Development of high-performance long-pulse discharge in KSTAR

High-performance long-pulse plasma operation is essential for producing economically viable fusion energy in tokamak devices. To achieve such discharges in KSTAR, firstly, the rapid increase in the temperature of plasma-facing components was mitigated. The temperature increase of the poloidal limiter, especially, was associated with beam-driven fast ion orbit loss and the discrepancy of the equilibrium reconstructed with heated magnetic probes of signal drift. The fast ions lost to the poloidal limiter were reduced by optimizing the plasma shape and the composition of neutral beam injection (NBI). This nonlinear signal drift was successfully reduced by a new thermal shielding protector on the magnetic probes. Secondly, a lower loop voltage approach was implemented to reduce a poloidal flux consumption rate. A plasma current of 400 kA and a line-averaged electron density of ∼2.0 × 1019 m−3 were chosen by considering the L–H power threshold, fast ion orbit loss, and beam shine-through power loss for low loop voltage in KSTAR. In addition, the application of electron cyclotron heating also helped maintain the plasma with low loop voltage (∼25 mV) by enhancing the NBI-driven current and achieving a high poloidal beta (β P) state. KSTAR has achieved a long pulse (∼90 s) operation with the high performance of β P ⩽ 2.7, thermal energy confinement enhancement factor (H98y2) ∼ 1.1, and fraction of non-inductive current (f NI) ⩽ 0.96. Still, gradual degradation of the plasma performance has been observed over time in the discharges. In one of the long-pulse discharges, β P reduced by ∼18% over the time of ∼8τ R (current relaxation time, τ R ∼ 5 s) and ∼1067τ E,th (thermal energy confinement time, τ E,th ∼ 45 ms). The degradation may be closely associated with weak, yet growing, and persistent toroidal Alfvén eigenmodes and their effect on fast ion confinement.

Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Introduction
Achieving long-pulse plasma operation in a tokamak device is a challenging objective.A tokamak device primarily relies on obtaining plasma current (I P ) induced by the current variation of the poloidal field (PF) coils, thereby inherently limiting its pulse length due to the current constraints of PF coils.However, nuclear fusion energy development heavily depends on the ability to sustain long-pulse plasma operation.Therefore, to accomplish long-pulse plasma operation, a tokamak must maximize the fraction of non-inductive current f NI (≡I NI /I P , I NI is non-inductively induced plasma current) rather than inductively obtaining plasma current I IND .
The development of long-pulse plasma operation scenarios in tokamak is being explored through two approaches to maximize f NI .One approach involves compensating for the designated plasma current by increasing the fraction of the bootstrap current f BS (≡I BS /I P , I BS is the bootstrap current), while the other approach focuses on offsetting it through an increase in the fraction of externally driven current f CD (≡I CD /I P , I CD is the current externally driven by heating and current drive (H&CD) systems).Both f BS (∝β P ) and f CD (∝ζ CD P CD β N B/n 2 ) can be expressed as functions of <β> [1], where β P is poloidal beta, ζ CD is dimensionless current drive efficiency, P CD is auxiliary heating power driven by H&CD systems, β N is normalized beta, B is toroidal magnetic field, n is plasma density, and <β> is volume averaged normalized plasma pressure in the tokamak.Increasing f CD through an increase in P CD could decrease the fusion gain Q (≡P fus /P CD, P fus is fusion power); therefore, it is considered beneficial to maximize f NI by not only increasing <β> but also keeping a favorable plasma state to enhance the dimensionless current drive efficiency ζ CD or utilizing H&CD sources which themselves have a relatively good ζ CD .
The development of long-pulse plasma operation scenarios should not only focus on achieving a high-performance plasma state with the maximization of f NI but also consider the ability to sustain that state over a long time.In order to address this, it is necessary to consider the two longest plasma characteristic times: the evolution of plasma current density profile and the interaction between plasma and plasma-facing components (PFCs).In medium-size tokamak devices like KSTAR, the current relaxation time is estimated to be ∼10 0 -10 1 s, and the plasma-wall equilibrium time is estimated to be ∼10 1 -10 2 s.Therefore, the complex and multiple interactions between the engineering and physics elements can be evaluated in the longpulse discharge over ∼10 2 s.Furthermore, the long-pulse discharge provides an opportunity to investigate physics issues that may not manifest within a relatively short-time scale but can accumulate substantial effects, potentially leading to significant issues over a long-time scale.
Remarkable achievements in high-performance long-pulse plasma operation have recently been reported in DIII-D/EAST joint experiments.Experiments have been conducted on both devices based on high β P plasma operation scenarios.In DIII-D, the experiments achieved the fully non-inductive state with β P ⩾ 3.0, f BS ⩾ 0.8, and H 98y2 ∼ 1.5 for a pulse length of several seconds, primarily utilizing the neutral beam injection (NBI) and electron cyclotron heating (ECH) H&CD systems [2].The DIII-D experiment forms the internal transport barrier (ITB) at a large minor radius (ρ ∼ 0.7) in all transport channels.The high β P state with ITB formation in the thermal channels is more favorable for the increase in f BS .Meanwhile, EAST also achieved fully non-inductive discharge with β P ∼ 2.0, f BS ∼ 0.5, and H 98y2 ∼ 1.3 for a pulse length of 60 s, mainly employing the lower hybrid current drive (LHCD) and ECH H&CD systems [3].Moreover, EAST successfully sustains a 1056 s pulse length with the super I-mode plasma state, demonstrating a stationary plasma state over a long time by the long-pulse operation of H&CD systems and control of the plasma-wall interactions [4].
The advancement of long-pulse discharges in KSTAR aims to develop stable and sustainable high-performance scenarios and test the long-pulse operation capabilities of the device, identifying and resolving any issues that may arise during such operations from the points of view of both plasma physics and device engineering.Since 2015, KSTAR has conducted long-pulse plasma operations and successfully produced high-performance long-pulse discharges lasting ∼90 s.Unlike EAST experiments, KSTAR does not currently employ LHCD, which has a relatively high ζ CD .Instead, the primary H&CD systems employed for long-pulse plasma operation at KSTAR are NBI and ECH, similar to the experiments conducted on DIII-D.This enables not only the evaluation of the long-pulse capability of the H&CD systems and other facilities in the KSTAR device but also the examination of NBIdriven fast ion behavior in a long-pulse discharge.In particular, the achievement and continuation of a burning plasma state in ITER heavily relies on effectively preventing the transport of NBI-driven fast ions and fusion-generated α-particles.In this sense, KSTAR can contribute to studying fast ion behavior in conducting long-pulse plasma operations.
KSTAR has conducted high-performance long-pulse experiments by adopting the high β P operation mode as the plasma operation scenario, similar to the DIII-D/EAST joint experiments.However, the high β P state observed in KSTAR exhibits distinct plasma characteristics compared to that observed in DIII-D.In KSTAR high β P (∼2.4-3.3)state, the presence of ITB in the thermal transport channels is absent, and the increase in β P is primarily attributed to mitigating/suppressing toroidal Alfvén eigenmodes (TAEs) through properly controlled electron cyclotron (EC)-wave deposition, which mainly contributes to the improvement of fast ion confinement [5].
This paper explores the development of high-performance long-pulse plasma discharge in KSTAR.KSTAR has identified and resolved several physical and engineering challenges encountered in high-performance long-pulse plasma experiments.During long-pulse plasma operation, KSTAR has experienced the following issues: (1) Rapid temperature increase in PFCs due to beam-driven fast ion orbit loss and nonlinear signal drift in magnetic probes.
Considering the challenges described in points 1 and 2, section 2 describes the optimization process to establish a long-pulse scenario by adopting a developed high β P scenario.Section 3 provides detailed descriptions of the experimental results for high-performance long-pulse discharges in KSTAR.Section 4 focuses on an extensive discussion of issue 3.Many of these long-pulse discharges in KSTAR have experienced gradual degradation in plasma performance over a long-time scale, typically lasting several tens of seconds.In some cases, performance degradation has reached up to ∼20%.Finally, a summary and conclusion are provided in section 5.

