Direct measurement of the electron turbulence-broadening edge transport barrier to facilitate core–edge integration in tokamak fusion plasmas

The integration of a high-performance core and a dissipative divertor, or the so-called ‘core–edge integration,’ has been widely identified as a critical gap in the design of future fusion reactors. In this letter, we report, for the first time, direct experimental evidence of electron turbulence at the DIII-D H-mode pedestal that correlates with the broadening of the pedestal and thus facilitates core–edge integration. In agreement with gyrokinetic simulations, this electron turbulence is enhanced by high η e (η e = Ln /LT e, where Ln is the density scale length and LT e is the electron temperature scale length), which is due to a strong shift between the density and temperature pedestal profiles associated with a closed divertor. The modeled turbulence drives significant heat transport with a lower pressure gradient that may broaden the pedestal to a greater degree than the empirical and theoretically predicted pedestal width scalings. Such a wide pedestal, coupled with a closed divertor, enables us to achieve a good core–edge scenario that integrates a high-temperature low-collisionality pedestal (pedestal top temperature T e,ped > 0.8 keV and a pedestal top collisionality ν*ped < 1) under detached divertor conditions. This paves a new path toward solving the core–edge integration issue in future fusion reactors.

Keywords: tokamak, H-mode pedestal, turbulence (Some figures may appear in colour only in the online journal) One of the key challenges facing the operation of a fusion reactor is to sustain a high-temperature, high-pressure plasma with sufficient confinement time while preventing damage to the plasma-facing components [1]. ITER will adopt highconfinement (H-mode) plasmas with a spontaneous edge transport barrier called a pedestal as the baseline scenario to achieve its scientific goal [2]. The formation of the edge transport barrier in the tokamak can inhibit substantial outflows and thus significantly improve global plasma confinement. In addition, the pedestal is the upstream source that determines the particle and heat fluxes toward the plasma-facing components, including the associated edge instabilities called edge-localized modes (ELMs [3]). To protect the plasmafacing materials, efficient boundary solutions with low particle energy and heat flux are highly desirable. However, in most of the present tokamak devices, it is commonly found that a strong dissipative boundary, such as a divertor detachment, can significantly cool the pedestal, increase collisionality, degrade the H-mode pedestal and thus the global performance [4][5][6]. Although alternative solutions, such as the X-point radiator [7] and detached high poloidal beta plasmas [1] exhibit strong advantages over core-edge solutions, the pedestal collisionality is much higher than that expected in future reactors. Understanding and thus optimizing the structure of H-mode pedestals is vitally important in order to explore the solution of integrating a hot and less-collisional core with a cold boundary, i.e. the so-called 'core-edge integration' in tokamak plasmas, which is one of the critical issues for a fusion reactor [1,8,9].
Based on experimental progress, the EPED model [10,11], which assumes that the peeling-ballooning mode (PBM) instability limits the achievable pressure ceiling and that the kinetic-ballooning mode (KBM) limits the achievable pressure gradient, has been developed to predict the plasma pressure and width at the top of the pedestal. The EPED predictions for the pedestal width and height prior to the ELM crash are consistent with the experimental data from multiple devices [10,12,13], particularly under attached divertor conditions. However, recent experiments in several tokamaks, including TCV [14], DIII-D closed divertor plasmas [15], JET, and ASDEX-Upgrade [16,17] H-mode plasmas with metal walls have found that the pedestal can be much wider than the EPED scaling when there is a strong shift between density and temperature pedestals. Such a pedestal shift may correlate with a low-density gradient resulting from weak pedestal fueling efficiency due to weak or shallow neutral ionization in the pedestal region. In future fusion reactors such as ITER, boundary simulations predict a weak-gradient density pedestal due to the highly opaque boundary plasmas [18,19]. The pedestal shift may cause large uncertainties in the pedestal prediction based on current modeling and thus the plasma behavior of ITER in both the core and the divertor.
