The influence of E× B drift on tungsten target erosion and W impurity transport during neon seeding on EAST

The E× B drift has a great impact on the redistribution of particles and energy in the divertor, which may result in divertor in-out asymmetry [5, 17–19]. Figure 2 shows the profiles of electron temperature T_e, electron density n_e and deposited heat flux q_dep along the inner and outer targets (OT) in different B_t directions, with the Ne puffing rate of 1 × 10²⁰ atoms/s. The divertor in-out asymmetry is changed significantly by E× B drift. Power exhaust in the whole region is dominated by Ne impurities, while radiation by the intrinsic W impurity is small (e.g. P_rad = 2.54 MW by Ne vs P_rad = 0.008 MW by W in the without-drift case). Figure 3 shows the 2D contours of total Ne density n_Ne and total Ne power radiation density P_rad,Ne in the divertor region in different B_t directions. In forward B_t, drift can increase the total Ne ion flux across the radial cut at the X-point through PFR and enhance the Ne recycling from the inner target (IT), while suppressing the Ne recycling from OT. However, the achievement of detachment (when T_e is very low) in the ID with drift reduces the Ne atom ionization. Therefore, more Ne atoms could penetrate the upstream region. Overall, the drift can drive the Ne impurity from the outer divertor (OD) to the ID through PFR, thus promoting the achievement of detachment in ID. Meanwhile, the drift also promotes the leakage of Ne impurity in ID to the upstream region in the high field side (HFS), thus the effective ion charge at CEI of OMP ${Z_{{\text{eff,CEI}}}}$ (which is defined to evaluate upstream impurity content) is increased from 2.51 to 2.81 and the total Ne radiation in the core P_core,Ne is increased from 0.47 MW to 0.83 MW. Radiation in the divertor is mainly contributed by line radiation due to excitation emission from Ne³⁻⁵⁺ ions, which mainly distribute near the separatrix. The front of the net Ne³⁻⁵⁺ source moves upstream of the HFS in forward B_t, which is attributed to the lower T_e near the target and the drift flux directed to the upstream region, thus the radiation near the X-point increases significantly, see figure 3(e). As a result, T_e and q_dep decrease at IT, while they increase significantly at OT, see figures 2(a) and (e). In reversed B_t, the transport of Ne ions from ID to OD through PFR is enhanced by drift, and it induces the increase of T_e and q_dep at IT due to lower P_rad,Ne in ID. However, even the peak T_e at OT is reduced compared to the forward B_t case, but it is still higher than the without-drift case. The strong radial drift near the separatrix drives Ne ions to the outer far SOL, thus reducing the radiation near the OSP where the peak T_e appears, as shown in figures 3(c) and (f). A shift of n_e profile along IT towards the inner common flux region (CFR) in forward B_t can be observed in figure 2(c). Similarly, the n_e profile along OT is shifted towards the outer CFR in reversed B_t, see figure 2(d).

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As we know, the influences of drift on the transport of the main plasma (D⁺) and impurity ions are equally important. The n_e and n_Ne in the divertor may increase/decrease simultaneously. Therefore, the Ne concentration (C_Ne= n_Ne/n_e) may not be changed significantly by drift. However, Ne impurities play a dominant role in the power radiation, thus it has a greater impact on T_e compared to D. It should be noted that since the electric field E is in direct proportion to T_e, the E× B drift as well as ion transport are also affected by Ne impurity, which is a strong nonlinear process.