Mitigation of the temperature increase in PFCs
KSTAR interlock systems [6], operated to protect the PFCs, continuously monitor the temperature of PFCs using thermocouples at a rate of 1 Hz.If the temperature of PFCs exceeds the designated threshold for more than 3 s after initial detection, the interlock system terminates the discharge process.
To protect the thermocouples from the intense heat of the plasma, they are positioned 5 mm below the surface of the PFC tiles [7].Consequently, the surface temperature of the tiles tends to be higher than the temperature measured by the thermocouples [8].In KSTAR, PFCs have bolted carbon tiles.According to [9], the surface temperature limit of a carbon tile due to particle erosion is theoretically analyzed to be ∼800 • C-2000 • C, depending on the plasma edge temperature.Therefore, KSTAR plasma experiments have been operated by ensuring that the thermocouple temperatures remain below 600 • C. In other words, managing heat sources and ensuring efficient heat transfer to the PFCs is essential for the successful development of long-pulse discharges.
To regulate the temperature increase of the PFCs, we must identify the underlying mechanism that leads to the temperature increase.For example, the temperature increase in the divertor is attributed to the heat flux flowing along the magnetic field lines, and extensive research has been conducted to control the heat flux incident on the divertor surface.In longpulse discharges of KSTAR, the temperature in the divertor also increased rapidly.To mitigate the temperature increase in the divertor, especially the temperatures of the central and outer divertor, the position of the striking point was adjusted over time.Using impurity gas injection to induce a detachment state on the divertor surface has deteriorated plasma performance in the KSTAR experiments.Ongoing research is focused on optimizing this technique, while the technique to access the detachment state has yet to be considered in the KSTAR highperformance long-pulse experiments.
It is worth noting that the temperature increase of the poloidal limiter was more pronounced than that of the divertor in the KSTAR experiments, as shown in figure 1(b).Within a few tens of seconds, the temperature of the thermocouples positioned in the poloidal limiter exceeded the limit of 600 • C, even with the diverted plasma shape.
The temperature increase in the poloidal limiter is primarily due to fast ion orbit loss [10].Firstly, the amount of fast ions lost to the poloidal limiter varies depending on the beamlines of the NBI sources.As described in [11,12], KSTAR has two NBI boxes: NBI1 and NBI2.Each NBI box consists of three ion sources named A, B, and C. According to the analysis of fast ion orbit loss using the NuBDeC code [10], among NBI sources, NBI1-C contributed significantly to the fast ion orbit loss to the poloidal limiter.NBI1-A, NBI1-B, NBI1-C, NBI2-A, NBI2-B, and NBI2-C contributed ∼19%, ∼1%, ∼38%, ∼9%, ∼17%, and ∼16%, respectively, of the total amount of fast ions lost to the poloidal limiter.This analysis was conducted with each NBI source injected with 2.0 MW of 100 kV, which has I P = 400 kA, B T = 2.4 T, and the plasma shape of discharge #21735 at t = 81 s.As reported in [10], fast ions ionized in the high-field side drift out and strike the PFCs as they rotate poloidally.The tangential radius of NBI1-C is 1.23 m, and its beamline touches the inboard limiter.Compared to other sources, NBI1-C produces a more significant number of fast ions on the high-field side.This indicates that the NBI1-C is unsuitable for long-pulse experiments where the rapid temperature increase in the poloidal limiter should be avoided.
Secondly, the amount of fast ions lost to the poloidal limiter depends on the plasma shape.Figure 2 also presents the NuBDeC analysis for the full discharge #21735 regarding the fast ion orbit loss to the poloidal limiter.As shown in figure 2(a), the outermost radial position at midplane (R out ) was evaluated as 2.21 m at ∼50 s.Subsequently, R out showed an almost linear increase, reaching R out = 2.27 m at 89 s.This observed increase was attributed to significant signal drift in the magnetic probes.Figure 2(b) implies that the increase in R out corresponded to the increase in fast ions lost to the poloidal limiter.We refer to [10] for a detailed interpretation of the correlation between R out and fast ion loss on the poloidal limiter.Consequently, as shown in figure 1, the poloidal limiter experienced rapid temperature growth after ∼50 s.
Therefore, to mitigate the temperature increase of the poloidal limiter, it is important to not only selectively utilize the appropriate NBI source but also control the plasma shape, mainly by keeping R out < ∼2.21 m under these plasma operating conditions in KSTAR.
Figure 3 shows the experimental results of how well the temperature increase of PFCs was mitigated by the change of the plasma shape and the selective application of NBI sources in the long-pulse discharge lasting more than 30 s. Generally, the subsequent discharge is usually conducted before the increased PFC temperature from the previous discharge is wholly dissipated.In KSTAR, a discharge can be carried out if all PFC temperatures are below 200 • C. For these reasons, the PFC temperatures are typically 100 • C-200 • C at the beginning of a discharge in the long-pulse experimental session, and there may be some differences between PFC positions.Therefore, as shown in figure 3, to facilitate a comparison between discharges or between PFCs, the temperature at the beginning of the discharge is adjusted to 0 • C. As shown in discharge #21735 in figure 3(a), the rate of increase in the poloidal limiter temperature was minimized and kept constant over time by controlling R out to be reduced to ∼2.21 m and replacing the injected NBI source NBI1-C with NBI1-A.This reduction in temperature increase can be interpreted as the result of reducing the fast ion orbit loss to the poloidal limiter.Furthermore, the rate of temperature increase in the inboard limiter was dramatically reduced when NBI1-C was removed, as shown in figure 3(b).As mentioned above, NBI1-C has a tangential radius of 1.23 m, causing its beamline to touch the inboard limiter.In the long-pulse discharges with a relatively low plasma density of ne ∼ 2.0-2.5 × 10 19 m −3 , the application of NBI1-C resulted in a rapid temperature increase in the inboard limiter due to relatively high shine-through power loss compared to the other beam sources.The rate of increase in the central divertor was significantly reduced by changing the position of the striking point, as shown in figure 3(c).However, the methods above did not contribute to lowering the temperature increase rate in the inboard divertor, as shown in figure 3(d), which we are still investigating a way to mitigate.Two techniques will be considered.One is the reduction of fast ion orbit loss to the inboard divertor by changing operating conditions.NuBDeC analysis indicates that the fast ion orbit loss also affects the inboard divertor.The other is to adjust the inboard striking point over time, as done to control the central divertor temperature.
In the high-temperature and long-pulse plasma experiment at KSTAR in 2018, significant nonlinear signal drift was observed in magnetic probes on the outboard side of the plasma.The nonlinear signal drift was likely attributed to the accumulation of plasma heat delivered to magnetic probes, which was associated with the temperature increase of PFCs.This nonlinear signal drift reduced the accuracy and reliability of real-time plasma shape control.As shown in discharge #21735 in figure 2, despite the actual increase in R out over time, real-time equilibrium fitting (EFIT) analyzed that R out was effectively controlled to a constant value.Eventually, this situation led to a rapid and further increase in the temperature  of the poloidal limiter.In order to solve this issue, an improvement was introduced in 2020 to mitigate the nonlinear signal drift by installing a thermal shielding protector on magnetic probes.
As shown in figure 4(a), in the KSTAR configuration, the PFC on the outboard side of the plasma in the midplane is open to the Vessel.As a result, magnetic probes installed on the inner surface of the Vessel were exposed to vacuum and plasma.This structural arrangement in KSTAR facilitates the transfer of plasma heat to these magnetic probes, potentially leading to nonlinear signal drift in the probes.The severity of this nonlinear signal drift is expected to increase with a longer pulse length.
The signal drift S using a G/s unit was evaluated from magnetic probes, MP Z and MP R , used to measure the magnitudes of the vertical magnetic field B z and the radial magnetic field B R on the plasma outboard side at the midplane.Figure 4(b) shows how much the signal drift S increases in KSTAR longpulse discharge compared to short-pulse discharge, as well as the impact of the thermal shielding protector on the signal drift.This analysis was interpreted as the absolute difference of the signal drift between long-pulse and short-pulse discharge, denoted as ∆|S| = |S long | − |S short |.A positive ∆|S| indicates that the signal drift in long-pulse discharge increased more than the inherent signal drift observed in the short-pulse discharge.This suggests the presence of nonlinear signal drift.In 2018, ∆|S| was observed to reach up to ∼4.0 G/s, predominantly observed in MP Z .The coils of MP Z are wound to face the plasma to measure the vertical magnetic field, making MP Z more susceptible to heat transfer from the plasma than MP R .In 2020, ∆|S| was close to 0, representing the effectiveness of the thermal shielding protector.
In order to compare the differences in the EFIT analysis results caused by the signal drift, two types of EFIT analyses were carried out: one employing drift-uncorrected magnetic probes and the other utilizing drift-corrected magnetic probes.The interpretation was performed by evaluating the difference in R out .As shown in figure 4(c), in discharge #21757 performed in 2018, ∆R out ∼ 10.0 cm was analyzed at the end of the discharge, as evidenced in MP Z in figure 4(b).Conversely, for discharge #27031 performed in 2020, ∆R out remained ⩽1.0 cm throughout the discharge.As a result, the thermal shielding protector has effectively mitigated the temperature increase in the poloidal limiter in the KSTAR long-pulse experiments.

