Validation of density pump-out by pedestal-foot magnetic island formation prior to ELM suppression in KSTAR and DIII-D tokamaks

TM1 nonlinear two-fluid simulations reveal key characteristics of density pump-out caused by pedestal-foot island formation when applying resonant magnetic perturbation (RMP). These characteristics include a bifurcation in pump-out with a low RMP coil current threshold, a sensitivity of pump-out magnitude to q 95, and the magnitude of pump-out scaling as the square root of the RMP coil current. Dedicated experiments are carried out in the KSTAR and DIII-D tokamaks to validate these features and show that: (1) a staircase bifurcation in density pump-out is observed when slowly ramping up the n = 1 RMP current, and the density fluctuations are found to be slightly decreased from the pedestal-foot to the pedestal-top; (2) the magnitude of density pump-out becomes weaker when decreasing q 95 from 5.5 to 4.9, and a partial recovery of density pump-out is observed when q 95 is ramped down to lower than 4.9; and (3) analysis of a DIII-D database of n = 3 RMP edge-localized mode control experiments finds that the magnitude of density pump-out is proportional to the square root of RMP coil current Δn e/n e ∝ IRMP0.5 . These experimental observations are consistent with TM1 simulations.

(Some figures may appear in colour only in the online journal) 6 Present address: Seoul National University, Seoul, Korea 7 Present address: Columbia University, New York, NY 10027, United States of America * Author to whom any correspondence should be addressed.
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Along with the application of RMP in tokamaks worldwide, understanding the underlying physics mechanism responsible for density pump-out has been a longstanding issue. Various mechanisms have been proposed to explain the phenomenology of density pump-out, including: (1) Edge magnetic field stochasticity. An analytical model [12] shows that the applied RMP produces edge-field stochasticity and modifies the ambipolar electric field, which in turn causes large particle fluxes and density pump-out. The edge-field stochasticity is based on the vacuum field assumption without taking into account the plasma response [13], which strongly reduces the field stochasticity near the plasma edge due to the plasma screening. According to this model, the magnitude of the particle flux caused by RMP is proportional to the magnetic perturbation δB r squared. Consequently, the magnitude of density pump-out is proportional to the RMP coil current squared. (2) Magnetic-flutter-induced transport [14][15][16]. Magneticflutter-induced plasma transport is thought to be caused by the non-stochastic spatial magnetic flutter induced by flow-screened RMP and it is dominantly an electron transport process. This model is based on two assumptions: first, the applied RMP is strongly screened by a large enough plasma toroidal rotation and only thin magnetic islands are induced without any overlap or formation of stochasticity. Second, only untrapped electrons around the pedestal-top that are sufficiently collisionless contribute to flutter transport [15]. (3) Turbulence effects. Both the analytical model [17] and gyrokinetic simulations [18,19] find that RMP enhances drift-wave turbulence. It is well known from experiments that turbulence level is observed to increase following the transition to ELM suppression [20][21][22][23][24][25][26]. (4) Neoclassical effects. The quasi-linear simulations by MARS-Q [27] found that the same physics that produces the toroidal neoclassical toroidal viscosity torque also acts to enhance an outward radial particle flux and results in density pump-out. The key physics is associated with the drift resonance between the RMP and the toroidal procession of trapped thermal particles. The model predicts that larger density pump-out occurs in plasmas with lower collisionality and slower toroidal rotation. Interestingly, the simulated density profiles always show a global downward shift with the separatrix density near zero at the end.
(5) Magnetic island effects. Nonlinear two-fluid MHD simulations using the TM1 code [28,29] have shown that magnetic island formation triggered by RMP penetration at the foot of the pedestal consistently produces the experimentally observed density pump-out. RMP is found to cause a strong kink response at the plasma edge and can easily penetrate into the highly collisional pedestal-foot [28,30]. The enhanced parallel collisional transport leads to density flattening across the magnetic islands and global density pump-out. One key attribute of magnetic island induced transport that distinguishes it from other transport effects is the transient bifurcation in density pump-out associated with RMP penetration [31].
It is most likely that all the above mechanisms are involved to some degree in density pump-out, but nonetheless it is very important to explore experimental evidence to validate aspects of the proposed mechanisms.
