We elaborate on the nature of the prompt core confinement improvement observed at the L–H transition in DIII-D, which is a long-standing issue unsolved for more than two decades and can impact future fusion reactor performance. Dynamic transport analysis suggests the essential role of the profile stiffness for understanding the mechanism of the prompt core confinement improvement. Beam emission spectroscopy shows that transport reduction at the core cannot be explained only by the ion scale turbulence density fluctuation suppression. Properties of nonlocal confinement improvement across the L–H transition are experimentally assessed in hydrogen (H) and deuterium (D) plasmas. Prompt core confinement improvement is found to be more rapid in the lighter hydrogen isotope.

After the first discovery of the high confinement mode (H-mode) transition,1 extensive effort has been made to understand the background mechanism of the edge transport barrier (ETB) formation. Although basic properties of the ETB formation, e.g., excitation of the E × B shear flow,2,3 turbulence transport suppression,3–5 and the isotope effects on the threshold condition,6–8 were successfully understood to a certain extent, some important enigmas still remain unresolved. One of these conundrums is the prompt core confinement improvement across the low to high confinement mode transition (L–H transition).9–11 That is, although the radial electric field as the turbulence regulator is only excited in a limited peripheral region,12 the turbulent transport is nonlocally suppressed in a wide radial region including the core. The nonlocal transport observed in L-mode plasmas13 is considered to have a link to the prompt core confinement improvement. Physics-based profile prediction in the H-mode core is extremely valuable for elaborated projection of future thermonuclear fusion reactor performance.14 

In this paper, the prompt core confinement improvement across the L–H transition in DIII-D is studied. Dynamic transport analysis suggests the essential role of the profile stiffness15,16 for understanding the mechanism of the prompt core confinement improvement. It is indicated that the transport reduction at the core cannot be explained only by the ion scale turbulence density fluctuation suppression experimentally measured. Motivated by the clear isotope effect in the L–H transition power threshold,6–8 properties of nonlocal confinement improvement across the L–H transition are experimentally assessed in hydrogen (H) and deuterium (D) plasmas for the first time. Prompt core confinement improvement is found to be more rapid in the lighter hydrogen isotope.

The experiments were conducted on the DIII-D tokamak with neutral beam (NB) heated ITER similar shape plasmas.7 The toroidal magnetic field Bt is 2.1T with the ion B drift toward the X-point. The safety factor at the 95% magnetic flux surface q95 is set to be 5 with the plasma current Ip of 1 MA. Before the L–H transition, the line averaged density n¯e is maintained to be 3×1019m3. In addition to regular D plasma discharges, H plasmas are generated by H beam and H puff with a high H purity more than 92% in a dedicated campaign. For the transport analysis discussed below, the electron temperature evolution is measured by the high time resolution electron cyclotron emission (ECE) radiometer, where the signal is cross-calibrated by the Thomson scattering (TS) data. Ion scale turbulent density fluctuation is measured by the beam emission spectroscopy (BES)17 in a one-dimensional radial array covering 0.65<ρ<1, where ρ=ΨN and ΨN are the normalized toroidal flux.

Figure 1 shows the typical time evolution of the hydrogen target discharge. For finding the L–H transition power threshold, the NB power is increased stepwise at the current and density flattops. The L–H transition time is tLH=1736.1 ms manifested by the drops in the edge Hα signal and the feedback-controlled gas injection rate as well as the abrupt increases in the energy confinement time and the line averaged density [Figs. 1(a) and 1(b)]. Radial profiles of the electron density ne and the electron temperature Te measured by the TS are shown in Figs. 2(a) and 2(b), respectively. Before the L–H transition, the ne profile is peaked, and no apparent pedestal structure exists in the Te profile. Once the L–H transition occurs, clear pedestal structures appear in the ne profile and the Te profile at the peripheral region ρ>0.95. Quick increase in the quantities at the peripheral region leads to the profile flattening at the inner side of the pedestal both in ne (ρ>0.5) and in Te (ρ>0.7). The location of the sheared E × B flow structure is determined as ρ>0.85 by the charge exchange recombination spectroscopy.

FIG. 1.

Time evolutions of (a) the line averaged density, the gas injection rate, and the energy confinement time, (b) the neutral beam power and the Hα emission intensity, and (c) and (f) the electron temperature traces at various radii; spatiotemporal evolutions of (d) and (g) the electron temperature and (e) and (h) the time derivative of the electron temperature with Hα emission intensity overlaid in the L-mode phase and across the L–H transition, respectively. The vertical dashed line indicates the L–H transition time of tLH=1736.1 ms.