Approaches for the lower loop voltage scenario
By achieving fully non-inductive discharge, the issue of flux consumption can be avoided.However, not only is it difficult to develop a fully non-inductive discharge, but it is also challenging to maintain the state for a long time.KSTAR successfully produced the fully non-inductive discharge, #13008, with a zero loop voltage.Nevertheless, the state was sustained for only ∼6 s within a 15 s pulse length.
The (Nb 3 Sn) conductors of PF1-PF5 are designed and manufactured with a maximum current of 25 kA/turn, but the operating current of the central solenoid composed of PF1-PF4 is currently limited to 15 kA/turn.This is relevant for the safe operation of the preload uncertainty of the central solenoid [13] and the apparent power limited to 140 MVA supplied by the KSTAR motor generator [14,15].The available poloidal flux is approximately estimated from the initial magnetization to the maximum PF coil current of 15 kA/turn.In order to evaluate this, the TES code [16] is adopted as an equilibrium solver, and the waveforms of PF coils are designated based on the typical scenario in the KSTAR discharges.From the TES analysis, as described in table 1, the total available poloidal flux is estimated to be ∼11.9Wb.Considering the standard plasma current ramp-up scenario of KSTAR discharges, the poloidal flux available for resistive flux consumption during the plasma current flat-top phase is ∼9.3 Wb at a plasma current of 400 kA.For plasma currents of 500 kA and 600 kA, the poloidal fluxes available during the plasma current flat-top phase are ∼9.0Wb and ∼8.2 Wb, respectively.As previously mentioned, KSTAR aims for a pulse length of 300 s.To achieve this, considering a discharge with the range of I P from 400 to 600 kA, the loop voltage (V loop ) should be kept constant at ∼27 mV or lower during the plasma current flat-top phase.Additionally, to approach a pulse length of at least 100 s, V loop should be ∼82 mV or lower.In other words, the long-pulse operation scenario requires an extremely low V loop over time, similar to the nearly fully-non inductive state.
Currently, the KSTAR long pulse scenario mainly targets I P = 400 kA and V loop < 93 mV.It is well known that approaches to reducing V loop must consider increasing f NI by maximizing f CD and increasing f BS .In our work, three approaches are considered as follows.
First, the plasma current was set as low as possible to induce lower flux consumption.The KSTAR long-pulse discharges mainly used a plasma current of 400 kA.However, as the plasma current decreased, not only did the plasma stored energy decrease, but the fast ion loss due to bad orbit also increased.As a result, the temperature of the poloidal limiter increased rapidly.According to KSTAR experimental results, using the plasma shape change mentioned in section 2.1, the plasma current that can operate within the temperature limit of the poloidal limiter was found to be 400 kA or higher.
In addition, lower plasma current typically results in relatively lower plasma density.A low plasma density allows for a large amount of current drive from H&CD systems.This helps reduce the loop voltage, which, in turn, reduces flux consumption; however, a low plasma density, especially in the case of KSTAR which primarily uses NBI as the main H&CD, increases the power loss through the beam shinethrough.Furthermore, it makes the transition to H-mode difficult due to the roll-over characteristic of the L-H threshold power against the line-averaged electron density in KSTAR [17].Based on these considerations, the KSTAR long-pulse discharges have been conducted at I P = 400 kA and the lineaveraged electron density (n e ) ∼ 2.0 × 10 19 m −3 .
Second, attempts were made to maximize the externally driven current (mainly an NBI-driven current).In [18], a regression analysis was performed on the driven current of KSTAR NBI sources to understand the characteristics of NBIdriven currents and increase their efficiency in various plasma conditions.The NUBEAM code was employed to calculate the NBI-driven currents and build a database for the regression analysis.The database includes a parametric scan with input variables such as I P in MA, B T in T, shafranov shift (∆ S ) in cm, ne in 10 19 m −3 , T e0 in keV, T i0 in keV, injected P NBI in MW, and anomalous fast ion anomalous diffusion coefficient (D f ) in m 2 s −1 .In the database, other variables, such as plasma shape, central safety factor (q 0 ), effective ion charge (Z eff ), and toroidal rotation profile (V T ), were held constant at q 0 ∼ 1.05, Z eff = 2.0, and V T0 = 200 km s −1 , respectively.As an example, the regression equation for the estimated NBIdriven current of the KSTAR NBI1-A source was obtained as follows, According to equation (1), although the input variables I P , ∆ S , and T i0 had little effect on the NBI-driven current, a higher NBI-driven current could be expected with relatively low ne , high T e0 , and high P NBI .As mentioned, the plasma discharges were carried out by