In this paper, we report that in DIII-D H-mode plasmas with a closed divertor, the strong gas puffing required to achieve detachment leads to a significant separation between density and temperature pedestals and a wider temperature pedestal than that predicted by the EPED scaling. Concomitantly, turbulence at k y ρ s values from one to two, which is limited by the measurement capability, is enhanced at the pedestal by the Doppler backscattering (DBS) measurement; here, k y and ρ s are the poloidal wave number and ion sound gyroradius, respectively. The appearance of turbulence is strongly correlated with high η e that results from the pedestal shift and is consistent with gyrokinetic simulation predictions. In addition, gyrokinetic simulations show that electron turbulence drives significant heat transport, which can broaden the pedestals so that they are wider than the EPED prediction. The wide temperature pedestal facilitates the achievement of a hightemperature, low-collisionality pedestal, i.e. T e,ped ⩾ 0.8 keV and ν * ⩽ 1, and the outward shift of the density pedestal facilitates access to detached divertor conditions at low temperatures and heat flux toward the target plate, which offers a promising approach for solving the core-edge integration issue.
The main results were obtained from a DIII-D impurity seeding detachment experiment with an upper closed divertor. Figure 1 shows two example discharges with plasma current I p = 1.3 & 1 MA, B t = 2 T, 9.2 MW NBI, and an upper single null shape with ion B × ∇B drift toward the upper divertor. With continuous D 2 gas puffing and N 2 injection (figures 1(a1) and (a2)), divertor detachment is achieved, and the divertor temperature T e,div is reduced from >20 eV to <5 eV, as measured by divertor Langmuir probes near the outer strike point (figures 1(b1) and (b2)). From divertor attachment to detachment, the electron pedestal pressure is reduced by ∼20% in the 1.3 MA case, while in the 1 MA case the reduction is very small. During divertor detachment, the temperature pedestal is significantly (>40%) wider than the EPED prediction ( figure 1(d)). Here, based on the KBM constraints, the EPED model gives a scaling law for the pedestal width, ∆ ψ N = cβ 1/2 p,ped , where the constant c = 0.089 [20], and ∆ ψ N and β p,ped are the pedestal width and pedestal poloidal beta, respectively. Note that, due to the flat density pedestal, the electron pressure pedestal width is close to the temperature width and larger than the EPED scaling at a similar ratio. In the meantime, the relative shift between the density and temperature pedestals is enhanced by the density increase. The pedestal shift is calculated as the relative distance in normalized poloidal flux space between the positions of the peak-gradient regions of the density and temperature pedestals. This shift can be even larger than 50% of the temperature or pressure pedestal width. In the pedestal's steep pressure gradient region, η e increases from 2 to ∼4 during divertor detachment, while η i remains nearly identical. Here, η e = L n /L Te and η i = L n /L Ti , where L n is the density scale length and L Te(i) is the electron (ion) temperature scale length at the pedestal's steepest pressure gradient region, calculated based on the fitted profiles.
The enhanced η e can potentially drive turbulent fluctuations and transport as predicted in [21][22][23][24][25], limiting the growth of the pedestal gradients. As shown in figure 1(f1), around 3500 ms, when η e increases from 2 to ∼4 and the temperature pedestal becomes wider than the EPED scaling, a quasi-coherent fluctuation (QCF) with a central frequency of ∼−2.5 MHz is significantly enhanced in the density fluctuations measured by a high-k DBS system. Here, DBS measures the wavenumber-resolved density fluctuations and associated Doppler shifts with high spatial (<5 mm) and temporal resolutions (∼0.2 µs). Profile reflectometry provides the edge density profile with high temporal resolution for the calculation of the scattering locations and wavenumbers using the 3D ray-tracing code GENRAY. In contrast, before 3500 ms, when the pedestal width is close to the EPED scaling, DBS only observes bursty broadband fluctuations, which correlate with the high-frequency small ELMs and low-frequency giant ELMs and exhibit different spectral features. During divertor detachment in the 1.3 MA case, small ELMs are suppressed and the frequency of giant ELMs remains nearly unchanged, leading to a clearer spectrum with strong QCF. At the lower plasma current with I p ∼ 1 MA, the QCF intensity gradually increases over time ( figure 1(f2)), which appears to be consistent with the gradual increases of η e , the pedestal shift,  a1) and (b1) the auto-power spectra of the innermost DBS channels. QCF can clearly be observed in the innermost two channels in shot #187032 and in the innermost three channels in shot #187038, which are marked with star symbols. ρ is the square root of the normalized toroidal flux. and the normalized temperature pedestal width. The QCF shows a larger spectral width than that in the higher-current case (which can also be seen in figure 2), while the ELMs with a mixture of giant and small ELMs are similar for both attached and detached divertors. Note that another DBS system observed fluctuations with lower k (k y ρ s ⩽ 0.5) in both attached and detached cases, which did not correlate with pedestal broadening. Note that no significant change in magnetic fluctuations is observed in the high-frequency internal magnetic coils for the 1 MA case, though the frequency range for the magnetic fluctuation measurement is <1 MHz. No significant change in the low-k (k y ∼ 0.25 cm −1 , k y ρ s ⩽ 0.1) density fluctuations is observed in the beam emission spectroscopy (BES) measurements at the pedestal.
