -H = 151 MW) whereas for Kr seeding PSOL only marginally exceeds the threshold close to the highest allowed seeding level. Important consequence of the higher PSOL is the possibility of working with higher puffing levels and the power to divertor plates (Pplate ) can be reduced to technologically acceptable value (<50 MW, assuming 5 m2 of wetted area (20% larger than in ITER) with large enough seeding. In case of Ar seeding and for larger radial transport in the SOL (DSOL = 0.5 m2 /s2 ) very favorable conditions might develop with strong seeding. It appears that for sufficiently large puff (>11 × 1022 el/s) PSOL increases well above PL -H threshold whereas PPLATE is reduced allowing for the development of the semi-detached plasma in the divertor region with TPLATE < 3 eV and total radiation above 78%. In case with Kr seeding, similar conditions can be achieved only for very large seeding puff > 13 × 1022 el/s. 3.2. Effect of the seeding impurity type: Ne, Ar, and Kr In the present day experiments, different gasses have been successfully used to mitigate the heat loads to the target plates: N, Ne, Ar, Kr [18]. In DEMO reactor, one would need good radiators in the SOL region like N or Ne but simultaneously it might be necessary to replace the W radiation in the core which can be done only by higher Z impurities (Ar, Kr, Xe). In order to give some insight on the proper impurity choice for fusion reactor, we have done simulations for three different gasses with different atomic number: Ne (Z = 10), Ar (Z = 18) and Kr (Z = 36) assuming favorable situation with higher SOL diffusion (DSOL = 0.5 m2 /s). Some plasma parameters are shown in Figs. 2 and 3. First, it should be noted that the overall fusion performance (alpha power, Q-factor) is weakly affected by the impurity type. Neon leads to the lowest core radiation (highest power to the SOL)
Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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a)
2,0
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c) 0
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a) c) Te
5 0
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d)
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plate
10
b)
0
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50
200 180
P
Te
plate
[eV]
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100
0,9
fRAD
300 25
SOL
320
150
160 140
0
2
4
6
8 10 12 14 22
Γpuff [x10 el/s]
Fig. 2. Plasma parameters versus seeding level for Ne, Ar and Kr: a) alpha power P˛, b) power to plate (PPLATE ), (c) radiation fraction and plate temperature, and (d) power to SOL (PSOL ).
but seems to be not acceptable as the seeding gas in the fusion reactor due to strongly reduced radiation efficiency leading to an excessive heat loads to the target plates. In case of both, Ar and Kr impurities, the power to the plate can be reduced to an acceptable values with seeding. However, since Kr radiates effectively in the SOL and core regions, it mitigates the heat load more efficiently than Ar. Moreover, Kr is able also to reduce significantly the W production (radiation) approaching 82% of the total radiation losses. But this significant core radiation in the case of Kr, leads to strong reduction of the power crossing the separatrix, which remains below the PL-H threshold for most of the seeding levels. Therefore, control of the H-mode operation might be more difficult/critical in the case of krypton as compared to argon.
260 240 220 200 180
a)
160
c)
120 90
Ne Ar Kr
60 30
0
2
4
6 8 10 12 14 22 Γpuff [x10 el/s]
SOL radiaton[MW]
PowerPLATE [MW]
Pα [MW]
360
Ne Ar Kr
Imp. radiation [MW]
200
Ne Ar Kr
380
W radiation [MW]
400
Total radiation [MW]
Fig. 1. Plasma parameters as functions of Kr (left) and Ar (right) injection rates for different SOL diffusion coefficient: a) Q-factor and Zeff , b) power to plate (PPLATE ), to SOL (PSOL ) and L-H power threshold (PL-H ) and c) radiation in SOL, W radiation in the core, and total radiation.
160
Ne Ar Kr
120 80 40
b)
0 80
Ne Ar Kr
60
d)
40 20 0
0
2
4
6
8 10 12 14 22
Γpuff [x10 el/s]
Fig. 3. Plasma parameters versus seeding level for Ne, Ar and Kr with radial diffusion D = 0.5 m2 /s: a) core radiation (RCORE ), b) SOL radiation (RSOL ), (c) W line radiation in the core and (d) Ne, Ar and Kr radiation in the core.
