Effects of strike point location on the divertor particle and energy flux decay widths on EAST by experiment and SOLPS modeling

The new lower tungsten divertor of EAST uses a right-angle shape consisted by horizontal and vertical targets, which has the capacity of increasing the divertor closure. The strike point (SP) sweeping experiment is carried out to (1) avoid long-term deposition of particle and heat flux at the same location, thus protecting the target, (2) study the dependence of power control capability on the SP location. The particle and energy flux densities to the target depends strongly on their decay width. Therefore, it is important to know how the SP location influences the outer target (OT) particle parallel λjs ,OT and OT parallel heat flux decay widths λq ,OT. In this work, SOLPS-ITER simulations combined with SP sweeping experiment are applied to study this issue. Four cases, which are taken from different time during SP sweeping (including both horizontal and vertical divertor) in L-mode experiment with high heating power, are selected for investigation. The simulation result is in satisfactory agreement with experiment data, suggesting the simulation is valid. The results indicate that the SP location can affect neutral particles accumulation and ionization positions, thus affecting λjs ,OT and λq ,OT. (1) When SP is located in horizontal target, the higher neutral particle ionization in common flux region leads to wider λjs ,OT than those of vertical target. (2) When SP is located on horizontal target, the divertor power radiation is higher than that of vertical target, resulting in wider λq ,OT. (3) Increasing upstream plasma density can effectively broaden λq ,OT, while λjs ,OT remains almost unchanged. This study improves the understanding of the influence of divertor shape on λjs ,OT and λq ,OT, and can be applied to heat flux control during long-pulse high-power discharges on EAST.


Introduction
During the long-pulse high-power discharge in a tokamak, particle and heat fluxes transport across the last closed flux surface and most of them will finally deposit onto the divertor target through the scrape-off layer (SOL).The parallel high particle flux (Γ ||,target ) and parallel heat flux density (q ||,target ) to the target can lead to target erosion and reduce the lifetime of the device [1].Additionally, impurities sputtered from the target may influence the steady-state discharge [2].It is essential to control Γ ||,target and q ||,target to sustain long-pulse high-power discharge, and the parallel particle flux decay width (λ js ) and parallel heat flux decay width (λ q ) in the SOL [3] are very important to determine the flux density.Eich et al found that λ q generally has an inverse proportional trend with the outer mid-plane (OMP) poloidal magnetic field (B p,OMP ) during Land H-mode discharges based on the experimental data from JET, AUG, DIII-D, and C-Mod [4][5][6], and the corresponding multi-mechanism scaling law is known as Eich's scaling law [4].
From 2010 to 2020, a series of experiments and simulations have been carried out on EAST to systematically study λ js and λ q [7][8][9][10][11], including with different magnetic field configurations (lower single null; upper single null; double null) [8,9], under different heating conditions (low-hybrid waves, LHW; neutral beam injection) [7,10] and different discharge modes (L-mode and H-mode) [8].Overall, EAST experiment results are consistent with Eich's scaling law: the inverse relationship between λ q and B p,OMP (or plasma current I p ) is always valid under various discharge conditions.Goldston et al developed a heuristic drift (HD) model and also found a negative correlation between λ q and I p [12], i.e. λ q ∼ q edge ρ 0 , where q edge is the boundary safety factor and ρ 0 is the mid-plane ion gyration radius, and the model explained the experimental results.However, the HD model has some limitations.For example, it assumes that particle turbulent on the boundary cannot exceed a certain level, and ignores collisions and radiation between the boundary plasma and neutral particles.
The parallel particle flux decay widths λ js,target and parallel heat flux decay widths λ q,target in the target () directly determines the Γ ||,target and q ||,target , and they depends on the widths in the SOL (λ q , λ js ).However, λ q,target (λ js,target ) are not always the same to λ q (λ js ).Recent studies found that there are other factors affecting λ q,target , e.g. both the B × ∇B direction λ q,target [13,14] and the turbulent particle motion on the boundary [13,15] have great impact on λ q,target .Moreover, the plasma behavior in divertor region, such as power radiation (P rad ), collisions and ionization, can also influence λ q,target [16][17][18][19].Our previous work has established a positive correlation between the collision rate in the SOL v * SOL and λ q,target [17,20], and we found the P rad in the divertor region can significantly broaden λ q,target , i.e. λ q,target increases as P rad increases [17].Previous EAST experimental studies found that the values of λ js,target and λ q,target are similar, i.e. λ js,target ≈ λ q,target [8,9,11].Due to the limitations of the diagnostics in EAST, the measurement of J sat on the target are more accurate than q || .Therefore, λ js,target is usually used instead of λ q,target experimentally [11].
EAST upgraded its lower graphite divertor to a tungsten divertor with a right-angle geometry [21] in 2021.The new divertor can flexibly adjust the X-point position through the controlling of poloidal field coils, thus allows the sweeping of strike point (SP) to form horizontal and vertical target [22][23][24][25].The SP sweeping can also avoid the prolonged deposition of particle and heat loads on a single location, thus preventing the damage of the target.Both of the preliminary SOLPS simulations and experimental measurement revealed that when the SP is located in the horizontal target (this case is called 'horizontal target' for simplification), it is easier to achieve plasma detachment than that of the SP located in the vertical target (this case is called 'vertical target' in this work) due to its more closed geometry [21,25].
In order to ascertain the changes of thermal load with the SP sweeping and to elucidate the effect of the SP location on the heat flux control, it is imperative to investigate the variation of λ js,target and λ q,target with the SP location.In this study, the SOLPS modeling is carried out to study the variation of λ js,target and λ q,target with the SP sweeping on EAST in attached regime, and the simulation results are benchmarked against the experiment measurement.In chapter 2, the experiment and the corresponding SOLPS modeling setup are introduced, and the comparison between simulation and experiment results are presented.In chapter 3, the effects of SP location on the λ js,target and λ q,target are analyzed and discussed based on the SOLPS simulation results.Finally, chapter 4 presents the conclusions.

