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Design of EAST lower divertor by considering target erosion and tungsten ion transport during the external impurity seeding

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Published 21 April 2021 © 2021 The Author(s). Published on behalf of IAEA by IOP Publishing Ltd
, , Citation Chaofeng Sang et al 2021 Nucl. Fusion 61 066004 DOI 10.1088/1741-4326/abecc9

0029-5515/61/6/066004

Abstract

To demonstrate the performance of tungsten (W) as the divertor target material and to solve the power handling problem during high power long-pulse discharge, the upgrade of EAST lower divertor is planned. In this work, the physical design of the W divertor is presented by using 2D edge plasma code SOLPS and Monte Carlo impurity transport code DIVIMP. The optimized divertor geometry is proposed after systematic examination of target shapes, target slant angles and the pump opening locations. The performance of the designed divertor is further assessed by impurity seeding. By comparing the medium and high power discharges with argon (Ar) seeding, the differences on the divertor power radiation and impurity core accumulation are distinguished. The simulated effective ion charge Zeff fits well the scaling law, which is based on multi-machine database. Ar seeding and neon (Ne) seeding scans are carried out separately. The simulation results indicate Ar has higher power radiation efficiency than that of Ne, thus promoting the achievement of plasma detachment. However, the core compatibility with Ar is worse than with Ne. The W target erosion and W impurity transport during impurity seeding are simulated by the DIVIMP–SOLPS coupled modeling. It illustrates that under the similar divertor plasma conditions, Ar seeding causes more serious W erosion and more severe core contamination by W impurity, than Ne seeding. Finally, the divertor in–out asymmetry is studied by considering electromagnetic drifts. The simulation results manifest that the designed open vertical inner target reduces in–out asymmetry due to that its weak power radiation capability is offset by the ion flow driven by the drifts. In addition, the designed divertor is compatible with the quasi snowflake magnetic configuration. These studies will improve the understanding of W target sputtering and W impurity transport control during the radiative divertor discharges for CFETR/DEMO.

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1. Introduction

The divertor target serves as the most intense plasma–surface interaction (PSI) area in tokamaks, and a majority of the particles and energy crossing the separatrix from core region finally deposit on the targets. To ensure the lifetime of the device and to maintain the steady-state operation, the control of the power load on targets becomes to a critical issue during high performance long-pulse discharges. As a superconducting tokamak, EAST has achieved H-mode operation with a duration of 101.2 s and total power injection of 0.3 GJ [1], which benefits by the ITER-like water-cooled tungsten (W) divertor at the top [2, 3]. However, the lower graphite divertor prevents its achievement of further high-power long-pulse discharges. Thus, the upgrade of the lower divertor of EAST device has been proposed.

EAST has gone through four generations of plasma-facing materials (PFMs) since the first plasma in 2006 [4]. Currently, it has graphite lower divertor target and W upper divertor target, while the main chamber PFCs (first wall) are molybdenum. The application of W as the PFM of upper divertor has demonstrated its advantage on steady-state high-performance H-mode plasmas. W has been chosen as the PFM of divertor target for ITER [5] and the main candidate for DEMO [6] and CFETR [7]. EAST provided a good platform for W divertor study prior to ITER, due to its unique long-pulse discharge capability. However, the current mixed PFMs make the PSIs very complicated. Our previous work found that during the deuterium discharge, the intrinsic carbon impurity, which is sputtered from lower graphite target, dominates upper W target erosion [8, 9]. The fully metallic PFM machine is required to better understand PSIs of W target. To demonstrate the performance of W divertor target for ITER and to solve the power handling problem, EAST is planned to upgrade its lower divertor by the usage of W as the PFM. Before the engineering construction, the physical design is necessary [5, 1014]. The goals of physical design are: (1) optimizing the divertor geometry to obtain best power radiation capability [15]; (2) reducing the heat flux q and electron temperature Te at the target below 10 MW m−2 and 10 eV [16], respectively, to avoid melting and target erosion; (3) increasing divertor shielding to control the impurity content in the core region and to maintain the energy confinement and core–edge compatibility.

The divertor geometry has great impact on the edge plasma. ITER will use the vertical divertor target (with small glancing angle), which can significantly increase the plasma wetted area, thus reducing the heat flux density [17]. The slant target can also promote the achievement of partial-detachment. On the other hand, increasing divertor closure has been taken as a promising way to optimize divertor geometry. Our previous modeling work showed that divertor with a closed baffle enables plasma detachment at much lower upstream density than that of the open divertor [18] and recent DIII-D experiment also confirmed this observation [19]. The slot divertor has been proposed as a potential candidate to DEMO [11, 12, 20] with the combination of the closed geometry and vertical target. The small-angle slot divertor [21], which has a small target angle in near-scrape-off layer (SOL) and progressive slot opening toward far-SOL, is the further optimization of the slot divertor. It solves the problem of high Te in the far SOL region [22]; however, it requires high precision control of strike point (SP) [23], which is a great challenge to EAST control system.

The creation of advanced magnetic equilibrium configurations, such as snowflake [24], X- [25] and super X divertors [26, 27], is another important direction for designing innovative divertor. Modeling and experiment results found that they can better handle the deposited heat flux to the divertor target [2832]. The quasi snowflake (QSF) divertor has been realized on EAST, which showed significant reduction of heat flux compared to the standard single null divertor [33]. The designed divertor shape should be compatible with QSF configuration. In additional, the fishtail divertor, i.e. swinging SP, is also proposed for the active heat load control with the new divertor [34]. This asks for the large target area, which should satisfy the SP sweeping requirement.