3.3. Influence of the prompt re-deposition All the results discussed so far, have been obtained without considering the possible reduction of the W sputtering yield due to prompt re-deposition process. In order to take this phenomena into account, a simple model for prompt re-deposition has been implemented in the COREDIV code (see Section 2). In Fig. 4, simulation results are shown for the cases with and without prompt re-deposition model and for all three impurities: Ne, Ar and Kr. It can be seen that the effect of the reduced sputtering yield due the prompt-re-deposition process is only important for relatively small levels of seeding, usually outside the DEMO operational window. It improves the fusion performance (larger Q-factor) due to reduced dilution effect with reduced W production.
Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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30 300 250 200 150 100 50 0 300 250 200 150 100 50 0
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PL_H
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34
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1,6
40
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Radiation[MW]
1,8
38
Power [MW]
Power [MW]
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32
Radiation [MW]
2,0
Radiation [MW]
Q
38
a)
Zeff
Zeff
w/o prompt with prompt
40
Zeff
4
PLATE SOL PL-H
TOTAL SOL W
0
2
4 Γ
6 Kr
8
1,25
b)
1,00
c)
10 12 14
22
[x10 el/s] puf
Fig. 4. Plasma parameters as functions of impurity injection rates and without and with prompt re-deposition for Neon (left), Argon (middle) and Krypton (right): a) Q-factor and Zeff , b) power to plate (PPLATE ), to SOL (PSOL ) and L-H power threshold (PL-H ) and c) radiation in SOL, W line radiation in the core, and total radiation.
ing space. However for Kr seeding, the prompt re-deposition leads to significantly larger operational window due to increase of the power crossing separatrix, which stays above the PL-H threshold.
1,0
0,8
1-fprompt
4. Conclusions 0,6
ne / m B=2T
-3
B = 6.5 T 19
10 20 10 21 10
0,4
0,2
0,0 10
Te / eV
100
1000
Fig. 5. The fraction of not promptly redeposited W ions escaping from divertor plate as a function of temperature in 2 and 6.5T magnetic field (DEMO scenario) for different electron densities.
Simultaneously, the W radiation is smaller and the power crossing separatrix rises to be above PL-H threshold for all considered impurities. However, the influence of the prompt re-deposition model on the DEMO working point is relatively week, since the reduction of the power to the target plates requires strong seeding, which leads to plasma condition in the divertor, close to target plates, with low plasma temperature (2–3 eV). Consequently the sputtering reduction factor due prompt re-deposition process is close to one and the sputtered tungsten flux is hardly reduced (see Fig. 5). In the case with Ne seeding, prompt re-deposition model allows for significantly larger seeding levels, but still the DEMO working point could not be achieved (PPLATE < 50 MW). For Ar seeding the prompt re-deposition model has almost no influence on the work-
The COREDIV code has been used to simulate DEMO inductive discharges with impurity seeding. The work was motivated by the need to develop DEMO scenarios which satisfy simultaneously the requirement for high radiation fractions and good H-mode confinement. It appears that the COREDIV code is well suited to analyze DEMO seeded discharges due to its ability to perform self-consistent simulations of the core and edge regions of the reactor, and taking into account the influence of different impurities (seeded and sputtered) on the discharge parameters. Simulations with the updated sputtering model taking into account prompt redeposition process, show that only for Ar and Kr, for strong enough radial transport in the SOL, it is possible to achieve H-mode plasma operation (power to the SOL > L-H transition threshold power) with acceptable level of the power to the target plates. For neon seeding such regime of operation seems not to be possible. Acknowledgments 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. The authors would like to thank Dr. R. Dux from IPP Garching for atomic data for Kr.
Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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References [1] R. Wenninger, et al., Advances in the physics basis for the European DEMO design, Nucl. Fusion 55 (6) (2015), 063003. [2] R. Zagórski, et al., Simulations with the COREDIV code of DEMO discharges, Nucl. Fusion 53 (7) (2013), 073030. [3] I. Ivanova-Stanik, R. Zagórski, Mitigation of the divertor heat load in DEMO reactor by impurity seeding, J. Nucl. Mater. 463 (2015) 596–600. [4] R. Kemp, et al., EFDA Report WP11-SYS-01-ACT5 (2012). [5] J. Rapp, et al., Strongly radiating type-III ELMy H-mode in JET—an integrated scenario for ITER, J. Nucl. Mater. 337–339 (2005) 826–830. [6] H. Zohm, et al., On the physics guidelines for a tokamak DEMO, Nucl. Fusion 53 (7) (2013), 073019. [7] T. Putterich, et al., Tungsten screening and impurity controlin JET, in: Proc. 24th IAEA Fusion Energy Conf. (FEC2012), San Diego, CA, 2012, 2012 http:// www-naweb.iaea.org/. [8] R. Neu, et al., Tungsten experiences in ASDEX Upgrade and JET, 2013 IEEE 25th Symp. Fusion Eng. SOFT (2013) 2013. [9] R. Stankiewicz, R. Zagorski, Self-consistent modelling of the tokamak core and SOL plasma with the COREDIV code, Czech. J. Phys. 52 (2002) D32–D37.
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[10] R. Zagórski, et al., Modelling with COREDIV code of JET ILW configuration, Contrib. Plasma Phys. 50 (3–5) (2010) 306–312. [11] D. Tskhakaya, et al., Modelling of tungsten re-deposition coefficient, J. Nucl. Mater. 463 (2015) 624–628. [12] A.V. Chankin, et al., Monte Carlo simulations of tungsten redeposition at the divertor target, Plasma Phys. Control. Fusion 56 (2) (2014) 025003. [13] G. Fussmann, et al., High-Z elements as target materials in fusion devices, Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research 2 (1995) 143–148. [14] R. Dux, et al., Main chamber sources and edge transport of tungsten in H-mode plasmas at ASDEX Upgrade, Nucl. Fusion 51 (5) (2011), 053002. [15] M. Wischmeier, High density operation for reactor-relevant power exhaust, J. Nucl. Mater. 463 (2015) 22–29. [16] R. Zagorski, et al., Influence of seeding and SOL transport on plasma parameters in JET ITER-like wall H-mode discharges, J. Nucl. Mater. 463 (2015) 649–653. [17] A.S. Kukushkin, et al., Consequences of a reduction of the upstream power SOL width in ITER, J. Nucl. Mater., 438 (2013) S203–S207. [18] A. Kallenbach, et al., Impurity seeding for tokamak power exhaust: form present devices via ITER to DEMO, Plama Phys. Control Fusion 55 (2013) 124041.
Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Divertor power spreading in DEMO reactor by impurity seeding ˛ Roman Zagórski ∗ , Krzysztof Gałazka, Irena Ivanova-Stanik Institute of Plasma Physics and Laser Microfusion, Hery Str. 23, 01-497 Warsaw, Poland
h i g h l i g h t s • The COREDIV code has been used to simulate DEMO inductive discharges with different impurity seeding (Ne, Ar, Kr) and different sputtering models (with and w/o prompt re-deposition process).
• It has been shown that only for Ar and Kr seeding it is possible to achieve H-mode plasma operation with acceptable level of the power to the tungsten target plates.
• For neon seeding, such regime of operation seems not to be possible. • Prompt re-deposition model extends the DEMO operation window.
a r t i c l e
i n f o
Article history: Received 29 July 2015 Received in revised form 29 February 2016 Accepted 14 March 2016 Available online xxx Keywords: Numerical modeling Edge plasma Impurity seeding Fusion reactor
a b s t r a c t Numerical simulation with COREDIV code of DEMO H-mode discharges (tungsten divertor and wall) are performed considering the influence of seeding impurities with different atomic numbers: Ne, Ar and Kr on the DEMO scenarios. The approach is based on integrated numerical modeling using the COREDIV code, which self-consistently solves radial transport equations in the core region and 2D multi-fluid transport in the SOL. In this paper we focus on investigations how the operational domain of DEMO can be influenced by seeding gasses. Simulations with the updated prompt re-deposition model implemented in the code show that only for Ar and Kr, for high enough radial diffusion in the SOL, it is possible to achieve H-mode plasma operation (power to the SOL> L-H transition threshold power) with acceptable level of the power to the target plates. For neon seeding such regime of operation seems not to be possible. © 2016 EURATOM. Published by Elsevier B.V. All rights reserved.