Experiment and simulation comparison
In the EAST experiment shot #98332 (L-mode), as shown in figure 1, the SP is changed from the horizontal target to the vertical target by controlling the RF coil, and the X-point is moved from R x ∼ 159 cm to R x ∼ 166 cm, where R x is the major radius of X-point.The movement of the X-point induces the variation of the plasma shape, thus resulting in the changes of the low triangularity δ, which may vary by 20%.During this process, however, other key parameters remained relatively stable, e.g. the variation of elongation κ remains below 2% (κ ∼ 1.7), the q 95 variation rate keeps about 0.5%, the connection length is still around 100 m, and the flux expansion factor f x is about 2.2.The SP position is controlled by ISOFLUX [26] to control the magnetic flux distribution and by EFIT to reconstruct magnetic equilibrium.The distance between SP and corner on target is defined as d.As shown in figure 1(d), the SP location on the outer target (OT) gradually moves from horizontal target to vertical target.The error in the reconstructed SP location is approximately 3.0 ± 1.2 mm, which is calculated by comparing the SP position obtained by fitting target deposition heat flux density q dep,OT of infrared (IR) camera and Langmuir probes (LPs) data with the distance from EFIT SP [27].During the discharge, the average line-averaged density n e in the midplane remains around 2.1 × 10 19 m −3 until 6.5 s, after which point it increases by about 10%.The I p is 500 KA, and ion B × ▽B drift pointed toward the upper divertor.The experiment uses 2 MW and 4.6 GHz LHW, 0.7 MW and 2.45 GHz LHW, and 0.5 MW electron cyclotron resonance heating, with a total auxiliary heating power of 3.2 MW.No external impurity gas is injected.
In the experiment, the plasma profiles along the OT (electron density n e,OT , ion saturation current J sat,OT , electron temperature T e,OT and parallel heat flux density q ||,OT ) are measured by divertor LP [28,29].However, the arrangement of LP leads to poor resolution of plasma profile.Moreover, the damage of the probes increases the diagnostic error of the plasma parameters.In this experiment, the time signal of a single probe is converted into a spatial signal to obtain complete plasma profiles, which assumes that the plasma profile is unchanged at the same target (horizontal or vertical), and the profile shifts with the SP.This measurement method can eliminate the uncertainty caused by the different degrees of damage of the probes and it can obtain a complete plasma profile along the target.The disadvantages are (1) it cannot simultaneously obtain the complete distribution of plasma on both horizontal and vertical targets, (2) there is some degree of inaccuracy, especially in the case that the SP is near the corner.Therefore, it is essential to numerically simulate the experiment to obtain complete plasma information, and this is necessary to understand the effect of SP location on the λ js,OT and λ q,OT .
In this study, we employ SOLPS-ITER code to simulate the EAST experiment shot #98332.The SOLPS-ITER code is a coupling of the fluid code B2.5 [30], which simulates electrons and ions, and the kinetic code EIRENE [31], which simulates neutral particles.It is widely used to simulate and interpret experimental results [32,33].In recent years, SOLPS-ITER has also been applied to study the impact of boundary plasma on λ q [14,17].Since the OT usually suffers stronger heat and particle fluxes than inner target, this study mainly focuses on the physical quantities in the outer divertor (OD).The plasma profiles along the OT can be taken from experimental diagnostics and numerical simulation.Then the obtained ion saturation current J sat,OT = eΓ ||,OT and q ||,OT are mapped to the OMP.Finally, the Eich formula [6] is used to calculate λ js,OT and λ q,OT q (r) = q 0 2 exp where q 0 is the peak parallel heat (particle)flux density, r = r − r sep (where r is the radial location projected to OMP, and r sep is the radial location of the separatrix at OMP), q BG is the background heat flux (particle flux), and the Gaussian width S represents the width of the heat (particle) flux in the private flux region (PFR).All the experimental and simulated cases are in attached regime, and Eich formula fits the J sat,OT , and q ||,OT well (R 2 > 0.97).
In this work, t = 3.6 s, 4.4 s, 5.6 s, and 6.3 s (i.e.d t=3.6 s = −3.0cm, d t=4.4 s = −1.2cm, d t=5.6 s = +1.0cm, and d t=6.3 s = +3.0cm) of shot #98332 are used to represent the magnetic equilibrium configurations with the SP locates at far corner and near corner of the horizontal target, and near corner and far corner of the vertical target, respectively.The simulations are first performed for the t = 4.4 s (SP is near to #13 LP on the horizontal target) and t = 6.3 s (SP is near to #8 LP on the vertical target), as shown in figure 1  domain ranges from the core-edge interface (CEI) to the outermost SOL boundary, i.e. r − r sep ⊂ (−4.3, +1.8 cm) at OMP.Since the impurity radiation in the core region is not considered in the simulation, it is assumed that 50% of the experiment heating power flowed into the simulation domain (P input = 1.6 MW) and the power is divided equally between electrons and ions [34,35].In the simulation, the recycling coefficient R rec is set to 1 except for the pumping port, where R rec is set to 0.95, and drift is currently not taken into consideration [33].The particle and energy reflection coefficients, which are functions of incident energy and angle, are calculated by TRIM [36].The angle of the reflected particle follows specular reflection, which is similar to previous SOLPS simulation [37].Note that we do not attempt to simulate the time-dependent evolution of the discharge, instead each time slice is taken as steady-state, which is simulated separately.
In the experiment, the upstream plasma density profile n e,omp was measured by a reflectometer, as shown in figures 2(c) and (d).The 20% uncertainty of the OMP plasma density is mainly caused by the error of reflectometry radial position, and it is affected by the plasma density cutoff layer [38].The horizontal error is due to the SP location reconstruction error mapped to OMP.In the simulation, by adjusting the radial anomalous particle transport coefficient D ⊥ , the simulated n e,omp profiles show good agreement with the reflectometry measurements.Both experiment and simulation show that the electron density at the separatrix of OMP n OMP e,sep is slightly higher in horizontal target than that of the vertical target.Due to the large diagnostic error of Thomson scattering in the SOL, the electron temperature T e,omp is not available.The radial anomalous thermal transport coefficients of electrons and ions [14,25,33] χ ⊥,e,i is mainly determined by comparing T e profile at the divertor target with LP measurement, i.e. the upstream χ ⊥,e,i is adjusted to match the divertor T e profile, while keeping the value T e in OMP separatrix T OMP e,sep ∼ 100 eV [39].The turbulence was not considered in experiment.In the simulation, the turbulent only determines the anomalous transport coefficients, which was adjusted according to the experimental profiles.