More details of the QCF are shown in figure 2. The eightchannel high-frequency DBS measures the fluctuations over a wide radial range spanning from the scrape-off layer (SOL) to the pedestal. The DBS measurements are shifted outward by the increased density but remain in the pedestal's steep gradient region. The perpendicular wavenumber of the density fluctuations measured by DBS is ∼10-13 cm −1 at the pedestal region inside the separatrix, and the corresponding k y ρ s is about 1-2; the innermost one is ∼2. As shown in figures 2(a1) and (b1), the QCF significantly increases from the attached phase to the detached phase, whereas during the attached phase, it does not appear. The QCF's central frequencies are ∼−2 MHz for 1 MA and ∼−2.5 MHz for 1.3 MA, which seem to scale with the plasma current; however more data from future experiments are needed to clarify this relationship. The QCF propagates in the electron diamagnetic drift direction in the lab frame (figures 2(a) and (b)). The mode phase velocity is larger than the E × B drift velocity inferred from the CER CVI measurement [26], suggesting that it propagates in the electron drift direction in the plasma frame. In addition, the QCF appears in the DBS channels with high poloidal velocity, which corresponds to the pedestal's steep pressure gradient region. The QCF is not detected in the SOL, either due to the lower Doppler shift or the diminished free energy drive, which requires further investigation.
A strong correlation between the pedestal shift η e in the steep pressure gradient region and the pedestal width can also be found in the statistical analysis shown in figure 3. This correlation is applicable to both non-impurity and impurity seeding detachment plasmas. The strong pedestal shift leads to high η e ( figure 3(a)), while high η e is in turn correlated with the wider electron temperature pedestal (figure 3(c)), which is hypothesized to be due to enhanced turbulence and transport as discussed for figures 1 and 2. The physical reason for the pedestal shift is still under investigation, but the outward shift of the density pedestal resulting from the shallow pedestal ionization due to the increased divertor closure or high gas puffing is a possible hypothesis, as discussed in [15,17,27]. It should be noted that such a pedestal shift has been observed across many devices, such as JET [16,28], TCV [14], ASDEX-Upgrade [29], and DIII-D [13], though the wall materials may play an important role in pedestal fueling and pedestal structure. Similar observations, including high η e and wider pedestal than the EPED scaling [16,17], have been found to be associated with a strong pedestal shift, indicating common physics.
