Observation of a stationary double transport barrier in KSTAR

We have observed a stationary high confinement regime with a double transport barrier (DTB), including both internal and edge transport barriers (ITB and ETB) but without edge-localized modes (ELMs), in KSTAR. The ELM-free DTB phase has high thermal confinement comparable to typical H-mode operation in KSTAR. We investigated the characteristics of the DTB phase through various analyses. Transport analysis shows a reduction of ion heat diffusivity to near neoclassical level after the transition from the ELMy H-mode phase to the DTB phase. This result supports the formation of an ion ITB during the DTB phase. Furthermore, we observed that the DTB phase had an edge thermal transport barrier in the ion temperature profile, comparable to that of the H-mode, without a particle transport barrier at the edge. Peeling-ballooning stability analysis indicates that a lower pressure gradient due to density decrease in the DTB phase is mainly responsible for the ELM-free operation. Linear gyrokinetic analysis shows that the real frequency of the most unstable mode in the core region ( ρtor = 0.32–0.47) is in the ion diamagnetic direction at both H-mode and DTB phases. At the DTB phase, the linear growth rate inside the ITB is reduced by 50% compared to the ITB foot, while the reduction is not shown at the H-mode phase. Further investigation including nonlinear effects will be needed to better understand the unique operation mode, which can contribute to applying the physical mechanism to fusion reactors in the future.


Introduction
To achieve self-sustainable fusion reactor conditions in magnetic fusion devices, enhancements to energy confinement have been pursued.The high confinement operation mode, or H-mode [1], has been considered a main operation scenario 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. in future tokamak experiments including ITER.In the conventional H-mode, high confinement is achieved through the formation of an edge transport barrier (ETB) on the pressure profile.However, the H-mode edge pressure, determined by the height of the ETB, is limited by edge-localized modes (ELMs), which are peeling-ballooning instabilities destabilized by a high edge pressure gradient and/or high edge current density.The concept of a double transport barrier (DTB) has been introduced as an ideal state of advanced tokamak confinement, achieved by sustaining an internal transport barrier (ITB) [2][3][4] and ETB simultaneously.Since ELMs can still be a problem in DTB operation scenarios, eliminating the ELM bursts during DTB operation is desirable, as shown in previous studies [5][6][7][8][9].We here report a recent observation of stationary DTB formation in KSTAR, sustaining both an ITB in the ion thermal transport channel and an ETB similar to the Hmode but without ELM bursts for ∼3 s, roughly 50 times the confinement time (∼0.06 s).
The DTB discharge reported in this study was selfgenerated.During the discharge, a sudden decrease in electron density was observed, accompanied by a remarkable increase in the core ion temperature.In contrast, the electron temperature remained the same, implying the formation of an ion ITB.It appeared that there was an upper limit in the electron density level allowed in this ion DTB operation without ELMs.When the electron density exceeded a specific value, ELMs were triggered again.Interestingly, a similar pattern reflecting changes in electron density and DTB formation was observed two times throughout the discharge.Both the first and second DTB phases exhibited a similar evolution, implying the existence of a certain physical mechanism behind the DTB formation and sustainment.In this study, we aimed to analyze the characteristics of the DTB discharge and investigate potential physical mechanisms driving the formation and sustainment of the DTB phases.
The structure of this paper is as follows.Section 2 describes the experimental setup, namely the access conditions of the discharge, and section 3 discusses the characteristics of the transport barriers in the core and edge regions.In section 4, we present possible mechanisms that may explain the formation and sustainment of the DTB and the transition from the ELMy H-mode to this particular regime.In section 5, we summarize and discuss the future work.