FIG. 1.

Time evolutions of (a) the line averaged density, the gas injection rate, and the energy confinement time, (b) the neutral beam power and the Hα emission intensity, and (c) and (f) the electron temperature traces at various radii; spatiotemporal evolutions of (d) and (g) the electron temperature and (e) and (h) the time derivative of the electron temperature with Hα emission intensity overlaid in the L-mode phase and across the L–H transition, respectively. The vertical dashed line indicates the L–H transition time of tLH=1736.1 ms.

Close modal
FIG. 2.

Radial profiles of (a) the electron density and (b) the electron temperature.

FIG. 2.

Radial profiles of (a) the electron density and (b) the electron temperature.

Close modal

Spatiotemporal evolution of Te measured by the ECE and its time derivative Te/t in the L-mode phase and across the L–H transition are shown in Figs. 1(c)–1(h). The radial region of interest, 0.6<ρ<1, is covered by six channels, having a radial interspacing of 2.5 cm. For suppressing the high frequency noise, a numerical low pass filter with the cutoff frequency of 650 Hz, which is much faster than the energy confinement timescale, is applied to the ECE data. In the L-mode phase at ttLH83 ms, an outward propagation of the increased Te is observed, which corresponds to the heat pulse induced by a sawtooth crash [Fig. 1(e)]. Another sawtooth heat pulse is seen at ttLH5 ms shortly before the L–H transition. Note that the sawtooth inversion radius is far inside (ρ0.22), and the heat pulse is rather less sharp in the edge region. At the L–H transition, an inward propagating pulse of the Te increase appears as implied in Ref. 18, after which Te continues to increase in a wide radial region. The pulse propagation speed in radius is 115 m/s, which is one order of magnitude smaller than the electron diamagnetic drift velocity (typical propagation speed of the turbulence spreading pulse19,20). This chained sequence of the Te increase corresponds to the inward transmission of the prompt transport suppression front starting from the edge E × B shear region.

First, we discuss a possible explanation of the prompt core confinement improvement. The electron heat flux qe is evaluated from the energy conservation equation as qe=V10r[P32(neTe)/t]Vdr, where P is the heating power density including the NB heating, the Ohmic heating, the radiation loss, and the ion–electron temperature equilibration and V is the radial derivative of the torus volume inside the flux surface labeled by r. Time evolutions of P and V are calculated by a transport analysis code ONETWO.21 For obtaining the ne profile evolution, the spatially smoothed TS data in t>tLH are fitted by ne,fit=ne,L+Δne[1e(ttLH)/Δt], where Δne and Δt are the fitting parameters and ne,L is the mean electron density profile in the L-mode, t<tLH. As an example, measured data and fitting curves are shown for different radial positions in Fig. 3. Uncertainness of the fitting is considered in the transport analysis below.

FIG. 3.

Time evolution of electron density measured by Thomson scattering and exponential fitting at (a) ρ=0.53, (b) 0.75, and (c) 0.89.

FIG. 3.

Time evolution of electron density measured by Thomson scattering and exponential fitting at (a) ρ=0.53, (b) 0.75, and (c) 0.89.

Close modal

Figure 4(a) is the time evolution of the electron heat flux divided by the electron density qe/ne and the electron temperature gradient Te at ρ0.74, far inside the E × B shear region. Across the L–H transition, qe/ne is quickly suppressed even though the local E × B shear is considered to remain unchanged. The value without the contribution of ne,fit/t is overlaid by the thin dashed curve to exclude uncertainness of fitting. This dashed curve corresponds to the possible upper boundary of qe/ne. Even only with the Te/t contribution, the prompt reduction of qe/ne is reproduced. Slight decrease in Te is due to the drastic increase in Te at the edge pedestal of ρ>0.95 with a moderate change in Te in the core as shown in Figs. 1(f) and 2(b). Figure 4(b) is the flux-gradient diagram, where time is shown by the color bar. Different phases, i.e., L–mode, transition phase, and H-mode, are shown by different symbols, i.e., circles, squares, and triangles, respectively. In addition, points for ttLH=0.9 and 1.3 ms are specially marked as representative data in the L-mode and H-mode. The slope between each point and the origin corresponds to the power balance thermal diffusivity χePB=qe/(neTe), and the derivative of the points shows the heat pulse thermal diffusivity χeHP=(qe/ne)/Te (Ref. 22). Across the L–H transition, χeHP18 m2/s is much larger than χePB3.4 m2/s, which corresponds to a representative feature of the profile stiffness.15,16 In the presence of the profile stiffness, the slight decrease in Te induced by the edge pedestal formation leads to the rapid and drastic drop in qe/ne. Then, the transport suppression front propagates inward in a chain reaction manner. Rapid decrease in the ne gradient possibly plays a role through an off diagonal contribution as well, as demonstrated in Refs. 23 and 24 for the nonlocal transport study. After the prompt reduction in qe/ne ceases at ttLH=1.3 ms, the trajectory in the flux-gradient diagram transits to a different branch with χeHPχePB, i.e., no stiffness.

