# Highest Fusion Performance without Harmful Edge Energy Bursts in Tokamak

S.K.Kim  Princeton Plasma Physics Laboratory  R.Shousha  Princeton University
S.M.Yang  Princeton Plasma Physics Laboratory  Q.Hu  Princeton Plasma Physics
Laboratory  S.H.Hahn  Korea Institute of Fusion Energy  A.Jalalvand  Princeton
University  J.-K.Park  Seoul National University  N.C.Logan  Columbia
University  A.O.Nelson  Columbia University  Y.-S.Na  Seoul National
University  R.Nazikian  General Atomics  R.Wilcox  Oak Ridge National
Laboratory  R.Hong  University of California Los Angeles  T.Rhodes  University
of California Los Angeles  C.Paz-Soldan  Columbia University  Y.M.Jeon  Korea
Institute of Fusion Energy  M.W.Kim  Korea Institute of Fusion Energy  W.H.Ko
Korea Institute of Fusion Energy  J.H.Lee  Korea Institute of Fusion Energy
A.Battey  Columbia University  G.Yu  University of California Davis
A.Bortolon  Princeton Plasma Physics Laboratory  J.Snipes  Princeton Plasma
Physics Laboratory  E.Kolemen<EMAIL_ADDRESS>Princeton Plasma Physics
Laboratory  Princeton University

(August 31, 2024)

###### Abstract

The path of tokamak fusion and ITER is maintaining high-performance plasma to
produce sufficient fusion power. This effort is hindered by the transient
energy burst arising from the instabilities at the boundary of high-
confinement plasmas. The application of 3D magnetic perturbations is the
method in ITER and possibly in future fusion power plants to suppress this
instability and avoid energy busts damaging the device. Unfortunately, the
conventional use of the 3D field in tokamaks typically leads to degraded
fusion performance and an increased risk of other plasma instabilities, two
severe issues for reactor implementation. In this work, we present an
innovative 3D field optimization, exploiting machine learning, real-time
adaptability, and multi-device capabilities to overcome these limitations.
This integrated scheme is successfully deployed on DIII-D and KSTAR tokamaks,
consistently achieving reactor-relevant core confinement and the highest
fusion performance without triggering damaging instabilities or bursts while
demonstrating ITER-relevant automated 3D optimization for the first time. This
is enabled both by advances in the physics understanding of self-organized
transport in the plasma edge and by advances in machine-learning technology,
which is used to optimize the 3D field spectrum for automated management of a
volatile and complex system. These findings establish real-time adaptive 3D
field optimization as a crucial tool for ITER and future reactors to maximize
fusion performance while simultaneously minimizing damage to machine
components.

$*$These authors equally contributed to this work.

For a fusion energy source to be economically competitive in the global energy
market, it must produce a high fusion triple product ($n\tau T$) Gormezano
_et al._ (2007) with sufficient plasma density ($n$), temperature ($T$), and
energy confinement time ($\tau$) while sustaining fusion reactions. In other
words, the fusion plasma requires sufficient figure of merit ($G\propto n\tau
T$) Gormezano  _et al._ (2007); Peeters, Angioni, and Sips (2007), which
increases with plasma confinement quality ($H_{\text{89}}$) Yushmanov  _et
al._ (1990), where $H_{\text{89}}$ is normalized energy confinement time. For
example, the International Thermonuclear Experimental Reactor (ITER) requires
$G_{\text{fus}}>0.4$ and $H_{\text{89}}>2$ to achieve Gormezano  _et al._
(2007) its objective (A fusion power ten times higher than the input heating
power). One of the leading approaches Han  _et al._ (2022) towards this goal
is a tokamak operated robustly in the high confinement mode (H-mode)Wagner
_et al._ (1984), characterized by a narrow edge transport barrier (or
confinement pedestal) responsible for significantly elevated plasma pressures
within the device. This "pedestal" has demonstrated notable benefits by
enhancing $G$, thereby improving the fusion economy. However, the H-mode has a
high-pressure gradient at the edge (pedestal), which introduces significant
risks to reactor operation, mainly due to emerging dangerous edge energy
bursts as a result of a plasma instability known as edge localized modes
(ELMs) Connor  _et al._ (1998). These edge bursts cause rapid relaxations in
pedestal plasma energy, leading to intense transient heat fluxes on reactor
walls, resulting in undesirable material erosion and surface melting. The
predicted heat energy reach $\sim 20\text{MJ/m}^{2}$, unacceptable in a fusion
reactor Loarte  _et al._ (2014); Gunn  _et al._ (2017). Consequently, for
tokamak designs to become a viable option for fusion reactors, reliable
methods must be developed to routinely suppress edge burst events without
affecting $G$.

Figure 1: 3D-field coil structure in tokamak. Schematic diagram of 3D field
coil and edge energy-burst in DIII-D tokamak. Color contour shows typical
3D-field amplitude formed by coils. Figure 2: Performance comparison of ELM-
free discharges in DIII-D and KSTAR tokamaks. $H_{89}$ versus figure of merit
($G$) at ELM-free state. These cover various non-ELMing scenarios, including
RMP, QH, L-mode, I-mode, and EDA-H mode in DIII-D. The red star and green
diamond markers show the adaptive RMP discharges in DIII-D and KSTAR,
respectively. The dashed lines indicate ITER-relevant level Transport,
Database, and Editors (1999); Gormezano  _et al._ (2007) required to achieve
their objectives. A detailed plot for this figure can be found in the
supplement material.

Resonant magnetic perturbations (RMPs) using external 3D field coils Evans
_et al._ (2006); Suttrop  _et al._ (2011); Jeon  _et al._ (2012); Sun  _et
al._ (2016) have proven to be one of the most promising methods for edge burst
control. The typical external coils surrounding the plasma to generate 3D
fields are shown in Fig. 1. By reducing the pedestal Fenstermacher  _et al._
(2008); Rozhansky  _et al._ (2010); Nazikian  _et al._ (2015); Paz-Soldan  _et
al._ (2015); Hu  _et al._ (2019); Fitzpatrick (2020); Liu  _et al._ (2020a);
Mordijck, Moyer, and McKee (2012); McKee  _et al._ (2013); Müller  _et al._
(2013); Liu  _et al._ (2020b), 3D-fields effectively stabilizes energy burst
in the edge region Snyder  _et al._ (2007). This stabilizing effect holds
significant advantage, and therefore, the ITER baseline scenario relies on
3D-field to achieve an edge-burst-free burning plasma in a tokamak for the
first time.

However, this scenario comes at a significant cost, resulting in a significant
deterioration of $H_{89}$ and $G$ compared to standard high-confinement plasma
regimes, thus depleting economic prospects. Moreover, the 3D field also raises
the risk of disastrous core instability, known as a disruption, which is even
more severe than an edge burst. Thus, the safe accessibility and compatibility
of edge-burst-free operation with high confinement operation requires urgent
exploration.

This work reports on an innovative and integrated 3D-field optimization on
both KSTAR and DIII-D tokamaks for the first time by combining machine
learning (ML), adaptiveLaggner  _et al._ (2020); Shousha  _et al._ (2022), and
multi-machine capabilities for automatically accessing and achieving an almost
fully edge-burst-free state while boosting the plasma fusion performance from
its initial burst-suppressed state, which is a significant milestone toward
edge-burst-free operation for future reactors. This is accomplished by real-
time exploitation of hysteresis between edge-burst-free onset and loss to
enhance plasma confinement while extending the ML capability in capturing
physics and optimizing nuclear fusion technology Kates-Harbeck, Svyatkovskiy,
and Tang (2019); Degrave  _et al._ (2022); Vega  _et al._ (2022).

This integration facilitates 1) highly enhanced plasma confinement, reaching
the highest fusion $G$ (see Fig. 2) among ELM-free scenarios in two machines
with the increase in $G$ up to 90%, 2) fully automated 3D-field optimization
for the first time by using an ML-based 3D-field simulator, and 3) concurrent
establishment of burst suppression from the very beginning of the plasma
operation, achieving nearly complete edge-burst-free operation close to the
ITER-relevant level. Such an achievement paves a vital step for future devices
such as ITER, where relying on empirical RMP optimization is no longer a
viable or acceptable approach.

This paper is organized as follows. We first explain the integrated 3D-field
optimization algorithms. The contribution of ML and adaptive schemes in the
optimization process is introduced in the following sections. Then, the
utilization of early 3D (or RMP) algorithms toward a complete ELM-free
operation and underlying physics phenomena allowing the burst-free operation
with high $G$ are presented. Lastly, the discussions on the application in
ITER and future reactors are drawn in summary.