Here, we present simulations and experimental work to validate the mechanism of density pump-out caused by magnetic island formation at the foot of the pedestal. Nonlinear twofluid simulations using the TM1 code are performed to provide a predict-first reference for designing validation experiments. Out of the five mechanisms described above, TM1 only captures the magnetic island mechanism. The simulation results show that: (1) bifurcation in density pump-out is more easily observed by slowly ramping up n = 1 RMP instead of n = 2 or 3 RMP, since there are fewer n = 1 rational surfaces at the foot of the pedestal and more distinct magnetic island chains form. Associated with the ramping of RMP current, magnetic island chains are triggered gradually from the outer to the inner side of the pedestal foot. The formation of each island chain leads to a bifurcated density pump-out. (2) As q 95 decreases (or increases), the radial locations of the n = 1 rational surfaces move outward (inward) and the density flattening region caused by magnetic islands at the pedestal foot becomes narrower (wider). Here, q 95 is the magnetic safety factor at 95% of the normalized poloidal magnetic flux. Consequently, for constant RMP strength, the magnitude of density pump-out is sensitive to q 95 . (3) The magnitude of density pump-out depends on the width of profile flattening, which is found to be proportional to the width of the magnetic island at the pedestal foot [29]. This leads to a square-root scaling of the density pump-out to the RMP coil current, ∆n e ∝ W ∝ B 0.5 r ∝ I 0.5 RMP [32]. Here, ∆n e , W, B r and I RMP are the reduction in density, magnetic island width, magnitude of magnetic perturbation generated by RMP and the RMP coil current, respectively. This scaling distinguishes it from the transport effects caused by magnetic stochasticity or magnetic flutter. Dedicated experiments are performed in the KSTAR and DIII-D tokamaks to validate the above features. Bifurcation in density pump-out and its sensitivity to q 95 are observed by carefully scanning the RMP coil current and q 95 . The dependence of the magnitude of density pump-out on the RMP coil current is obtained by analyzing the n = 3 RMP ELM control database in the DIII-D tokamak.
This paper is organized as follows. Key features of density pump-out associated with magnetic island formation based on TM1 nonlinear simulations are introduced in section 2. The experiential setups for the KSTAR and DIII-D experiments are introduced in section 3.1. In section 3.2, the KSTAR and DIII-D experimental results on resolving the bifurcated density pump-out and sensitivity to q 95 are introduced. The scaling of density pump-out of RMP coil current based on DIII-D experiments and TM1 simulations is introduced in section 3.3. A discussion and summary of the results are given in section 4.

TM1 nonlinear simulations on the features of density pump-out
To obtain the simulation results in this section, we use the TM1 code [33,34] to simulate the RMP penetration in the KSTAR and DIII-D pedestals with multiple helical magnetic boundary conditions [28,29,35,36]. TM1 is a nonlinear twofluid MHD code with cylindrical geometry and circular crosssection. The details of the model are introduced in [29], including the equations, assumptions and limitations, its input and its output. Toroidicity and plasma-shaping effects are introduced through the use of the toroidal ideal MHD code GPEC [37], which calculates the ideal MHD plasma response to the 3D vacuum field and decomposes the total magnetic perturbation into helical harmonics that serve as the boundary conditions for TM1. The equilibrium and profiles for the TM1 simulation and GPEC analysis are obtained from a typical KSTAR H-mode plasma for n = 1 RMP ELM control [36]. In order to avoid too many magnetic island chains forming at the foot of the pedestal for high-n RMP, n = 1 RMP is used. The perpendicular transport coefficients for the TM1 simulation are obtained from power and particle balance analysis using TRANSP [38]. With these initial conditions, TM1 then calculates the resonant field penetration and/or screening for all the relevant resonant components in the pedestal region and evolves the profiles according to simulations of collisional parallel transport across these islands.