The strong pedestal shift and wider pedestal induced by the enhanced fluctuations can greatly facilitate core-edge integration. The outward shift of the density pedestal with lower gradient and larger width leads to relatively high density in the SOL. Based on the two-point model [30], high separatrix and SOL density can decrease the divertor temperature T e,div ∝ n −2 sep , increase the divertor density n e,div ∝ n 3 sep and also enhance divertor radiation, all of which facilitate the achievement of a dissipative divertor. The high separatrix density is also beneficial for the screening of impurities and neutrals due to its high neutral opacity. In addition, the wider temperature pedestal directly helps achieve a high-temperature core and expands the region isolating the hot core and cold boundary. are the entire profiles from the core to the edge. Divertor particle flux (d), temperature (e) and electron pressure (f ) profiles were measured by a divertor Langmuir probe. The red profiles are a reference for the attached divertor in the early phase of the same discharge. (g) the radial profiles of the density gradient (dne/dψ n) and temperature gradient (dTe/dψ n) versus the normalized poloidal flux ψ n; the pedestal shift is also indicated by an arrow. (h) 2D CIII radiation from a tangential TV system indicates divertor detachment.
As shown in figure 4, partially detached divertor plasma has been achieved, as manifested by strong (>80%) pressure loss (figure 4(f )) and reduction of particle flux (figure 4(d)) near the outer strike point compared to the attached divertor, low divertor temperature (T e < 10 eV) measured by divertor Langmuir probes across the entire target plate (figure 4(e)), and a carbon radiation front that moved off the target plate ( figure 4(h)). For the upstream profiles, the pedestal top electron temperature is ∼0.82 keV from the fitting, corresponding to a normalized pedestal collisionality ν * ∼ 0.7, including both carbon and nitrogen density at the pedestal, and the normalized pedestal beta β N,ped ∼ 0.9. The density gradient peaks around the separatrix and the high separatrix density correlate with the strong divertor dissipation ( figure 4(g)). The temperature gradient peaks further inside, leading to a high pedestal temperature and facilitating the achievement of high core performance. In this case, we have achieved a normalized global beta β N ∼ 2.8, a normalized energy confinement factor H 98 ∼ 1.35, a core electron temperature T e ∼ 4 keV, and a core ion temperature T i ∼ 5.5 keV. Such a high-performance core and detached divertor are non-transient and can be sustained for more than eight energy confinement times, demonstrating the advantages of this integrated scenario. Note that, in contrast to the pedestal improvement obtained via impurity seeding in metal-wall machines [31], additional N 2 puffing does not significantly change the relationship between the pedestal parameters in figure 3 but greatly facilitates the achievement of divertor detachment [32], thus improving core-edge integration.
To further understand the nature of these fluctuations, a set of comprehensive gyrokinetic simulations was performed using the CGYRO code [33] for the 1 MA cases. The kinetic EFIT equilibrium using the measured experimental profiles with a 70%-99% ELM phase was used as the background input for the calculations. More details about the CGYRO settings can be found in [34]. In these simulations, we focus our analysis on a representative flux surface in the pedestal region, with ρ ∼ 0.93, where the QCF is significantly enhanced during divertor detachment with high η e . The linear calculation performed by CGYRO shows consistent behavior as seen in experiments. As can be seen in figure 5(a), at an early stage, i.e. 2500 ms of shot #187038, the linear growth rate with 0.4 < k y ρ s < 3.0 is close to but slightly higher than the normalized shearing rate of the E × B flow γ E . In contrast, as shown in figure 5(b), during the later phase with divertor detachment, the linear growth rate for the same k y ρ s range close to the experiment is well above the normalized E × B shearing rate, suggesting possible excitation and enhancement of the pedestal instability, which agrees with experimental observations. Here γ E = a Cs r q ∂ω0 ∂r , where ω 0 = E r /RB p is the toroidal rotation frequency induced by the radial electric field E r . B p , a, c s , and q are the poloidal magnetic field, plasma minor radius, ion sound speed, and safety factor, respectively. At a similar wavelength to that used in the experiment, the CGYRO simulations exhibit a ballooning-mode structure with even parity in the electrostatic potential and odd parity in A || , while the amplitude of the magnetic component is much smaller than the electrostatic potential. This can help to exclude the possibility of electromagnetic modes, such as the KBM [35] and the microtearing mode [36][37][38].