FIG. 4.

(a) Time evolutions of the electron heat flux divided by the electron density and the electron temperature gradient at ρ=0.74 and (b) its flux–gradient diagram; radial profiles of (c) the electron heat flux and (d) the electron thermal diffusivity. Thin dashed curves in (a), (c), and (d) correspond the values without considering the electron density evolution. Colored lines and symbols in (b)–(d) correspond to the data at the time indicated in (a) by the vertical lines.

FIG. 4.

(a) Time evolutions of the electron heat flux divided by the electron density and the electron temperature gradient at ρ=0.74 and (b) its flux–gradient diagram; radial profiles of (c) the electron heat flux and (d) the electron thermal diffusivity. Thin dashed curves in (a), (c), and (d) correspond the values without considering the electron density evolution. Colored lines and symbols in (b)–(d) correspond to the data at the time indicated in (a) by the vertical lines.

Close modal

Figure 4(c) shows the radial profile of qe for the specific time slices and time period. Before the L–H transition, ttLH=0.9 ms, qe monotonically increases in radius, which is mainly driven by the NB heating having a wide absorption profile. Shortly after the L–H transition, ttLH=1.3 ms, qe is significantly reduced by the positive value of Te/t in a wide radial region. Even without considering the contribution of ne,fit/t,qe is substantially reduced as shown by the thin dashed curve. In the later time period, ttLH=1020 ms, qe remains reduced. Note that the reduced heat flux is maintained in the temperature rising phase and eventually returns to the original value in the confinement timescale. The heat flux in the later H-mode is driven by some other mechanisms under the increased gradient. The evolution of χePB profile shown in Fig. 4(d) exhibits a similar global reduction across the L–H transition as previously reported in Ref. 10.

Next, the role of the ion scale turbulent density fluctuation amplitude ñe on the prompt core confinement improvement is studied through the BES measurement. Turbulent transport reduction away from the E × B shear region was previously reported in Refs. 5 and 25. Figures 5(a) and 5(b) compare the spatiotemporal evolution of Te/t to that of ñe/(ñe)L, where (ñe)L is the mean turbulence amplitude in the L-mode. The turbulence amplitude is defined by the moving averaged cross power spectrum (CPS) of the density fluctuations measured at radially adjacent sample volumes. The CPS components in the frequency range from 65 to 200 kHz are integrated, and the numerical low pass filter used for the ECE signals is applied afterward. In the E × B shear region of ρ>0.85,ñe/(ñe)L is immediately suppressed. Detailed physics of the turbulence suppression at the ETB region was discussed in Ref. 26. In contrast, further in, substantial reduction in ñe/(ñe)L is not seen, although a temporary decrease appears in 0.75<ρ<0.85. Another gradual diminishing with a slow timescale of O(10ms) is observed in ρ<0.85. The timescale of the slow turbulence decay coincides with the timescale of the local gradient change as shown in Fig. 4(a). No front propagation in ñe/(ñe)L reduction as reported in Ref. 27 is found; therefore, the prompt core confinement improvement is not fully explained by the ion scale turbulence measured here. Radial profile of the normalized density fluctuation amplitude ñe/ne shown in Fig. 5(c) confirms the immediate drop in the E × B shear region of ρ>0.85 and the slower decrease in the inner radii. Relation between the turbulence and the transport is displayed as the ñe/ne vs qe/ne diagram in Fig. 5(d). Here, two radial positions ρ0.73 and 0.93 are chosen for representing turbulence dynamics outside and inside the E × B shear region, respectively. Radial distance between these two points is 8 cm, which is approximately a hundred times larger than the ion gyro radius and several times larger than the turbulence correlation length.28 In the E × B shear region of ρ0.93, the transport reduction is likely linked with the turbulence reduction. However, outside the E × B shear region at ρ0.73, only the transport is suppressed without an apparent change in the turbulence. This observation implies that the transport reduction in the core should be accounted for by unmeasured quantities, e.g., the electron temperature fluctuation and its cross phase with respect to the potential fluctuation or higher-wavenumber turbulence not detected by BES, which is sensitive to low-wavenumber density fluctuations. As a quick assessment for the turbulence energy source, inverse gradient lengths of the electron density, electron temperature, and ion temperature at 0.8<ρ<0.9 are compared. They are defined as LΨ1Ψ1Ψ/ρ, where Ψ is either ne,Te, or Ti. In the L-mode phase, they are Lne1=1.6,LTe1=4.5, and LTi1=2.8; therefore, a dominant role of the electron temperature gradient driven turbulence in driving transport is suggested. For more detailed investigation, a numerical approach is planned in future.