setting ne ∼ 2.0 × 10 19 m −3 : close to the minimum density level.NBI and ECH are our primary H&CD systems.As reported in [19], the efficiency of ECHdriven current η ECCD (10 20 AW −1 m −2 ) is typically ∼0.015, which is lower than the efficiency of NBI-driven current η NBCD at ∼0.026.Since the injected P ECH is lower than ∼25% of the injected P NBI in the KSTAR experiments, it is difficult to expect a significant amount of ECH-driven current.However, the injection of ECH can help increase the NBI-driven current.According to equation ( 1), the injection of ECH raises the electron temperature at the same electron density, which may result in a larger amount of NBI-driven current.Moreover, the increased electron temperature has the additional effect of reducing plasma resistivity.From this point of view, the injection of ECH is crucial for the lower V loop scenario in KSTAR long-pulse discharge.
Third, a high β P discharge was adopted to enhance f BS for KSTAR long-pulse discharge.In KSTAR, when subjected to NBI injection, discharges with lower plasma currents (I P = 400-500 kA) have often faced challenges from TAEs that cause significant and substantial fast ion transport and a reduction in plasma β.Recent KSTAR experiments have demonstrated that these TAE activities can be mitigated/suppressed through precisely controlled EC-wave deposition [20,21].
As reported in [5], to achieve a high β P state at KSTAR, ECH/electron cyclotron current drive (ECCD) deposition must be accurately controlled to a narrow vicinity near the magnetic axis.For instance, figure 5 illustrates the time evolution of the high β P discharge #18602 (β P ∼ 2.9) compared with a typical H-mode discharge #18597 (β P ∼ 2.2).As described in table 1, β P ∼ 2.2 represents the typical plasma performance achievable at I P = 400 kA, while KSTAR high β P plasma exhibits significantly higher performance than this.As shown in figures 5(a) and (b), both discharges shared nearly identical operating conditions, except for B T .Specifically, I P = 400 kA, ne ∼ 4.2-4.7 × 10 19 m −3 , P NBI = 3.9 MW, P ECH = 0.7 MW, with B T at 1.8 T for discharge #18602 and 1.9 T for discharge #18597, resulting in distinct ECH/ECCD deposition.As shown in figures 5(c) and (d), the high β P discharge #18602 exhibited ∼30% improvement in β P and ∼50% reduction in V loop compared to the typical H-mode discharge #18597.This improvement is attributed to the improved fast ion confinement as indicated by neutron rate measurements due to TAE stabilization by ECH/ECCD injection, as shown in figures 5(e)-(g).That is, in addition to enhancing the NBI-driven current, ECH/ECCD injection plays an important role in achieving a high β P state in KSTAR.
Furthermore, experimental observations indicated that the valid deposition of ECH/ECCD, in terms of its radial position with respect to the EC-wave resonance, was confined to a specific region, denoted as R res ∼ 1.72 ± 0.025 m (equivalent to ∆R res ∼ 5 cm and ψ N ∼ 0.2), with B T = 1.8 T. This was highly reproducible in KSTAR experiments.It is important to note that conventional high β P mode, as observed in DIII-D and EAST, often attributes the improvement of β P to the formation of ITB by applying strong off-axis ECH/ECCD.In contrast, KSTAR high β P mode relied on ECH/ECCD applied in close proximity to the on-axis, which led to the expectation of no ITB formation in KSTAR high β P discharge.
Figure 6 presents experimental results describing V loop with various plasma operating conditions such as β P , B T , P EC , and P NBI in the database developed for the KSTAR longpulse scenario.The discharges in the database had a similar plasma shape, and the difference in the last closed flux surface between them was less than 3 cm.I P was 400 kA with ne ∼ 1.8-2.5 × 10 19 m −3 for all data points.
Figure 6 shows that V loop decreased with a β P increase (figure 6(a)) and P ECH increase (figure 6(b)), while a clear trend in V loop for B T (figure 6(c)) and P NBI (figure 6(d)) is difficult to discern.For clarification, discharges represented by I, II, III, and IV in figure 6 were selected to examine the effects of P ECH and β P in achieving a lower V loop .These four discharges have similar B T and P NBI conditions, as shown in figures 6(c) and (d).In discharges I, II, and III, the V loop decreased effectively and almost linearly as P ECH increased, despite little change in β P .This may be attributed to the second approach, which focuses on maximizing the NBIdriven current and reducing plasma resistivity through the ECH injection.In discharges III and IV, despite little change in P ECH , β P increased significantly from 2.0 to 2.5 through the controlled ECH injection technique by properly adjusting the ECH resonance location to mitigate/suppress TAEs.Consequently, the V loop reached ∼25 mV.Finally, discharge IV represents the reproduced high β P discharge corresponding to the third approach mentioned above, which has been considered as the plasma operating scenario for the highperformance long-pulse discharge in KSTAR.