Figure 3 shows the profiles of the main plasma quantities along the OT obtained from both the simulation and experiment.It is possible that the noisy in LP data was caused by: (1) the variation of discharge plasma parameters, as shown in figures 1(b) and (c); (2) the measurement errors of LP.In the simulation, by setting divertor region D ⊥ = 1.5 m −2 s −1 and χ ⊥,e,i = 1.0 m −2 s −1 , n e,OT and T e,OT are in reasonable agreement with LP measurement [40,41].
By comparing the SOLPS simulation with LP data, it can be seen that the peak values of n e,OT and T e,OT are similar, while inconsistencies in the peak values positions and shapes of the profiles are observed, which were also found in other SOLPS simulation works [41].The reason for the inconsistency may lies in: (1) in experiment, the SP position is determined by the peak of T e,OT , which may have some deviation from the actual SP.The plasma profiles obtained from the LP may also have some errors, determined by the discharge condition; (2) the main plasma profiles along the target are influenced by radial transport (i.e.E × B drift, ballooning mode), which were not considered in the current simulation.However, the J sat,OT and q ||,OT of SOLPS are both larger than the LP diagnostic, i.e. the maximum ion saturation current (J peak sat,OT ) and parallel heat flux (q ∥,OT peak ) are about 150% and 200% of the experimental values, respectively.The differences between SOLPS simulation and experiment were also observed in other works, such as EAST [41,42], C-Mod [43], Globus-M2 [44].Both simulation and experiment find that the difference of J peak sat,OT is small (<20%) between t = 4.4 s and 6.3 s, while the T peak e,OT and q peak ∥,OT at t = 4.4 s are over 50% large than that of t = 6.3 s.Simulation results show similar trend to experiments at different time, suggesting the simulation is valid and consistent with experiment.EAST is equipped with IR to measure the target temperature and to obtain the q dep,OT , which can be expressed as: where θ is the angle between the poloidal magnetic field lines and the target, ψ is the angle between the toroidal magnetic field and the target.The intersection angle in different t (d) are listed in table 1.
The q dep,OT profiles obtained from IR, LP and SOLPS-ITER simulation in horizontal OT (t = 3.6 s, 4.4 s) are compared.As shown in figure 4, SOLPS-ITER simulation coincides with IR measurement when the SP is far from the corner (t = 3.6 s); while when the SP is close to the corner (t = 4.4 s), IR data is larger than simulation due to that the SP is further away from water-cooling than that of t = 3.6 s.The peak value of q dep,OT obtained from LP is about 40% of IR measured value, which is consistent with the observation in AUG [45,46].The possible reason is that: (1) LP measurement does not include contributions such as neutral particles, radiation, recombination heat fluxes, which are about 40% contribution to total deposition heat flux; (2) there are inevitable errors in the q dep,OT data from LP and IR measurements.For IR, due to the extended tail of heat flux away from separatrix, and the q dep,OT is calculated via surface temperature, which is influenced by the non-uniform distribution of water-cooling distribution and target thickness, the measured q dep,OT value may be overestimated.For LP, the damage of probes during the discharge lead to the underestimation.The peak value of q IR dep,OT is much larger than q LP dep,OT , resulting in a steeper gradient of q dep,OT in common flux region (CFR), and a smaller λ IR q,dep,OT .At t = 3.6 s, the decay width of q dep,OT measured by LP λ LP q,OT = 9.7 mm, which is about 154% of that measured by IR λ IR q,OT = 6.3 mm.In additional, it was also founded that λ LP q,dep,OT is 30% larger than λ IR q,dep,OT in previous EAST work [8].
Moreover, in the simulation, the peak q dep,OT at t = 3.6 s is q peak dep,OT ∼ 1.5 MW m −2 , which is about 150% of the value at t = 6.3 s (q peak dep,OT ∼ 1.0 MW m −2 ), and it is mainly caused by the difference of θ in the horizontal and vertical targets (as table 1 lists), which resulting plasma-wetted area A wet of vertical target is 236% of horizontal target.To eliminate the influence of the target geometry on λ q,OT estimation, the parallel  flux density, i.e.J sat,OT and q ||,OT , are used to calculate the decay width.
To facilitate a clear comparison of the λ js,OT and λ q,OT between the SOLPS-ITER simulation and experiment, the normalized profiles are used.Figure 5 shows the normalized profiles of Ĵsat = J sat,OT /J peak sat,OT and q∥,OT = q ∥,OT /q peak ∥,OT , and the corresponding λ js,OT and λ q,OT .Due to the underestimation of LP data, the peak values of J sat,OT and q ||,OT by SOLPS simulation are much larger than that of LP data, while in far SOL region the difference is smaller.The gradient of J sat,OT and q ||,OT in CFR from SOLPS simulation is steeper than that by LP measurement, resulting λ js,OT and λ q,OT from SOLPS simulation are smaller than from experiment.For example, in t = 4.4 s case, the experimental λ js,OT and λ q,OT are 180% and 170% of the simulation values, respectively; in t = 6.3 s case, they are 140% and 150% of the simulation values, respectively.Both experiment and simulation find that λ js,OT and λ q,OT at t = 4.4 s are larger than those at t = 6.3 s, e.g. at t = 4.4 s, λ js,OT is 207% and 172% (λ q,OT is 145% and 130%) of those at t = 6.3 s in the experiment and simulation, respectively.In previous EAST upper divertor experiment, it was found the values of λ js,OT and λ q,OT were similar (i.e.λ js,OT /λ q,OT ≈ 1) [7][8][9]11].In this work, large difference between λ js,OT and λ q,OT are found in both experiment and simulation at t = 4.4 s (λ js,OT /λ q,OT are 1.6 and 1.48, respectively), while at t = 6.3 s, λ js,OT /λ q,OT are 1.13 and 1.22 in experiment and simulation, respectively, which is more consistent with previous EAST upper divertor experiment.This indicates that it is not accuracy any more to use λ js,OT instead of λ q,OT in experiment in the case of horizontal target.
In summary, due to the limitations of diagnostic methods and probe distribution on EAST, the mechanism of how the SP location influences λ js,OT , λ q,OT , and λ js,OT /λ q,OT is not clear.Although the simulated λ js,OT and λ q,OT are smaller than those measured by LP probe [7], the effect of SP location on λ js,OT , λ q,OT , and λ js,OT /λ q,OT in the simulation is consistent with the experiment.Thus, it is crucial to simulate the experiment by SOLPS-ITER for further analysis.In this work, SOLPS is used to simulate the divertor plasma with SP at different locations, and the changes of λ js,OT , λ q,OT , and λ js,OT /λ q,OT with high upstream plasma density are clarified.