For W divertor, due to the absence of radiative species in the divertor region and the high particle/energy reflection rate, its power radiation capability is weak compared to carbon target [8, 35]. This can be solved by introducing seeded impurities, such as nitrogen (N), neon (Ne) and argon (Ar), which can significantly reduce the heat flux and plasma temperature. However, the impurity may transport to the core region and cool the plasma down to temperatures where momentum losses start to become effective, which becomes to a big threat to the plasma confinement and stability [36]. Therefore, the choice of seed impurity species for the designed divertor should be assessed. There are two important factors to be taken into account: enhancement of edge (including divertor) radiation and avoidance of core radiation and fuel dilution. Impurity control can be achieved by optimum gas puffing and divertor pumping, and by the optimization of divertor geometry for impurity shielding [37]. Apart from reducing plasma temperature in front of target, the seeded impurity can also dominate the W target sputtering [38], which influences the lifetime of the device and the contamination of the core plasma. Therefore, the W target erosion and W impurity transport are very crucial for the designed divertor and the assessment should be implemented.

In this work, we report the physical design of EAST lower W divertor. By using the 2D edge plasma code SOLPS modeling [14, 39], the optimized divertor shape is proposed after a systematic examination of target shapes, target angles and the pump opening locations. With the designed divertor, the Ar and Ne seeding have been assessed by the consideration of achieving plasma detachment, the impurity content in the core region, the erosion of the W target and the resulting W impurity accumulation. The transport of the W impurity is simulated by DIVIMP code. We mainly focus on the optimization of the outer divertor (OD). Finally, the inner divertor (ID) and the divertor in–out asymmetry is studied including drift effect. The paper is organized as follows; a brief description of the model setup is given in section 2. In section 3, simulation results are presented for divertor optimization, impurity seeding, target erosion and W impurity transport during seeding, and divertor in–out asymmetry. Discussion and conclusions are summarized in section 4.

2. Simulation model

The edge plasma code package SOLPS, which consists of the multi-fluid transport code B2.5 [39] and the kinetic neutral transport code EIRENE [40], is used for divertor design. Here, the coupled version of SOLPS5.0 with neutrals simulated kinetically by EIRENE is applied, unless otherwise stated. The typical EAST lower-single null magnetic equilibrium with favorable BT (the direction of the ion B × B points to the lower divertor) is selected for the modeling. The sketch of EAST tokamak with one proposed lower divertor geometry and the corresponding simulation domain is shown in figure 1(a).

Figure 1.

Figure 1. (a) Sketch of the EAST tokamak with one designed lower W divertor and the corresponding mesh for SOLPS modeling. The modeled impurity seed location is labeled. (b) Flow chart of the physical design processes.

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The power across the core–edge-interface (CEI) PSOL and the deuterium ion density nD+,CEI (at rrsep = −4.3 cm of the outer mid-plane, OMP) are fixed at various values. The fluxes of other ions and neutrals are assumed to be zero at CEI. The leakage boundary condition at the SOL & private flux region (PFR) and the sheath boundary condition at the targets are applied, please find details in references [8, 41]. The radial particle transport coefficient D = 0.3 m2 s−1 and electron/ion heat conductivity coefficients χ⊥,e = χ⊥,i = 1.0 m2 s−1 are applied, in accordance with series of EAST design simulation [4244], and the corresponding power decay length λq in the SOL is about 4.5 mm. It should be noted the mesh width of the SOL (outside the separatrix) mapped to the OMP is only 1.5 cm due to technical restrictions. This may lead to underestimation of the neutral source (ionization source), resulting in the underestimation of the power radiation. Moreover, the absent of plasma information in the far SOL region of the horizontal target case may lead to inaccurate peak Te. This might be overcome with future versions of SOLPS-ITER. The location of cryopumps are labeled in figure 1(a), with the recycling rate R = 0.9 at pump port [45].

The objective of the present work is to design the EAST lower W divertor. To this end, it is divided into two modeling steps. (1) Optimizing the divertor shape to obtain the highest power radiation capability. (2) Assessing the performance of the designed W divertor during impurity seeding. The flow chart of the design processes can be found in figure 1(b).

In a first step, to simplify the influencing factors and to model the plasma detachment, the carbon target is assumed. Deuterium plasma species (D0, D2, D+ and D2 +) and intrinsic sputtered carbon impurities are considered (C0, C+–C6+). The chemical sputtering yield is fixed to YC,chem = 0.01 [8, 46], while the physical sputtering yield YC,phys is calculated by the modified Roth–Bohdansky formula [47]. The transport of hydrocarbons is not included and the sputtered material is treated as atomic carbon. No gas puffing is considered in this step and the deuterium is fueled by core. In a second step, after confirming the divertor geometry, the W target is used. However, since it is too time consuming for SOLPS to directly simulate the transport of W impurities, the trajectories of W impurities are ignored. Due to the absence of the radiative impurity in the divertor region, the external impurity (Ar or Ne) seeding is implanted from the seed location as shown in figure 1(a). This choice of simulation neglects the combination of divertor shape and impurity gas puff location effects, which may influence the far-SOL plasma [48], and requires to be investigated in the future work.