In the simulations, m/n = 5/1, 6/1 and 7/1 resonant components and their harmonics are included. The RMP current is slowly ramped up from 0 to 4 kAt to explore magnetic island formation at the foot of the pedestal and the current is not high enough to trigger magnetic island formation at the pedestaltop (q = 5). A typical example of such a simulation is shown in figure 1 for the time evolution of the RMP coil current, normalized magnetic island width and the pedestal density. As the RMP coil current ramps up (figure 1(a)), the 7/1 and 6/1 resonant field components penetrate successively at t = 0.3 s and 0.65 s with threshold current ∼1.2 kAt and 2.6 kAt, as indicated by the fast jump in the 7/1 and 6/1 magnetic island width in figure 1(b). Associated with the penetration of the 7/1 and 6/1 magnetic island chains, a sudden drop appears in the pedestal density, which is especially obvious when the 6/1 penetration happens. The bifurcation in the pedestal density is due to the flattening of the density profile in the magnetic island region and a global drop in the profiles beyond the magnetic island [29]. Here, the 5/1 component RMP is shielded throughout the simulation and not shown here. A stronger RMP current will trigger 5/1 magnetic island formation at the pedestal-top, which will cause ELM suppression and an additional staircase density pump-out, as observed in EAST and simulations [9,28,36]. Figure 2 shows the Poincaré plots of the magnetic surface during 7/1 penetration at t = 0.6 s and both 7/1 and 6/1 penetration at t = 0.8 s. The very edge of the plasma (ψ N > 0.99) becomes stochastic when the 7/1 magnetic island opens, as shown in figure 2(a). The screening current at the 5/1 and 6/1 rational surfaces drives small magnetic islands with width ∼0.005ψ N . The later opening of the 6/1 magnetic island chain overlaps with the 7/1 magnetic island chains and produces a wider stochastic region (ψ N > 0.975), as shown in figure 2(b). Although this thin 3D magnetic structure cannot be directly measured with any available diagnostics, the bifurcation in the pedestal density is a unique feature that indirectly indicates the appearance of the magnetic island at the pedestal foot and can be validated in the experiment. Interestingly, staircase density evolution was observed in the EAST n = 1 RMP ELM control experiments [9].
A dependence of the magnitude of density pump-out on q 95 is reasonably expected according to the results shown in figure 2. Taking figure 2(b) for example, lowering q 95 will move all the rational surfaces outward. For the same RMP strength strong enough to open the 6/1 and 7/1 magnetic islands, the width of the flattening region across the stochastic region will become narrower, resulting in less density pump-out. TM1 simulations are performed to scan q 95 from 5.4 to 4.6 with 4 kAt RMP coil current, and the results are shown in figure 3. It is found that RMP triggers 6/1 and 7/1 magnetic island chains at the pedestal-foot when 4.9 ⩽ q 95 ⩽ 5.4, which leads to wider flattening in the density profile and a stronger reduction in the pedestal density as shown in figure 3(b). However, the flattening region becomes a bit narrower, and the pedestal density recovers slightly when 4.6 ⩽ q 95 < 4.9. Figures 3(c) and (d) clearly show the dependence of the region of magnetic islands and normalized pedestal density on q 95 . Here, the locations of the rational surfaces are shown in circles, and the width of the magnetic islands are shown in bars. The stronger density pump-out is dominated by the 6/1 and 7/1 magnetic islands for 4.9 ⩽ q 95 ⩽ 5.4, the loss of 7/1 magnetic island results in the ∼10% recovery in the density pump-out. It should be pointed out that further lowering down q 95 to 4.4 or even lower will open the 5/1 magnetic island at the pedestal foot and produce stronger density pump-out again. Contrary to n = 1 RMP, the dependence of density pump-out on q 95 is negligible for n = 2 and 3 RMP, since there are always more than two magnetic island chains opened at the pedestal foot.
The results shown in figure 3 implicitly include the effect of resistivity and plasma rotation on RMP penetration. It is well understood that field penetration becomes harder for plasmas with higher rotation and lower resistivity [29,39,40]. For the H-mode plasma studied here, the strong E × B rotation together with the strong diamagnetic drift frequency in the steep pedestal region shields the RMP, as indicated by the screened 5/1 island when its rational surface moves from the pedestal-top to the steep pedestal region. At the foot of the pedestal, however, the plasma rotation is much lower, but the plasma resistivity is usually one order higher than that at the pedestal-top, resulting in a minimal screening effect of RMP. Consequently, the applied RMP very easily penetrates into the pedestal-foot to form magnetic islands [28,29], and the rotation effect will not be further discussed in this paper.