The parametric dependence of the linear growth rate predicted by CGYRO agrees well with experimental observations. As shown in figures 5(c)-(e), the instability is driven by a lower density gradient and a higher T e gradient [39] but is weakly sensitive to the ion temperature gradient, suggesting that it is likely to be an electron temperature gradient (ETG) mode. This dependence agrees with experimental findings that strong gas puffing increases the ratio n sep /n ped , reduces the density gradient, and leads to high η e and enhanced QCF. It is also worth pointing out that in MAST, experiments and simulations have found that a low-k ETG mode with a similar k y ρ s range to that used in this study plays a role in inter-ELM pedestal evolution at the pedestal top [40].
In order to assess the transport enhancement that comes with the mode, a series of nonlinear gyrokinetic simulations including extensive convergence and sensitivity tests were performed using the CGYRO code [33]. We begin with 32 toroidal modes with ∆k y ρ s = 0.1, so (k y ρ s ) max = 3.1 for both cases. Some key results are listed in table 1. From the attached to the detached case, the increase in high η e significantly increases the energy flux Q e /Q GB from 22 to 62, which is consistent with the increased growth rate with a lower density gradient and a higher T e gradient given by linear calculations (figures 5(c) and (d)). Here, Q GB = n e T e c s (ρ s /a) 2 is the gyro-Bohm energy flux. The predicted energy flux is also increased from 1.9 MW to 2.5 MW, which is consistent with the experimental energy flux that increased from 2.8 MW to 3.6 MW. The neoclassical electron energy fluxes, Q e,neo ∼ 0.9Q GB and 2.1Q GB for these two cases, are much smaller than the turbulent ones. Note that the correlation between the increased electron energy fluxes and η e is consistent with previous studies [22,25]. The underestimation of the energy fluxes in the simulations compared to the experimental results could be due to the higher k contribution as shown in [25], while these new CGYRO simulations highlight the important contributions made by the low k turbulence. As can be seen in figure 6, compared to the attached case, in the detached case both density and heat flux fluctuations exhibit strong amplitudes at k y ρ s > 0.6, while at k y ρ s < 0.6, the differences are very small, which demonstrates the important role of the enhanced turbulence observed in the experiment on the transport and thus the pedestal structure. Evidenced by the nonlinear analysis above and in line with experimental findings, the enhanced turbulence driven by high η e gives rise to the transport level, correlates with the lower pressure gradient, and leads to a pedestal wider than that predicted by KBM-dominant theory. A wide pedestal would compensate for the gradient reduction (figures 3(c)-(d)), which would facilitate the achievement of a high-temperature, low-collisionality pedestal and thus significantly improve core-edge integration. Note that, given the assumption of a constant profile of transport coefficients in the SOLPS simulations, the density pedestal gradient is expected to be weak in ITER [18,19], similar to the cases we report here, due to much weaker neutral ionization in the pedestal region. The physics of the correlation between the weak density gradient and the associated enhanced fluctuations and pedestal width could be applicable to ITER and future tokamak fusion reactors. Another related topic, namely whether this enhanced turbulence could broaden the SOL heat flux in future reactors, such as those predicted in XGC1 modeling with a trappped electron mode (TEM) streamer [41], would be interesting to explore in the future.
In DIII-D, the detached closed divertor plasma leads to a strong pedestal shift between density and temperature, which directly results in a high-η e pedestal that is well above the threshold of microinstability. We find for the first time in experiments that electron fluctuations with k y ρ s > 1 at the pedestal steep pressure gradient region are significantly enhanced by high η e . As confirmed by gyrokinetic simulations, these electron fluctuations are consistent with the expectation of a low-k branch of the ETG mode. This electron turbulence drives significant heat transport and broadens the pedestals so that they are wider than the empirical and theoretically predicted pedestal width scalings. This wide pedestal and closed divertor enable the achievement of a good core-edge scenario with a high-temperature, low-collisionality pedestal and a high-performance, high-confinement core, together with detached divertor conditions, thus offering a new approach toward resolving core-edge integration as one of the critical issues for future fusion reactors. and DE-AC04-94AL85000. We would like to thank the DIII-D operation team for the support and effort for the experiment work. Author HW would like to thank Richard Groebner and Pengjun Sun for useful discussions. 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.