The creation, transport and core accumulation of W impurity are the key issues for the application of W as the PFM. In this work, the production of W impurities is calculated by the erosion of W target via empirical physical sputtering yield formula [49], and the details can be found in references [8, 38]. With the calculated W source and plasma background provided by SOLPS modeling, the transport of W impurity is simulated by DIVIMP code [50], which uses the Monte Carlo method to track particles and their charge states in the plasma. The details of the SOLPS–DIVIMP coupling for EAST W divertor can be found in the recent work [51].

Only steady-state conditions are simulated, and the condition during edge localized modes (ELMs) is not considered. Unless otherwise statement, electromagnetic drifts are switched off in the simulation.

3. Modeling results and discussions

3.1. Design of the geometry of EAST lower divertor

To optimize the divertor shape, carbon PFM is assumed at the beginning with the focus on the inherent power radiation capability of the divertor. The systematic examination of different target shapes, target angles and the pump locations has been carried out. Firstly, the horizontal target with outer strike point (OSP) at different positions and the vertical target are compared. PSOL = 4 MW is fixed unless otherwise stated. Sketches of the divertor geometry/mesh and the main plasma quantities at the outer target as functions of electron density at the separatrix of OMP ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}$ are shown in figure 2. It can be seen that vertical target and horizontal target with OSP close to corner (called Horiz-near) cases have similar maximum and OSP values of the heat flux density qdep, while the horizontal target with OSP far from corner (named Horiz-far) has much higher qdep, indicating Horiz-far case is not applicable for power handling. The controlling of Te is another important requirement for divertor. Figure 2(d) shows the vertical target can hardly reduce peak Te compared to horizontal target, and Horiz-near case has the lowest Te. From requirements for qdep and Te reduction, the Horiz-near divertor is preferred. Here we define the rollover of target ion flux at OSP as the indication of detachment onset [46, 52]. The detachment onset density is ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\mathrm{O}\mathrm{M}\mathrm{P},\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{t}}=2.1{\times}1{0}^{19}\enspace {\mathrm{m}}^{-3}$, 1.6 × 1019 m−3, 1.9 × 1019 m−3, respectively, for cases figures 2(a)–(c), showing Horiz-near case can promote the occurrence of plasma detachment. This is in agreement with recent EAST experiment observation [53].

Figure 2.

Figure 2. Sketches of the divertor with OSP at different positions (a) horizontal target with OSP far from the corner, (b) horizontal target with OSP close to the corner, (c) vertical target. (d)–(f) The maximum values of electron temperature Tet, deposited heat flux density qdep and deposited particle flux density Γdep to the outer target, (g)–(i) the OSP values of Tet, qdep, Γdep, respectively, as functions of ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}$. The dash line in figures 2(d)–(f) indicates the selected upstream density for further analysis.

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To show the differences among three divertor cases, similar upstream density ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}\sim 2.65{\times}1{0}^{19}\enspace {\mathrm{m}}^{-3}$ (as marked by the dash line in figures 2(d)–(f)) is selected for comparison. The profiles of main plasma quantities and neutral density along the outer target are shown in figure 3. The divertor shape changes divertor plasma remarkably. For the vertical target, the main features are: (1) Te and qdep near the OSP can be well reduced; (2) Te in the far SOL region is much higher than that of horizontal target due to much lower neutral particle compression there, which may be problematic for resulting in net erosion of W target; (3) qdep can be controlled in the far SOL region due to low plasma density, and the location of peak qdep is away from OSP; (4) the plasma wetted area is larger than that of horizontal target, which can lower deposited particle and energy flux density. These are similar to previous DIII-D modeling results [14]. For the horizontal target, when the OSP is close to corner, neutral particle can be well compressed in a small region, resulting in significant reduction of both Te and qdep, i.e. the peak Te and q are ∼1.7 eV and ∼0.8 MW m−2 compared to ∼4.4 eV and ∼1.5 MW m−2 of Horiz-far divertor, and it achieves fully detachment. These show the advantages of Horiz-near divertor. The corresponding 2D contours of Te, molecular D2 density nD2t and total energy radiation Prad are shown in figure 4. A clear 'gas cushion' is created in front of the target of Horiz-near divertor (figure 4(e)), leading to significant falling down of Te (figure 4(b)), in agreement with previous finding of strong correlation between nD2t and Te [5, 54]. nD2t in the SOL of the vertical target case is very small, thus Te is high. The essential problem for vertical target is that neutral particles can hardly be compressed in the far SOL region and only partial detachment can be easily obtained.

Figure 3.

Figure 3. For similar upstream density ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}\sim 2.65{\times}1{0}^{19}\enspace {\mathrm{m}}^{-3}$, the outer target profiles of (a) net, (b) Tet, (c) qdep, (d) atomic deuterium density nDt, (e) nD2t and (f) Γdep for three divertor cases.

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Figure 4.

Figure 4. For similar upstream density ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}\sim 2.65{\times}1{0}^{19}\enspace {\mathrm{m}}^{-3}$, the 2D contours of Te, nD2t and Prad for (a), (d), and (g) Horiz-far, (b), (e), and (h) Horiz-near, and (c), (f), and (i) vertical target, respectively.