In addition to the above features of bifurcated density pump-out and its dependence on q 95 , the TM1 simulations usually show a dependence of the magnitude of density pump-out on the RMP coil current, which is ∆n e /n e ∝ I 0.5 RMP . This scaling is valid for RMPs with different toroidal mode number n [29,32], and the simulated scaling for n = 3 RMP is compared with the RMP ELM control database in DIII-D. In the following section, these three features of density pump-out caused by magnetic island formation are explored in the KSTAR and DIII-D experiments.

Experimental setup
Dedicated experiments are designed in the KSTAR and DIII-D tokamaks to explore the features of density pump-out caused by n = 1 RMP, as introduced in section 2.
The KSTAR discharges presented here are configured in a lower single null configuration with lower triangularity ∆ low ∼ 0.85 and upper triangularity ∆ up ∼ 0.35, as shown by the poloidal cross section of poloidal flux surfaces in figure 4(a). The major and minor radii are R = 1.8, a = 0.5 m, aspect ratio A = R/a = 3.6, toroidal field B t = 1.8 T, neutral beam injection power ≈3.2 MW, and the plasma current ranges from 500 kA to 600 kA to change the edge safety factor q 95 from 5.5 to 4.5, normalized beta β N ≈ 2.3, normalized electron pedestal collisionality ν * e ≈ 0.3-0.5. The in-vessel control-coil (IVCC) system [41] consists of the top, middle and bottom rows, as shown in figure 4(b). In the experiment, the IVCC coils are configured to produce n = 1 RMP, and only the middle row coils (middle IVCC) are used in order to trigger the bifurcation in density pump-out at higher coil current threshold compared to the three-row coils. According to the GPEC calculation, the amplitude of the edge resonant field generated by the middle row coils is 60% of that generated by the three row coils in +90 • configuration.  The DIII-D low-collisionality discharges presented here are configured to KSTAR similar shape but with a slightly smaller aspect ratio A = R/a = 1.7 m/0.6 m = 2.83, as shown in figure 4(b). The in-vessel coils [42], consisting of a lower row (IL) and an upper row (IU), are configured to generate n = 1 RMPs. The toroidal phase difference ∆Φ UL = 120 • between the IU and IL coil currents is used to achieve optimal resonant coupling with the plasma pedestal. The total injected power is ∼5.7 MW to match the pedestal collisionality in the KSTAR experiments, consisting of ∼4.5 MW neutral beam injection and ∼1.2 MW electron cyclotron heating. The toroidal field B t = 2 T and the plasma current is varied from 1 MA to 1.3 MA to change the edge safety factor q 95 from 5.6 to 4.5. In addition to the experiments with n = 1 RMP, the ELM control database by using n = 3 RMP in the ITER similar shape (ISS) low collisionality plasma [43] is analyzed to obtain the dependence of density pump-out on RMP coil current.

Resolving the bifurcated density pump-out and dependence on q 95
Experiments are designed in the KSTAR tokmak to explore the bifurcation events in density pump-out with slowly rampingup and ramping-down the middle row RMP coil current. In the experiment, constant D 2 puffing is applied. An example of bifurcated density pump-out during the ramp-up of n = 1 RMP current is shown in figure 5 for shot 28442. Here the top trace shows the q 95 , which is kept constant at 5.35. The n = 1 RMP current from the middle row coil is gradually increased from 0 to 4 kAt in 3 s, as shown in figure 5(b). Two steps of staircase bifurcated density pump-out are observed in the edge line-averaged density at 5.6 s and 7 s during the increase of RMP amplitude, as shown in figure 5(c), which corresponds to a threshold current of 1.45 kAt and 3.3 kAt, respectively. The observed bifurcation in density pump-out is qualitatively consistent with TM1 simulations, as shown in figure 1, and indicates bifurcation in magnetic island formation. Interestingly, the density recovers partially after the first bifurcation, which is associated with a fast change in toroidal rotation and ion temperature. In addition, n = 1 RMP causes slight mitigation of the ELMs. The density recovers gradually when the RMP current is ramped down from 8.5 s to 11.5 s. Additional experiments, using three-row RMP coils in +90 • configuration, show that the threshold current for triggering the bifurcation in density pump-out is about 0.6-0.8 kAt.