Experimental setup and access conditions
The stationary DTB regime was accessed in a typical ELMy H-mode discharge in an early-diverting scenario to enhance the plasma beta (β = ⟨p⟩ B 2 /2µ0 , where ⟨p⟩ is volume averaged plasma pressure, B is the total magnetic field strength, and µ 0 is the vacuum permeability) during the plasma current (I p ) flat top period [10].The direction of I p , clockwise when viewed from the device top, was parallel to B T , so that the ion ∇B drift could be set to a favorable direction in the lower single null configuration toward the dominant X-point, located in the lower region, as shown in figure 1.We used four co-current tangential neutral beam sources in this experiment.They are NB1A/B/C with beam voltages of 90/90/75 kV, respectively, and NB2B, a new beam source operated at a beam voltage of 55 kV with a power of 0.6 MW [11].The total injected beam power was approximately 5.0 MW. Figure 1 briefly describes the geometry of each beam line; the newly added off-axis beam source (NB2B) [12] has a longer radial excursion than the onaxis beams (NB1A, B, and C) by entering the plasma bulk in the z > 0 region.By the off-axis injection, NB2B is expected to affect the beam deposition profiles and efficiency of the current drive.
In the previous studies in Alcator C-Mod, DTB formation using ion cyclotron range of frequencies heating was investigated [5,6], focusing on the changes of E × B shearing by off-axis heating.However, as for the role of the offaxis NB in terms of E × B shearing and DTB formation in KSTAR, we could find both differences and possible similarities compared to the C-Mod results.As shown in figures 2(b) and (g), the toroidal rotation velocity (V tor ) was increased near 5 s, when the off-axis NB was started to inject.However, we also observed that V tor actually started to increase from 4.9 s, earlier than off-axis beam injection.It is likely that the increase in V tor is correlated with the cessation of one gyrotron (EC4) shown in figure 2(a).Moreover, after 5 s, V tor steadily decreased to the previous level before entering the DTB phase while the off-axis NB was still injected.Therefore, the changes in V tor by off-axis beam were not significant in this discharge.Nevertheless, in figure 2(g), it can be also seen that the difference in V tor between ρ tor ∼ 0.05 and 0.45 becomes larger in the DTB phase compared to the H-mode phase.This observation suggests that E × B shearing can have a role in the DTB formation, as found in the previous studies [5][6][7][8][9].The role of E × B shearing in the DTB formation will be further discussed in section 4.2.In addition to the neutral beam heating, one gyrotron (EC2) was injected at the period of interest, t = 5-10 s, with approximately 0.6 MW power.The target deposition region of the EC2 injection (ρ tor ∼ 0.01, where ρ tor is the square-root of the normalized toroidal flux) was fixed during the injection period.No resonant magnetic perturbation or additional impurities were applied.The fully pumped divertor condition with two in-vessel cryopumps was maintained in this discharge.
Figure 2 shows the temporal evolution of the main parameters in the DTB discharge (shot #26980).Under the on-axis toroidal field, B T = 2.6 T (at major radius, R = 1.8 m), I p was set to 0.5 MA at the current flat top, resulting in an edge safety factor of q 95 = 8.1-8.4.The resultant normalized beta, β N , was 1.7-1.8before entering the DTB regime.A DTB was established twice in this discharge.The first DTB phase was detected at t = 6.64 s accompanied by the elimination of ELM bursts, as shown in figure 2(c).The first ELM-free DTB phase lasted for ∼1.2 s until 7.85 s.It was observed that the lineaveraged density (n e ) measured by a two-color interferometer (TCI) [14] decreased at the beginning of the first DTB phase, from 6.64 s to 7.09 s.Afterward, the density increased gradually until the ELM bursts reappeared at t = 7.85 s.With the return of the ELM bursts, the DTB phase disappeared and the discharge transited back to the ELMy H-mode phase.
After several large bursts for ∼0.35 ms, we can see a similar process to the first DTB phase, including a density drop.The second onset of the DTB phase occurred around t = 8.2 s and lasted more than 3 s.The DTB sustainment seems to have an upper limit of the density level (∼2.2 × 10 19 m −3 ), and once ne reached to this level at t = 7.85 s and t = 10.68 s, ELM bursts started again.It is interesting that the onset processes occurring at two different time points commonly accompany a relatively rapid reduction of n e .Notably, as shown in figure 2(d), n e in both first and second DTB phases decreased to a similar level, after which it increased to nearly similar levels.As plotted in figure 2(e), although the density dropped in the DTB phases, we observed a similar level of the confined energy and H 89 factor [9] during the DTB phases compared to that of the H-mode, indicating that this DTB regime has comparable confinement performance to the H-mode.We also observed that β N maintained at a similar level from 7 s to 10 s, regardless of the operation phase (either DTB or ELMy H-mode), as shown in figure 2(f ).This indicates that the DTB formation process is not affected by the absolute value of β N .In KSTAR, the β N threshold on the stability of high-confinement scenarios has been studied [15], but the DTB process is likely to be irrelevant to the β N threshold.