The W target erosion can be roughly calculated by ${{\Gamma }}_W^{ERO} = \sum\nolimits_{i,j} {Y_{phys}^{i,j}{{{\Gamma }}_{i,j}}}$, where i and j represent incident ion species and different charge states, respectively, $Y_{{\text{phys}}}^{\,i,j}$ is sputtering yield and ${{{\Gamma }}_{i,j}}$ is the incident ion flux to the target. ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ can be affected by drift in two ways. On the one hand, drift induces the divertor in-out asymmetry, and at least one of the divertors (depends on the B_t direction) becomes hotter than in the without-drift case. As a result, $Y_{{\text{phys}}}^{\,i,j}$ is enhanced. On the other hand, drift contributes to the redistribution of charged particles, which influences ${{{\Gamma }}_{i,j}}$. The total eroded W flux ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ along the targets are shown in figure 4. W target erosion is dominated by Ne ions, see the explanation in [4]. In forward B_t, the peak value of T_e at OT increases from 3.0 eV in the without-drift case to 16.2 eV. The incident energy of Ne ions is in direct proportion to T_e, and an ion with high incident energy has larger ${Y_{{\text{phys}}}}$. Therefore, ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at OT is increased significantly by the drift. The erosion of the IT is suppressed by the drift mainly due to T_e being reduced. While in reversed B_t, W erosion at IT is strongly enhanced as T_e increases significantly. ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at OT is also increased owing to higher T_e near the OSP compared to the without-drift case. The integrated W eroded flux at the IT and OT are summarized in table 2. The total integrated ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ values at the targets are increased by two orders of magnitude (from ∼10¹⁷ to ∼10¹⁹) with the drift term switched on.

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Table 2. Integrated W eroded flux at inner and outer targets in different B_t directions.

	Integrated W eroded flux at targets (s−1)
	Inner target	Outer target
W/O drift	$9.68\, \times \,{10^{17}}$	$7.42 \times {10^{16}}$
Forward	$2.48 \times {10^{16}}$	$3.95 \times {10^{19}}$
Reversed	$7.46 \times {10^{19}}$	$2.95 \times {10^{18}}$

Next, the effect of drift on W impurity distribution is investigated. Figure 5 shows the 2D distribution of total W density n_W. When the drift term is turned on, n_W in the whole simulation domain is increased due to the stronger W impurity source, as shown in table 2. In forward B_t, the integrated ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ is larger at the OT than that at the IT, while n_W in the HFS is higher than that in the low field side (LFS), see figure 5(b). The E× B drift influences the W transport as follows: the sputtered W atoms are ionized, and then they are driven from the outer CFR to the PFR in the OD by radial E× B drift. Thus, n_W in PFR increases. The poloidal E× B drift prompts more W ions to transport from OD to ID through PFR. The ratios of the integrated W eroded flux along IT and along OT to the total W ion flux across the radial cut at the X-point through PFR are 0.05 and 8.4, respectively. This indicates that in the HFS the transport dominates the W flux balance, while in the LFS the W erosion is the dominant term. Moreover, some of the W particles in the OD transport to the upstream region in the near SOL of the LFS. It should be noted that the W concentration (C_W = n_W/n_e) in both the HFS and the LFS of the forward B_t case is much higher than that in the without-drift case, which is attributed to the increase of n_W, as shown in figures 5(a) and (b). In reversed B_t, ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at both targets is enhanced compared to the case without drift, as illustrated in figure 4, thus n_W in the whole region is increased. Due to the transport of W ions from ID to OD through PFR by E× B drift, n_W at LFS is higher than that at HFS and even more W atoms are sputtered from IT (table 2), which is contrary to the forward B_t case, see figure 5(c). Figure 6 shows the profiles of n_W along the inner (IMP) and outer mid-plane (OMP) in SOL. n_W at mid-planes is uplifted by drift. W ions mainly transport to the upstream from the inner divertor entrance (IDE) in forward B_t and from the outer divertor entrance (ODE) in reversed B_t, respectively. Comparing the reversed B_t case with the forward B_t case, n_W at both IMP and OMP are higher due to stronger target erosion. It is worth noting that the integrated ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ (9.68 × 10¹⁷ s⁻¹) at IT is an order of magnitude higher than that at OT (7.42 × 10¹⁶s⁻¹) in the without-drift case, as indicated in table 2. However, n_W along IMP (peak value of 1.80 × 10¹⁴ m⁻³) is lower than that at OMP (peak value of 2.17 × 10¹⁴ m⁻³). This is attributed to the impurity leak mechanism in the divertor region. We will turn to the impurity leakage analysis next.