The dependence of density pump-out magnitude on q 95 is investigated by changing q 95 shot by shot and keeping the RMP waveform the same as shot 28442. The time trace of shot 28444 with q 95 = 4.75 is also shown in figure 5 in red color. The ramping up n = 1 RMP only causes one bifurcation in the density pump-out at t = 5.7 s, and the magnitude of density pump-out during the flattop of the RMP coil current is lower than shot 28442. Another discharge (not shown) with q 95 = 5.05 also shows one distinguishable bifurcation in density pump-out, and the density pump-out magnitude is larger than shot 28444 but lower than 28442, which is consistent with the prediction of TM1 simulations.
The density fluctuations measured by beam emission spectroscopy (BES) [44] are examined to understand the change in turbulent fluctuations during density pump-out caused by RMP. The density fluctuations during the inter-ELM phase are found to slightly decrease when applying an n = 1 RMP. Figure 6 shows the spectrogram of the density fluctuations measured by BES at different locations and times. Here, the BES data during the inter-ELM phase (30%-90% of ELM period) are analyzed. Compared to t = 4.0 s without RMP, the intensity of density fluctuations at both the pedestal-top and pedestal-foot are decreased slightly in the low frequency range of f < 50 kHz after the first and second bifurcations of the density pump-out. Figure 6(c) shows the time evolution of the profile of the relative density fluctuations integrated in the frequency range of 0-50 kHz, which clearly shows gradually decreasing density fluctuations. Further analysis shows that the level of density fluctuations recovers to the initial state when turning off the RMP after 11.5 s. Different from the observed increase after accessing ELM suppression [20,21,25,26], these fluctuation measurements suggest that the density pump-out prior to ELM suppression is irrelevant with turbulent transport.
Experiments with continuously scanning q 95 are performed to document the q 95 window for stronger density pump-out. Figure 7 shows the time evolution of q 95 , D α , n = 1 RMP coil current and the edge density for discharges 28437 and 28440. The RMP coil current is kept constant with 4 kAt from 4.5 s to 11 s, and q 95 is ramped downward from 5.6 to 4.5 in the same time range. For shot 28437, the RMP causes 30% density pump-out at the beginning and stays almost constant with decreasing q 95 . The density pump-out magnitude recovers to 20% at 9.2 s when q 95 is lowered to 4.75, as indicated by the jump up in the density marked by the dashed line in figure 7(c). The weaker density pump-out continues till the end of the scan at 11 s with q 95 = 4.5. For comparison, shot 28440 with q 95 ramping upward also shows a similar q 95 window for stronger density pump-out. Specifically, the RMP causes stronger density pump-out for either q 95 < 4.5 or q 95 > 4.75, and the density recovers only partially when 4.5 < q 95 < 4.75, qualitatively consistent with TM1 simulations in figure 3. A more detailed comparison of the dependence of density pump-out on q 95 is shown in figure 7(d), which shows the same q 95 window of 4.5 < q 95 < 4.75 (yellow shaded region) for partial recovery of density, although the baseline density is different. For the KSTAR experiments presented here, the value of q 95 is from the magnetic equilibrium, which is about 0.15-0.2 below the q 95 from the kinetic equilibrium constrained by the measured profiles. Consequently, the q 95 window for partial recovery of the density pump-out is 4.65 < q 95 < 4.9, which is consistent with the TM1 simulations in figure 3.