FIG. 5.

Spatiotemporal evolutions of (a) the time derivative of the electron temperature with Hα emission intensity overlaid and (b) the relative turbulence amplitude with respect to its L-mode value; (c) radial profile of the turbulence amplitude; and (d) relation between the turbulence amplitude and the electron heat flux divided by the electron density.

FIG. 5.

Spatiotemporal evolutions of (a) the time derivative of the electron temperature with Hα emission intensity overlaid and (b) the relative turbulence amplitude with respect to its L-mode value; (c) radial profile of the turbulence amplitude; and (d) relation between the turbulence amplitude and the electron heat flux divided by the electron density.

Close modal

Finally, the isotope effect on the prompt core confinement improvement is addressed. Here, the discussion is based on the propagation properties of the inverse time constant of Te,τTe1Te1Te/t. Figures 6(a) and 6(b) exemplify spatiotemporal evolutions of τTe1 for D and H plasmas across the L–H transition. These are routinely reproduced in all discharges in the dataset at a fixed line averaged density of n¯e3×1019m3 and different L–H power threshold loss power Ploss shown in Fig. 7(a). Here, Ploss is defined as Ploss=PNB+PohmicdW/dtPrad at the transition, where PNB is the NB heating power, Pohmic is the Ohmic heating power, W is the plasma stored energy, and Prad is the total radiation loss. Because of the strong isotope dependence in the L–H power threshold, comparison between D and H plasmas at an identical condition cannot be performed. Comparing Figs. 6(a) and 6(b), the H plasma looks to have a faster and larger magnitude inward propagating τTe1 pulse. For taking a statistical approach, we utilize three different quantities of the propagating τTe1 pulse, i.e., the penetration depth, Δrpenet; the propagation velocity, vprop; and the maximum value of τTe1,τTe,max1. We define four specific points to obtain those parameters. The first one is the radius and time of τTe,max1. Following three are the inner most radii and corresponding times in which the contours of τTe1=70, 50, and 30 s−1 reach. These points are shown by blue open circles in Figs. 6(a) and 6(b). The penetration depth is determined by Δrpenet=a(1ρ30), where a is the minor radius and ρ30 is the radius where the contour of τTe1=30 s−1 reaches. The slope of the linear fitting for those four points gives the definition of vprop. Those quantities are plotted as a function of Ploss for D and H plasmas in Fig. 7. Overall, deeper penetration, faster propagation velocity, and larger value of τTe,max1 are obtained in H plasmas than D plasmas. This can also be interpreted that the pulse having a larger amplitude (τTe,max1) can produce a deeper and faster propagation. In order to prove that the propagation parameters in D and H plasmas are different, the student’s t-test is performed. Student’s t values, tst, for the mean difference between D and H datasets are displayed in each panel. Except for the line averaged density, tst>3.7, indicating the hypothesis that the mean difference is the same is rejected with more than 99% confidence. This implies that the H plasmas have more significant prompt core confinement improvement than D plasmas. Each of D and H plasmas shows no clear dependence of the propagation properties on Ploss. Therefore, those differences in D and H plasmas are not merely due to different Ploss. Improvement of confinement was more significant in H plasmas according to the TS profile measurement (not shown here for D plasmas). This means that the H plasmas has more room for confinement improvement compared to D plasmas in L-mode, which can be a possible origin for the H/D difference.