Characteristics of transport barriers in the DTB discharge
Figure 3 illustrates the changes in the fitted T i profiles between H-mode and DTB phases, along with the electron temperature (T e ) profiles.In the DTB regime, an increase in core T i for ρ tor < 0.45 was observed while a steep edge pedestal was maintained.The increased T i was maintained in the DTB regime, and the level of the increased T i on-axis was ∼4.8 keV, which is 20% higher than the level during the Hmode phase (∼4.0 keV).To analyze the structure of the transport barrier formed in the T i channel, the second derivative of T i was calculated.The foot position of the ITB was evaluated around ρ tor ∼ 0.47, shown as the vertical dashed line in figure 3(a), based on the maximum value of the second derivative.Changes in the electron temperature (T e ) between the Hmode and DTB phases are not distinct, as shown in figure 3(b), and likewise, T e does not show notable changes between core and edge regions.Therefore, the ITB is formed only in the T i channel while preserving the edge pedestal.During the DTB phase, n e decreases in the whole region including both core and edge regions compared to the H-mode phase, as shown in figure 3(c).The profiles of toroidal rotation velocity (V tor ) are also shown in figure 3(d).
To investigate the changes in the transport associated with the formation of the ITB, TRANSP [19] analysis was conducted based on electron temperature, density, ion temperature obtained from diagnostic measurements, and the effective ion charge (Z eff = ∑ j Z 2 j n j /Z j n j , j is ion species) measured using the visible bremsstrahlung diagnostic [20].In the TRANSP analysis, an anomalous fast ion diffusion coefficient was adjusted to minimize the difference between the stored energy obtained through TRANSP calculations and the energy estimated from the equilibrium reconstruction constrained by magnetics.A coefficient of approximately 0.5 m 2 s −1 was applied to both H-mode and DTB phases.The calculated thermal confinement scaling, H 98y,2 [21], from TRANSP remained consistent around 1 for both H-mode and DTB phases.Accordingly, we confirmed that even after the n e drop and the disappearance of ELMs in the DTB regime, a stable thermal confinement time comparable to the H-mode was maintained.Figure 4 illustrates the results of the TRANSP calculations for thermal transport.In figure 4(a), the ion heat flux is much reduced at the DTB phase, down to ∼50% of the level of the H-mode.Figures 4(b) and (c) show the ion and electron heat diffusivities, respectively.The neoclassical diffusivities plotted in dashed lines in figure 4(b) were calculated using the NCLASS module [22] in TRANSP.In the DTB regime, the experimental value of ion heat diffusivity approached the neoclassical transport level inside the ITB, which suggests that transport mechanisms other than collisional transport, such as turbulent transport, are suppressed  inside the ITB region.On the other hand, electron heat diffusivity showed little change, consistent with the small change in the T e profile across the DTB transition.The analysis on the ion and electron heat diffusivities suggests that transport variations mainly occur in the ion thermal transport channel, forming an ion ITB, which has also been reported in previous studies [23,24].
Along with the ITB, we investigated the characteristics of the ETB in the DTB regime using kinetic profiles.Figure 5 shows the difference in the edge profiles between the DTB and H-mode phases.The T i profile is obtained by CES [16], and T e profiles are fitted on the ECE [17] and Thomson scattering [18] data.For the n e profiles, we combined the Thomson and TCI [14] data.To get local data points using tangentially lineintegrated n e from TCI, we applied Abel inversion [25] to 5channel TCI data.From the inversion data, we obtained two data points (ρ tor ∼ 0.8 and ρ tor ∼ 0.9) at the edge region in figure 5(c), which is helpful to determine the pedestal height of n e .The ion and electron temperature pedestals of the DTB (7.4 s) remained similar to those of the H-mode (6.45 s), as shown in figures 5(a) and (b).However, as shown in figure 5(c), n e decreased in the DTB regime, where the maximum density decrease was about 20% of the level of n e in the H-mode phase.As a consequence, the pressure gradient was relieved, as shown in figure 5(d).Throughout the DTB regime, the discharge showed ELM-free characteristics while preserving the ETB in the thermal transport channel, as observed in figures 5(a) and (b).In the next section, we discuss the edge stability and effect of lowered edge pressure.