A similar tendency is also observed in the DIII-D experiment with n = 1 RMP. Figure 8 shows the time trace of the signals similar to KSTAR discharges with q 95 scan. For discharge 173744, q 95 is ramped downward from 5.6 to 4.6 in 2 s, and n = 1 RMP with 4 kA coil current is applied throughout the scan. During the ramp-up phase of RMP coil current, it first increases the pedestal density and lowers the ELM frequency at 2.6-2.7 s with around 1 kA coil current. The increased density (called pump-in) is found to be correlated with decreased turbulence transport [45]. Further increase of the RMP current to 4 kA leads to 55% density pump-out and strong ELM mitigation, as shown in figures 8(b) and (c). The strong density pump-out is due to the formation of 6/1 and 7/1 island chains at the pedestal-foot. While the strong ELM mitigation is due to the combined effects of strongly degraded plasma confinement, steeper but narrower pedestal and formation of pedestaltop magnetic island, which are not the subject of this paper. However, the pedestal density begins to recover gradually after 4.3 s when q 95 is lower than 4.8. The pedestal density even recovers to the initial level at the end of q 95 scan with little ELM mitigation. For discharge 173741, the scan starts with q 95 = 5.15 and the same RMP current waveform. However, the pedestal density stops decreasing at 3.3 s when q 95 is decreased to 4.95 and the magnitude of density pump-out is about 20%, which is much weaker compared to shot 173744. It also leads to little ELM mitigation. Similar to shot 173744, the pedestal density begins to recover at 4.4 s when q 95 is lower than 4.8. Figure 9(a) and (b) shows the evolution of the profiles of safety factor and electron density versus q 95 for discharge 173 744. Here, the profiles of q are obtained by running kinetic EFIT construction, and constraints of current density and pressure profiles are included based on derivation of the measured electron and ion density and temperature profiles. The density profiles are mapped by the kinetic EFIT by assuming 85 eV separatrix electron temperature [46]. At the beginning of q 95 scan around 5.6, the q = 7, 6 and 5 rational surfaces locate around ψ N = 0.991, 0.975 and 0.91 respectively. All the rational surfaces move outward to ψ N = 0.999, 0.99 and 0.97 when decreasing q 95 to 4.6. In contrast to TM1 simulations, the density profile throughout the pedestal region continues to decrease slightly for 4.8 < q 95 < 5.3, which is probably due to the enhanced particle transport caused by the smaller but higher frequency ELMs. GPEC calculations show that the magnetic response is strongly decreased due to the confinement degradation with β N strongly decreased from 2 to 1.4 as shown in figure 9(c). It is well known that RMP causes a stronger plasma response in plasmas with higher β N [47]. However, the strong density pump-out is sustained for more than about 1 s with that lower magnetic perturbation, until the recovery of density pump-out when q 95 is deceased to 4.75. This indicates that the density recovery is a consequence of the change in q 95 instead of the reduced magnetic response [48].
We note that, due to density pump-in at the early ramp-up of RMP current and the non-stationary ELM dynamics, it is hard to identify bifurcations in the density pump-out when slowly ramping up the RMP coil current. In addition, for the DIII-D experiment with n = 1 RMP, the neutral particle pressure in the scrape-off layer region decreases when density pump-out happens. This indicates that the particle source may change during the application of RMP, which is different from the assumption of a fixed particle source in the TM1 simulations.
Further DIII-D experiments confirm that, for the same 4 kA RMP coil current, the magnitude of density pump-out at q 95 = 4.8 is weaker than q 95 = 5.2, which is consistent with TM1 simulations introduced in section 2.

Scaling of density pump-out on RMP current
Ideally, the dependence of density pump-out on RMP coil current would be obtained by a single discharge with continuous ramping-up the RMP current, similar to the results shown in figure 5. However, it turns out that there is a time delay in the density pump-out due to a longer particle confinement time compared to the energy confinement time, which results in a decreasing density even after the RMP current reaches the flattop. Consequently, this section presents the analysis of n = 3 RMP ELM control database from DIII-D to show the dependence of density pump-out on the RMP coil current. Figure 10 shows three discharges with the same plasma parameters except for different n = 3 RMP current. In the experiment, the RMP coil current is ramped up to the flattop in 50 ms and kept constant thereafter. It shows that higher RMP current leads to both stronger density pump-out and stronger ELM mitigation. The pedestal density saturates 100-200 ms after turning on the RMP current and then remains stationary.