Effect of SP location on λ js,OT
Firstly, the SOLPS simulated different SP location cases (corresponding to t = 3.6, 4.4, 5.6 and 6.3 s in experiment) are selected for analysis, and the SP locations are shown in figure 1(a).The upstream density is consistent with the experiment (n e ∼ 2.1 × 10 19 m −3 , n OMP e,sep ∼ 0.92 × 10 19 m −3 ). Figure 6 displays the profiles of n e,OT , J sat,OT and their normalization, and the corresponding λ js,OT is calculated.At t = 3.6 s, the SP locates in the horizontal target and it is far from the corner.The radial gradients of n e,OT and J sat,OT in the far SOL region are the flattest, and the λ js,OT is maximum in all the cases.At t = 4.4 s, the peak n e,OT and J sat,OT become slightly higher, and the radial gradients become steeper, resulting in about 91% lower of λ js,OT than that of t = 3.6 s.It indicates that in the case of horizontal target, λ js,OT is affected by the distance between the SP and the corner d.While in the cases of vertical target (t = 5.6 and 6.3 s), the changes of n e,OT and J sat,OT are less than 5%, and λ js,OT is almost unaffected by d.In addition, in the cases of vertical target (t = 5.6 and 6.3 s), n peak e,OT is about 75% of that of horizontal target (t = 4.4 s), and the radial gradients of n e,OT and J sat,OT at vertical target are much steeper than those of horizontal target.As a result, the λ js,OT in vertical target is significantly smaller than in the horizontal target, e.g. at t = 6.3 s it was only around 58% and 62% of the λ js,OT at t = 3.6 and 4.4 s, respectively.
To further investigate the reason for the difference of λ js,OT with the horizontal and vertical target, and to understand the mechanism of how does d influence λ js,OT , the ion flux load on the CFR of OT is analyzed.According to particle conservation, the ion flux in the CFR Φ OT can be expressed as where Φ in represents the poloidal ion flux from upstream to the region, Φ ⊥ is the integrated radial ion flux (positive/negative value means the flow into/out of the region), and Φ ion indicates the sum of ion sources by recombination (negative value) and ionization (positive value).Φ in is similar at different time due to the similar upstream plasma density, and Φ ⊥ is also similar because the radial particle transportation coefficient in the divertor region is fixed.Previous studies showed that the ionization and recombination have significant impact on the particle flux density and distribution near the target [17].Therefore, we can assume that the difference of λ js,OT at different time is mainly caused by Φ ion .Figures 7(a) and (b) shows the total neutral particle density n D+D2 and D atom ionization rate along the OT.It reveals that in horizontal target (at t = 3.6 s and 4.4 s), both the peak values of n D+D2 and ionization rate are located at CFR, and in the far SOL region they are higher at t = 3.6 s than at t = 4.4 s.In the cases of vertical target (t = 5.6 s and 6.3 s), the peak values of n D+D2 is located in the PFR, while the peak ionization rate appears near the SP.To illustrate the effect of the target configuration on the distributions of neutral particles and ionization more directly, figures 7(c)-(f ) present the n D+D2 in the OD region.It is found that neutral particles tend to accumulate near the corner of the horizontal target regardless of whether the SP is on the horizontal or vertical target.This can be explained as follows: (1) in the horizontal target, most of the D atoms produced by the incident ions on the target will be reflected toward the vertical target, which also acts as a baffle to reflect the atoms toward the corner of the horizontal target again, causing the accumulation of neutral particles; (2) in the vertical target, the recycling neutral particles are directly reflected toward the horizontal target, causing the accumulation near the corner.Figures 7(g)-(j) show the 2D contours of D atoms ionization rate in the OD region.In the horizontal target, the ionization rate in CFR is higher due to the accumulation of neutral particles and the high T e (>15 eV) in this area.Conversely, in vertical target, the ionization rate in CFR is lower because the neutral particles tend to accumulate in the PFR, where T e is lower than the ionization threshold, and the ionization mainly occurs near the SP.As shown in figures 7(c)-(j), neutral particle accumulation and ionization mainly occur near the target.In order to quantitatively analyze their effect on λ js,OT , the CFR region near the target (i.e. the region about 5.1 cm away from the target) is divided into two parts: the near SP region (NSR, i.e. 18 < ix < 25) and the far SP region (FSR, i.e. ix > 25). Figure 7(g) shows the sketch of each parts in the mesh.The boundary between NSR and FSR (ix = 25) mapped to OMP is shown by the dashed line in figure 7(b).The values of each terms in equation ( 3) at different regions are listed in table 2. In NSR, due to the existence of n peak e,OT , the radial particle flux point toward the lower density region (PFR and FSR), and the contribution of Φ ⊥ to Φ OT is negative, i.e.Φ ⊥ /Φ OT ∼ −20%.At t = 3.6, 5.6, and 6.3 s, the contribution of Φ in to Φ OT (i.e.Φ in /Φ OT ) is close to 46%, which is slightly higher than that at t = 4.4 s (Φ in /Φ OT ∼ 38%).The reason is that the SP is closer to the corner, and the n D+D2 and ionization rate are higher at t = 4.4 s, thus Φ ion /Φ OT ∼ 81% is higher than at the other three times (Φ ion./Φ OT ∼ 71%).In FSR, although the values of Φ in are almost the same in all the cases, their contribution to Φ OT depends strongly on the SP location.In vertical target (t = 5.6 and 6.3 s) Φ in /Φ OT ∼ 74% is much larger than that of the horizontal target (Φ in /Φ OT ∼ 48% and 54% at t = 3.6 and 4.4 s, respectively).The reason is that the contribution of Φ ion to Φ OT is very different.At vertical target (t = 5.6 and 6.3 s) Φ ion /Φ OT ∼ 24% is much smaller than the horizontal target (Φ ion./Φ OT ∼ 51% and 44% at t = 3.6 and 4.4 s, respectively).
Overall, it can be considered that λ js,OT and Φ OT,FSR /Φ OT,NSR are positively correlated, which means the larger the particle flux flow to the FSR relative to the NSR (i.e. the larger Φ OT,FSR /Φ OT,NSR ), the flatter radial particle flux gradient and the larger λ js,OT .In the vertical target cases (t = 5.6 and 6.3 s), most of the neutral particles accumulate in the PFR and ionized near the SP, and the contribution of Φ ion to Φ OT in both FSR and NSR changes slightly with d.We obtain Φ OT,FSR /Φ OT,NSR ∼ 1.15.In the cases of horizontal target (t = 3.6 and 4.4 s), Φ ion can significantly increase Φ OT .At t = 3.6 s, (1) the neutral particles accumulate in the FSR resulting in higher ionization rate, thus Φ ion /Φ OT is larger than that of t = 4.4 s case; (2) while in NSR the Φ ion /Φ OT is smaller than that of t = 4.4 s case.Therefore, Φ OT,FSR /Φ OT,NSR ∼ 1.85 at t = 3.6 s is 26% larger than that at t = 4.4 s (Φ OT,FSR /Φ OT,NSR ∼ 1.46).Φ OT,FSR /Φ OT,NSR in horizontal target (t = 4.4 s) is further more than 27% larger than in vertical target.As a result, we obtain larger λ js,OT in horizontal target than in vertical target, i.e. λ js,OT = 3.36, 3.08, 1.95 mm at t = 3.6, 4.4 and 5.6 (6.3) s, respectively.