Stability analysis on the ETB
To understand the ELM-free characteristics of the two DTB phases, a peeling-ballooning stability analysis was performed for both ELMy H-mode and DTB phases.As shown in figure 5(d), the edge pressure gradient was reduced in the DTB phases along with the decreased density.To evaluate the impact of the reduced pressure gradient on the edge stability, the equilibrium of each phase was calculated from the kinetic equilibrium reconstruction constrained by the kinetic pressure profiles as well as by magnetic diagnostics, using the code EFIT [26,27].The core pitch angle measured by the motional Stark effect (MSE) diagnostic [28] was also included with the edge current profile calculated by TRANSP.The reconstructed equilibria were then modulated using the code CHEASE [29] by varying the pressure and current profiles while maintaining the plasma boundary.These modulated equilibria were used to calculate the peeling-ballooning stability with each pressure and current profile by the code ELITE [30].
Figures 6(a) and (b) present peeling-ballooning stability diagrams of the H-mode and DTB phases.The operation points of the H-mode and DTB phases are marked with black crosses in each figure .From the stability analysis, it was found that the H-mode phase operated near the stability boundary, as shown in figure 6(a).Since it is possible that the real operation point is in the unstable region within the uncertainties of the input profiles, this result is consistent with the experimental results that showed ELMs.In figure 6(b), the operation point moved to the peeling-ballooning stable region as the pressure gradient decreased in the DTB phases, also consistent with the experiment.These results suggest that the relieved pedestal pressure gradient due to the reduced density in the DTB phases is the main cause of the ELM-free ETB.The density decrease and eased pedestal gradient also affect the edge current by reducing the edge bootstrap current, contributing to stability in the DTB phases for the peeling-ballooning mode.As the density gradually increased during the DTB phases, the edge pressure and current also increased and finally reached the previous H-mode levels, approaching the unstable region.As mentioned above, the peeling-ballooning stability analysis can explain the ELM-free phases with the reduced density and the reappearance of the ELMs as the density recovers a certain density level, as observed in the DTB discharge shown in figure 2.

