Optimization of 3D controlled ELM-free state with recovered global connement for tokamak fusion plasmas

Mitigation of deleterious heat ﬂux from edge-localized modes (ELMs) on fusion reactors is often attempted with 3D perturbations of the conﬁning magnetic ﬁelds. However, the established technique of resonant magnetic perturbations (RMPs) also degrades plasma performance, complicating implementation on future fusion reactors. In this paper, we introduce an adaptive real-time control scheme as a viable approach to simultaneously achieve both ELM-free states and recovered high-conﬁnement ( β N ∼ 1 . 91, β p ∼ 1 . 53, and H 98 ∼ 0 . 9), demonstrating successful handling of a volatile complex system through adap- tive measures. We show that, by exploiting a salient hysteresis process to adaptively min- imize the RMP strength, stable ELM suppression can be achieved while actively encour- aging conﬁnement recovery. This is made possible by a self-organized transport response in the plasma edge which reinforces the conﬁnement improvement through a widening of 22 the ion pedestal and promotes control stability, in contrast to the deteriorating effect on 23 performance observed in standard RMP experiments. These results establish the real-time approach as an up-and-coming solution towards an optimized ELM-free state, which is 25 an important step for the operation of ITER and reactor-grade tokamak plasmas. Notably, 26

a RMP coil current (blue), D α emission (green) near outer divertor target, and detected ELM frequency (red). b H 98 (blue), β N (green), and β p (red). c Pedestal height of ion (red), electron (blue) temperature, and NBI heating power (green). d Pedestal height of electron density (blue) and toroidal rotation of carbon (6+) impurity (red). performance close to the ITER-baseline level, reaching β N ∼ 1.91, β p ∼ 1.53, and H 98 ∼ 0.9. 62 Here, β N = aB T I p p B 2 /2µ 0 is the normalized beta, β p = p B 2 p /2µ 0 is the poloidal beta, and H 98 = τ exp /τ 98 63 is the thermal energy confinement quality compared to the standard H-mode plasmas, where p is 64 the averaged plasma pressure, a is the minor radius, I p is the total plasma, B T is the toroidal mag-65 netic field, B p is the poloidal magnetic field, B is the total magnetic field, τ exp is the experimental 66 thermal energy confinement time, and τ 98 is the empirically derived confinement time using stan-   (ω E ) at pedestal are shown for five different time slices. c 70% of ELM stability limit for β p,ped with (orange) and without (gray) wide ion pedestal, calculated from EPED code. Experimentally measured β p,ped (magenta) and D α emission (black) are also shown. The dotted lines show β p,ped limits during ELM-free state imposed by pedestal stability with (gray) and without (orange) wide ion pedestal.
s. Before ELM suppression (5.3-6.3 s), T i,ped decreases with I RMP , while the pedestal gradient is 168 well sustained (or even slightly increased). After ELM suppression (> 6.5 s), however, the pedestal 169 stiffness starts to change. The transition from 6.6 to 7.1 s shows broadening of the ion pedestal and 170 decreasing of its gradient. This widening is maintained in the pedestal recovery phase up to 7.7 171 s. The decrease in pedestal height and gradient are both due to RMP-induced transport. However, 172 the rapid broadening of the ion pedestal after ELM suppression indicates that its gradient is not 173 governed by the transport affecting the pedestal height but instead by an "additional" transport 174 source that occurs in the ELM suppression phase.

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The change in ion pedestal width improves the ELM stability. In theory, pedestal pressure 176 (P ped ) or pedestal poloidal beta (β p,ped = P ped B 2 p /2µ 0 ) should stay under the stability limit to avoid 177 the reappearance of ELM crashes. Stability analysis confirms that β p,ped stays below 70% of the 178 stability limit during the ELM suppression phase. This stability limit is known to improve with 179 increased pedestal width 35 . Therefore, widened pressure pedestal via ion-pedestal broadening 180 allows for higher β p,ped during the ELM-free phase. Numerical analysis reveals that the β p,ped 181 limit increases by 53% due to ion pedestal broadening. This change is presented in Fig.4c where W m,n and ∇T ped are the (m, n) island width and pedestal gradient, respectively. q ped is an 188 edge safety factor on the pedestal top. This expression is based on the concept where ∆T ped is 189 the accumulation of profile flattening by the islands in the pedestal region. We note that constant 190 ∇T ped over the pedestal region is assumed to make interpretation easier. This expression addresses 191 that pedestal height changes more rapidly with RMP strength as the pedestal gradient grows and 192 q ped decreases. With the given q profile monotonic, q ped is reduced by increasing pedestal width.