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The benefits of Horiz-near divertor to plasma detachment are confirmed. Next, we want to know the impact of target slant angle on divertor plasma performance. Three angles, i.e. θ = 0°, 10°, and 20°, which is defined by the angle between horizontal plane and target as shown in figures 5(a)–(c), are selected for comparison. By varying the upstream plasma density, the variations of main divertor plasma parameters (maximum and OSP values) with ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}$ are shown in figures 5(d)–(i). It illustrates that the target slant angle influences the divertor plasma slightly. The reason may lie in that the poloidal incident angle is still large. Therefore, θ = 0° target is preferred to reduce the complexity of engineering construction. It should be noted that the total magnetic field incident angle varies slightly with the target angle, i.e. 1.5°–2.5° during the target angle variation.

Figure 5.

Figure 5. Sketches of the divertor target with different slant angles θ = (a) 0°, (b) 10°, (c) 20°. (d)–(f) The maximum values of Tet, qdep and Γdep to the outer target, and (g)–(i) the values of Tet, qdep, Γdep, at the OSP, as functions of ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}$.

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Particle exhaust is another important issue for divertor [46]. The impact of pump opening location at common flux region (CFR) side on the divertor plasma is thus assessed. Four cases, i.e. pump opening at the bottom of CFR side, no pump opening at CFR side, pump opening at CFR side with a baffle height of 1.5 cm and with a baffle height of 2.5 cm, are simulated. Sketches of the divertor target with different pump opening locations and corresponding divertor plasma parameters are shown in figure 6. It can be seen that the pump location has remarkable impact on divertor plasma. Setting the pump opening at the CFR bottom makes it a relative open divertor, while as the baffle height increases, it becomes to a more and more closed divertor. The case without CFR pumping opening is a relative closed divertor. The simulation results demonstrate that the more closed divertor enhances divertor power radiation more distinctly. As the baffle height increases, the detachment onset density reduces. The main reason is that the pump location influences effective particle exhaust. As the pump opening moves further away from OSP, the exhausted particle reduces and the neutral density in the divertor region increases significantly, which in turn influences divertor plasma [46].

Figure 6.

Figure 6. (a) Sketches of the divertor target with four pump locations, i.e. pump opening at bottom of CFR (divertor 7A, open geometry), no pump opening at CFR (divertor 7A, closed geometry), pump opening at CFR with baffle height of 1.5 cm (divertor 8A) and with baffle height of 2.5 cm (divertor 8C). The maximum (b) Tet, (c) qdep and (d) Γdep to the outer target as functions of ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}$ for four divertor cases.

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Our previous work confirmed that for a closed divertor with flat target configuration both pump opening at the bottom of CFR side and PFR side are good to improve particle exhaust [46]. The present work finds that making the pump opening at the bottom of both PFR and CFR sides simultaneously can hardly maintain the energy radiation in the divertor region, i.e. divertor 7A in figure 6(a). Therefore, keeping the pump opening at the bottom of PFR, while in the CFR side either setting the pump opening with a certain baffle height (e.g. divertor 8C in figure 6(a)) or leaving no pump opening, is preferred. However, an additional pump to be placed under the PFR should be considered with this design.

3.2. Tungsten divertor with argon seeding

After the optimization of the divertor geometry, the horizontal target with OSP close to corner and a pump duct above 4.0 cm height baffle is chosen, which has similar performance to that of the closed one in figure 6. Note that it was not shown in figure 6 to avoid too many similar lines and to make the figure more distinguishable. The sketch of the divertor is shown in figure 7(a), and its performance with W target is further investigated. Since W impurity is not included by the present SOLPS modeling, we first simulate pure deuterium discharge (no impurity included), as shown in figures 7(b)–(g) the maximum and OSP values of Tet, qdep and Γdep, as functions of PSOL and ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}$, respectively. It can be seen that the maximum values and OSP values are very similar. As PSOL increases from 2 MW to 8 MW, while maintaining nD+,CEI = 6.0 × 1019 m−3, Te at OSP increases from ∼5.5 eV to ∼177.7 eV and qdep at OSP raises from ∼1.0 MW m−2 to ∼17.8 MW m−2, exceeding the tolerance of W target, i.e. (1) Tet should be below 44 eV, assuming D+ accelerated through a sheath drop of 3kTe with an impact energy of ∼5kTe [55] and the sputtering threshold for D+ incident into W of 220 eV [38]; (2) qdep should be under 10 MW m−2 [43, 56]. Fixing PSOL = 4 MW and varying upstream plasma density, the plasma detachment is not observed even ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}$ reaches 4.0 × 1019 m−3. These indicate that for W divertor edge power exhaust will be a great challenge during pure D discharge and the external impurity seeding is necessary, which is consistent with JET experiment and modeling [57].

Figure 7.

Figure 7. (a) Sketch of the proposed divertor geometry. Pure deuterium discharge, the maximum and OSP values of Tet, qdep and Γdep at outer target (b)–(d) as functions of PSOL while nD+,CEI = 6.0 × 1019 m−3, and (e)–(g) as functions of ${n}_{\mathrm{e},\mathrm{s}\mathrm{e}\mathrm{p}}^{\text{OMP}}$ with PSOL = 4 MW.

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To raise the power radiation in the W divertor, Ar impurity is seeded from the puffing location shown in figure 7(a). The medium and high input power cases, i.e. PSOL = 4 MW and 10 MW, are compared by varying the seeding rate. The power radiation can be expressed as Prad = Vne nimp LZ, where V is the plasma volume, nimp is the impurity density and LZ is the radiative loss factor of impurity. For a specified tokamak with fixed V and nD+, both nimp and LZ are important to the power radiation.