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Sputtered W impurity has two typical transport paths: (1) returning to the targets after ionization (including prompt redeposition, which is defined as the redeposition of W⁺ during the first gyration) and retaining in divertor; (2) escaping to the upstream region and entering core plasma through cross-field transport. The process of W ions leakage and retention in the divertor dominates W core accumulation.

Friction force with main ions and thermal force due to the ion and electron temperature gradients dominate the parallel momentum balance of impurity. While the contribution of electric force and impurity pressure gradient are small, as illustrated by SOLPS-ITER simulation on DIII-D [20]. The W ion velocity can be deduced by the force balance summed over all the charge states [21]:

$$\begin{align}& {m_D}{n_D}\sum\nolimits_a {{n_a}\left\langle {{\sigma _i}\upsilon } \right\rangle \frac{1}{{\left\langle {{n_W}} \right\rangle }}\left( {{v_{\parallel ,D}} - \left\langle {{v_{\parallel ,W}}} \right\rangle } \right)} + \sum\nolimits_a {\frac{{{\alpha _{{a_i}}}Z_a^2{n_a}}}{{\left\langle {{n_W}} \right\rangle }}{\nabla _\parallel }{T_i}}\nonumber\\ & \quad + \sum\nolimits_a {\frac{{{\alpha _{{a_e}}}Z_a^2{n_a}}}{{\left\langle {{n_W}} \right\rangle }}{\nabla _\parallel }{T_e} \approx 0} \end{align} \tag{ 1 }$$

where the subscript 'a' denotes the individual charge state of all W plasma species, ${m_{\text{D}}}$, ${n_{\text{D}}}$ and ${v_{\parallel ,{\text{D}}}}$ represent the mass, density and parallel velocity of the main ion (D⁺), respectively. The average W parallel velocity is $\left\langle {{v_{\parallel ,W}}} \right\rangle = \sum\nolimits_a {Z_a^2{n_a}{v_{\parallel a}}/\left\langle {{n_W}} \right\rangle }$ with $\left\langle {{n_W}} \right\rangle = \sum\nolimits_a {Z_a^2{n_a}}$. The rate coefficient for momentum exchange between W and D ions is ${\sigma _i}\upsilon = KZ_a^2$ with proportional coefficient $K$, ${\alpha _{{a_i}}}$ and ${\alpha _{{a_e}}}$ are kinetic coefficients. The W leakage from the divertor depends mainly on the relative position of the stagnation point ($\left\langle {v_{\parallel ,{\text{W}}}}\right\rangle = 0$) and the W ionization front. If the sputtered W atom is ionized below the stagnation point, it will return to the targets. When the ionization occurs above the stagnation point, the W ions can escape from the divertor and have the possibility of entering the core plasma. The velocity of each charge state W ions ${v_{\parallel a}}$ almost equals the average velocity $\left\langle{v_{\parallel ,{\text{W}}}}\right\rangle$ when terms except for the friction force and thermal force in the force balance are relatively small. The validity of this approximation has been demonstrated in [21]. According to the balance between friction force and thermal force, ${v_{\parallel a}}$ satisfies the equation:

$$\begin{equation}{m_{\text{D}}}{n_{\text{D}}}{n_a}\langle{\sigma _i}\upsilon\rangle \left( {{v_{\parallel ,{\text{D}}}} - {v_{\parallel a}}} \right)\, + \,{\alpha _{{a_i}}}Z_a^2{n_a}{\nabla _\parallel }{T_i}\, + \,{\alpha _{{a_e}}}Z_a^2{n_a}{\nabla _\parallel }{T_{\text{e}}}\, \approx \,0.\end{equation} \tag{ 2 }$$

It can be concluded from equation (2) that W ion velocity depends on ${v_{\parallel ,{\text{D}}}}$.