The dependence of density pump-out magnitude on the n = 3 RMP coil current is obtained as shown by blue circles in figure 11. Here, totally 25 discharges with the same plasma parameters are used for this analysis, the stationary pedestal density (n e ) after pump-out is normalized by the initial pedestal density (n e,ped ) before RMP is turned on, and the RMP does not suppress ELMs for 1 s after density pump-out. A least-squares fitting (the magenta dotted line), in the term of n e /n e,ped = 1 − A I α RMP , for the experimental results (the blue circles) shows that n e /n e,ped = 1-0.147 I 0.508±0.05 RMP , or the magnitude of pump-out ∆n e /n e,ped = 0.147 I 0.508±0.05 RMP . Nonlinear TM1 simulations for discharge 158075 are performed to scan the RMP current from 0.1 kA to 6.5 kA by using the equilibrium and profiles 200 ms before the RMP is turned on, the results are shown in red circles. The linear fitting of the simulation results shows ∆n e /n e,ped = 0.144 I 0.492±0.01 RMP , which is consistent with the experimental results, although it is slightly lower. The observed scaling of density pump-out on RMP current has not yet been predicted by other transport mechanisms except for the magnetic island formation [29]. The scaling of ∆n e /n e,ped ∝ W ∝ I 0.5 RMP is valid for RMPs with different toroidal mode numbers and different plasma parameters (i.e. collisionality and q 95 ), while the staircase bifurcation in density pump-out is only observed for n = 1 RMP. Here, W is the width of the magnetic island. However, it should be pointed out that theoretically the magnitude of density pump-out depends on both the width of the magnetic island and the plasma collisionality [29,34]. Qualitatively, for the same RMP current and β N , the density pump-out is expected to be stronger for RMPs with lower n compared to higher n, lower q 95 and lower collisionality.
We note that there are two upper limits for this ∆n e /n e,ped ∝ I 0.5 RMP scaling. The first one is the RMP current threshold to open the magnetic island at the top of the pedestal and cause ELM suppression [29]. The pump-out caused by the pedestal-top island still obeys the scaling, but the constant coefficient A (∆n e /n e,ped = A I α RMP ) will be smaller due to the weaker density gradient at the pedestal-top. The second limit is the RMP current threshold to open the magnetic island in the steep pedestal. The pedestal will not be preserved anymore when the magnetic island appears in the steep pedestal region, and it will lead to pedestal collapse and H-L transition [29,49]. The scaling is only valid for RMP currents below the second limit.

Discussion and summary
The experiments presented in this work are consistent with bifurcated magnetic island formation causing density pumpout. However, direct evidence for the existence of magnetic islands at the pedestal-foot is still missing, since it is very challenging to measure the possible flattening of the profiles by the magnetic island at the pedestal-foot. This is because, on the one hand, the spatial resolution of recent diagnostics is inadequate to resolve such narrow (∆ψ N ∼ 0.01-0.02) profile structures around the separatrix. On the other hand, as illustrated in figure 2, the magnetic surface becomes stochastic as long as magnetic islands form at the pedestal foot, and the enhanced radial transport [50] in this chaotic region will further destroy the flattening profiles. Future studies should aim to resolve these structures by measuring profiles in the flux expansion region near the X-point; for example, by using the divertor Thomson scattering in DIII-D.
It should be pointed out that both the observed decreased density fluctuations and the sensitivity of pump-out on q 95 are unique for n = 1 RMP. Running the KSTAR experiment with q 95 around 5.35 makes the n = 1 rational surfaces either located at the top or at the foot of the pedestal to avoid change in the magnetic structure by n = 1 RMP in the steep pedestal region. n = 2 or 3 RMP usually drives screening current and affects the profiles in the steep pedestal region, which in turn may also affect the density fluctuations. The implication of the scaling of density pump-out on RMP current is that RMP with higher n will lead to weaker density pump-out and will be more favorable to minimize the confinement degradation when controlling ELM [32,51], as illustrated by the TM1 simulation results in figure 7 of reference [32]. An extension of the scaling to include the dependence on plasma collisionality and toroidal mode number will enable a simplified model for the prediction of density pump-out quickly.
In conclusion, dedicated experiments in KSTAR and DIII-D by using n = 1 RMP are carried out to validate the features of density pump-out caused by magnetic island formation at the pedestal-foot, with qualitative consistency observed. A staircase-like bifurcation in the density pump-out is observed when slowly ramping up the n = 1 RMP current, and the density fluctuations are slightly decreased from the pedestal-foot to the pedestal-top. The magnitude of density pump-out becomes weaker when decreasing q 95 from 5.5 to 4.9, and the density pump-out partially recovers when q 95 is ramped down to lower than 4.9. Analysis of the DIII-D database of n = 3 RMP ELM control experiments finds that the magnitude of density pump-out is proportional to the square root of RMP coil current ∆n e /n e ∝I 0.5 RMP , consistent with simulations.
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