Effect of SP location on λq ,OT
The q ||,OT could be expressed as where γ is fixed to 7. It indicates that q ||,OT depends not only on J sat,OT , but also on T e,OT .Therefore, it is necessary to analyze T e,OT to understand the variations of q ||,OT and λ q,OT .Table 3 lists P rad in different regions of each case.At t = 4.4 s, due to the accumulation of neutral particles in the CFR region and higher ionization rate, P rad in the OD is the highest, about 160% of that of t = 6.3 s case, which result in 50% lower T peak e,OT and q peak ∥,OT than t = 6.3 s in both experiment and simulation, see figures 8(a) and (c).Figures 8(b) and (d) show the normalized profiles of T e,OT and q ||,OT .In the horizontal target cases (t = 3.6 and 4.4 s), t = 3.6 s has larger P rad in FSR and lower P rad in NSR than those of t = 4.4 s case, resulting in a steeper radial gradient of T e,OT .In the vertical target cases (t = 5.6 and 6.3 s), T e,OT is higher in the FSR compared to that of the horizontal target cases, which result in the smoother radial T e,OT gradient.Overall, in the cases of vertical target, i.e. t = 5.6 and 6.3 s, T e,OT profile is almost unaffected by the SP location due to the relative open divertor configuration, and T e,OT is higher in the CFR and its radial gradient is smooth.Thus, λ q,OT is mainly affected by λ js,OT , with λ js,OT /λ q,OT ∼ 1.2, which is close to the results of EAST upper divertor experiment (λ js,OT /λq ,OT ∼ 1) [7,11].In the cases of horizontal target, T e,OT plays more important role in  λ q,OT than the case of vertical target.At t = 3.6 s, the high P rad in FSR leads to low T e,OT , resulting in the steepest radial T e,OT gradient.However, the λ js,OT is significantly higher than other cases, thus the λ q,OT is only 112% of that vertical target.As a result, the difference between λ js,OT and λ q,OT is very large, i.e. λ js,OT /λ q,OT ∼ 189%.At t = 4.4 s, the combination of a smaller radial T e,OT gradient and a larger λ js,OT causes largest λ q,OT in all the cases, λ q,OT is about 116% of that of t = 3.6 s case and 135% of that of vertical target.The λ js,OT /λ q,OT ∼ 149% is obtained.