When E× B drift is taken into consideration, the poloidal velocity of W ${v_{{\text{p,W}}}}$ mainly consists of the poloidal projection of parallel velocity and poloidal E_r × B drift velocity ${v_{{\text{p}},E \times B}}$, and other components such as impurity anomalous diffusion make little contribution. Therefore, thr average poloidal velocity of W $\left\langle{v_{{\text{p,W}}}}\right\rangle$ can be written as

$$\begin{equation}\langle{v_{{\text{p,W}}}}\rangle = \langle{b_x}{v_{\parallel ,{\text{W}}}}\rangle + {v_{{\text{p}},E \times B}}\end{equation} \tag{ 3 }$$

where ${b_x}$ is the sine of the pitch angle. Drift may change the position of the W velocity stagnation point, and thus affect the poloidal W flow pattern. Moreover, drift can change ${v_{\parallel ,{\text{D}}}}$, which in turn influences ${v_{\parallel ,{\text{W}}}}$ according to equation (2).

The poloidal W flow pattern with the drift term switched off is first analyzed. The positions of the velocity stagnation point ($\left\langle{b_x}{v_{\parallel ,{\text{W}}}}\right\rangle = 0$) calculated by $\left\langle{v_{\parallel ,{\text{W}}}}\right\rangle$ in equation (1) and the W ionization source ${S_{{\text{W,Ion}}}}$ in the SOL in the without-drift case are illustrated in figure 7(a). The stagnation points are in the vicinity of the ODE at LSF, while there are no stagnation points at HFS. The W erosion peak at OT locates near the OSP, where ${S_{{\text{W,Ion}}}}$ is intense. Nevertheless, most of the W atoms sputtered from the OT are ionized below the stagnation point. These ionized W impurities are retained in the divertor and can hardly escape. ${S_{{\text{W,Ion}}}}$ is compressed to the hot OT region especially near the OSP, while the stagnation points in the corresponding flux tubes are located above the ODE. Therefore, the transport of W ions to the upstream region is suppressedin the near SOL due to W ion flux directed to the OT, which leads to low n_W in the near SOL at OD, see figure 7(b). Due to the erosion of the baffle, an obvious W ionization zone can be seen in the far SOL near the ODE, where part of the W ionization appears above the stagnation points. Thus, n_W at the OMP is slightly higher than that at the IMP, as indicated in figure 6. W target erosion at the upper divertor by high energy neutral particles contributes to ${S_{{\text{W,Ion}}}}$ in the top region. The $\left\langle{b_x}{v_{\parallel ,{\text{W}}}}\right\rangle$ near the top region is directed towards HFS, thus some W ions can transport to the IMP and deposit onto the IT.

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Next, the influence of drift on W impurity transport is investigated. Figure 8(a) shows the positions of the stagnation point ($\left\langle{v_{{\text{p,W}}}}\right\rangle = 0$) and W ionization source ${S_{{\text{W,Ion}}}}$ in the SOL in forward B_t. The position of the stagnation points is changed by drift flow. As a result, almost all of the sputtered W atoms are ionized below the stagnation point at both LFS and HFS. Thus, the W impurity can hardly escape from the divertor region. Even though ${S_{W,Ion}}$ at the OD is much stronger than at the ID due to the larger ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ of the OT, n_W at the IDE is higher than that at the ODE, see figure 8(b). This is attributed to the W ions redistribution in the divertor induced by poloidal and radial E× B drift. In addition, the cross-field transport of W ions from the far SOL to the near SOL in the OD driven by radial E_p × B drift enhances the n_W near the separatrix, figure 8(b).