1. Introduction The operating point of a future DEMO fusion reactor will be optimized to fulfill the following criteria: (1) maximize the fusion power output, (2) allow for an H-mode operation through keeping the power flux to scrape-off layer (SOL) considerably higher than H-L transition threshold and (3) minimize the heat load to divertor plates [1]. One of the ways to manage the plasma performance and power exhaust to realize these requirements is by controlling the impurity content in the plasma. From our earlier simulations [2], it comes out that the level of the power going to the scrape-off layer (SOL) depends strongly on the tungsten radiation in the core, the latter being quite significant. It is expected that by increasing the seeding level, the radiation in the SOL region is increased leading to the decrease of the power to
∗ Corresponding author. E-mail address: [email protected] (R. Zagórski).
the plate and tungsten production. But, smaller tungsten concentration in the core results in the reduction of the tungsten radiation and increase of the power to the SOL, which in turn, increases the tungsten production. In order to account properly on this strongly nonlinear behavior, only integrated approach can to be used taking into account the coupling between the core and edge regions. In this paper, numerical simulations with COREDIV code [3] of DEMO discharges with tungsten as armor material (divertor and wall) for H-mode scenarios are presented. Calculations are performed for inductive DEMO 2012 steady-state configuration [4] and focus on two especially important issues related to DEMO operation: finding an appropriate kind and amount of seeded impurity to mitigate the heat load to the divertor to an acceptable level (5–10 MW/m2 ) [5], [6] and replacing the intrinsic W impurity in the core which by high line radiation might lead to radiative collapse [7]. In existing devices (JET, ASDEX-Upgrade) a beneficial influence of nitrogen puffing on lowering the L-H threshold, improvement in the pedestal stability and reduction of the divertor heat load was observed [8]. This results were reproduced by numerical modeling
http://dx.doi.org/10.1016/j.fusengdes.2016.03.058 0920-3796/© 2016 EURATOM. Published by Elsevier B.V. All rights reserved.
Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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by COREDIV code [9], which brought some insight in the JET operational domain [10]. COREDIV was applied also to DEMO scenarios to study various impurities (Ne, Ar, Ni) and the main conclusion was that for DEMO an element with atomic number Z ≥ 18 would be suitable [2], [3]. Referring to a recent publication on an optimal impurity mix for DEMO [1] we would like to present here a systematic study on Kr seeding and compare it to Ar and Ne impurities analyzed before. Additionally, the calculations included a simple model for prompt re-deposition processes for W on the divertor plate, as described below. 2. Model The simulations were performed by using COREDIV code which is based on an integrated approach coupling the radial transport in the core and the 2D multifluid description of the SOL. The interaction between seeded and intrinsic impurities as well as the effect of the impurities on the fusion power significantly affects the particles and energy flows in the plasma, therefore the self-consistent approach is essential for a correct evaluation of the average power to the divertor plate. As this work is a follow-up of our previous calculations the detailed description and parameters used can be found in Refs. [2,3] and only the main points of the model are reported here. In the core, the 1D radial transport equations for bulk ions, for each ionization state of impurity ions and for the electron and ion temperatures are solved. For auxiliary heating paraboliclike deposition profile is assumed and heating due to alpha power is calculated self-consistently taking into account the dilution effect due to helium transport. The energy losses are determined by Bremstrahlung and synchrotron radiation together with ionization and line radiation losses. The energy and particle transport are defined by the local transport model with prescribed profile of transport coefficients taking into account the barrier formation in the edge region and which reproduces a prescribed energy confinement law. In the present simulations, the radial impurity transport is described only by anomalous transport with only relatively small pinch term. That would correspond to the situation with the ECRH control of the central electron temperature leading to mitigation of W accumulation in the core. In the SOL, the 2D fluid equations are solved in the simplified slab geometry but taking into account plasma recycling in the divertor and sputtering