Figure 3: Machine-learning based real-time RMP optimization algorithm.
Schematic diagram of integrated RMP optimization scheme in KSTAR with ML-
surrogate model (ML-3D). Figure 4: ML-3D model performance. a-d Validating
comparison of the model using test case, showing actual (blue), predicted
(orange), and low-pass filtered (green) $R_{\text{M,B}}$,$\phi_{\text{T,B}}$
values in time. Figure 5: Plasma parameters for a fully automated ELM
suppression discharge (#31873) with integrated RMP optimization. a
$I_{\text{RMP}}$ (blue) and $D_{\alpha}$ emission (orange) near outer divertor
target. c $H_{89}$(blue) and $G$ (orange). c Phasing between top/middle
($\phi_{\text{T}}$, blue) and middle/bottom coils ($\phi_{\text{B}}$, orange).
d Current amplitude ratio between of top/middle ($R_{\text{M}}$, blue) and
top/bottom coils ($R_{\text{B}}$, orange). e Ratio
($\epsilon$=$r_{\text{B,ML}}/r_{\text{B,STD}}$) of 3D-coil induced
$r_{\text{B}}$ from ML-3D ($r_{\text{B,ML}}$) and predicted one using a
empirical configuration ($r_{\text{B,STD}}$) . Smaller $\epsilon$ means lower
$r_{\text{B}}$ than the one by standard (empirical) setup. The gray dotted
line in c,d shows the 3D-coil configurations from a standard (empirical)
setup. The red-colored area highlights the automated access to the ELM-
suppressed state without pre-programmed 3D fields. The optimization algorithm
is triggered at 4.5 s

##  I Results

Fully automated optimization of 3D-field using ML-surrogate model. The key to
stable and robust ELM suppression is maintaining a sufficient edge 3D field
($B_{\text{edge}}$) for the ELM suppression while minimizing the core
perturbation ($B_{\text{core}}$) or
$r_{\text{B}}=B_{\text{core}}/B_{\text{edge}}$ to avoid disruption.
$B_{\text{edge}}$ and $r_{\text{B}}$ can be controlled by adjusting the RMP
current (or amplitude, $I_{\text{RMP}}$) and current distribution among
external 3D coils (.e.g. 3D waveform). For these reasons, in the present
experiments, a series of discharges are used to find an optimized 3D waveform
for safe ELM suppression. The successful ELM suppression in the previous
studies also relies on the empirically derived 3D setup. However, this trial-
and-error approach isn’t viable in a fusion reactor, where a single
unmitigated disruption terminates the machine’s life. Achieving reliable ELM
suppression in a reactor requires a first-principle strategy to determine the
3D waveform adaptively.

In this context, this work introduces the machine learning technique to
develop the novel path of automated 3D coil optimization and demonstrate the
concept for the first time. This approach exploits the physics-based
optimization scheme of 3D waveform Yang  _et al._ (2023) based on plasma
equilibrium and ideal 3D response from GPEC simulation Park, Boozer, and
Glasser (2007). This method has been validated across multiple devices Park
_et al._ (2018, 2021) and extensively tested on KSTAR, which has flexible 3D
coils with three rows, resembling ITER’s configuration. This approach
effectively predicts the optimal 3D coil setup that minimizes $r_{\text{B}}$
to ensure safe ELM suppression. However, its computational time, taking tens
of seconds, hinders real-time applicability, limiting its use to pre-
programmed or feed-forward strategies.

To overcome such limitations, a surrogate model (ML-3D) of GPEC code has been
developed to leverage the physics-based model in real time. This model uses
machine learning algorithms to accelerate the calculation time to the "ms"
scale, and it is integrated into the adaptive RMP optimizer in KSTAR. ML-3D
consists of a fully connected multi-layer perceptron (MLP) which is driven by
nine inputs, the total plasma current ($I_{\text{P}}$), edge safety factor
($q_{\text{95}}$), global poloidal beta ($\beta_{\text{P}}$), global internal
inductance ($l_{\text{i}}$), the coordinates of X-points on the R-Z plane
($R_{\text{X}}$, $Z_{\text{X}}$), and the plasma elongation ($\kappa$). These
parameters are derived from real-time equilibrium Ferron  _et al._ (1998)
calculations and are normalized to have zero mean and unit variance per input
feature overall training set. The outputs of the model are coil configuration
parameters ($R_{\text{M}},R_{\text{B}},\phi_{\text{T}},\phi_{\text{B}}$),
which determines the relations between coil current distribution across the
top ($I_{\text{TOP}}$), middle ($I_{\text{MID}}$), and bottom
($I_{\text{BOT}}$) 3D coils. Here, $R_{\text{M}}$ =
$I_{\text{MID}}/I_{\text{TOP}}$, $R_{\text{B}}$ =
$I_{\text{BOT}}/I_{\text{TOP}}$, and $\phi_{\text{T,B}}$ is the toroidal
phasing of the top and bottom coil currents relative to the middle coil (see
Fig. 3). In order to train this model, the GPEC simulations from 8490 KSTAR
equilibria are utilized.

As shown in Fig. 3, the algorithm adaptively changes $I_{\text{RMP}}$ in real-
time by monitoring the ELM state using $D_{\alpha}$ signal. This maintains a
sufficient edge 3D field to access and sustain the ELM suppression. At the
same time, the 3D-field optimizer adjusts the current distribution across the
3D coils using the output of ML-3D, which guarantees a safe 3D field for
disruption avoidance. This model generates the relations between coil currents
($R_{\text{M,B}}$, $\phi_{\text{T,B}}$) at every 1 ms given equilibrium state.
Figure 4(a-d) illustrates the performance of ML-3D with a randomly selected
test discharge, showing good agreement between the offline and ML-3D outputs.
A low-pass filter is applied to prevent overly rapid changes in the 3D-coil
commands that could result in damage to the coils.

In KSTAR discharge (#31873) with plasma current, $I_{p}=0.51\text{ MA}$, edge
magnetic pitch angle, $q_{95}\sim 5.1$, and $\sim 2.5$ MW of neutral beam
injection heating, the ML-integrated adaptive RMP optimizer is triggered at
4.5 s and successfully achieves fully-automated ELM suppression without the
need for pre-programmed waveforms. Shown in Fig. 5a, $I_{\text{RMP}}$ starts
increasing at 4.5 s with a rate of 3 kA/s to access the ELM suppression, while
$R_{\text{M,B}}$ and $\phi_{\text{T,B}}$ adjust simultaneously. As a 3D coil
setup is automatically optimized by ML-3D during the entire discharge, safe
ELM suppression is achieved at 6.2 s.

During the optimization process (see Fig. 5d), ML-3D maintains $r_{\text{B}}$
at a level similar to the empirically optimized 3D setup (standard,
$R_{\text{M,B}}$=1, $\phi_{\text{T,B}}$$=\pi/2$). Interestingly, ML-3D
achieves such a favorable $r_{\text{B}}$ even with different coil
configurations from the empirical (standard) case, highlighting the capability
of ML-3D in finding totally new physics-informed path of 3D-field
optimization. It is clear that $\epsilon$
(=$r_{\text{B,ML}}/r_{\text{B,STD}}$) stays near or below unity, where
$r_{\text{B,ML}}$ and $r_{\text{B,STD}}$ are$r_{\text{B}}$ from ML-3D and
standard setup, respectively. Furthermore, ML-3D performs better than the
empirical setup in the early stages of ELM suppression (<6 s), showing much
lower $r_{\text{B}}$ than the standard case (or $\epsilon<1$). This behavior
is particularly beneficial as keeping $r_{\text{B}}$ small in the early ELM
control phase is key to avoiding disruption, explaining how the successful
automated ELM suppression is achieved. Therefore, these results show the 3D-ML
as a viable solution for automated ELM-free access. Notably, ML-3D is based on
a physics-based model and doesn’t require experimental data, making its
extension to ITER and future fusion reactors straightforward. This robust
applicability to future devices highlights the advantage of the ML-integrated
3D-field optimization scheme. It is worth pointing out that the operational
limits of the KSTAR-3D coils are restricting the ML-3D’s ability to further
optimize $r_{\text{B}}$ in #31873. In future devices with higher current
limits for 3D coils, better field optimization and improved fusion performance
are expected.

As shown in Fig. 5a, the plasma performance significantly decreases from
$G\sim 0.17$ (4 s, before 3D-field application) to $G\sim 0.1$ after the first
ELM suppression at 6.2 s, which is the major disadvantage of 3D-field. Here,
$G=\beta_{\text{N}}H_{89}/q_{95}^{2}$ is the figure of merit,
$\beta_{\text{N}}$ is the normalized beta,
$H_{89}=\tau_{\text{exp}}/\tau_{89}$ is the energy confinement quality
compared to the standard tokamak plasmas, $\tau_{\text{exp}}$ is the
experimental energy confinement time, and $\tau_{89}$ is the empirically
derived confinement time using standard tokamak plasma database Yushmanov  _et
al._ (1990). Following the initial degradation, however, the confinement
starts to increase, eventually reaching a converged state by 8.7 s with an
enhanced final state of $G\sim 0.16$, reaching the initial high-confinement
state. This corresponds to a 60% boost from $G$ in a standard ELM-suppressed
state. Such a notable fusion performance boost is an outcome of adaptive
amplitude ($I_{\text{RMP}}$) optimization starting at 6.2 s, which will be
described in the next section.

Enhanced fusion performance using adaptive optimization. Figure 6 presents a
compelling illustration of H-mode plasmas from both DIII-D
($n_{\text{RMP}}=3$) and KSTAR ($n_{\text{RMP}}=1$), effectively achieving
fully suppressed ELMs through adaptive feedback RMP amplitude optimization.
The RMP-hysteresis from the plasma response is harnessed in these discharges,
allowing for sustained ELM suppression with lower RMP strength than initially
required to access the ELM suppression regime Nazikian  _et al._ (2014). As
the RMP amplitude is reduced, the pressure pedestal height increases, leading
to a notable global confinement boost in an ELM-suppressed state. In this
section, we employ a pre-set RMP waveform or 3D spectrum and apply real-time
feedback to control its amplitude ($I_{\text{RMP}}$). Therefore, the results
illustrate the pure effect of adaptive amplitude optimization.