The main plasma quantities at outer target as functions of Ar seeding rate can be seen in figure 8. With the increasing of seeding rate, both Tet and qdep fall first gradually due to the raising of nimp, then remarkably until fully detachment is achieved. The sudden drop occurs when Tet ∼ 130 eV for both PSOL cases, which is caused by more than one order of magnitude increment of LZ as Te raises higher than ∼130 eV [58]. Larger PSOL requires higher seeding rate to dissipate energy. To reduce Te at OSP below 5 eV, the required Ar seeding rate is 1.5 × 1020 argon atoms s−1 and 3.0 × 1020 argon atoms s−1 for PSOL = 4 MW and 10 MW, respectively. Plasma detachment can be achieved with remarkable reduction of Γdep as seeding rate is adding. The trends of peak and OSP values with seeding rate are similar. This indicates the power dissipation problem of W divertor can be solved by Ar gas seeding with appropriate seeding rate.

Figure 8.

Figure 8. The (a)–(c) OSP values and (d)–(f) maximum values of Tet, qdep, Γdep at the outer target, as functions of Ar seeding rate, for both PSOL = 4 MW and 10 MW cases. nD+,CEI = 4.5 × 1019 m−3 is fixed.

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Previous work showed strong influence of the divertor plasma on the main SOL and pedestal electron density, especially during highly dissipative conditions [59]. DIII-D experiment found that the seed impurity leads to increment of pedestal pressure, and a significant amount of the impurity has been found in pedestal [60]. The accumulation of the impurities in the core region causes a harmful effect to the sustaining of the high-performance plasma by radiation cooling and dilution [61]. Therefore, the understanding of SOL and pedestal changes associated with impurity injection is crucial for future reactors. For the designed divertor, it is important to know the core–edge compatibility during the impurity seeding, and the impurity content in the core region should be well controlled.

The effective ion charge Zeff in the core is usually taken as one of the important parameters to quantify the impurity content and divertor shielding. Zeff at CEI of OMP during Ar seeding is shown in figure 9, and it is proportional to impurity puffing rate for both PSOL, i.e. higher seeding rate leads to larger Zeff in the core region, figure 9(a). The scaling law for Zeff based on multi-machine database has been estimated by Matthews [62] as:

Equation (1)

where Prad is power radiation in MW, $\bar{{n}_{\mathrm{e}}}$ is line averaged electron density in unit of 1020 m−3, Z is the atomic number of impurity, α and β are fitting factors. The present simulation results can be fitted by specified α and β, and the scaling law becomes to

Equation (2)

Figure 9.

Figure 9.  Zeff at the CEI of OMP (a) as functions of Ar seeding rate, versus the scaling law of (b) equation (2) and (c) equation (3), for both PSOL = 4 MW and 10 MW cases. The neon seeding case is also included to verify the scaling. nD+,CEI = 4.5 × 1019 m−3 is fixed.

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Here Prad is the total radiation in the simulation domain, $\bar{{n}_{\mathrm{e}}}$ is the averaged ne along OMP, and $\bar{{T}_{\mathrm{e}}}$ is the averaged Te along OMP with unit of keV. The comparison of fitted Zeff with simulated value is shown in figure 9(b), indicating the fitting law can roughly describe the dependence of Zeff. However, the agreement is not very good for some points, due to the simple model omits radiation in different region and different discharge regimes of divertor plasma [30]. Since the line averaged values are taken from upstream region, and divertor plasma is not included, the power radiation in the core region Prad,core can be used instead of Prad. The corresponding scaling law becomes to:

Equation (3)

Figure 9(c) shows that equation (3) scales much better Zeff than that of equation (2). The scaling relations indicate that in a specified tokamak with fixed upstream density $\bar{{n}_{\mathrm{e}}}$, by seeding impurity to dissipate heat flux to divertor target, larger PSOL requires higher Prad, and leading to higher Zeff.

A pair of similar OD plasma condition cases, i.e. maximum Tet ∼ 5 eV, is chosen with seeding rate of 1.5 × 1020 and 3.0 × 1020 argon atoms s−1 for PSOL = 4 MW and 10 MW (as labeled by the dash lines in figure 8), respectively. The corresponding power radiation is Prad = 1.3 MW and 3.2 MW, and the fractional power radiation are similar frad = Prad/PSOL ∼ 0.32. It can be seen from figure 10 that the profiles trends of different quantities are similar for both PSOL cases, and qdep of PSOL = 10 MW case is much larger than that of PSOL = 4 MW case due to larger incident particle flux and higher plasma density. Zeff at CEI of OMP is 1.62 and 3.98, respectively.

Figure 10.

Figure 10. For similar maximum Te ∼ 5 eV at the outer target, the outer target profiles of (a) net, (b) Tet, (c) qdep, (d) total neutral deuterium density nDt + nD2t, (e) Ar impurity density nimp and (f) Γdep of PSOL = 4 MW and 10 MW cases, with seeding rate of 1.5 × 1020 and 3.0 × 1020 argon atoms s−1, respectively. nD+,CEI = 4.5 × 1019 m−3 is fixed.

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By the comparison between different input power, the simulation results demonstrate that higher PSOL requires larger seeding rate to achieve same frad, while it results in much higher impurity content in the core region and the corresponding core radiation is accordingly increased, scaled well by equation (3).