processes due to all ions: D, T, He, Ne, (or Ar Kr) and W at the target plate. It is assumed that the seeding gasses are puffed at the side wall in the divertor region. We are looking for steady state solutions and the model provides, from a number of inputs like the heating power, the average density and the confinement enhancement factor H98 , the core temperature and density profiles, the effective ion charge Zeff , the radiated and fusion power, the W flux and concentration and the plasma parameters in the divertor/SOL region. The prompt re-deposition process in case of W plate was recently modeled with PIC and Monte Carlo methods [11,12], but here we use a relatively simple description taking into account only single ionization process. The fraction of the re-deposited W to all sputtered W atoms fprompt is given by fprompt =
1 + ion /W +
2 −1
,(1)
where ion is the ionization length calculated from ionization frequency and average thermal velocity and W + is the gyroradius of singly ionized W in magnetic field [13,14]. The resulting fprompt is incorporated into W sputtering yield Y as follows: Y = Y 1 − fprompt . The simulations are prepared for the European DEMO configuration with the following main parameters [4]: toroidal radius RT = 9m, minor plasma radius a = 2.49 m, plasma current
Ip = 16.79 MA, toroidal magnetic field BT = 6.5T, elongation ε = 1.56, volume averaged electron density
Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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a)
2,0
32 PPLATE
30
PSOL
1,50
PPLATE
30
PSOL
200
PL-H
Power [MW]
PL-H
1,75
34 32
1,0
b)
1,25
b)
150
150 100
100
50
50
0 300 250 200 150 100 50 0
0 300 250 200 150 100 50 0 0
Radiation[MW]
Power [MW]
200
1,5
ZEFF Q
Q
36 Q
Zeff
Q
34
2,00
a)
ZEFF
38
36
Radiation[MW]
40
2,5
2
D=0.25m /s 2 D=0.5m /s
Zeff
40
3
TOTAL SOL W
c) 0
2
4
6
Γ
8
Kr
10
12 14
TOTAL SOL W
c) 3
22
6 Γ
[x10 el/s] puf
Ar
9
12
15
22
[x10 el/s] puf
340
a) c) Te
5 0
2
4
6
8 10 12 14 22
Γpuff [x10 el/s]
0,7 0,6 0,5
Ne Ar Kr PL-H
d)
220 [MW]
plate
10
b)
0
0,8
15
0
50
200 180
P
Te
plate
[eV]
20
100
0,9
fRAD
300 25
SOL
320
150
160 140
0
2
4
6
8 10 12 14 22
Γpuff [x10 el/s]
Fig. 2. Plasma parameters versus seeding level for Ne, Ar and Kr: a) alpha power P˛, b) power to plate (PPLATE ), (c) radiation fraction and plate temperature, and (d) power to SOL (PSOL ).
but seems to be not acceptable as the seeding gas in the fusion reactor due to strongly reduced radiation efficiency leading to an excessive heat loads to the target plates. In case of both, Ar and Kr impurities, the power to the plate can be reduced to an acceptable values with seeding. However, since Kr radiates effectively in the SOL and core regions, it mitigates the heat load more efficiently than Ar. Moreover, Kr is able also to reduce significantly the W production (radiation) approaching 82% of the total radiation losses. But this significant core radiation in the case of Kr, leads to strong reduction of the power crossing the separatrix, which remains below the PL-H threshold for most of the seeding levels. Therefore, control of the H-mode operation might be more difficult/critical in the case of krypton as compared to argon.
260 240 220 200 180
a)
160
c)
120 90
Ne Ar Kr
60 30
0
2
4
6 8 10 12 14 22 Γpuff [x10 el/s]
SOL radiaton[MW]
PowerPLATE [MW]
Pα [MW]
360
Ne Ar Kr
Imp. radiation [MW]
200
Ne Ar Kr
380
W radiation [MW]
400
Total radiation [MW]
Fig. 1. Plasma parameters as functions of Kr (left) and Ar (right) injection rates for different SOL diffusion coefficient: a) Q-factor and Zeff , b) power to plate (PPLATE ), to SOL (PSOL ) and L-H power threshold (PL-H ) and c) radiation in SOL, W radiation in the core, and total radiation.
160
Ne Ar Kr
120 80 40
b)
0 80
Ne Ar Kr
60
d)
40 20 0
0
2
4
6
8 10 12 14 22
Γpuff [x10 el/s]
Fig. 3. Plasma parameters versus seeding level for Ne, Ar and Kr with radial diffusion D = 0.5 m2 /s: a) core radiation (RCORE ), b) SOL radiation (RSOL ), (c) W line radiation in the core and (d) Ne, Ar and Kr radiation in the core.
3.3. Influence of the prompt re-deposition All the results discussed so far, have been obtained without considering the possible reduction of the W sputtering yield due to prompt re-deposition process. In order to take this phenomena into account, a simple model for prompt re-deposition has been implemented in the COREDIV code (see Section 2). In Fig. 4, simulation results are shown for the cases with and without prompt re-deposition model and for all three impurities: Ne, Ar and Kr. It can be seen that the effect of the reduced sputtering yield due the prompt-re-deposition process is only important for relatively small levels of seeding, usually outside the DEMO operational window. It improves the fusion performance (larger Q-factor) due to reduced dilution effect with reduced W production.
Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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30 300 250 200 150 100 50 0 300 250 200 150 100 50 0
PPLATE
Q
PSOL
b)
PL_H
32
1,2
30
1,0
28 300 250 200 150 100 50 0 300 250 200 150 100 50 0
c) TOTAL SOL W
0
1
2
3 Γ
4
Ne
5
6
7
8
9
Q Zeff
PPLATE
1,25
a)
PSOL
b) TOTAL SOL W
c) 0
3
6 Γ
22
[x10 el/s] puf
9
Ar
12
15
18
22
[x10 el/s] puf
a)
2,25 Zeff
1,75
34
30 300 250 200 150 100 50 0 300 250 200 150 100 50 0
2,50 2,00 1,50
32
1,00
PL-H
ZEFF
36 Q
1,4
1,50
Power [MW]
34
34
Q
38
1,75
36 Q
1,6
40
2,00
Radiation[MW]
1,8
38
Power [MW]
Power [MW]
40
36
32
Radiation [MW]
2,0
Radiation [MW]
Q
38
a)
Zeff
Zeff
w/o prompt with prompt
40
Zeff
4
PLATE SOL PL-H
TOTAL SOL W
0
2
4 Γ
6 Kr
8
1,25
b)
1,00
c)
10 12 14
22
[x10 el/s] puf
Fig. 4. Plasma parameters as functions of impurity injection rates and without and with prompt re-deposition for Neon (left), Argon (middle) and Krypton (right): a) Q-factor and Zeff , b) power to plate (PPLATE ), to SOL (PSOL ) and L-H power threshold (PL-H ) and c) radiation in SOL, W line radiation in the core, and total radiation.
ing space. However for Kr seeding, the prompt re-deposition leads to significantly larger operational window due to increase of the power crossing separatrix, which stays above the PL-H threshold.
1,0
0,8
1-fprompt
4. Conclusions 0,6
ne / m B=2T
-3
B = 6.5 T 19
10 20 10 21 10
0,4
0,2
0,0 10
Te / eV
100
1000
Fig. 5. The fraction of not promptly redeposited W ions escaping from divertor plate as a function of temperature in 2 and 6.5T magnetic field (DEMO scenario) for different electron densities.
Simultaneously, the W radiation is smaller and the power crossing separatrix rises to be above PL-H threshold for all considered impurities. However, the influence of the prompt re-deposition model on the DEMO working point is relatively week, since the reduction of the power to the target plates requires strong seeding, which leads to plasma condition in the divertor, close to target plates, with low plasma temperature (2–3 eV). Consequently the sputtering reduction factor due prompt re-deposition process is close to one and the sputtered tungsten flux is hardly reduced (see Fig. 5). In the case with Ne seeding, prompt re-deposition model allows for significantly larger seeding levels, but still the DEMO working point could not be achieved (PPLATE < 50 MW). For Ar seeding the prompt re-deposition model has almost no influence on the work-
The COREDIV code has been used to simulate DEMO inductive discharges with impurity seeding. The work was motivated by the need to develop DEMO scenarios which satisfy simultaneously the requirement for high radiation fractions and good H-mode confinement. It appears that the COREDIV code is well suited to analyze DEMO seeded discharges due to its ability to perform self-consistent simulations of the core and edge regions of the reactor, and taking into account the influence of different impurities (seeded and sputtered) on the discharge parameters. Simulations with the updated sputtering model taking into account prompt redeposition process, show that only for Ar and Kr, for strong enough radial transport in the SOL, it is possible to achieve H-mode plasma operation (power to the SOL > L-H transition threshold power) with acceptable level of the power to the target plates. For neon seeding such regime of operation seems not to be possible. Acknowledgments 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. The authors would like to thank Dr. R. Dux from IPP Garching for atomic data for Kr.
Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058
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Please cite this article in press as: R. Zagórski, et al., Divertor power spreading in DEMO reactor by impurity seeding, Fusion Eng. Des. (2016), http://dx.doi.org/10.1016/j.fusengdes.2016.03.058