Experimental results of high-performance long-pulse discharges
KSTAR has been establishing plasma operation scenarios since 2015 and conducting experiments aimed at achieving high-performance long-pulse discharges.KSTAR high-performance long-pulse experiments have mainly been attempted under the following operating conditions: I P = 400 kA, B T ∼ 1.8 T or ∼2.5 T, ne ∼ 1.8-2.5 × 10 19 m −3 , and maximum available P NBI and P EC in each experimental campaign.The variation in the toroidal magnetic field operated in a discharge is determined by the available frequency of the ECH gyrotron.The KSTAR ECH gyrotron is a dual-frequency source that can operate at both 105 GHz and 140 GHz.KSTAR has utilized up to two ECH sources in the long-pulse experiments so far, with each ECH source capable of delivering a maximum power of ∼0.8 MW.The KSTAR NBI system has six beamline sources, each capable of delivering 2.0 MW, resulting in a total maximum available power of ∼12.0 MW.However, for long-pulse experiments, NBI sources injecting power below ∼5.5 MW have been utilized, considering the maintenance requirements of the NBI sources and the temperature limitation of PFC.Starting from the 2023 experimental campaign, KSTAR plans to experiment with an upgraded PFC material, transitioning from carbon tiles to tungsten monoblocks.This upgrade will enable a higher NBI heating power to be injected into long-pulse experiments within the newly established temperature limitations of the PFCs.
Here, an overview of the development process and plasma characteristics of high-performance long-pulse discharges at KSTAR spanning from 2015 to 2022, with pulse lengths of 50 s or longer, is presented in figure 7.While all discharges were designed to have a pulse-length target of 100 s or longer, ∼57% of discharges were terminated by device operation limits, as indicated by the L PF and L TC labels, before reaching the target.Without the L PF and L TC labels, discharges were terminated due to NBI operational faults.In the KSTAR experiments, unlike ECH operational faults, NBI operational faults result in discharge termination through the interlock system [6].In figure 7, the β P and V loop values only up to 40 s are displayed because, in most long-pulse discharges, the injection of ECH usually remains consistently stable until 40 s.Thus, the influence of changes in ECH injection can be excluded as a factor in the variations of β P and V loop over time.
In the initial phase of the development of high-performance long-pulse discharges in KSTAR before 2018 (see figure 7(a)), the discharges produced sporadic and inconsistent performance in terms of β P , performance degradation over time, and subsequent increases in V loop .Consequently, due to relatively high flux consumption, the PF coil current reached its limit even in discharges lasting less than ∼75 s.
In the 2018 experimental campaign, experiments were focused on optimizing the high β P scenario to be suitable for long-pulse discharge (see figure 7(b)).This was carried out in the approaches described in sections 2.1 and 2.2, which involved optimizing factors such as plasma shape and operating conditions.Subsequent experiments were then conducted to increase the pulse length up to ∼90 s.As shown in discharges #21735, #21757, and #21758, it was possible to minimize performance degradation with β P ∼ 2.2-2.3 for up to a pulse length of ∼40 s as well as extend the time reaching L PF .However, as the pulse length increased, the thermal load on the PFC increased, making the discharge reach the PFC temperature limit (see L TC markers).Simultaneously, significant nonlinear signal drift was also observed in magnetic probes, which produced a deviation of the controlled plasma shape from the originally designed target shape.This inaccurate control of the plasma shape led to a further increase in PFC temperature, as shown in figure 2.
In 2020, the thermal shielding protector was installed on the magnetic probes exposed to the vacuum.The mitigation of nonlinear signal drift in magnetic probes was confirmed, as mentioned in section 2.1.More ECH and NBI power were injected to achieve a higher β P state and increase the pulse length.As shown in figure 7(c), increasing the P ECH was particularly effective in facilitating V loop reduction in conjunction with the increase of β P .This ensured V loop < 30 mV and β P > 2.5, as shown in discharge #27031.However, performance degradation phenomena frequently reappeared even within a 40 s pulse length.Therefore, since 2021, long-pulse experiments have focused on investigating plasma performance degradation over a long time.
In KSTAR, long-pulse experiments have commonly encountered several events, including plasma performance degradation, magnetohydrodynamic (MHD) instabilities, reaching operational limits, abnormal operation of H&CD systems, and abnormal operation of real-time EFIT associated with linear/nonlinear signal drift.The representative discharges #30291 and #32768 are examples that have encountered some of these events, as shown in figure 8.These two discharges had a pulse length of ∼80-90 s.Although the target pulse length was over 100 s, they were unable to sustain the discharge until the designed pulse length due to events occurring during the discharge.
Discharge #30291 demonstrated relatively high performance with β P ⩾ 2.7 with a V loop ∼ 34 mV in the early phase of discharge compared to discharge #32768.However, as the pulse length increased, β P gradually decreased, accordingly leading to a gradual increase in V loop , as shown in figure 8(I.a) and (I.c).Just before a specific event occurred at t ∼ 48 s, β P experienced ∼18% reduction compared to the initial value, and V loop increased by over two times to ∼73 mV.During the discharge, an abnormal operation of the ECH, which was not designed in the scenario, occurred.One of the two ECH gyrotrons turned off at t ∼ 48 s, and the remaining ECH gyrotron turned off at t ∼ 78 s, which resulted in a further and drastic decrease in β P (∼2.3 → ∼2.1 → ∼1.8) and an increase in V loop (∼73 → ∼93 → ∼185 mV).While the V loop ∼ 34 mV was expected to achieve a pulse length of over 100 s, the events that occurred during the discharge caused an increase in V loop , pushing PF1, PF3, and PF4 to rapidly approach their limit of 15 kA/turn, as shown in figure 8(I.f ).In discharge #30291,  at t ∼ 91 s, plasma collapsed due to insufficient flux supply to sustain the discharge and the loss of plasma shaping control.
The PFC temperature of discharge #30291 was successfully maintained within 600 • C until the end of the discharge by optimizing and controlling the plasma shape, as described in section 2.1.The poloidal limiter temperature was kept within the limit by reducing the R out of the plasma shape by ∼2-4 cm compared to the reference plasma shape, as described in figures 2 and 3.The divertor temperature was maintained within the limit by changing the position of the striking point over time, as described in figure 3. Discharge #30291 showed plasma parameters of ne ∼ 2.6 × 10 19 m −3 , T e (ψ N ∼ 0.1) ∼ 3.4 keV, and T i (ψ N ∼ 0.1) ∼ 2.1 keV with almost constant for t ∼ 10-48 s, which implies that the thermal plasma conditions were not changed much.The current relaxation time (τ R ) and the thermal energy confinement time (τ E,th ) for discharge #30291 were analyzed to ∼4.3-5.6 s and ∼42-48 ms, respectively, until t = 48 s.
Discharge #32768 had a relatively moderate plasma performance of β P ∼ 2.3 compared to discharge #30291.Initially, it showed β P ⩾ 2.4, but the performance linearly decreased until reaching β P ∼ 2.3 by t ∼ 12 s.Subsequently, it maintained a nearly constant β P until t ∼ 57 s.It also held V loop ∼ 82 mV, which only marginally met the requirement to achieve the target pulse length of 100 s, as explained in section 2.2.The ECH sources of discharge #32768 operated well throughout the discharge period.As shown in figure 8(II.f ), PF4 reached the PF coil current limit at t ∼ 79 s, and PF1 and PF3 would likely have also reached their limits shortly after.Similar to discharge #30291, discharge #32768 likely encountered challenges with insufficient flux supply and the loss of plasma shaping control, ultimately resulting in plasma collapse within a short time.
Discharge #32768 was conducted with the same plasma shape target as in discharge #30291.The relatively high PFC temperature of discharge #32768 compared to discharge #30291 is estimated to be attributed to larger external heating power and lower plasma performance.Nevertheless, like the approach used in discharge #30291, discharge #32768 successfully maintained the PFC temperature within 600 • C until the end of the discharge.Discharge #32768 showed plasma parameters of ne ∼2.5 × 10 19 m −3 , T e (ψ N ∼ 0.1) ∼ 2.5 keV, and T i (ψ N ∼ 0.1) ∼ 2.1 keV with almost constant for t ∼ 12-57 s. τ R and τ E,th for discharge #32768 were analyzed to ∼4.3-5.0 s and ∼44-52 ms, respectively, until t = 57 s.
Discharge #32768 experienced an unplanned event different from discharge #30291, which occurred at t ∼ 57 s.This event was related to a specific operational option of real-time EFIT.This option excludes a magnetic measurement from EFIT analysis during the discharge if χ 2 of that measurement exceeds a pre-defined threshold.χ 2 is defined as ((M − C)/σ) 2 , where M, C, and σ denote the measured value, the computed value, and the measurement uncertainty, respectively.In discharge #32768, the χ 2 of a specific magnetic probe exceeded the threshold at t ∼ 57 s due to the signal drift.Simultaneously, the option abruptly excluded this magnetic probe from realtime EFIT analysis.This sudden exclusion resulted in a rapid change of the plasma shape that real-time EFIT could not promptly handle.As a result, β P dropped sharply from ∼2.3 to ∼1.9.As mentioned in section 2.2, for long-pulse experiments at KSTAR, significant progress has been made in improving the signal drift caused by thermal loads on magnetic probes.