3.3. The comparison of argon and neon seeding

Ne has been proposed as the main seed impurity for ITER [5, 63]. In this work, the implantation of Ne seeding to EAST is also carried out and is compared to Ar seeding. Figure 11 shows the main plasma quantities at OSP as functions of the puffing rate of Ar and Ne, respectively. With the increase of seeding rate, significant energy loss is found for both impurities, and plasma detachment can be achieved. The rollover of ${{\Gamma}}_{\text{dep}}^{\text{OSP}}$ occurs with seeding rate of 1.1 × 1020 Ar atoms s−1 and 2.6 × 1020 Ne atoms s−1, respectively, showing that detachment requires a factor of 2.4 higher Ne seeding rate than Ar. The main reason can be attributed to that Ar has much higher radiative loss factor LZ than that of Ne [64]. This indicates power dissipation problem can be solved and Ar is more efficient than Ne. The remain question is what is the difference of two seed impurities to the core plasma? We turn to that next.

Figure 11.

Figure 11. The OSP values of (a) Tet, (b) qdep, (c) Γdep as functions of impurity seeding rate of Ar and Ne, respectively.

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From the power radiation point of view, the difference between Ar and Ne lies in the seeding amount. Since the required divertor plasma condition can be achieved by sufficient seed impurity, it is important to know the difference of the upstream plasma under similar plasma condition. We use ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$ and radiated power in the divertor region Prad,div to represent divertor condition, respectively, and Zeff is used to represent the influence on the core plasma. The Zeff scaling law equations (2) and (3) also fit Ne seeding case well, figures 9(b) and (c). Zeff at CEI of OMP as functions of ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$ and Prad,div are shown in figure 12. Smaller ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$ corresponds to larger Zeff. When ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$ < 20 eV, Ne seeding leads to larger Zeff than Ar seeding with same ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$; while ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$ > 20 eV, Zeff is similar with same ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$. The correlation between Zeff and Prad,div is the inverse of that between Zeff and ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$, due to that larger Prad,div leads to lower ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$. It should be noted that there is a reversal of Prad,div vs Zeff when Prad,div reaches the highest value, figure 12(b). It is attributed to that after detachment the energy radiation front moves from divertor region to upstream, leading to the reduction of Prad,div [59], thus impurity screening by divertor becomes worse.

Figure 12.

Figure 12.  Zeff at the CEI of OMP as functions of (a) Tet at OSP and (b) divertor power radiation Prad,div with Ar and Ne seeding, respectively.

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The plasma state with similar energy radiation in the simulation domain Prad ∼ 2.1 MW is chosen for further comparison. The seeding rate is 1.8 × 1020 Ar atoms s−1 and 3.0 × 1020 Ne atoms s−1, respectively, as labeled in figure 11 by the dash lines. Profiles along the outer target are shown in figure 13. It can be seen that peak Te is similar ∼3 eV, while peak qdep of Ne seeding case is about two times of Ar seeding case. More Ar accumulates in the vicinity the divertor target than that of Ne impurity, figure 13(e). The corresponding 2D contours of impurity density are shown in figure 14. It is clear that the Ne density in the core region is much higher than that of the Ar density, resulting in higher Zeff at the CEI 2.4 vs 2.0. The energy radiation distribution in the physical and computational regions are shown in figure 15. Ne impurity has larger radiation area, while Ar impurity focuses on radiating energy along the separatrix in the divertor region. The total radiated power in the divertor region is similar for two cases ∼1.2 MW. However, it should be noticed that power radiation in the core region by Ar is even higher than that by Ne, 0.71 MW vs 0.56 MW, as shown in figure 16, due to that LZ of Ar is much larger than that of Ne [64]. Again, it demonstrates that heavier impurities are more efficient seed species for core radiation, which should be limited to avoid the degradation of the energy confinement. The ionization potential of the Ne atom is 21.6 eV, larger than that of Ar atom (15.8 eV). This leads to a deeper penetration of recycling Ne from divertor targets and correspondingly weaker screening for the Ne ions. Furthermore, it may also lead to a larger residence time of neon impurity, which is unfavorable for radiation [30].

Figure 13.

Figure 13. For similar total power radiation Prad ∼ 2.1 MW, the outer target profiles of (a) net, (b) Tet, (c) qdep, (d) nDt + nD2t, (e) nimp and (f) Γdep for PSOL = 4 MW with seeding rate of 1.8 × 1020 Ar atoms s−1 and of 3.0 × 1020 Ne atoms s−1, respectively.

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Figure 14.

Figure 14. 2D contours of (a) Ne impurity density, (b) Ar impurity density, and (c) the corresponding Zeff along OMP. The seeding rates are 3.0 × 1020 neon atoms s−1 and 1.8 × 1020 argon atoms s−1, respectively. PSOL = 4 MW is fixed.

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Figure 15.

Figure 15. The power radiation distribution in the physical region (a), and (c) and computational region (b), and (d) during Ne and Ar seeding, respectively. The seeding rates are 3.0 × 1020 neon atoms s−1 and 1.8 × 1020 argon atoms s−1, respectively. PSOL = 4 MW is fixed.

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Figure 16.

Figure 16. Total power radiation in different regions for Ne and Ar seeding cases, PSOL = 4 MW. Definitions of each regions: total—all the simulation domain, OD, ID, SOL, core—inside the separatrix.