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Figure 9 shows the distribution of ${S_{{\text{W,Ion}}}}$ and n_W in the inner and outer PFR in the without-drift and forward B_t case. The direction of W impurity flux is illustrated in figures 9(a) and (c). In forward B_t, massive ${S_{{\text{W,Ion}}}}$ at some distance away from the OT in the outer PFR comes from dome sputtering, which is contributed by enhanced charge exchange neutrals. These W ions can transport to the inner PFR and then cross the separatrix and enter the ID. Thus, n_W is high near the X-point, figure 9(d). As shown in figure 8(a), the stagnation points are located close to the IDE in the near SOL. Therefore, the W can easily escape from the inner PFR to the core region through the X-point. The W flow pattern is similar in reversed B_t and only the direction of drift flow is changed, thus it is not shown here. W impurity transport can also be influenced by the ionization mean free path (MFP) of the W atom [22] $\lambda _{\text{W}}^{{\text{mfp}}} = \frac{{{v_{\text{W}}}}}{{{n_{\text{e}}}{{\langle \sigma \upsilon \rangle }_{EI}}}}$, where ${v_{\text{W}}} = \sqrt {\frac{{2{T_i}e}}{{{m_i}}}}$ is W atom velocity, ${\langle \sigma \upsilon \rangle _{EI}}$ is the ionization rate coefficient. The radial E_p × B drift, which drives plasma from the inner PFR to the inner CFR, leads to a decline of n_e in the inner PFR compared to the without-drift case, see figures 2(c) and (d). Thus, $\lambda _{\text{W}}^{{\text{mfp}}}$ in the inner PFR is larger in forward B_t and the ionization front extends closer to the X-point, which contributes to the enhanced W leakage from ID.

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To quantitatively analyze the effect of E× B drift on W transport, the total W flux and E× B drift W flux integrated over different segments are summarized in table 3. The sketch of corresponding segment locations is shown in figure 10(b), where L1 is the interface of inner and outer PFR, L2 and L3 are radial surfaces of ODE and IDE, respectively, L4 and L5 are segments between the X-point and strike points. The radial E_p × B drift facilitates the cross-field transport from the outer CFR to the outer PFR and the integrated E× B drift flux through L4 is −7.66 × 10¹⁸ s⁻¹, which is comparable to the integrated total W flux of −5.54 × 10¹⁸ s⁻¹. Thus, n_W in the PFR is increased. The integrated total W flux (−4.72 × 10¹⁷ s⁻¹) from the OD to the ID through L1 is dominated by poloidal E_r × B drift flux (−4.66 × 10¹⁷ s⁻¹), which conduces to W ion redistribution in the divertor. W ions in the inner PFR enter the SOL through L5 by radial E_p × B drift, and the integrated drift flux (2.59 × 10¹⁷ s⁻¹) is almost a factor of two larger than the integrated total W flux (1.40 × 10¹⁷ s⁻¹), as shown in table 3. Both the integrated total W flux and E_r × B drift flux through L2 is directed towards the OT, thus W ions in the OD can hardly transport to the upstream region in the LFS. At the IDE, the integrated E_r × B drift flux through L3 is directed upstream, while the integrated total W flux points towards the IT. Overall, both of the integrated total W fluxes along the IDE and the ODE are directed towards targets. The net W flux from upstream is balanced by (1) W impurity escaping from the X-point and (2) the W atoms ionized above the divertor entrance. Note that the E× B drift flux may be higher than the total flux, mainly due to the components of total flux being in different directions.

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Table 3. Total flux and E× B drift flux of W impurity integrated over different segments as shown in figure 10(b) in forward B_t.

	Total flux (s−1)	E × B drift flux (s−1)
From OD to ID (L1)	$- 4.72 \times {10^{17}}$	$- 4.66 \times {10^{17}}$
From OD to upstream (L2)	$1.47 \times {10^{16}}$	$5.11 \times {10^{16}}$
From ID to upstream (L3)	$- 9.20 \times {10^{17}}$	$5.18 \times {10^{17}}$
From outer CFR to outer PFR (L4)	$- 5.54 \times {10^{18}}$	$- 7.66 \times {10^{18}}$
From inner PFR to inner CFR (L5)	$1.40 \times {10^{17}}$	$2.59 \times {10^{17}}$

The W impurity transport in forward B_t can be summarized as follows, and the sketch of W impurity transport is given in figure 10(a).