Effect of SP location on λ js,OT and λq ,OT in high density condition
In the experimental conditions (n e ∼ 2.1 × 10 19 m −3 , n OMP e,sep ∼ 0.92 × 10 19 m −3 ), T peak e,OT is higher than 30 eV, and the target is eroded easily [47,48].Therefore, it is necessary to increase the upstream plasma density to reduce T peak e,OT , and to investigate the effect of SP location on λ js,OT and q,OT in high density condition.As in table 2, as the upstream plasma density is increased from n e,CEI ∼ 1.3 × 10 19 −3 (n OMP ∼ 0.92 × 10 19 m −3 ) to e,CEI ∼ 1.6 × 10 19 m −3 (n OMP e,sep ∼ 1.24 × 10 m −3 ), Φ OT is raised by about 140%.However, in both horizontal and vertical contributions of Φ in /Φ ion to in NSR and FSR are similar to the low upstream density condition.The Φ OT,FSR /Φ OT,NSR of high density is also similar to that under low density condition.Therefore, as shown in figure 9(a) and (c), the profiles of ne,OT and Ĵsat,OT in high density cases are similar to those in low density cases, and λ js,OT shows little variation as upstream density increases.
As the upstream density increases, particle recycling is enhanced, resulting in an increase in the neutral particle density near the target and an increase in P rad .Comparing with the low density cases, in horizontal target (t = 4.4 s), P rad is increased by about 53% and 43% in NSR and FSR, respectively, the corresponding T peak e,OT is reduced by about 58% (from 36.0 eV to 15.2 eV), and q peak ∥,OT is decreased by about 35% (from 27.6 MW m −2 to 18.2 MW m −2 ).The increase of P rad mainly occurs in NSR, while in FSR the changes of P rad is small.Therefore, the radial gradient of T e,OT is smaller in high density than in low density, as shown in figure 9(b).As a result, λ q,OT is increased by about 17%, which can be attributed to: (i) v * SOL is increased with upstream density, leading to the enhancement of SOL heat flux decay width λ q ; (ii) a significant increase of P rad in the divertor region raises the broadening effect on λ q,OT [17].
In vertical target (t = 6.3 s), due to the relative open divertor configuration, comparing with the low density cases, the neutral particle density in the CFR is increased moderately, and P rad in NSR and FSR is enhanced by about 37% and 10%, respectively; T peak e,OT and q peak ∥,OT are decreased by 34% (from 58.2 eV to 38.9 eV) and 12% (from 48.8 MW m −2 to 44.5 MW m −2 ), respectively.The reduction of T peak e,OT and q peak ∥,OT is smaller than that of t = 4.4 s.Therefore, the radial gradient of T e,OT at t = 6.3 s is steeper compared to t = 4.4 s, and λ q,OT only increases by about 6% compared to low density condition.
Our previous study [17] demonstrated that λ q,OT is affected by the v * SOL .In this work, we further investigated the effects of SP locations on λ js,OT , λ q,OT , and λ js,OT /λ q,OT by changing the upstream plasma density, and the results are shown in figure 10.Firstly, the simulation results indicate that λ js,OT is mainly influenced by the SP location, but depends slightly on v * SOL (corresponds to upstream plasma density).The main reason is that the SP location determine neutral particle accumulation and ionization, which affects the contribution of Φ ion to Φ OT , thus it has a significant impact on the profile of J sat,OT .While within the selected range of upstream density, the changes of contribution of Φ ion to Φ OT in same SP location case are small.
Secondly, the simulation results show that λ q,OT is influenced by both SP location and v * SOL : (i) in horizontal target, the presence of corner increases the neutral particles accumulation and P rad , resulting in a wider λ q,OT compared to vertical target, and λ q,OT increases as SP approaches toward the corner.(ii) As v * SOL increases, the recycled neutral particles increases, resulting in the increment of P rad and thus λ q,OT .The increment of λ q,OT with v * SOL in horizontal target cases is larger than on vertical target cases.Moreover, at low upstream density, the SP location has a larger influence on λ js,OT than on λ q,OT , and λ js,OT /λ q,OT is much larger than 1 in horizontal target.As the upstream density increases, T e,OT becomes flatter, thus λ q,OT increases.However, λ js,OT changes slightly.Therefore, at high density, the ratio of λ js,OT /λ q,OT approaches 1, which is consistent with previous EAST upper divertor experiment [7,11].
In summary, in the EAST lower divertor, the SP location can affect the ionization and P rad by influencing the neutral particles accumulation position to change λ js,OT and λ q,OT .In the horizontal target, the neutral particle accumulation is dominated by the target geometry, thus λ js,OT is much larger than vertical target.The simulation results show that although λ js,OT has a relatively weak dependence on the upstream density, increasing upstream density can raise P rad in the divertor region, thereby broadening λ q,OT .Moreover, both the experiment and simulation show that in low density there is big difference between λ q,OT and λ js,OT in horizontal target, thus using λ js,OT instead of λ q,OT may result in deviation.In high density, T peak e,OT decreases and T e,OT profile becomes flat, and λ js,OT can be used instead of λ q,OT .Overall, horizontal target has lower T peak e,OT and q peak ∥,OT as well as wider λ q,OT than those in vertical target.Therefore, in long-pulse highpower discharge, the horizontal target plate with SP close to the corner can effectively widen λ q,OT and λ js,OT , reducing J sat,OT and q ||,OT to the target and preventing the target damage.