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The simulation results show the advantage of Ar impurity on the power radiation efficiency and divertor impurity screening, compared to Ne impurity. The potential disadvantage of Ar is the strong core radiation, which is fatal for ITER due to the power flux across the separatrix has to stay above the H–L threshold [65]. The successful application of Ar requires further compression in the divertor region, which can be obtained by 'puff-pump' as realized in DIII-D experiment [66]. Our previous work found that the seed impurity plays a dominant role in the W erosion [38], which is another critical issue since the acceptable central concentration of W is below 10−5 in ITER [67, 68]. The last question is which seed impurity is better from aspects of the W target erosion and W impurity accumulation.

The erosion of the W target during the Ar and Ne seeding is calculated, respectively. The eroded W flux ΓW can be expressed by

where ΓImp is the incident impurity flux density and YPhy,W is physical sputtering yield. YPhy,W depends on incident species, incident energy and angle. It increases as the incident energy increases once the energy exceeds energy threshold. Figure 17 shows the correlations between the peak ΓW at outer target and puffing rate, ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$, and Prad,OD, respectively. With the increasing of seeding rate, ΓW first increases, then decreases until to be neglectable. The reason has been discussed in reference [38]. Similarly, higher Tet corresponds to lower puffing rate (figure 11(a)), and the competition between reduction of ΓImp and the increment of YPhy,W makes ΓW first increase and then decrease with the enhancement of ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$, which is similar to JET experiment with nitrogen seeding [69]. Heavier incident species (e.g. Ar) have lower energy threshold and higher YPhy,W [49]. This explains the reason of much larger ΓW with Ar seeding than that with Ne seeding with the same ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$ or Prad,OD. ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$ should be controlled below 10 eV with Ne seeding or below 5 eV with Ar seeding to effectively eliminate the eroded W source, as shown in figure 17(b).

Figure 17.

Figure 17. The peak eroded W flux at outer target as functions of (a) impurity seeding rate, (b) ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$ and (c) power radiation in the OD Prad,OD, with Ar and Ne seeding, respectively.

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The eroded W then transports in the plasma. The contamination of the core plasma has been observed with Ar seeding owing to the sputtering of upper W divertor on EAST experiment [70]. Thus, it is important to know the corresponding W impurity accumulation in the core region. To this end, the transport of W impurity is simulated by the coupling of DIVIMP and SOLPS modeling. The eroded W flux, i.e. figure 17, is taken as W source, the corresponding plasma state is used as plasma background, and the W impurities are tracked by DIVIMP. Figure 18 shows the dependence of W density at CEI on impurity seeding rate and ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$, respectively. It can be seen that Ar seeding leads to higher W density in the core region than that of Ne seeding with insufficient seeding rate (i.e. <1.6 × 1020 argon atoms s−1). For the same ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$, Ar seeding leads to more W impurity accumulated in the core plasma region, which can be explained by the eroded W source (figure 17(b)).

Figure 18.

Figure 18. The W density at the CEI as functions of (a) impurity seeding rate and (b) ${T}_{\mathrm{e}\mathrm{t}}^{\text{OSP}}$.

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To further investigate the difference of W impurity distribution between Ne and Ar seeding, the seeding rate of 1.8 × 1020 Ar atoms s−1 and 3.0 × 1020 Ne atoms s−1 (with similar energy radiation in the simulation domain, the same cases to figures 1316) are selected for comparison. From figure 13(b) we can see that both peak Te at outer target is smaller than 3 eV, therefore the erosion of outer target is well suppressed as shown in figure 17(a). However, there is still W impurity in the CEI of the two cases. The reason is that the ID is still in partial detached, i.e. Te at the far SOL is above 10 eV as shown in the inset graph of figure 19(a). As a result, the erosion of inner target is still remarkable. Ar seeding also causes stronger sputtered W flux than that of Ne seeding at inner target, which leads to higher W density at CEI as shown in figure 19(b). The total W impurity density distributions are demonstrated in figures 19(c) and (d). The highest density appears in the divertor region, where the W impurity is produced. This indicates the prompt redeposition is the dominant processes for W impurity during transport.

Figure 19.

Figure 19. (a) The eroded W flux along the inner target, (b) the W ion density at OMP of 3.0 × 1020 neon atoms s−1 and 1.8 × 1020 argon atoms s−1 seeding cases, total W impurity density of (c) Ar seeding case, and (d) Ne seeding case. The inset-graph of (a) is Te along the inner target.

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3.4. The divertor in–out asymmetry

The ID usually shows general more pronounced detachment compared to the OD and it is thus noncritical for most of tokamaks operated with normal Bt direction [71], even without the consideration of drifts [59]. Therefore, we prefer to use as simple shape of the ID target as possible, as shown in figure 1. One should be noted that in the present modeling, the drifts are switched off by default since it is very time consuming to obtain a steady-state solution due to numerical difficulty. For the normal Bt direction, the drifts drive the ion flux from outboard divertor to inboard divertor, resulting in the in–out asymmetry [7274]. The EAST lower divertor is designed to have an open vertical inner target, plus the related closed outer horizontal target. This will naturally lead to much weaker power radiation capability of the ID than that of the OD. Therefore, Te is higher in inner target than that of outer target when drifts are neglected, figure 19(a) vs figure 13(b).