Plasma performance degradation over a long-time scale
As described in figure 7, most of the KSTAR long-pulse discharges have experienced a degradation in plasma performance.Figure 8 depicts two discharges exhibiting contrasting plasma performance trends over time.The β P of discharge #30291 demonstrated a nearly linear decrease over time and showed an ∼18% reduction compared to the initial β P until t ∼ 48 s, while the discharge was maintained under constant experimental conditions.Conversely, the β P of discharge #32768 initially experienced a slight decrease for ∼12 s, but subsequently showed a nearly constant plasma performance with a slight reduction of ∼3% until t ∼ 57 s.
In order to investigate the plasma performance degradation, the 0D plasma characteristics of these two discharges were analyzed at every 5 s intervals using the KSTAR kinetic-EFIT package involving NUBEAM analysis.As shown in figures 9(I.d) and (II.d), these two discharges were characterized as typical H-mode plasmas with the thermal energy confinement enhancement factor (H 98y2 ) ∼ 1.1.This implies that both discharges had similar thermal energy confinement, which was analyzed to τ E,th ∼ 42-52 ms.
However, figures 9(I.c) and (II.c) reveal noticeable differences in fast ion stored energy (W f ) between the two discharges.In discharge #30291, the decrease in total stored energy (W mhd ) representing plasma performance degradation occurred primarily due to the decrease of W f rather than thermal stored energy (W th ).Conversely, in discharge #32768, which experienced minimal performance degradation, W f remained almost constant over time.In other words, the β P degradation primarily resulted from the decrease of fast ion pressure, as thermal pressure remained relatively stable.
The decreasing trend in fast ion stored energy of discharge #30291 closely matched the trend in neutron rate measured in the fission chamber, as shown in figure 9(I.e).The neutron rate measured in the fission chamber aligned closely with the neutron rate calculated by NUBEAM.This implies that the analyzed results obtained by using the above tool were reliable.The TAEs in these discharges were analyzed concerning the decrease in fast ion stored energy.Figure 10 compares the TAE analysis results for discharges #30291, #32768, and #27033.As shown in figure 10(c), in discharge #30291, which exhibits high performance (β P ⩾ 2.7) in the early phase of the discharge, TAEs with n = 2 in the 130-150 kHz frequency range and n = 3 in the 170-220 kHz frequency range were observed, along with performance degradation.It is important to highlight that the amplitudes of these TAEs were relatively low by an order of magnitude compared to the amplitudes typically observed and analyzed in KSTAR, which is reported in [21].Also, note that the amplitude of the n = 3 TAE was increased over time.In high-performance discharge #27033 with β P ∼ 2.6, TAE with n = 2 in the frequency range of 130-150 kHz was observed, and its amplitude was similar to the amplitude of the n = 2 TAE in discharge #30291, as shown in figure 10(d).On the other hand, no significant TAEs were observed for discharge #32768, as shown in figure 10(e).
The comparison between discharge #30291 and discharge #27033 implies that performance degradation in discharge #30291 was likely associated with the n = 3 TAE rather than the n = 2 TAE.The trend of n = 3 TAE amplitude was likely to have a strong correlation with analyzed and measured data shown in figure 9, such as D f in (I.a), W f in (I.c), and neutron rate in (I.e).In other words, the observed TAE was likely closely associated with the degradation of fast ion stored energy through an increase in fast ion transport.The underlying physical mechanisms explaining the absence of n = 3 TAE in discharge #27033 are still being investigated, even with similar β P to discharge #30291.
As mentioned in section 2.2, the KSTAR long pulse discharges adopted the high β P scenario developed in [5,21].The developed high β P scenario is characterized by the increase of fast ion confinement through controlling TAEs with precise ECH/ECCD deposition, which was successfully reproduced in discharge #30291 in the early phase of the discharge (t ⩽ ∼8 s).
However, even when TAEs are mitigated/suppressed through ECH/ECCD in the early phase of the discharge, changes in the plasma state as the discharge evolves may lead to reduced mitigation/suppression effects and excitation of TAEs due to the fixed deposition of ECH/ECCD during the discharge.This likely explains that even though the observed n = 3 TAE was mitigated for t ⩽ ∼8 s, which was similar to the time scale of τ R (∼5 s), this low-amplitude TAE was sustained and its amplitude was increased again, as shown in figure 10(c) of discharge #30291.The sustained TAE is supposed to result in a decrease in fast ion pressure.As shown in figures 10(b), (c) and (e), it is likely that when β P of fast ions (β P,fast ) in discharge #30291 decreased to closely match β P,fast ∼ 0.9 in discharge #32768, the n = 3 TAE in discharge #30291 was stabilized at t > ∼40 s.The physical mechanism behind the timedependent TAE amplitude, even with ECH/ECCD injection in the KSTAR long-pulse discharges, as well as the relation between TAEs and fast ion transport, will be further investigated through additional studies, which involve fast ion D α (FIDA) measurement and NOVA-k analysis.
Figure 11 shows the characteristics of performance degradation observed in the KSTAR high-performance long-pulse experiments.Discharges with t degraded ⩽ 20 s (black circles) showed a β P,based ∼ 1.8-2.5 and R β P (≡β P,degraded /β P,based ) ∼ 0.9-1.1.In other words, when the pulse length was relatively short, the performance was well maintained, or its degradation was not severe.However, discharges lasting longer than 40 s (t degraded ⩾ 40 s, red circles) are classified into two categories based on the β P,based criterion to investigate their characteristics.One category consists of discharges within the range of β P,based ⩽ ∼2.2.These discharges showed R β P ⩾ ∼0.9 and did not experience significant performance degradation, similar to discharges lasting shorter than 20 s.The other category includes discharges within the range of β P,based ⩾ ∼2.2, where β P,based increased while R β P decreased even further.These discharges showed even more significant performance degradation as R β P ∼ 0.8.This implies that performance degradation appeared more severe as the discharge had higher plasma performance.
Furthermore, discharges within the range of β P,based ⩾ ∼2.2 showed a notable feature that β P,degraded values converged after experiencing performance degradation.This converged value is estimated to be β P,degraded ∼ 2.0-2.2, as highlighted by the red-shaded region in figure 11.Phenomena involving the convergence of β P as pulse length increased were likely associated with the TAE activities, as discussed through the comparison and analysis of discharge #30291 and discharge #32768 in figures 9-11.