Analysis and discussion on ITB formation
The formation of the ion ITB was investigated by observing the temporal evolution of T i and n e , as shown in figure 7. From figure 7(a), it can be seen that the line-averaged electron density decreased globally.The T i in the core region, shown in figure 7(c), started to increase from almost the same time as the density started to drop.At 6.640 s, core T i started to increase abruptly, and afterwards, it gradually decreased until n e reached its minimum level.Then n e started to increase again with the increased core T i .In the first DTB phase, a neutral beam blip was included for diagnostic purposes, as shown in figure 7(c).After the beam blip, core T i decreased.It is possible that the plasma condition was changed by the beam blip in the first phase, resulting in its shorter period than the second DTB phase.As mentioned in section 2, when n e increased to the previous H-mode level, the ELMs reappeared (7.865 s).It is noteworthy that the increased core T i also collapses, as shown in figure 7(c), implying the disappearance of the ITB.The same process was repeated throughout the discharge.At 8.252 s, n e decreased while T i increased, similar to the pattern observed in the first DTB phase.The increased T i was steadily sustained as n e gradually increased.It follows that the ITB was not caused by the reduced n e level after the density drop.From figures 7(a) and (b), we can also notice that n e already started to decrease before the time when the core T i started to rapidly rise, denoted by the green dashed line.Therefore, a certain event that increased only particle transport occurred prior to the abrupt increase in core T i , which is likely an indicator of the ITB.Interestingly, the core line-averaged density decreased to ∼1.4 × 10 19 m −3 , then started to increase until ELMs appeared again in both the first and second DTB phases.This result may indicate that the certain event enhancing particle transport can exist only above a certain density level.Since the raised core T i was maintained even as the reduced density level was recovered, this event may not critically contribute to sustaining the ITB.We can speculate that a certain mechanism accompanying this event caused the increased T i in the core region, forming the ITB.Identification of this event resulting in density reduction is out of the scope of this study and will be investigated in the future.
To investigate the mechanism of ITB formation, changes in the profiles of the safety factor and magnetic shear in the H-mode and DTB phases were examined, as shown in figure 8, since the effects of a negative or flat magnetic shear on ITB formation have been reported in several tokamaks [31][32][33].Figure 8(a) shows the safety factor profiles (q) before and after the DTB transition, calculated using the aforementioned kinetic equilibrium reconstruction.In the H-mode phase before the DTB transition, the on-axis safety factor (q 0 ) was around 1.4.Even after the transition to the DTB phase, the q profiles remained similar to those of the H-mode, except for minor changes in the edge pedestal region caused by the changes in the edge pressure shown in figure 5(d).Figure 8(b) plots the changes in the magnetic shear (s = r q dq dr ) profiles in the H-mode and DTB phases.These changes are not distinct between the phases, and the magnetic shear remains positive.These results suggest that the influences of equilibrium and magnetic shear are not dominant factors for the ITB formation in the DTB regime.The change of q profiles can also be checked in the measured data of magnetic field pitch angle.In figure 8(c), the lines and error bars show the pitch angle from the MSE measurements [28], and the marked points represent calculated pitch angle values from the EFIT reconstruction.The MSE data at both H-mode and DTB phases were similar, so we can infer that the q profiles were not much changed between the phases.Moreover, the calculated pitch angles were within the uncertainty of the MSE data, thus showing that the analysis was within reasonable bounds of the diagnostic measurements.
Linear stability analyses using the code CGYRO [34] were performed to study the potential contribution of the changes in the turbulence to the ITB formation.Figures 9(a) and (b) show the changes in the real frequency of the most unstable mode at the ITB foot (ρ tor = 0.47) and inside the ITB (ρ tor = 0.32) in the H-mode and DTB phases, respectively.The real frequency of the most unstable mode is in the ion diamagnetic direction in both locations for both phases, which was negative in these simulations.We also checked that the linear growth rate of the modes increased with higher ion temperature gradients, so the modes are presumably ion temperature gradient modes.In figures 9(a) and (b), a sudden jump appeared in the low k y ρ s region, suggesting a different origin of the related modes.We observed that these modes exist only when fast ion species were included in the simulation; therefore, the existence of fast ion-related modes was predicted in the linear analysis.Figures 9(c) and (d) present the linear growth rate of the most unstable mode in the H-mode and DTB phases, respectively, at the same analysis points.In figure 9(c), the growth rate in the H-mode phase was reduced for k y ρ s < 0.6 inside the ITB region compared to the ITB foot.However, the reduction was not prominent except for the fast ion-related modes, and the growth rate increased for 0.6 < k y ρ s .In the DTB phase, the reduction in the growth rate was quite distinct, as shown in figure 9(d).Here, the growth rate inside the ITB region was reduced by about 50% compared to the ITB foot, for all k y ρ s values.Moreover, the growth rate inside the ITB was lower compared to the H-mode.The reduction in the linear growth rate as the location moves from the ITB foot to inside the ITB in the DTB phase is consistent with the reduction in heat diffusivity to the neoclassical level inside the ITB region in the DTB phase observed in the transport analysis (section 3).
We then compared the linear growth rate of the most unstable mode in the H-mode and DTB phases with the equilibrium E × B shearing rate, γ E×B , which is defined as [35], where R and q are the major radius and safety factor, respectively, B θ is a poloidal magnetic field, and E r is a radial electric field estimated from the force balance equation [36] of the impurity species, carbon, in this study.In the calculation of E r , we used the toroidal velocity measured by charge exchange spectroscopy [16] using carbon line emission, and the neoclassical poloidal velocity (V pol ) simulated by the code NEO [37].Figure 10(a) shows neoclassical V pol profiles, and figure 10(b) represents total E r profiles calculated from the measured V tor from CES carbon lines, neoclassical V pol , and the gradient of carbon pressure.These E r profiles were used for calculating γ E×B shown in equation ( 1) in this study.The calculated γ E×B values are shown in figures 9(c) and (d) for comparison with the growth rates.γ E×B in the DTB phases is about 4 times higher compared to that in the H-mode.Although γ E×B increased in the DTB regime, it remained lower than the linear growth rates in the same regime.Similar results were obtained for the H-mode phase.Lower γ E×B values compared to the growth rates were observed at both analysis points in the H-mode.Even in the DTB regime with a reduced growth rate, γ E×B was of an order lower compared to the maximum growth rate.Therefore, ITB formation in the DTB regime cannot be covered by a linear picture explaining the formation of transport barriers through turbulence suppression via equilibrium E × B shearing [38].In figure 2(g) of section 2, we could observe a consistent change in the V tor at the DTB phase, implying a correlation between E × B shearing and DTB formation.Nevertheless, the effect of E × B shearing on turbulence suppression in the linear analysis was insufficient to fully explain the DTB formation.However, the analysis conducted in this paper used the calculated V pol to obtain E r rather than direct measurements from experiments, which can represent the correlation of rotation change and turbulence suppression [39].The previous research demonstrated direct measurements of E r using MSE [40].The research on direct E r measurements using MSE is also ongoing in KSTAR.In the future, we will utilize the directly measured E r for further investigation of the effect of E × B shearing in the DTB formation.Moreover, we compared the linear growth rate only with the equilibrium E × B shearing rate.Therefore, we will conduct nonlinear simulation to include nonlinear effects including zonal shearing [41,42].Further analysis including a nonlinear picture will be conducted to better understand ITB formation during the DTB phase.
Another factor that can impact the reduction of turbulence and ITB formation is the turbulence suppression effect by fast ions.Previous studies have mentioned that the dilution effect on main ions [43,44] is caused by the fast ion population.It is also known that increases in the zonal flow level due to fast ion modes [42,45] can influence the turbulence suppression.In the DTB regime here, it was observed that the core fast ion fraction (n fast /n e , where n fast is the fast ion density) increased from 13% to a maximum of 20% due to the decrease in density level and increased penetration of fast ions to the plasma core.However, this increase is significantly lower than the fraction of ∼40% shown in previous research [46], so it appears to be insufficient to consider the dilution effect as the major cause of ITB formation in this study.Research on nonlinear mode couplings and their influence on turbulence suppression will be performed in the future.