In DIII-D discharge (#190736) with $I_{p}=1.62\text{ MA}$, $q_{95}\sim 3.35$,
and $\sim 5.8$ MW of neutral beam injection heating, the plasma exhibits
initial performance of $G\sim 0.39$ and $H_{89}\sim 2.15$, closely aligned
with the target of the ITER baseline scenario, including plasma shape.

However, after the first stable ELM suppression is achieved through
conventional RMP-ramp up ($n_{\text{RMP}}=3$), the plasma performance notably
decreases to $G\sim 0.18$ and $H_{89}\sim 1.45$. This 54% reduction in $G$ is
mainly attributed to the degradation in density and temperature pedestals, as
depicted in Fig. 6d,e. Similarly, in the KSTAR discharge with
$I_{p}=0.51\text{ MA}$, $q_{95}\sim 5$, and $\sim 3$ MW of neutral beam
heating, significant performance degradation is observed from $G\sim 0.19$ and
$H_{89}\sim 2.24$ to $G\sim 0.11$ and $H_{89}\sim 1.69$ after ELM suppression
by $n_{\text{RMP}}$=1 RMPs (Fig. 6h). These extensive degradations are a well-
known general trend in RMP experiments Suttrop  _et al._ (2016); Sun  _et al._
(2016); Kim  _et al._ (2020); Paz-Soldan (2021). Such $H_{\text{89}}$ and $G$
degradation cannot be accepted in future fusion reactors due to the
substantial deviation from the ITER baseline level ($H_{\text{89}}=$2,
$G=$0.4) and increase in fusion cost.

Following the initial degradation, the real-time adaptive RMP optimization
scheme improves fusion performance while maintaining stable ELM suppression.
The controller relies on the $D_{\alpha}$ emission signal near the outer
divertor target to monitor the ELM events. To achieve ELM suppression, the RMP
amplitude ($I_{\text{RMP}}$) is increased until ELM suppression. Subsequently,
during the ensuing ELM-suppressed phase, the controller lowers
$I_{\text{RMP}}$ to raise the pedestal height until ELMs reappear, at which
point the control ramps up the RMP amplitude again to achieve suppression
(Fig. 6b). A 0.5 s RMP flattop interval is introduced between the RMP-ramp up
and down phases in the experiment to achieve a saturated RMP response. As
mentioned earlier, the 3D shape of RMP is pre-programmed for safe ELM
suppression and only adjusts the amplitude.

Figure 6: Plasma parameters for an ELM suppression discharges (#190736 [a-e]
and #26004 [f-j]) with adaptive amplitude optimization. a,f Plasma current
($I_{\text{P}}$, blue), NBI heating ($P_{\text{NB}}$, orange), and torque
($T_{\text{NB}}$, green). b,g RMP coil current ($I_{\text{RMP}}$, blue) and
$D_{\alpha}$ emission (orange) near outer divertor target. c,h $H_{89}$(blue)
and $G$ (orange). d,i Pedestal height of electron ($T_{\text{e,ped}}$, blue)
and ion ($T_{\text{i,ped}}$, orange) temperature. e,j Pedestal height of
electron density ($n_{\text{e,ped}}$, blue) and toroidal rotation frequency of
carbon (6+) impurity ($\omega_{\text{tor,ped}}$, orange). Figure 7:
Performance enhancement in discharge with adaptive RMP optimization. $G$ at
initial (standard) ELM-suppressed state versus finally achieved $G$ from the
initial state by adaptive RMP optimization. The circle (orange), triangle
(green), and diamond (blue) dots correspond to $n=$1 (KSTAR), $n=$2 (KSTAR),
and $n=$3 (DIII-D) cases, respectively. The dotted grey lines show the degree
of $G$ enhancement by the adaptive scheme.

With the adaptive RMP optimization, the plasma performance of discharge
#190736 is enhanced to $G\sim 0.33$ and $H_{89}\sim 2.05$, which corresponds
to 83% and 41% improvement of $G$ and $H_{89}$ of standard RMP-ELM suppressed
state, respectively. Notably, the increase in $G_{fus}$ is particularly
significant, reaching the ITER-relevant level, highlighting the advantage of
adaptive optimization. We note that the further performance increase during
the transient ELM-free period (>2.95s) with rapid density increase is not
considered to avoid overestimating the control performance. The improved
confinement quality is attributed to enhanced temperature and density
pedestals. As shown in Fig. 6(d,e), all pedestals are improved compared to the
initial ELM suppression phase. For example, the electron ($T_{\text{e,ped}}$)
and ion ($T_{\text{i,ped}}$) temperature pedestals increase by 25% and 28%,
respectively. The electron density pedestal ($n_{\text{e,ped}}$) also shows a
23% increase during the same period.

The strong performance boost is similarly achieved in KSTAR discharge #26004.
To leverage the long-pulse feasibility (>10 s) of KSTAR, the adaptive
optimization scheme is implemented with the lower bound of $I_{\text{RMP}}$
set slightly higher (by $0.1\text{kA}$) than where the most recent ELM
returns. This adaptive constraint reduces control oscillation and enables the
plasma to converge to an operating point after sufficient iterations,
optimizing both ELM stability and confinement. In the selected discharge, the
adaptive scheme reaches a stable ELM-suppressed phase after 10 s, with
enhanced global confinement, as illustrated in Fig. 6(g,h). The plasma
performance in this final state shows $G\sim 0.15$ and $H_{89}\sim 1.98$,
increasing up to 37% and 17% of $G$ and $H_{89}$ at initial ELM suppression.
This successful iteration of the adaptation scheme in longer pulses also
supports its applicability in ITER long pulses.

The adaptive scheme has been extensively tested in both tokamaks over $30$
discharges with multi-toroidal wave number of RMP ($n_{\text{RMP}}$) of
$n_{\text{RMP}}=1-2$ (KSTAR) and 3 (DIII-D), demonstrating its robust
performance in boosting ELM-suppressed plasma performance. It is noteworthy
that ITER-tokamak will utilize high-$n$ ($n_{\text{RMP}}$=3) while fusion
reactor may rely on low-$n$ due to the engineering limitations Yang  _et al._
(2020). Therefore, it is important to confirm the multi-$n$ capability of the
adaptive RMP scheme. As shown in Fig. 7, we observe an effective $G$
enhancement from the standard ELM-suppressed state regardless of
$n_{\text{RMP}}$, affirming the multi-n compatibility of the adaptive RMP
optimization for ITER and future fusion reactors. With such success, the ELM-
suppressed discharges with RMP optimization perform the best $G$ among the
various ELM-free scenarios (see Fig. 2) in DIII-D and KSTAR, including Non-ELM
scenarios Paz-Soldan (2021) where ELMs are intrinsically suppressed without
using 3D-fields. This highlights that adaptive 3D-field optimization is one of
the most effective ways to achieve a high-performance ELM-free scenario.
Furthermore, the enhanced $H_{\text{89}}$ can result in an increased non-
inductive current fraction. This improvement reduces the flux consumption in
the central solenoid, thereby extending the pulse length. Therefore, the
adaptive RMP scheme has contributed to notable ELM-suppression long-pulse
records J.-K.Park  _et al._ (2023) over 45s in KSTAR, which is also an
essential advantage for ITER operations. We emphasize that the feasibility of
utilizing RMP-hysteresis in a feed-forward approach is restricted. This
limitation stems from the challenges in precisely predicting the required RMP
strength to achieve and sustain ELM suppression. Notably, such an advantage
remains exclusive to the adaptive real-time scheme.

Interestingly, a very high fusion $G$ boost over 80% is observed in the
$n_{\text{RMP}}=3$ results for the DIII-D cases, recovering most of the
performance lost by RMP (see Fig. 7). This further highlights the performance
of adaptive RMP optimization, a key to accessing ELM-suppressed high-
confinement scenarios. We’ll revisit the analysis and insights behind these
strong performance enhancements in the last part of this paper.

Figure 8: Plasma parameters with an integrated RMP optimization (#191754),
reaching near-zero ELMs. a $q_{\text{9}}5$ (blue) and $P_{\text{NB}}$
(orange). b $I_{\text{RMP}}$ (blue) and $D_{\alpha}$ emission (orange) near
outer divertor target. c $H_{89}$(blue) and $G$ (orange). The red-colored area
highlights the H-mode access without early ELMs. The green dotted lines in b
show the sawteeth timing.

Nearly complete ELM-free operation with high performance by integrated RMP
optimization. It is worth pointing out that the amplitude optimization process
results in multiple ELMs before accessing the optimized state. As shown in
Fig. 6(b,g), the ELMs reappear during RMP amplitude optimization. These can be
considered acceptable as they can be reduced with control tuning, and also,
few ELMs are tolerable in future fusion machines. However, avoiding extensive
ELMs between the LH transition and the first ELM suppression is vital.
Previous research has demonstrated that early RMP-ramp up Evans and the DIII-D
Team (2012); Shin  _et al._ (2022) before the first ELM reduces ELMs during
the early H-mode phase. Nevertheless, this approach often faced limitations
due to uncertainties in determining the required conditions, including initial
RMP amplitude for suppressing the first ELMs. While using a sufficiently large
RMP could guarantee early ELM suppression, it leads to poor confinement.