• (a)  
  Retention in the divertor region: the sputtered W atoms from the targets and baffle are ionized below the velocity stagnation points, thus flowing back towards targets.
• (b)  
  Redistribution in the divertor region: W particles produced in the OD transport to the ID through PFR, which is dominated by the combined effect of radial and poloidal E× B drifts.
• (c)  
  Leakage from the divertor region: W ions in the PFR (including ionized W source from the dome, baffle and targets) transport through the separatrix by radial E× B drift and leak from the ID to the upstream region in the near SOL. There are also a few W ions from the PFR entering the OD through cross-field transport and flowing to upstream region in the near SOL of LFS.

Seeded impurities have a great impact on divertor plasma and thus change $\Gamma _{\text{W}}^{{\text{ERO}}}$ at targets. When the impurity seeding rate is increased, radiation exhaust caused by impurities is enhanced, which can prompt the achievement of divertor detachment [10, 23, 24]. Drifts may trigger the movement of the radiation front and affect plasma parameters in the divertor [25, 26]. Moreover, the production and transport of W impurity are varied by drift. Therefore, the Ne puffing rate is scanned to further investigate the influence of impurity levels on target erosion and W transport. The magnetic field is fixed to forward B_t, and only the puffing rate is varied. The without-drift cases are used for comparison. In forward B_t, when the puffing rate is low, the corresponding E is large. As a result, E× B drift is enhanced significantly, which causes a serious numerical converge problem. Therefore, there are no values for forward B_t for low puffing rates in the present work.

Figure 11 shows the peak value of electron temperature ${ }T_{\text{e}}^{\,{\text{peak}}}$, peak ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ and integral ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the IT and OT as functions of the Ne puffing rate. In without-drift cases, $T_{\text{e}}^{\,{\text{peak}}}$ and peak $\Gamma _{\text{W}}^{{\text{ERO}}}$ at the OT are higher than IT when the puffing rate is low (<7 × 10¹⁹ Ne atoms/s), see figures 11(a) and (b). However, from figure 11(c) it can be seen that the integral ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the IT dominates over the OT due to the larger W erosion area of the IT. The effect of drift is more obvious in the high recycling regime (upstream T_e is much higher than that at targets and $T_{\text{e}}^{\,{\text{peak}}} \leqslant 10\,{\text{eV}}$ at targets) than that in the low recycling regime [5, 27, 28]. In forward B_t, the divertor in-out asymmetry is enhanced drastically by drift in the high recycling regime and T_e at the OT is increased significantly compared to without-drift cases, thus W erosion at the OT is aggravated remarkably and the integral ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the OT is much higher than that at the IT, see figure 11(c). It should be noticed that $T_{\text{e}}^{\,{\text{peak}}}$ at the OT is similar (∼30 eV) with the Ne puffing rate of 1 × 10¹⁹ atoms/s in without-drift case and 7 × 10¹⁹ atoms/s in the forward B_t case, while both the peak ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ and integral ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the OT in the drift case are much higher than that in the without-drift case, with a difference of about an order of magnitude. The suppressed W erosion without the drift term activated is due to the fact that incident Ne ion flux is much smaller than that of the drift case. Therefore, we can see that the W source from targets is generally enhanced by drift.

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To determine which factor dominates the W transport and accumulation in the core region, the W concentration at the CEI of the midplanes $C_{\text{W}}^{\,{\text{CEI}}}$ as functions of $T_{\text{e}}^{\,{\text{peak}}}$ at the OT ($T_{{\text{e,OT}}}^{\,{\text{peak}}}$) in the without-drift case and forward B_t case are given, and the correlations between integrated ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at targets and $T_{{\text{e,OT}}}^{\,{\text{peak}}}$ are also established, as shown in figure 12. In the without-drift cases, $C_{\text{W}}^{\,{\text{CEI}}}$ at the OMP is higher than at the IMP, even the W source from the IT is predominant, see figures 11(c) and 12(a). This is due to the fact that W ions escape easily from the OD in the far SOL while W ions tend to remain in the ID, as discussed in section 3.2. The integrated OT ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ first increases when $T_{{\text{e,OT}}}^{\,{\text{peak}}}$ is lower than about 30 eV, followed by a drop with decreasing $T_{{\text{e,OT}}}^{\,{\text{peak}}}$ , as shown in figure 12(c). In forward B_t cases, a similar trend of integrated OT ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ with $T_{{\text{e,OT}}}^{\,{\text{peak}}}$ is also observed, see figure 12(d). This is due to the fact that inadequate seeded impurities can give rise to larger ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ depending on the competition between lower T_e and increased incident Ne ion flux [4], which is in accordance with the measurement of sputtered W flux during the Ne seeding experiment on EAST [29]. However, larger ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ does not necessarily raise $C_{\text{W}}^{\,{\text{CEI}}}$ (figures 12(a) and (c)) since the divertor regime also plays an important role in W accumulation in the core, which was demonstrated by our previous work [3] and DIVIMP simulations on EAST [22].