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The largely broadened ion pedestal can lead to a stronger response of T i,ped despite the decrease of entry changes as 4.9 → 3.6 → 3.53 → 3.5 kA, as seen in Fig.1(a), resulting in fast and stable sys-234 tem optimization. This interesting example shows uncommon positive effect 43,44 of self-organized 235 transport on pedestal confinement. 236 We note that such an RMP-induced hysteresis shown in Fig5 is not trivial to be produced in 237 the experiment as it conventionally requires a delicate pre-programmed RMP waveform. This 238 leads to difficulties in investigating and exploiting the hysteresis, which is critical to optimize 239 the ELM-free state. In this respect, adaptive RMP control is an effective methodology as it can 240 automatically generate the hysteresis and utilize it. In addition, the adaptive scheme has been suc-241 cessfully operated for more than a hundred confinement times (∼ 5 s) of KSTAR, and therefore, 242 this control is also expected to be applicable to long pulse plasma in ITER.
The origin of broadened ion-pedestal. It is worth pointing out that successful adaptive con-245 trol in these experiments is mainly due to a broadened ion pedestal during the ELM suppression fluctuations. Furthermore, they are both insensitive to RMP strength. Therefore, these similarities 266 support the claim that the ion pedestal is widened primarily due to increased heat diffusivity by 267 edge turbulence.

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Linear gyrokinetic simulations confirms that enhanced edge turbulence may occur in the ELM 269 suppression phase. As shown in Fig.7b, the linear growth rates (γ/γ E ) of turbulence mode exceed 270 the onset limit (>1) after the transitions to the ELM-free state. This is mainly due to decreased 271 stabilizing effect from the ExB shearing rate (γ E ) 46,47 , which comes from the degraded pressure 272 pedestal (Fig.4b). It turns out that the excited modes are correlated with the ITG/TEM hybrid.
Here, the bi-normal wave length k y ρ s ∼ 0.3 and real frequency ∼ 51 kHz of the most unstable to achieve stable ELM-free access by preventing RMP-induced disruption. It is noteworthy that 294 the remarkable recovery of confinement is not solely attributable to adaptive RMP control but also 295 to a widened ion pedestal resulting from RMP-induced transport that promotes pedestal recovery 296 by improving the ion response and ELM stability and facilitates fast, stable, and reinforced control 297 optimization (Fig.8). This feature, which can be correlated to the turbulent process, is a good ex-298 ample of a system that transitions to an optimal state through a self-organized response to adaptive 299 modulation. These results with low n = 1 RMP confirm that adaptive ELM control is a highly 300 promising approach towards optimizing the ELM-free state, potentially solving one of the most 301 challenging obstacles for viable and economical fusion energy.

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However, there are remaining features to be improved for a "complete" adaptive ELM control 303 picture. As shown in Fig.1a, the current approach is based on ELM detection and thereby in-304 evitably faces several ELMs during control. This limitation could be critical at the reactor level, 305 where a single ELM can already be dangerous. Thus, a way to detect the loss of ELM suppression 306 in advance of the ELM re-occurrence is needed. Here, the behavior of edge turbulence suggests 307 the potential solution. The amplitude of magnetic fluctuation during the ELM-free phase shows a 308 rapid decrease 70 ms before the return of ELMs at 7.75 s (Fig.7f). Such an abrupt change in mag-309 netic signals is an effective indicator of suppression loss. Therefore, this property can be utilized 310 in real-time to entirely avoid the return of ELM to achieve truly ELM-free optimization.

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Previous work has shown that the effectiveness of RMP ELM suppression can be enhanced by