The integration of early RMP and 3D-field optimization schemes provides an
effective solution to address these limitations. Figure 8 illustrates a DIII-D
discharge (#191754) of near-zero ELMs, where the adaptive RMP optimization is
integrated with early RMP ramp-up. Notably, establishing a strong RMP of
$I_{\text{RMP}}$=4.7 kA (at 0.8s) successfully suppresses early ELMs, enabling
ELM-free access to H-mode. Subsequently, the RMP optimization improves the
performance from 2.7s, leading to the boost of $G$= 0.28 and
$H_{\text{89}}$=1.83 at standard ELM-suppressed state to $G$= 0.39 and
$H_{\text{89}}$=2.18. Despite the successful integration of optimizing
schemes, complete ELM suppression remains challenging due to a few sporadic
ELMs induced by sawteeth activity during the ELM suppressed phase, as shown in
Fig. 8b. These sporadic ELMs lead the controller to overestimate the ELM
instability, thereby hindering further optimizations (or decreases) of the RMP
amplitude, ultimately limiting the additional improvement in confinement.
Nevertheless, the plasma performance still exceeds the ITER-relevant baseline
($H_{\text{89}}$=2), highlighting the benefits of the adaptive scheme. In the
future, further progress can be pursued by exploring scenarios with reduced or
mitigated sawtooth, potentially leading to even greater improvements in ELM
control and optimization performance.

Figure 9: Plasma parameters of an optimized RMP amplitude (#190738) with
highly enhanced performance. a $I_{\text{RMP}}$ (blue) and $D_{\alpha}$
emission (orange) near the outer divertor target. b $H_{89}$(blue) and $G$
(orange). c $\omega_{\text{tor,ped}}$ (blue) and $T_{\text{i,ped}}$ (orange).
c $T_{\text{e,ped}}$ (blue) and $n_{\text{e,ped}}$ (orange). e ExB rotation
frequency ($\omega_{\text{E}}$) at $q$=10/3 (blue). The red and green colored
regions show the transient ELM-free phase and $|\omega_{\text{E}}|$<5 krad/s,
respectively.

Physics behind on accessing highly enhanced Edge-Energy-Burst-free phase by
adaptive optimization. The achievement of the ELM-suppressed state by resonant
magnetic perturbation (RMP) is generally understood to be due to field
penetration and pedestal gradient reduction. When RMP is applied externally,
the plasma response mainly shields it, and a sufficiently strong amplitude is
required to penetrate the plasma and form magnetic islands that cause
additional pedestal transport. The plasma flow ($\omega_{E}$), formed by ExB
forces due to electric ($E$) and magnetic ($B$) fields, is known to strengthen
the RMP shielding effect, causing the amplitude threshold
($I_{\text{RMP,th}}$) required to access and maintain the ELM-suppressed state
to increase. In particular, it is found that the value of $\omega_{E}$ on the
rational surfaces near the electron pedestal top mainly increases
$I_{\text{RMP,th}}$ because magnetic islands on these surfaces are key to the
ELM suppression Hu  _et al._ (2020). Following the penetration of RMPs, the
pedestal gradient decreases due to RMP-induced transport, and ELM suppression
is attained once the gradient falls below the ELM stability limit. In theory,
the pressure gradient at the pedestal center should stay under the stability
limit to avoid the reappearance of ELMs Hu  _et al._ (2021). Here, this
gradient reduction results in a decrease in pedestal height and global
confinement. Considering these factors, strict control boundaries exist for
the RMP amplitude and pedestal gradient to ensure stable ELM suppression.
These limitations often constrain the strong confinement to boost through
adaptive RMP optimization. Remarkably, however, the highly optimized cases
exhibiting more than an 80% $G$ enhancement, as shown in Figure 7, offer an
insight to overcome limitations in a performance boost.

Figure 9 shows an ELM-suppressed discharge in DIII-D (#190738), which achieves
>80% $G$ enhancement by adaptive $n=3$ RMP optimization. After the first
stable ELM suppression at 2.45s with $I_{\text{RMP}}$=5.4 kA, the plasma
performance improves from $G\sim 0.22$ and $H_{89}\sim 1.58$ up to $G\sim
0.49$ and $H_{89}\sim 2.42$ at 3.55s. This significant performance boost is
characterized by a gradual change that differs from the transient confinement
increase typically observed in transient ELM-free periods (>3.7 s) in that a
sharp increase in density pedestal is not observed before 3.65 s. In these
highly enhanced states, the ELM suppression is maintained until
$I_{\text{RMP}}\sim$1.5 kA, exhibiting more than 70% of RMP-hysteresis, as
shown in Fig. 9a, which dramatically exceeds typical values ($\sim$40%) in
other cases Kim  _et al._ (2022). Because a smaller RMP amplitude means higher
performance, such a strong hysteresis is the main contributor to performance
enhancement.

The strong RMP-hysteresis observed in this experiment is correlated with the
self-consistent evolution of the plasma flow in the RMP control. As shown in
Fig. 9c, the toroidal rotation at the pedestal top ($\omega_{\text{tor,
ped}}$) increases as the RMP decreases. Then, the increase in
$\omega_{\text{tor, ped}}$ alters the momentum balance of the plasma, causing
$\omega_{\text{E,10/3}}$ to decrease toward zero in the electron pedestal top
region, located at the $q=10/3$ rational surface. Figure 9(c,e) shows this
correlation between increasing $\omega_{\text{tor, ped}}$ and
$\omega_{\text{E,10/3}}\rightarrow 0$. As a result, $I_{\text{RMP,th}}$ is
relaxed, and the RMP amplitude can be further reduced. Here, an additional
decrease in RMP weakens the rotation damping by the 3D field, resulting in a
further increase in $\omega_{\text{tor, ped}}$, and allows
$\omega_{\text{E,10/3}}$ and $I_{\text{RMP,th}}$ to decrease favorably once
again. This synergy between $I_{\text{RMP,th}}$ and $\omega_{\text{tor, ped}}$
is key to maintaining ELM suppression with very low RMP, leading to a strong
confinement enhancement (and rotation), as shown in Fig. 9(a-d). The ELM
suppression ($\sim$4.2 s) in Fig. 6a with a very low RMP (1.5 kA) also shares
the same feature. We note that achieving such a reinforced RMP-induced
hysteresis is not trivial in the experiment, requiring pre-programmed and
dedicated RMP waveforms. In this respect, adaptive RMP optimization is an
effective methodology, as it can automatically generate and utilize the
hysteresis without manual intervention.

The enhanced RMP-hysteresis and rotation increase observed in the experiments
also offer promising aspects for future fusion devices. Maintaining thermal
and energetic particle confinements in a fusion reactor is essential for
achieving high fusion $G$. However, the presence of RMPs leads to undesired
perturbed fields in the core region that adversely affect the fast ion
confinement. Additionally, RMP-induced rotation damping poses a critical
challenge for ITER, where externally driven torque may not be sufficient to
suppress core instabilities and turbulent transport. The strengthened RMP-
hysteresis and rotation boost during adaptive RMP optimization can
significantly mitigate these unfavorable aspects of RMPs by enabling ELM
suppression with very low RMP amplitudes. By reducing the negative impacts of
RMPs on fast ion and core confinements, the prospects of an adaptive scheme
for achieving high fusion $G$ within future fusion devices become more
favorable.

It is noteworthy that the $\omega_{\text{tor,ped}}$ increase in the early RMP-
ramp down phase still leaves a question. This may simply be due to the reduced
damping caused by the 3D fields Logan  _et al._ (2013); Park and Logan (2017).
However, the increase in $\omega_{\text{tor,ped}}$ starts 0.3 s later than the
2.6 s that RMP-ramp down starts. This delayed response may indicate that
additional mechanisms, such as field penetration or turbulence, are
participating in the rotation response. In fact, the change in turbulence
along with rotation change is also observed in the experiment. Future studies
on plasma rotation in the presence of RMPs will provide further insight into
the projection of the RMP-ELM scenario onto ITER and future devices.

##  II Discussion

We have successfully optimized controlled ELM-free states with highly enhanced
fusion performance in the KSTAR and DIII-D devices, covering low-$n$ RMPs
relevant for future reactors to ITER-relevant $n$=3 RMPs and achieving the
highest fusion among various ELM-free scenarios in both machines. Furthermore,
the innovative integration of the ML algorithm with RMP control enables fully
automated 3D-field optimization and ELM-free operation for the first time with
strong performance enhancement, supported by an adaptive optimization process.
This adaptive approach exhibits compatibility between RMP ELM suppression and
high confinement. Additionally, it provides a robust strategy for achieving
stable ELM suppression in long-pulse scenarios J.-K.Park  _et al._ (2023)
(lasting more than 45 seconds) by minimizing the loss of confinement and non-
inductive current fraction Kim  _et al._ (2023). Notably, a remarkable
performance ($G$) boost is observed in DIII-D with $n$=3 RMPs, showing over a
90% increase from the initial standard ELM-suppressed state. This enhancement
isn’t solely attributed to adaptive RMP control but also to the self-
consistent evolution of plasma rotation. This response enables ELM suppression
with very low RMP amplitudes, leading to enhanced pedestal. This feature is a
good example of a system that transitions to an optimal state through a self-
organized response to adaptive modulation. In addition, the adaptive scheme is
integrated with early RMP-ramp methods, achieving an ITER-relevant ELM-free
scenario with nearly complete ELM-free operation. These results confirm that
the integrated adaptive RMP control is a highly promising approach for
optimizing the ELM-suppressed state, potentially addressing one of the most
formidable challenges in achieving practical and economically viable fusion
energy.