Summary and conclusion
KSTAR aims to achieve a pulse length of 300 s and highperformance plasma.In order to develop long pulse discharges in KSTAR, the approaches have focused on achieving an extremely low V loop and mitigating the temperature increase of the PFCs.Since KSTAR employs NBI as the primary H&CD system, research on fast ion behavior is crucial.In high-performance long-pulse discharges of KSTAR, it was analyzed that fast ion behavior was related to the rapid temperature increase in the poloidal limiter and ∼18% of gradual plasma performance degradation.
To mitigate the temperature increase in the poloidal limiter, based on the analysis of fast ion orbit loss, R out of plasma shape was optimized, and appropriate NBI sources were selected.Furthermore, selecting an NBI source, not using the NBI1-C source, also reduced temperature increase in other PFC components, such as the inboard limiter heated up by NBI1-C beam shine-through.The temperature increase in the central divertor or the outer divertor was mitigated by adjusting the position of the striking point over time.The optimization of the H&CD injection scenario, especially ECH, was important for achieving low V loop to ∼25 mV with high-performance plasma.One or two ECH injections enabled lower V loop operation for a longer pulse discharge by enhancing the NBI-driven current through the T e increase.ECH/ECCD is able to stabilize TAEs through properly controlled EC-wave deposition, as reported in [5,21].In this work, the high β P discharge developed in [5], which improves fast ion confinement, was adopted and optimized for conducting long-pulse discharges.The improved fast ion confinement in the high β P state contributed to mitigating the temperature increase of PFCs as well as improved plasma performance.In addition, KSTAR experienced nonlinear signal drift in the magnetic probes in the long-pulse discharges.The nonlinear signal drift in a discharge impacted the accuracy and reliability of EFIT analysis and led to unintentional errors in the real-time plasma shape control.A thermal shielding protector was installed on the magnetic probes to effectively resolve this issue, which successfully reduced the nonlinear signal drift.
However, KSTAR long-pulse discharges suffer from plasma performance degradation over time.It was figured out that the reduction of the total stored energy of plasma was attributed to the reduction of fast ion stored energy rather than the thermal stored energy.Based on the correlation with the analyzed fast ion anomalous diffusion coefficient, the measured neutron rate, and the TAE analysis under stable plasma conditions, it is likely that the degradation of fast ion stored energy was associated with the degradation of fast ion confinement coupled with long-lasting, weak, and growing amplitude of TAE.
In other words, despite achieving the β P state by controlling TAEs through the precise deposition of ECH/ECCD in the early phase of the long-pulse discharge (t ⩽ 8 s), it is still observed that the low-amplitude TAEs were sustained and grown, which is thought to influence the decrease in fast ion pressure.Furthermore, as the pulse length increased to over 40 s, β P likely converged to ∼2.0-2.2, which seemed to be associated with the TAE activities.The performance degradation related to TAEs in KSTAR high-performance long-pulse discharges will be further investigated through FIDA measurements and NOVA-k analysis to uncover the underlying indepth physical mechanism.