To fully evaluate the performance of both ID and OD, SOLPS-ITER [75] with new version of B2.5 code [76], which can better handle drifts, is applied to model the drift case with Ar as the seed gas. The in–out asymmetry of Te has been offset by introducing drifts as shown in figure 20. It can be explained by the poloidal (Er × B) and radial (Ep × B) drift flows. Figure 21 demonstrates the Ar impurity distributions. In the outer target the radial drift flow drives Ar impurity from SOL towards the separatrix and into PFR, while in the ID it drives the impurity from PFR across the separatrix into the SOL. The poloidal drift pushes the impurity from OD to ID. As a result, Ar impurity accumulates in the inner SOL region with drifts as shown in figure 21, leading to the reduction of Te even in the far SOL region. In addition, drifts lead to the impurity flow reversal due to the competition with fluxes by thermal forces, parallel electric fields and the friction coupling between impurities and main plasma ions [77]. More ionized Ar appears upon the stagnation point with drifts, leading to the increment of impurity leakage [78]. Therefore, the Ar density at OMP is higher with drifts than that of without drifts. However, the increment of impurity core accumulation by drifts may also depend on the impurity species, divertor plasma states, divertor magnetic field configurations, or divertor shapes, which is required to be further studied. It should be noted that on EAST the drifts also lead to the formation of high field side high density, please see the detailed explanation in reference [78].

Figure 20.

Figure 20.  Te along the (a) inner target and (b) outer target, for drifts switched on/off cases with seeding rate of 1.0 × 1020 argon atoms s−1.

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Figure 21.

Figure 21. 2D contours of total Ar density for with and without drifts cases and corresponding profiles along the OMP. The seeding rate is 1.0 × 1020 argon atoms s−1.

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In general, with the consideration of drifts, the ion flow to inner target driven by drifts offsets the particle leakage in the inner open vertical divertor, resulting in the more symmetrical in–out divertor. This is one of the advantages of the designed divertor, which assists the W impurity control. It should be noted that the drifts change the absolute plasma values of the OD. However, the main conclusions of sections 3.13.3 do not change.

The designed OD target has enough area to swing the OSP for the 'fishtail divertor' operation. It is also compatible with the advanced magnetic configuration. A divertor coil (DC) with current |IDC| = 0–10 KA/turn is planned to be added under the lower divertor with the aim to create QSF divertor configuration. Our simulation results show that with impurity seeding, QSF divertor can significantly increase the divertor power dissipation, thus promoting the achievement of the plasma detachment compared to standard divertor [45]. Finally, to make it more flexible, the pumping opening in the CFR side can also be removed without remarkable influence of the divertor performance.

4. Summary and conclusions

The physical design of EAST lower tungsten (W) divertor is presented with the assistance of SOLPS and DIVIMP modeling. The divertor geometry is optimized by considering horizontal target with OSP at different positions, vertical target, target with different slant angle, and pump opening at different locations. The simulation results indicate the horizontal target with the OSP close to the corner, which creates a relative closed divertor, can promote the achievement of the fully detachment across the target. The target slant angle has slightly influence on the divertor plasma. The pump opening is placed on the PFR to ensure the required particle exhaust, while keeping enough power exhaust. The performance of the designed divertor with W target is evaluated by argon (Ar) seeding with different heating power (PSOL). SOLPS simulation demonstrates the plasma temperature and power load to the target can be significantly reduced, and the plasma detachment can be achieved by sufficient Ar seeding. Larger PSOL requires higher seeding rate to dissipate the energy. The power dissipation problem for W divertor can be solved by Ar seeding with appropriate seeding rate. However, the accumulation of seeded Ar in the core region is another important limitation. The scaling law of effective ion charge Zeff is fitted by the simulation results. It explains that why larger PSOL leads to higher Zeff with similar divertor plasma conditions. By comparing Ne and Ar seeding, it is found the advantage of Ar impurity is the higher power radiation efficiency and better divertor impurity screening. While the disadvantage of Ar is the stronger core radiation. The W target erosion and W impurity accumulation in the core region are finally evaluated by the coupling of DIVIMP and SOLPS modeling, the simulation results demonstrate that Ar seeding causes more serious target erosion and core plasma contamination problem than that of Ne seeding.

The ID is designed to have an open vertical target, which is naturally characterized by the weak power radiation capability. However, this can be offset by the ion flow driven by the drifts. As a result, the designed divertor becomes more in–out symmetrical with the favorable Bt direction. Moreover, the divertor is compatible with the QSF magnetic configuration, which can further promote the power handling capability, especially during impurity seeding.

This work presents the physical design of the EAST lower divertor to find out the optimized geometry to achieve further high performance long-pulse discharge. It illustrates the application of external impurity seeding to achieve the radiative divertor with W target and the resulting W accumulation in the core region. These studies will improve the understanding of the plasma detachment of W divertor, and the control of W target sputtering and W impurity core accumulation for future fusion device. However, the present study could be taken as the first step of the EAST W divertor design, further quantitative investigations are required. The systematic work with full drifts switched on will be carried on in the future work.

Acknowledgments

This work is supported by National Key R&D Program of China Nos. 2017YFA0402500, 2018YFE0301101, 2017YFE0301206, 2017YFE0300402 and 2019YFE03030000, National Natural Science Foundation of China under Grant Nos. 11775044, 12011530053, 12022511, 11922513 and U19A20113, CASHIPS Director's Fund under Grant No. BJPY2019A01, the key Research Program of Frontier Sciences, CAS with No. ZDBS-LYSLH010, and AHNSF under Contract No. 1808085J07. The authors thank the anonymous referees for their constructive comments.

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