However, there are remaining features to be improved for a “complete” adaptive
RMP optimization. The present strategy, relying on ELM detection, unavoidably
encounters several ELMs during the optimization process. This drawback is
unfavorable for fusion reactors, where any potential risks must be minimized.
Earlier research Kim  _et al._ (2022) has revealed a "precursor pattern" in
$D_{\alpha}$ and turbulence signals, emerging about 20 ms ahead of ELM
reappearances during the suppression phase. This distinctive pattern can be
harnessed in real-time to prevent ELM reappearance by initiating early RMP
actions upon precursor detection, ultimately achieving a genuinely ELM-free
optimization. As an extension of these findings, this concept has been
successfully demonstrated in KSTAR R.Shousha  _et al._ (2023) by using
precursors in $D_{\alpha}$ signals, leading to nearly complete ELM suppression
by monitoring the precursors. In future work, enhanced ELM control performance
will be enabled through advanced ELM-loss precursor detection methods
incorporating real-time high-frequency fluctuation measurements.

Lastly, achieving robust access to H-mode without ELMs is a non-trivial task.
Here, it turns out that the stable $q_{\text{95}}$ control within the ELM
suppression window before the RMP ramp is key, as shown in Fig. 8a. This
significance is demonstrated by achieving more than ten sequential discharges
with ELM-free H-mode transitions via delicate $q_{\text{95}}$ tailoring.
However, the early RMP ramp required for achieving complete ELM suppression
might potentially affect the H-mode access by raising the LH-transition
threshold Leonard  _et al._ (1991); Kaye  _et al._ (2011); Gohil  _et al._
(2011); Ryter  _et al._ (2012); In  _et al._ (2017); Schmitz  _et al._ (2019).
This concern must be addressed through fine-tuned early heating and RMP ramp
timings to minimize their effect on robust LH transition Shin  _et al._
(2022). The future integration of these features will be expanding operational
flexibility, enhancing fusion performance boost, and developing advanced ELM
control techniques for ITER and future tokamaks.

##  III Methods

DIII-D tokamak. The DIII-D tokamak is the largest operating national tokamak
device in U.S.A. The reference discharge has the plasma major radius
$R_{0}=1.68\text{ m}$, minor radius $a_{0}=0.59\text{ m}$, and the toroidal
magnetic field $B_{\text{T}}=1.92\text{ T}$ at major radius $R_{0}$. The $n=3$
RMP ELM suppression discharge is reproduced with a plasma shape having
elongation $\kappa\sim 1.81$, upper triangularity $\delta_{\text{up}}\sim
0.35$, and lower triangularity $\delta_{\text{low}}\sim 0.69$.

KSTAR tokamak. The KSTAR tokamak is the largest magnetic fusion device in the
Republic of Korea, supported by the Korea Institute of Fusion Energy (KFE) and
Government funds. The reference discharge has the plasma major radius
$R_{0}=1.8\text{ m}$, minor radius $a_{0}=0.45\text{ m}$, and the toroidal
magnetic field $B_{\text{T}}=1.8\text{ T}$ at major radius $R_{0}$. The $n=1$
RMP ELM suppression discharge on KSTAR can be reproduced with a plasma shape
having elongation $\kappa\sim 1.71$, upper triangularity
$\delta_{\text{up}}\sim 0.37$, and lower triangularity
$\delta_{\text{low}}\sim 0.85$.

ELM-free database. The ELM-free database in DIII-D tokamak comes from Ref.Paz-
Soldan (2021). Here, the previous database uses 300 ms time averaging, while
the data point of discharge with adaptive RMP optimization uses a shorter time
scale (100 ms) to capture the performance variation with adaptive RMP
optimization. The KSTAR database is also constructed using the same process.

Ideal plasma response calculation. The perturbed radial fields ($\delta
B_{\text{r}}$) from an ideal plasma response by RMP are calculated using GPEC
code Park, Boozer, and Glasser (2007) under given magnetic equilibria and 3D
coil configuration. The core ($B_{\text{core}}$) and edge ($B_{\text{edge}}$)
responses are derived through radially averaging $\delta B_{\text{r}}$ at
$\psi_{\text{N}}=0-0.9$ and $0.9-1.0$, respectively. The optimal 3D coil
configurations ($R_{\text{M}},R_{\text{B}},\phi_{\text{T}},\phi_{\text{B}}$)
of the edge-localized-RMP (ERMP) model are derived using calculated perturbed
fields.

Surrogate 3D model. The surrogate model is developed using the dense layer
model within the Keras library. The hidden neurons are equipped with ReLU
activation function, and they are organized in two layers with 40 and 10
neurons, respectively. In order to train this model, we collected data from
8490 KSTAR time slices in the past three years. The data was split randomly
into 6790 and 1700 samples for training and testing the model. In total, this
MLP consists of 800 trainable parameters (connection weights), and the
training iterations continue for 150 epochs or if the error rates converge.
The final R2 score on the test set is 0.91.

Kinetic profile and equilibria reconstruction. Core ion temperature is
measured by charge exchange recombination system Seraydarian and Burrell
(1986); Won-Ha Ko, Seungtae Oh, and Myeun Kwon (2010) for Carbon (6+)
impurities at outboard mid-plane. Core electron temperature and density are
measured by the Thomson Scattering system Carlstrom  _et al._ (1992); Eldon
_et al._ (2012); Lee  _et al._ (2016). To obtain well-resolved profiles, the
data are averaged over 50 ms. The pedestal height is obtained from hyperbolic
tangent fits with edge profiles. Kinetic equilibria are reconstructed for the
plasma transport and stability analysis. This equilibrium is calculated from
the magnetic reconstruction using EFIT code Lao  _et al._ (1985) with the
reconstructed radial profiles. The OMFIT package Logan  _et al._ (2018);
Meneghini  _et al._ (2015) is used to achieve well-converged equilibrium with
automated iteration processes.

Plasma fluctuation measurements. In this work, edge $n_{\text{e}}$
fluctuations are measured from the doppler backscattering system (DBS)
Hillesheim  _et al._ (2009). Here, the measured density fluctuation captures
the ion-scale turbulence $k_{\text{y}}\rho_{\text{s}}=0.3-1.5$, rotating in
the electron direction, where $k_{\text{y}}$ is the bi-normal wave number,
$\rho_{\text{s}}=\sqrt{2m_{i}T_{e}}/eB$ is the hybrid Larmor radius, and
$m_{i}$ is deuterium mass.

##  IV acknowledgments

The authors would like to express their deepest gratitude to KSTAR and the
DIII-D team. This material was supported by the U.S. Department of Energy,
under Awards DE-SC0020372, DE-AC52-07NA27344, DE-AC05-00OR22725, DE-SC0022270,
DE-SC0022272, and DE-SC0019352. The U.S. Department of Energy also supported
this work under contract number DEAC02-09CH11466 (Princeton Plasma Physics
Laboratory). The United States Government retains a non-exclusive, paidup,
irrevocable, worldwide license to publish or reproduce the published form of
this manuscript or allow others to do so for United States Government
purposes. This material is based upon work supported by the U.S. Department of
Energy, Office of Science, Office of Fusion Energy Sciences, using the DIII-D
National Fusion Facility, a DOE Office of Science user facility, under
Award(s) DE-FC02-04ER54698. This research was also supported by R&D Program of
"KSTAR Experimental Collaboration and Fusion Plasma Research(EN2301-14)"
through the Korea Institute of Fusion Energy(KFE), funded by the Government
funds. Disclaimer: This report was prepared as an account of work sponsored by
an agency of the United States Government. Neither the United States
Government nor any agency thereof, nor any of their employees, makes any
warranty, express or implied, or assumes any legal liability or responsibility
for the accuracy, completeness, or usefulness of any information, apparatus,
product, or process disclosed, or represents that its use would not infringe
privately owned rights. Reference herein to any specific commercial product,
process, or service by trade name, trademark, manufacturer, or otherwise does
not necessarily constitute or imply its endorsement, recommendation, or
favoring by the United States Government or any agency thereof. The views and
opinions of authors expressed herein do not necessarily state or reflect those
of the United States Government or any agency thereof.