Figure 1 (
a) presents the temperature disparity between the infrared television (IRTV) and the thermocouples at the poloidal limiter in the long-pulse experiment, discharge #21735, terminated at 89 s.At that point, the IRTV recorded the highest temperature of 1182 • C, while the thermocouple registered 609 • C at 93 s: a time difference of 4 s and a temperature difference of 573 • C. Discharge #21735 was operated with I P of 400 kA, toroidal magnetic field (B T ) of 2.4 T, NBI power (P NBI ) of 2.8 MW, and ECH power

Figure 1 .
Figure 1.Temperature of PFCs over time at discharge #21735, (a) the temperature of the poloidal limiter measured by the IRTV (red) and the thermocouples (blue) and (b) the temperature measured by the thermocouples for all the PFCs, the inboard limiter (black), the inboard divertor (blue), the central divertor (magenta), the outer divertor (green), and the poloidal limiter (red).

Figure 2 .
Figure 2. NuBDeC analysis of long-pulse discharge #21735.This figure shows (a) Rout and R in of the plasma shape over time and (b) the amount of fast ions lost to the poloidal limiter over time.

Figure 3 .
Figure 3. Experimental results describing the effect of plasma shape and NBI source on changes of temperature increases in PFCs.This figure shows the thermocouple temperatures in (a) the poloidal limiter, (b) the inboard limiter, (c) the central divertor, and (d) the inboard divertor, and (e) the plasma shapes at 6 s and the NBI injection condition in the discharges of #20812 (black), #20878 (magenta), and #21735 (blue).

Figure 4 .
Figure 4. Analysis of nonlinear signal drift from magnetic probes located on the outboard side of the plasma in the high-temperature long-pulse plasma operation.Figure (a) describes a schematic cross-section of the KSTAR device, including the vessel, PFCs, and magnetic probes.In the KSTAR configuration, the PFC on the outboard side of the plasma in the midplane is open to the vessel.Figure (b) presents the signal drift S analysis obtained from magnetic probes, MP Z and MP R , on the plasma outboard side at the midplane.Figure (c) presents ∆Rout obtained from EFIT analyses in long-pulse discharges.
Figure 4. Analysis of nonlinear signal drift from magnetic probes located on the outboard side of the plasma in the high-temperature long-pulse plasma operation.Figure (a) describes a schematic cross-section of the KSTAR device, including the vessel, PFCs, and magnetic probes.In the KSTAR configuration, the PFC on the outboard side of the plasma in the midplane is open to the vessel.Figure (b) presents the signal drift S analysis obtained from magnetic probes, MP Z and MP R , on the plasma outboard side at the midplane.Figure (c) presents ∆Rout obtained from EFIT analyses in long-pulse discharges.

Figure 5 .
Figure 5.Comparison of two similar discharges with different ECH/ECCD depositions.A high β P discharge #18602 (red) was obtained by EC resonance line Rres ∼ 1.72 m at B T = 1.8 T, while a typical H-mode discharge #18597 (blue) was done by Rres ∼ 1.82 m at B T = 1.9 T. The figure presents (a) EC-wave ray tracing, (b) I P and Paux, (c) β P , (d) V loop , (e) neutron rate measured by fission chamber, and the magnetic spectrogram of the Mirnov coil signal for (f ) discharge #18597 and (g) discharge #18602.The analysis of the magnetic spectrogram was conducted within the TAE-relevant frequency range of 80-220 kHz.TAEs were substantially mitigated or almost suppressed in discharge #18602, while TAEs were activated and sustained in discharge #18597.

Figure 6 .
Figure 6.V loop versus (a) β P , (b) P EC , (c) B T , and (d) P NBI in the database corresponding to the development of the KSTAR long-pulse scenario.The unshaded area indicates that a pulse length of at least 100 s is expected at a plasma current of 400 kA.

Figure 7 .
Figure 7. Discharge set with a pulse length > 50 s performed during the 2015-2022 KSTAR experimental campaign.This shows β P and V loop against t pulse for (a) 2015-2017, (b) 2018, and (c) 2020-2022 KSTAR experimental campaigns.The circles represent the values of β P and V loop at 10 s.The arrows for β P and V loop indicate a decrease and increase of up to 40 s, respectively.L PF and L TC markers indicate that the PF coil current limit and the PFC temperature limit were reached during the discharge, respectively.Discharges without L PF and L TC markers were terminated due to the NBI faults.The unshaded region, characterized by relatively higher β P and lower V loop , represents the range sought by KSTAR long pulse discharges.

Figure 9 (
I.a) indicates stable P NBI,absorbed .Figure 9(I.f ) shows little change in line-averaged effective ion charge ( Zeff ).This implies that there was little change in the source of fast ions, which Zeff , ne , and T e (ψ N ∼ 0.1) did not significantly contribute to the change in fast ion stored energy.Therefore, the reduction in fast ion stored energy in discharge #30291 (∼23%, 125 kJ → 96 kJ in W f ) was influenced by the increased D f , as shown in figure 9(I.a).

Figure 9 .
Figure 9. 0D plasma characteristics for discharge #30291 (I.a)-(I.g)and #32768 (II.a)-(II.g).This figure shows temporal changes in the following parameters: (a) P NBI,injected (black line), P NBI,absorbed (black circle on the line), and the estimated anomalous fast ion diffusion coefficient D f (red circle on the line) which satisfies W f with a radially flat D f profile, (b) P ECH , (c) total stored energy W mhd (black), thermal stored energy W th (blue), and fast ion stored energy W f (red), (d) thermal energy confinement enhancement factor H 98y2 , (e) neutron rate measured by fission chamber (black) and calculated by NUBEAM (red circle), (f ) Zeff , and (g) measured total radiation power P rad .The parameters, such as P NBI,absorbed , D f , W mhd , W th , W f , H 98y2 , and calculated neutron rate, are analyzed using the KSTAR kinetic-EFIT package involving NUBEAM analysis.

Figure 10 .
Figure 10.Comparison of β P , β P,fast , and TAEs between discharges #30291, #27033, and #32768.This figure describes the (a) β P , (b) β P,fast , and (c)-(e) magnetic spectrogram of the Mirnov coil signal and mode amplitudes of TAEs in a.u.for each discharge.The analysis of the magnetic spectrogram was conducted within the TAE-relevant frequency range of 80-270 kHz.Among the plotted long-pulse discharges, #30291 has a relatively high-performance discharge with significant performance degradation (t ⩽ ∼48 s), #27033 has a relatively high-performance discharge without performance degradation (t ⩽ ∼37 s), and #32768 has a relatively low-performance discharge with minimal performance degradation (t ⩽ ∼57 s).

Figure 11 .
Figure 11.β P,based versus β P,degraded describing performance degradation over time.The black and red circles represent discharges with t degraded ⩽ 20 s and t degraded ⩾ 40 s, respectively.β P,based represents the β P value at the early phase of the discharge, and β P,degraded represents the β P value before the occurrence of any unintended event, with the corresponding time defined as t degraded , which represents the maximum duration for which the operating conditions of the discharge remain relatively stable.β P,based and β P,degraded are represented in figure 8.

Table 1 .
Summary of V loop targets and KSTAR experimental results for I P = 400, 500, and 600 kA regarding the flux consumption.