FIG. 6.

Spatiotemporal evolutions of the inverse time constant of the electron temperature evolution τTe1 in (a) H and (b) D plasmas, and (c) and (d) their time evolutions at specific radii, respectively.

FIG. 6.

Spatiotemporal evolutions of the inverse time constant of the electron temperature evolution τTe1 in (a) H and (b) D plasmas, and (c) and (d) their time evolutions at specific radii, respectively.

Close modal
FIG. 7.

Loss power dependences of (a) the line averaged density and the properties of the prompt core confinement improvement: (b) the penetration depth, (c) the propagation velocity, and (d) the maximum value of τTe1.

FIG. 7.

Loss power dependences of (a) the line averaged density and the properties of the prompt core confinement improvement: (b) the penetration depth, (c) the propagation velocity, and (d) the maximum value of τTe1.

Close modal

As a background mechanism of the prompt core confinement improvement, the turbulence spreading theory19,20 is considered. The turbulence spreading theory describes nonlocal turbulence packet transmission across magnetic surfaces having a potential impact on turbulence transport. It was demonstrated in the TJ-II stellarator that turbulence excited at the edge spreads into the core region in the L-mode, which was terminated by the edge E × B shear structure in the H-mode.29 Here, we also hypothesize that the turbulence spreading is continuously occurring in the L-mode, which enhances the profile stiffness.30 Once the L–H transition occurs, the turbulence supply into the core is depleted because the turbulence source at the edge region is quenched by the E × B shear. The improved confinement front is expected to appear as the inward transmission of the turbulent transport reduction. At the same time, local temperature gradient is weakened by temperature increase at the edge-side, which further reduces the local transport and chains the edge and the core. According to the turbulence spreading theory,19,20 the penetration length and the propagation velocity of a turbulence packet are predicted to be proportional to DT, where DT is the thermal diffusivity. Considering the isotope effect of confinement,31DT is generally larger in H plasmas than in D plasmas. Therefore, deeper penetration and faster propagation of the turbulence packet are expected in H plasmas, as observed experimentally.

The effect of zonal flows is another candidate for the interpretation. As presented in theory32 and exhibited in numerical simulation33 and experiment,34 zonal flows are more activated in D plasmas than in H plasmas. With the reinforced zonal flow in D plasmas, the turbulence spreading is expected to be less pronounced. Direct detection of zonal flows affected by the isotope mass is a future task.

In this paper, we discussed the properties of the prompt core confinement improvement in DIII-D plasmas. The prompt core confinement improvement was observed as an inward propagation of the increasing rate change in the electron temperature profile. Through the transient transport analysis, an important role of the profile stiffness was pointed out. Ion scale turbulence measurement by the beam emission spectroscopy was performed. Presently, a decoupled dynamics between the heat flux reduction and the turbulence amplitude suppression in the core was observed. For discussing isotope dependence of the properties of the prompt core confinement improvement, propagation velocity and penetration depth of the confinement improvement front were characterized. Faster and deeper propagation of the confinement improvement front was systematically found in hydrogen plasmas than deuterium plasmas.

The authors thank C. Petty, S. Smith, and L. Schmitz for useful discussions, and one of the authors (T. K.) acknowledges K. Ida, Y. Suzuki, K. Nagasaki, M. Nakata, and S. Sakakibara for strong support. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Awards Nos. DE-FC02–04ER54698, DE-FG02–08ER54999, DE-AC02–09CH11466, and DE-FG02–97ER54415. T. K. was also supported by JSPS Core-to-Core Program, A. Advanced Research Networks (PLADyS), JSPS Grant-in-Aid for Scientific Research (Nos. 17K14898 and 21K13902), and JapanE-FG02–08ER54999, DE-AC02‐09CH11466, and DE-FG02‐97ER5.

This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. 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 U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.

The authors have no conflicts to disclose.

Tatsuya Kobayashi: Conceptualization (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Writing – original draft (lead). Zheng Yan: Data curation (equal); Investigation (equal); Supervision (equal); Validation (equal). George R. McKee: Data curation (equal); Investigation (equal); Supervision (equal); Validation (equal). Max E. Austin: Data curation (equal). Brian A. Grierson: Data curation (equal). Punit Gohil: Data curation (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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