##  V Author contributions

S.K., R.S., S.Y. led the control development, experimental demonstration, and
analysis. E.K. conceived the original idea of adaptive control. Q.H. gave and
shared the fundamental guidance of the experimental plan and analysis. A.O.N.
analyzed the micro instability with Gyro-kinetic code. S.H., R.W., N.L., Y.J.,
M.K., and A.B. supported the experimental procedures. R.N. and C.P.S.
discussed the critical physics picture of transports at the pedestal. J.P. and
N.L. discussed the role of RMP response, stability, and transport analysis of
the pedestal region. H.R., T.R., W.K., and J.L. analyzed the profile and
fluctuation measurements. A.J. supported the development of the surrogate
model. Y.N., A.B., and J.S. advise the scope of the experimental analysis.
S.K. wrote the main manuscript text, and A.O.N. and all authors reviewed it.

##  VI Additional information

Competing financial interests: The authors declare no competing financial
interests.

## References

  * Gormezano  _et al._ (2007) C. Gormezano, A. Sips, T. Luce, S. Ide, A. Becoulet, X. Litaudon, A. Isayama, J. Hobirk, M. Wade, T. Oikawa, R. Prater, A. Zvonkov, B. Lloyd, T. Suzuki, E. Barbato, P. Bonoli, C. Phillips, V. Vdovin, E. Joffrin, T. Casper, J. Ferron, D. Mazon, D. Moreau, R. Bundy, C. Kessel, A. Fukuyama, N. Hayashi, F. Imbeaux, M. Murakami, A. Polevoi, and H. S. John, “Chapter 6: Steady state operation,” Nuclear Fusion 47, S285–S336 (2007).
  * Peeters, Angioni, and Sips (2007) A. Peeters, C. Angioni, and A. Sips, “On the extrapolation to ITER of discharges in present tokamaks,” Nuclear Fusion 47, 1341–1345 (2007).
  * Yushmanov  _et al._ (1990) P. Yushmanov, T. Takizuka, K. Riedel, O. Kardaun, J. Cordey, S. Kaye, and D. Post, “Scalings for tokamak energy confinement,” Nuclear Fusion 30, 1999–2006 (1990).
  * Han  _et al._ (2022) H. Han, S. J. Park, C. Sung, J. Kang, Y. H. Lee, J. Chung, T. S. Hahm, B. Kim, J.-K. Park, J. G. Bak, M. S. Cha, G. J. Choi, M. J. Choi, J. Gwak, S. H. Hahn, J. Jang, K. C. Lee, J. H. Kim, S. K. Kim, W. C. Kim, J. Ko, W. H. Ko, C. Y. Lee, J. H. Lee, J. H. Lee, J. K. Lee, J. P. Lee, K. D. Lee, Y. S. Park, J. Seo, S. M. Yang, S. W. Yoon, and Y.-S. Na, “A sustained high-temperature fusion plasma regime facilitated by fast ions,” Nature 609, 269–275 (2022).
  * Wagner  _et al._ (1984) F. Wagner, G. Fussmann, T. Grave, M. Keilhacker, M. Kornherr, K. Lackner, K. McCormick, E. R. Müller, A. Stäbler, G. Becker, K. Bernhardi, U. Ditte, A. Eberhagen, O. Gehre, J. Gernhardt, G. v. Gierke, E. Glock, O. Gruber, G. Haas, M. Hesse, G. Janeschitz, F. Karger, S. Kissel, O. Klüber, G. Lisitano, H. M. Mayer, D. Meisel, V. Mertens, H. Murmann, W. Poschenrieder, H. Rapp, H. Röhr, F. Ryter, F. Schneider, G. Siller, P. Smeulders, F. Söldner, E. Speth, K. H. Steuer, Z. Szymanski, and O. Vollmer, “Development of an Edge Transport Barrier at the H-Mode Transition of ASDEX,” Physical Review Letters 53, 1453–1456 (1984).
  * Connor  _et al._ (1998) J. W. Connor, R. J. Hastie, H. R. Wilson, and R. L. Miller, “Magnetohydrodynamic stability of tokamak edge plasmas,” Physics of Plasmas 5, 2687–2700 (1998).
  * Loarte  _et al._ (2014) A. Loarte, G. Huijsmans, S. Futatani, L. Baylor, T. Evans, D. M. Orlov, O. Schmitz, M. Becoulet, P. Cahyna, Y. Gribov, A. Kavin, A. Sashala Naik, D. Campbell, T. Casper, E. Daly, H. Frerichs, A. Kischner, R. Laengner, S. Lisgo, R. Pitts, G. Saibene, and A. Wingen, “Progress on the application of ELM control schemes to ITER scenarios from the non-active phase to DT operation,” Nuclear Fusion 54, 033007 (2014).
  * Gunn  _et al._ (2017) J. Gunn, S. Carpentier-Chouchana, F. Escourbiac, T. Hirai, S. Panayotis, R. Pitts, Y. Corre, R. Dejarnac, M. Firdaouss, M. Kočan, M. Komm, A. Kukushkin, P. Languille, M. Missirlian, W. Zhao, and G. Zhong, “Surface heat loads on the ITER divertor vertical targets,” Nuclear Fusion 57, 046025 (2017).
  * Transport, Database, and Editors (1999) I. P. E. G. o. C. Transport, I. P. E. G. o. C. Database, and I. P. B. Editors, “Chapter 2: Plasma confinement and transport,” Nuclear Fusion 39, 2175–2249 (1999).
  * Evans  _et al._ (2006) T. E. Evans, R. A. Moyer, K. H. Burrell, M. E. Fenstermacher, I. Joseph, A. W. Leonard, T. H. Osborne, G. D. Porter, M. J. Schaffer, P. B. Snyder, P. R. Thomas, J. G. Watkins, and W. P. West, “Edge stability and transport control with resonant magnetic perturbations in collisionless tokamak plasmas,” Nature Physics 2, 419–423 (2006).
  * Suttrop  _et al._ (2011) W. Suttrop, T. Eich, J. C. Fuchs, S. Günter, A. Janzer, A. Herrmann, A. Kallenbach, P. T. Lang, T. Lunt, M. Maraschek, R. M. McDermott, A. Mlynek, T. Pütterich, M. Rott, T. Vierle, E. Wolfrum, Q. Yu, I. Zammuto, and H. Zohm, “First Observation of Edge Localized Modes Mitigation with Resonant and Nonresonant Magnetic Perturbations in ASDEX Upgrade,” Physical Review Letters 106, 225004 (2011).
  * Jeon  _et al._ (2012) Y. M. Jeon, J.-K. Park, S. W. Yoon, W. H. Ko, S. G. Lee, K. D. Lee, G. S. Yun, Y. U. Nam, W. C. Kim, J.-G. Kwak, K. S. Lee, H. K. Kim, and H. L. Yang, “Suppression of Edge Localized Modes in High-Confinement KSTAR Plasmas by Nonaxisymmetric Magnetic Perturbations,” Physical Review Letters 109 (2012), 10.1103/physrevlett.109.035004.
  * Sun  _et al._ (2016) Y. Sun, Y. Liang, Y. \\. e. Liu, S. Gu, X. Yang, W. Guo, T. Shi, M. Jia, L. Wang, B. Lyu, C. Zhou, A. Liu, Q. Zang, H. Liu, N. Chu, H. \\. e. Wang, T. Zhang, J. Qian, L. Xu, K. He, D. Chen, B. Shen, X. Gong, X. Ji, S. Wang, M. Qi, Y. Song, Q. Yuan, Z. Sheng, G. Gao, P. Fu, and B. Wan, “Nonlinear Transition from Mitigation to Suppression of the Edge Localized Mode with Resonant Magnetic Perturbations in the EAST Tokamak,” Physical Review Letters 117 (2016), 10.1103/physrevlett.117.115001.
  * Fenstermacher  _et al._ (2008) M. E. Fenstermacher, T. E. Evans, T. H. Osborne, M. J. Schaffer, M. P. Aldan, J. S. deGrassie, P. Gohil, I. Joseph, R. A. Moyer, P. B. Snyder, R. J. Groebner, M. Jakubowski, A. W. Leonard, O. Schmitz, and the DIII-D Team, “Effect of island overlap on edge localized mode suppression by resonant magnetic perturbations in DIII-D,” Physics of Plasmas 15, 056122 (2008).
  * Rozhansky  _et al._ (2010) V. Rozhansky, E. Kaveeva, P. Molchanov, I. Veselova, S. Voskoboynikov, D. Coster, A. Kirk, S. Lisgo, and E. Nardon, “Modification of the edge transport barrier by resonant magnetic perturbations,” Nuclear Fusion 50, 034005 (2010).
  * Nazikian  _et al._ (2015) R. Nazikian, C. Paz-Soldan, J. Callen, J. deGrassie, D. Eldon, T. Evans, N. Ferraro, B. Grierson, R. Groebner, S. Haskey, C. Hegna, J. King, N. Logan, G. McKee, R. Moyer, M. Okabayashi, D. Orlov, T. Osborne, J.-K. Park, T. Rhodes, M. Shafer, P. Snyder, W. Solomon, E. Strait, and M. Wade, “Pedestal Bifurcation and Resonant Field Penetration at the Threshold of Edge-Localized Mode Suppression in the DIII-D Tokamak,” Physical Review Letters 114, 105002 (2015).