Conclusion
An ELM-free DTB regime achieving high confinement comparable to the ELMy H-mode was observed in KSTAR.During this ELM-free period, which lasted approximately 3 s, a stationary ITB and ETB were formed and sustained, composing an ELM-free DTB phase that showed comparable thermal confinement to the H-mode.The ITB formation was more prominent in the ion channel than in the electron channel, with ion thermal diffusivity reduced to neoclassical transport levels.Moreover, thermal ETBs in ion and electron channels were also sustained comparable to the H-mode, while the edge electron density was decreased.
Various analyses on the ETB and ITB were conducted.Changes in the edge density reduced the pressure gradient, and the edge stability analysis showed that the operation point moved to the peeling-ballooning stable region, resulting in ELM-free characteristics during the DTB phases.To understand the ITB formation, we first observed its sequence and found that the ITB formed immediately after the density started to decrease, indicating that the density level was not a main factor affecting the ITB formation.Nonetheless, we note that the ITB collapses once ELMs reappear as the density recovers to the previous level in the H-mode phase.
Possible ITB formation mechanisms were also investigated.It was found that magnetic shear was not a critical factor in the ITB formation in this case based on the similar magnetic shear profiles between H-mode and DTB phases.The linear gyrokinetic analysis showed that the growth rate of the dominant mode reduced inside the ITB compared to the ITB foot location, consistent with the transport analysis results.However, when comparing the linear growth rate of the DTB regime with the equilibrium E × B shearing rate, the linear analysis was not consistent with the conventional explanation of ITB formation through turbulence suppression by equilibrium E × B shearing.Further analysis is required to understand the ITB formation mechanism during the DTB regime, including direct measurement of E r and nonlinear influences such as zonal shearing.
The analyses performed in this study will contribute to understanding the physical mechanism behind the DTB.Following this, the stable, high-performance regime found in this study can be utilized as an advanced operation scenario for fusion reactors in the future.