Conclusion
The lower divertor with right-angle shape of EAST has the capacity of increasing the divertor closure and the creation of both horizontal and vertical target.In this study, the SP sweeping experiment (shot #98332) and corresponding SOLPS-ITER simulation are carried out to study the variations of particle/heat flux decay widths in the divertor with the SP location (in both horizontal and vertical target) and the corresponding mechanism.By comparing the cases of SP locations in four locations, i.e. two cases of horizontal target and two cases of vertical target (both including SP near and far from the corner), the simulation result is in satisfactory agreement with experiment data and the trends are the same.This study demonstrates that when the SP location is on the horizontal target, both λ q,OT and λ js,OT are wider than those of the vertical target.
Firstly, the location of the SP can affect ionization by influencing the accumulation position of neutral particles on divertor, which further affects the J sat,OT profile as well as λ js,OT .In horizontal target, the ionization of the recycled neutral particles can flatten J sat,OT , thus leading a larger λ js,OT than that of vertical target.In addition, λ js,OT is increased as the distance of SOL to the corner d increases, while it varies slightly with d in vertical target.
Secondly, λ q,OT in horizontal target is larger than that of vertical target, the maximum λ q,OT appears in horizontal target with SP near the corner case.The main reason is that in horizontal target, the neutral particles accumulate in the CFR and P rad in the OD region is much higher than that of vertical target.Therefore, both T peak e,OT and q peak ∥,OT are significantly lower than that in vertical target.Moreover, the difference between λ js,OT and λ q,OT is large in horizontal target.In vertical target, due to the open configuration, the T e,OT profile is less affected by the location of the SP, thus λ q,OT is mainly governed by λ js,OT , and λ js,OT can be used instead of λ q,OT .
As the upstream density increases, the contribution of neutral particle accumulation and ionization to λ js,OT are unchanged, and consequently, there is no significant change in λ js,OT .However, raising the upstream plasma density can effectively enhance P rad and reduce T peak e,OT , thus flattening T e,OT and widening λ q,OT .Therefore, λ q,OT approaches to λ js,OT , and λ js,OT can be taken as the substitute for λ q,OT in high density condition of horizontal target.
Through the experiment and simulation, this work reveals the mechanism of how the SP location influence λ js,OT and λ q,OT in EAST lower divertor.The horizontal target with SP close to the corner is proposed for EAST high-power longpulse discharges to broaden λ js,OT and λ q,OT , thus protecting the target.