  * Paz-Soldan  _et al._ (2015) C. Paz-Soldan, R. Nazikian, S. Haskey, N. Logan, E. Strait, N. Ferraro, J. Hanson, J. King, M. Lanctot, R. Moyer, M. Okabayashi, J.-K. Park, M. Shafer, and B. Tobias, “Observation of a Multimode Plasma Response and its Relationship to Density Pumpout and Edge-Localized Mode Suppression,” Physical Review Letters 114, 105001 (2015).
  * Hu  _et al._ (2019) Q. M. Hu, R. Nazikian, B. A. Grierson, N. C. Logan, J.-K. Park, C. Paz-Soldan, and Q. Yu, “The density dependence of edge-localized-mode suppression and pump-out by resonant magnetic perturbations in the DIII-D tokamak,” Physics of Plasmas 26, 120702 (2019), publisher: AIP Publishing.
  * Fitzpatrick (2020) R. Fitzpatrick, “Theory of edge localized mode suppression by static resonant magnetic perturbations in the DIII-D tokamak,” Physics of Plasmas 27, 042506 (2020).
  * Liu  _et al._ (2020a) Y. Liu, C. Paz-Soldan, L. Li, and Y. Sun, “Role of 3D neoclassical particle flux in density pump-out during ELM control by RMP in DIII-D,” Nuclear Fusion 60, 036018 (2020a).
  * Mordijck, Moyer, and McKee (2012) S. Mordijck, R. A. Moyer, and G. R. McKee, “Changes in density fluctuations as a result of resonant magnetic perturbations correlate with the density inverse scale length,” Physics of Plasmas 19, 024504 (2012).
  * McKee  _et al._ (2013) G. McKee, Z. Yan, C. Holland, R. Buttery, T. Evans, R. Moyer, S. Mordijck, R. Nazikian, T. Rhodes, O. Schmitz, and M. Wade, “Increase of turbulence and transport with resonant magnetic perturbations in ELM-suppressed plasmas on DIII-D,” Nuclear Fusion 53, 113011 (2013).
  * Müller  _et al._ (2013) H. Müller, T. Lunt, W. Suttrop, T. Eich, R. Fischer, J. Fuchs, A. Herrmann, M. Kočan, P. de Marné, and E. Wolfrum, “Modification of scrape-off layer transport and turbulence by non-axisymmetric magnetic perturbations in ASDEX Upgrade,” Journal of Nuclear Materials 438, S64–S71 (2013).
  * Liu  _et al._ (2020b) S. Liu, N. Yan, Y. Liang, H. Zhang, J. Xu, G. Xu, L. Wang, R. Chen, G. Hu, Y. Ye, Y. Sun, T. Shi, H. Wang, M. Wu, X. Wu, S. Gu, M. Jia, N. Chu, Q. Ma, Y. Wang, T. Zhang, X. Han, L. Chen, J. Liu, S. Xu, H. Wang, N. Zhao, W. Zhang, J. Qian, L. Zeng, L. Xu, S. Wang, H. Liu, Q. Zang, Y. Yu, L. Liao, X. Gong, and EAST, “Edge turbulence characteristics and transport during the ELM mitigation with n = 1 resonant magnetic perturbation on EAST,” Nuclear Fusion 60, 082001 (2020b).
  * Snyder  _et al._ (2007) P. Snyder, K. Burrell, H. Wilson, M. Chu, M. Fenstermacher, A. Leonard, R. Moyer, T. Osborne, M. Umansky, W. West, and X. Xu, “Stability and dynamics of the edge pedestal in the low collisionality regime: physics mechanisms for steady-state ELM-free operation,” Nuclear Fusion 47, 961–968 (2007).
  * Laggner  _et al._ (2020) F. Laggner, D. Eldon, A. Nelson, C. Paz-Soldan, A. Bortolon, T. Evans, M. Fenstermacher, B. Grierson, Q. Hu, D. Humphreys, A. Hyatt, R. Nazikian, O. Meneghini, P. Snyder, E. Unterberg, E. Kolemen, and t. DIII-D team, “Real-time pedestal optimization and ELM control with 3D fields and gas flows on DIII-D,” Nuclear Fusion 60, 076004 (2020).
  * Shousha  _et al._ (2022) R. Shousha, S. K. Kim, K. G. Erickson, S. H. Hahn, A. O. Nelson, S. M. Yang, J.-K. Park, J. Wai, Y. M. Jeon, J. H. Lee, J. Jang, D. Seo, and E. Kolemen, “Design and experimental demonstration of feedback adaptive RMP ELM controller toward complete long pulse ELM suppression on KSTAR,” Physics of Plasmas 29, 032514 (2022).
  * Kates-Harbeck, Svyatkovskiy, and Tang (2019) J. Kates-Harbeck, A. Svyatkovskiy, and W. Tang, “Predicting disruptive instabilities in controlled fusion plasmas through deep learning,” Nature 568, 526–531 (2019).
  * Degrave  _et al._ (2022) J. Degrave, F. Felici, J. Buchli, M. Neunert, B. Tracey, F. Carpanese, T. Ewalds, R. Hafner, A. Abdolmaleki, D. de las Casas, C. Donner, L. Fritz, C. Galperti, A. Huber, J. Keeling, M. Tsimpoukelli, J. Kay, A. Merle, J.-M. Moret, S. Noury, F. Pesamosca, D. Pfau, O. Sauter, C. Sommariva, S. Coda, B. Duval, A. Fasoli, P. Kohli, K. Kavukcuoglu, D. Hassabis, and M. Riedmiller, “Magnetic control of tokamak plasmas through deep reinforcement learning,” Nature 602, 414–419 (2022).
  * Vega  _et al._ (2022) J. Vega, A. Murari, S. Dormido-Canto, G. A. Rattá, M. Gelfusa, and JET Contributors, “Disruption prediction with artificial intelligence techniques in tokamak plasmas,” Nature Physics 18, 741–750 (2022).
  * Yang  _et al._ (2023) S. Yang, J.-K. Park, Y. Jeon, N. Logan, J. Lee, Q. Hu, S. Lee, J.H. Kim, J. Kim, Y. Na, T. Hahm, and G. Choi, “Tailoring tokamak error fields to control plasma instabilities and transport,” Nature communications, accepted (2023).
  * Park, Boozer, and Glasser (2007) J.-k. Park, A. H. Boozer, and A. H. Glasser, “Computation of three-dimensional tokamak and spherical torus equilibria,” Physics of Plasmas 14, 052110 (2007).
  * Park  _et al._ (2018) J.-K. Park, Y. Jeon, Y. In, J.-W. Ahn, R. Nazikian, G. Park, J. Kim, H. Lee, W. Ko, H.-S. Kim, N. C. Logan, Z. Wang, E. A. Feibush, J. E. Menard, and M. C. Zarnstroff, “3D field phase-space control in tokamak plasmas,” Nature Physics 14, 1223–1228 (2018).
  * Park  _et al._ (2021) J.-K. Park, S. Yang, N. Logan, Q. Hu, C. Zhu, M. Zarnstorff, R. Nazikian, C. Paz-Soldan, Y. Jeon, and W. Ko, “Quasisymmetric Optimization of Nonaxisymmetry in Tokamaks,” Physical Review Letters 126, 125001 (2021).
  * Ferron  _et al._ (1998) J. Ferron, M. Walker, L. Lao, H. S. John, D. Humphreys, and J. Leuer, “Real time equilibrium reconstruction for tokamak discharge control,” Nuclear Fusion 38, 1055–1066 (1998).
  * Nazikian  _et al._ (2014) R. Nazikian, E. Eldon, T. Evans, N. Ferraro, B. Grierson, and R. Groebner, “Advances in the understanding of elm suppression by resonant magnetic perturbations (rmps) in diii-d and implications for iter,” in  _25th IAEA Fusion Energy Conference (FEC 2014)_ (2014).
  * Suttrop  _et al._ (2016) W. Suttrop, A. Kirk, R. Nazikian, N. Leuthold, E. Strumberger, M. Willensdorfer, M. Cavedon, M. Dunne, R. Fischer, S. Fietz, J. C. Fuchs, Y. Q. Liu, R. M. McDermott, F. Orain, D. A. Ryan, E. Viezzer, and a. and, “Experimental studies of high-confinement mode plasma response to non-axisymmetric magnetic perturbations in ASDEX Upgrade,” Plasma Physics and Controlled Fusion 59, 014049 (2016), publisher: IOP Publishing.
  * Kim  _et al._ (2020) M. Kim, J. Lee, W. H. Ko, S.-H. Hahn, Y. In, Y. M. Jeon, W. Suttrop, S. K. Kim, G. Y. Park, J.-W. Juhn, and J. H. Lee, “Pedestal electron collisionality and toroidal rotation during ELM-crash suppression phase under n = 1 RMP in KSTAR,” Physics of Plasmas 27, 112501 (2020).
  * Paz-Soldan (2021) C. Paz-Soldan, “Plasma performance and operational space without ELMs in DIII-D,” Plasma Physics and Controlled Fusion 63, 083001 (2021).
  * Yang  _et al._ (2020) S. Yang, J.-K. Park, N. Logan, C. Zhu, Q. Hu, Y. Jeon, Y. In, W. Ko, S. Kim, Y. Lee, and Y. Na, “Localizing resonant magnetic perturbations for edge localized mode control in KSTAR,” Nuclear Fusion 60, 096023 (2020).