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In forward B_t, the W impurity source mainly comes from the OT, as shown in figure 11(c). $C_{\text{W}}^{\,{\text{CEI}}}$ at the IMP is much higher than at the OMP when $T_{{\text{e,OT}}}^{\,{\text{peak}}}$ becomes larger than 20 eV, see figure 12(b), which is attributed to the influence of E× B drift on W transport. Higher $T_{{\text{e,OT}}}^{\,{\text{peak}}}$ results in larger electric potential, which corresponds to higher electric field, thus the E× B drift is enhanced [5, 30]. W leakage is reinforced and $C_{\text{W}}^{\,{\text{CEI}}}$ at midplanes is increased consequently.

Figure 12(b) also demonstrates that drift can vary the asymmetry of W impurity poloidal distribution by affecting the W source and impurity transport. We define the degree of $C_{\text{W}}^{\,{\text{CEI}}}$ asymmetry as ${\text{AD}} = \frac{{C_{\text{W}}^{\,{\text{CEI,IMP}}} - C_{\text{W}}^{\,{\text{CEI,OMP}}}}}{{C_{\text{W}}^{\,{\text{CEI,OMP}}}}}$, where the positive value indicates $C_{\text{W}}^{\,{\text{CEI}}}$ at the IMP is higher than that at the OMP and the negative value indicates $C_{\text{W}}^{\,{\text{CEI}}}$ at the IMP is lower than that at the OMP. Figure 13 shows AD as functions of $T_{{\text{e}},{\text{OT}}}^{\,{\text{peak}}}$ in both cases. In without-drift cases, AD varies slightly (between −0.15 and −0.25) with $T_{{\text{e,OT}}}^{\,{\text{peak}}}$. It should be noticed that the absolute value of AD becomes smaller in without-drift case as $T_{{\text{e,OT}}}^{\,{\text{peak}}}$ increases. The reason for the reduced asymmetry is that the velocity stagnation point of W impurity also exists below the ${S_{{\text{W,Ion}}}}$ front in the near SOL region of the LFS, thus W impurity from the IT can escape from the divertor region. In forward B_t, AD ∼ −0.15 when detachment ($T_{{\text{e,OT}}}^{\,{\text{peak}}} \leqslant$ 5 eV) is achieved in the OD. In the attached regime ($T_{{\text{e,OT}}}^{\,{\text{peak}}}$ > 5 eV), AD is increased to 0.82 with $T_{{\text{e,OT}}}^{{\text{peak}}}$ = 20.8 eV due to the enhanced drift flow. AD decreases to some extent as puffing rate declines with $T_{{\text{e,OT}}}^{\,{\text{peak}}} > 20\,{\text{eV}}$, see figure 13. This is due to the fact that the total integral ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at targets, which is determined by the incident energy (i.e. $T_{{\text{e}},{\text{OT}}}^{\,{\text{peak}}}$) and incident Ne ion flux, rises relatively slowly and then falls with $T_{{\text{e,OT}}}^{\,{\text{peak}}}$, as shown in figure 12(d). With the consideration of drift, the poloidal asymmetry in W distribution is only obvious when one divertor is much hotter and has a stronger W source than the other, thus it leads to considerable W ion transport to another divertor through the PFR and then the leakage to the upstream region due to E× B drift. When detachment is achieved in both divertors, the W source from both targets declines and the redistribution of W impurity is weakened owing to the reduced drift flow.