Figure 1 .
Figure 1.Configurations of the main heating sources depicting the injected neutral beams and electron cyclotron heating (ECH, blue) during the DTB discharge.Three on-axis beams (NB1-A, B, C) are plotted as the red line, and the off-axis line for the NB2B ion source is plotted as the green line.

Figure 2 .
Figure 2. Time trace of the discharge (shot #26980).The DTB phases are the green-shaded regions.(a) Plasma current (Ip) and injected power of electron cyclotron (EC) heating.(b) Injected power of neutral beam heating.Power of off-axis beam (NB2B) is plotted as blue line.(c) Dα line emission showing ELM-free characteristics in the DTB phases.(d) Line-averaged electron density (ne).(e) Plasma stored energy (W mhd ) and H 89 scaling [13].(f ) Normalized beta (β N = β aBT Ip , a = minor radius).(g) Toroidal rotation velocity at ρtor ∼ 0.05 and ρtor ∼ 0.45, where ρtor is the square-root of the normalized toroidal flux.

Figure 4 .
Figure 4. Results of the transport analysis of the H-mode (6.45 s) and DTB (7.4 s) phases.(a) Ion heat flux and (b) ion heat diffusivity.The neoclassical values were calculated via NCLASS.(c) Electron heat diffusivity.

Figure 6 .
Figure 6.Edge peeling-ballooning stability diagrams of the same time points for the (a) H-mode and (b) DTB phases.The operation points of the analysis times are marked as black crosses.

Figure 7 .
Figure 7. (a) Line-averaged electron density (ne) from a TCI core-crossing channel and edge-crossing channel.(b) Dα line emission.(c) T i from a core CES channel.The data at the ELM burst timings are filtered out.The time points of the start of the T i increases are marked with green dashed lines (6.640 s, 8.252 s).The first ELM burst after the first DTB phase is marked with the red line (7.865s).

8 .
(a) Safety factor (q) profiles in the H-mode (dashed) and DTB (solid) phases.(b) Magnetic shear profiles.(c) Magnetic field pitch angles.The lines and error bars show measured MSE data, and the marked points represent the calculated values from the EFIT reconstruction.

Figure 9 .
Figure 9. Real frequency of the most unstable mode in the (a) H-mode and (b) DTB phases.The horizontal axis is kyρs, where ky is a poloidal wavenumber and ρs is the ion sound gyroradius defined as cs eB/(m i c) .The unit is cs/a, where cs ≡ √ Te/m i with ion mass m i .The minus sign of the real frequency indicates the ion diamagnetic direction.(c) Mode growth rate of different radial positions in the H-mode.The E × B shearing rate (γ E×B ) of each position is plotted as the black lines.(d) Growth rate and γ E×B in the DTB phase.

Figure 10 .
Figure 10.(a) Neoclassical poloidal velocity (V pol ) computed by the code NEO.The solid lines represent main ion (deuterium), and dashed lines are for impurity (carbon).(b) Total radial electric field (Er) profiles.