  * J.-K.Park  _et al._ (2023) J.-K.Park, S. Kim, S. Yang, Q. Hu, J. Snipes, G. W. Shin, M. W. Kim, H. S. Han, Y. M. Jeon, H.-S. Kim, T. Rhee, G. Park, W. H. Ko, J. H. Lee, J. W. Juhn, R. Shousha, E. Kolemen, N. Logan, and C. Paz-Soldan, “Progress towards elm-less h-mode operations in kstar long pulses with resonant magnetic perturbations,” in  _29th IAEA Fusion Energy Conference (FEC 2023)_ (2023).
  * Evans and the DIII-D Team (2012) T. E. Evans and the DIII-D Team, “Suppression and Mitigation of Edge Localized Modes in the DIII-D Tokamak with 3D Magnetic Perturbations,” Plasma and Fusion Research 7, 2402046–2402046 (2012).
  * Shin  _et al._ (2022) G. Shin, H. Han, M. Kim, S.-H. Hahn, W. Ko, G. Park, Y. Lee, M. Lee, M. Kim, J.-W. Juhn, D. Seo, J. Jang, H. Kim, J. Lee, and H. Kim, “Preemptive RMP-driven ELM crash suppression automated by a real-time machine-learning classifier in KSTAR,” Nuclear Fusion 62, 026035 (2022).
  * Hu  _et al._ (2020) Q. Hu, R. Nazikian, B. Grierson, N. Logan, D. Orlov, C. Paz-Soldan, and Q. Yu, “Wide Operational Windows of Edge-Localized Mode Suppression by Resonant Magnetic Perturbations in the DIII-D Tokamak,” Physical Review Letters 125, 045001 (2020).
  * Hu  _et al._ (2021) Q. M. Hu, R. Nazikian, N. C. Logan, J.-K. Park, C. Paz-Soldan, S. M. Yang, B. A. Grierson, Y. In, Y. M. Jeon, M. Kim, S. K. Kim, D. M. Orlov, G. Y. Park, and Q. Yu, “Predicting operational windows of ELMs suppression by resonant magnetic perturbations in the DIII-D and KSTAR tokamaks,” Physics of Plasmas 28, 052505 (2021).
  * Kim  _et al._ (2022) S. Kim, R. Shousha, S. Hahn, A. Nelson, J. Wai, S. Yang, J.-K. Park, R. Nazikian, N. Logan, Y. Jeon, Y. In, J. Lee, J. Kim, C. Lee, Y.-S. Na, and E. Kolemen, “Optimization of 3D controlled ELM-free state with recovered global confinement for KSTAR with n = 1 resonant magnetic field perturbation,” Nuclear Fusion 62, 026043 (2022).
  * Logan  _et al._ (2013) N. C. Logan, J.-K. Park, K. Kim, Z. Wang, and J. W. Berkery, “Neoclassical toroidal viscosity in perturbed equilibria with general tokamak geometry,” Physics of Plasmas 20, 122507 (2013).
  * Park and Logan (2017) J.-K. Park and N. C. Logan, “Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks,” Physics of Plasmas 24, 032505 (2017), publisher: AIP Publishing.
  * Kim  _et al._ (2023) M. Kim, G. Shin, J. Lee, W. Ko, H. Hahn, S.-H. Hahn, S. Kim, S. Yang, R. Shousha, H.-S. Kim, J.-W. Juhn, G. Park, and E. Kolemen, “Integrated RMP-based ELM-crash-control process for plasma performance enhancement during ELM crash suppression in KSTAR,” Nuclear Fusion (2023), 10.1088/1741-4326/ace460.
  * R.Shousha  _et al._ (2023) R.Shousha, S. KIM, K. ERICKSON, J.-K. PARK, S. YANG, A. NELSON, and N. LOGAN, “Closed loop rmp elm suppression with minimized confinement degradation using adaptive control demonstrated,” in  _29th IAEA Fusion Energy Conference (FEC 2023)_ (2023).
  * Leonard  _et al._ (1991) A. Leonard, A. Howald, A. Hyatt, T. Shoji, T. Fujita, M. Miura, N. Suzuki, S. Tsuji, and JFT-2M Group, “Effects of applied error fields on the H-mode power threshold of JFT-2M,” Nuclear Fusion 31, 1511–1518 (1991).
  * Kaye  _et al._ (2011) S. Kaye, R. Maingi, D. Battaglia, R. Bell, C. Chang, J. Hosea, H. Kugel, B. LeBlanc, H. Meyer, G. Park, and J. Wilson, “L–H threshold studies in NSTX,” Nuclear Fusion 51, 113019 (2011).
  * Gohil  _et al._ (2011) P. Gohil, T. Evans, M. Fenstermacher, J. Ferron, T. Osborne, J. Park, O. Schmitz, J. Scoville, and E. Unterberg, “L–H transition studies on DIII-D to determine H-mode access for operational scenarios in ITER,” Nuclear Fusion 51, 103020 (2011).
  * Ryter  _et al._ (2012) F. Ryter, S. Rathgeber, E. Viezzer, W. Suttrop, A. Burckhart, R. Fischer, B. Kurzan, S. Potzel, and T. Pütterich, “L–H transition in the presence of magnetic perturbations in ASDEX Upgrade,” Nuclear Fusion 52, 114014 (2012).
  * In  _et al._ (2017) Y. In, J.-K. Park, Y. M. Jeon, J. Kim, G. Y. Park, J.-W. Ahn, A. Loarte, W. H. Ko, H. H. Lee, J. W. Yoo, J. W. Juhn, S. W. Yoon, and H. P. and, “Enhanced understanding of non-axisymmetric intrinsic and controlled field impacts in tokamaks,” Nuclear Fusion 57, 116054 (2017), publisher: IOP Publishing.
  * Schmitz  _et al._ (2019) L. Schmitz, D. Kriete, R. Wilcox, T. Rhodes, L. Zeng, Z. Yan, G. McKee, T. Evans, C. Paz-Soldan, P. Gohil, B. Lyons, C. Petty, D. Orlov, and A. Marinoni, “L – H transition trigger physics in ITER-similar plasmas with applied n = 3 magnetic perturbations,” Nuclear Fusion 59, 126010 (2019).
  * Seraydarian and Burrell (1986) R. P. Seraydarian and K. H. Burrell, “Multichordal charge-exchange recombination spectroscopy on the DIII-D tokamak,” Review of Scientific Instruments 57, 2012–2014 (1986).
  * Won-Ha Ko, Seungtae Oh, and Myeun Kwon (2010) Won-Ha Ko, Seungtae Oh, and Myeun Kwon, “KSTAR Charge Exchange Spectroscopy System,” IEEE Transactions on Plasma Science 38, 996–1000 (2010).
  * Carlstrom  _et al._ (1992) T. N. Carlstrom, G. L. Campbell, J. C. DeBoo, R. Evanko, J. Evans, C. M. Greenfield, J. Haskovec, C. L. Hsieh, E. McKee, R. T. Snider, R. Stockdale, P. K. Trost, and M. P. Thomas, “Design and operation of the multipulse Thomson scattering diagnostic on DIII-D (invited),” Review of Scientific Instruments 63, 4901–4906 (1992).
  * Eldon  _et al._ (2012) D. Eldon, B. D. Bray, T. M. Deterly, C. Liu, M. Watkins, R. J. Groebner, A. W. Leonard, T. H. Osborne, P. B. Snyder, R. L. Boivin, and G. R. Tynan, “Initial results of the high resolution edge Thomson scattering upgrade at DIII-D,” Review of Scientific Instruments 83, 10E343 (2012).
  * Lee  _et al._ (2016) K. Lee, J.-W. Juhn, Y. Nam, Y. Kim, H. Wi, S. Kim, and Y.-c. Ghim, “The design of two color interferometer system for the 3-dimensional analysis of plasma density evolution on KSTAR,” Fusion Engineering and Design 113, 87–91 (2016).
  * Lao  _et al._ (1985) L. Lao, H. St. John, R. Stambaugh, A. Kellman, and W. Pfeiffer, “Reconstruction of current profile parameters and plasma shapes in tokamaks,” Nuclear Fusion 25, 1611–1622 (1985).
  * Logan  _et al._ (2018) N. C. Logan, B. A. Grierson, S. R. Haskey, S. P. Smith, O. Meneghini, and D. Eldon, “OMFIT Tokamak Profile Data Fitting and Physics Analysis,” Fusion Science and Technology 74, 125–134 (2018).
  * Meneghini  _et al._ (2015) O. Meneghini, S. Smith, L. Lao, O. Izacard, Q. Ren, J. Park, J. Candy, Z. Wang, C. Luna, V. Izzo, B. Grierson, P. Snyder, C. Holland, J. Penna, G. Lu, P. Raum, A. McCubbin, D. Orlov, E. Belli, N. Ferraro, R. Prater, T. Osborne, A. Turnbull, and G. Staebler, “Integrated modeling applications for tokamak experiments with OMFIT,” Nuclear Fusion 55, 083008 (2015).
  * Hillesheim  _et al._ (2009) J. C. Hillesheim, W. A. Peebles, T. L. Rhodes, L. Schmitz, T. A. Carter, P.-A. Gourdain, and G. Wang, “A multichannel, frequency-modulated, tunable Doppler backscattering and reflectometry system,” Review of Scientific Instruments 80, 083507 (2009).