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The average W concentration in the core plasma $\bar C_{\text{W}}^{\,{\text{CORE}}}$ is also evaluated to clarify the relationship between the W source and accumulation in the core. Figure 14 displays the $\bar C_{\text{W}}^{\,{\text{CORE}}}$ as functions of total integral ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at targets. It can be seen that when $\Gamma _{\text{W}}^{{\text{ERO}}}$ is smaller than 10¹⁹ s⁻¹, the drift can reduce $\bar C_{\text{W}}^{\,{\text{CORE}}}$ significantly with the same ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ compared to the without-drift case. As we have discussed above, W ions in the core mainly come from the HFS in forward B_t and the LFS in the without-drift case, respectively. Drift flow is decreased after divertor plasma detachment and thus fewer W ions transport to HFS, which gives rise to the suppressed W accumulation in the core compared to without-drift cases. $\bar C_{\text{W}}^{\,{\text{CORE}}}$ decreases as the total integral ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the targets reduce in forward B_t, which can be ascribed to the suppressed W erosion and enhanced W screening in the divertor. With a high puffing rate, T_e at the OT is reduced significantly, thus ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ is reduced due to the low sputtering yield, and the corresponding n_e in the divertor becomes large. As a result, $\lambda _{\text{W}}^{{\text{mfp}}}$ is reduced and W impurities retention in the divertor is increased. However, when the total integral ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the targets is higher than ∼10¹⁹ s⁻¹, $\bar C_{\text{W}}^{\,{\text{CORE}}}$ is increased remarkably by drift. This is due to the fact that T_e at the OT is high with a lower puffing rate (<1.2 × 10²⁰ atoms/s), as can be seen from figure 11(a) and the OD is in the attached regime, which contributes to the intense W sputtering at the targets and strong W leakage from the divertor. Plenty of W ions transport from the OD to the ID through the PFR by E× B drift and escape from the divertor in the near SOL at the IDE, as discussed in section 3.2. Therefore, W accumulation in the core is enhanced by the drift. In general, W accumulation in the core becomes severe when the divertor in-out asymmetry is enhanced by drift in the attached regime, while the W content in the core can be controlled effectively in the detached regime of both divertors when considering drifts.

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To directly illustrate the effect of drift on the W transport and the core accumulation, two cases in different B_t directions, with similar total integrated ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the targets, were chosen. The two cases are converted from the drift cases discussed in sections 3.1 and 3.2. Here, only physical sputtering from targets is included (erosion from other wall elements is turned off), and the redeposition rates at the IT and OT are varied so that the W source in forward B_t is in accordance with that in reversed B_t. The integrated ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the OT is 3.05 × 10¹⁸ s⁻¹ and 3.00 × 10¹⁸ s⁻¹ in forward and reversed B_t, respectively, and the eroded W profiles at the OT are shown in figure 15(a). ${{\Gamma }}_{\text{W}}^{{\text{ERO}}}$ at the IT is two orders of magnitude smaller than at the OT. As we can see from figure 15(b), n_W along the OMP in reversed B_t is higher than in forward B_t, especially in the near SOL. W ions are driven toward the separatrix from the outer CFR due to E_p × B drift in forward B_t, while they are driven away from the separatrix in reversed B_t, thus n_W below the ODE in the near SOL of the OD is higher in forward B_t than in reversed B_t, see figure 15(c). It is also visible in figure 15(c) that in the near SOL of the ID, n_W in forward B_t is also higher than in reversed B_t. In forward B_t, W ions transport from the OD to the ID through PFR by E_p × B and E_r × B drift, while W ion flux is in the opposite direction in reversed B_t, which contributes to higher n_W of HFS in forward B_t compared to reversed B_t. Nevertheless, we should keep in mind that the background plasma in the OD is different between forward and reversed B_t. The drift flux is stronger due to the higher T_e of the OD in forward B_t. Thus, it can be inferred that W transport caused by E× B drift is of vital importance and has a great influence on core accumulation.

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