Figure 1 .
Figure 1.In EAST experiment shot #98332, (a) the SP location at different time and the location of divertor Langmuir probes; (b) the line-averaged electron density and plasma current, (c) the auxiliary heating, and (d) the distance between the SP location and the corner d (negative value means the SP locates on the horizontal target and positive value indicates SP locates on the vertical target), varying with discharge time.
(a).The simulation meshes are shown in figures 2(a) and (b) and the plasma profiles obtained from the simulation includes information of both horizontal and vertical target regions.The simulation

Figure 2 .
Figure 2. (a), (b) The SOLPS meshes corresponding to the magnetic field configurations at t = 4.4 s and 6.3 s of the shot #98832; (c) the ne profiles obtained from reflectometry measurements and SOLPS simulations, and Te profiles from SOLPS at the OMP; (d) the upstream anomalous particle transport and electron/ion heat conductivity coefficients used in SOLPS modeling.

Figure 3 .
Figure 3.Comparison of profiles of the main plasma quantities along the OT between the LP measurement from experiment and SOLPS simulation: (a) ne ,OT , (b) J sat,OT , (c) Te ,OT , (d) q ||,OT , mapped to the OMP.The positions of corner map to OMP corresponding to different time are also marked.

Figure 4 .
Figure 4.In horizontal target (t = 3.6 s and 4.4 s), the deposited heat flux profile to the OT q dep,OT from both experiment and simulation.The experimental results are obtained by LP (circle symbol) and infrared cameras (IR, triangle), respectively.

Figure 5 .
Figure 5.The normalized (a) J sat,OT and (b) q ||,OT at t = 4.4 s and 6.3 s cases.The dotted lines represent the Eich fitting of LP data, the hollow dots represent the SOLPS simulation results and the dashed line corresponds to Eich fitting of SOLPS result.

Figure
Figure At t = 3.6 s, 4.4 s, 5.6 s, and 6.3 s, the SOLPS simulations of (a) total neutral particle density (n D+D2 = n D +2n D2 ) and (b) D atom ionization rate, along the OT; 2D contours of (c)-(f ) total neutral particle density and (e)-(j) deuterium ionization rate in the OD region.The schematic of the near strike point region (NSR) and far strike point region (FSR) near the outer target is shown in figure (g), and the boundaries of NSR and FSR are mapped to OMP as illustrated in figure (b).

Figure 10 .
Figure 10.The (a) λ js,OT , (b) λq ,OT , and (c) λ js,OT /λq ,OT as a functions of d.The data includes different upstream density (represented by v * SOL ) and SP location (represented by d) from both SOLPS simulation and experiment.

Table 1 .
At t = 3.6 s, 4.4 s, 5.6 s and 6.3 s, the toroidal magnetic field and the target angle ψ, and poloidal magnetic field and the target angle θ.

Table 2 .
The ion flux Φ OT and its components Φ in , Φ ion , Φ ⊥ , which are defined in equation (3), to the NSR and FSR of the outer target.Low density case corresponds to the upstream density in the experiment (ne ∼ 2.1 × 10 19 m −3 , n OMP e,sep ∼ 0.92 × 10 19 m −3 ), while high density case corresponds to n OMP e,sep ∼ 1.24 × 10 19 m −3 .