Investigation of core transport changes in DIII-D discharges with off-axis T e profile peaks

DIII-D discharges that transition to H-mode solely with off-axis electron cyclotron heating (ECH) often exhibit strong off-axis peaking of electron temperature profiles at the heating location. Electron heat transport properties near these off-axis temperature peaks have been studied using modulated ECH. The Fourier analyzed electron temperature data have been used to infer electron thermal diffusivity. Comparisons with numerical solutions of the time-dependent electron thermal equation find that the data are consistent with a narrow region with electron diffusivity χ e an order of magnitude lower than the average value across the plasma, suggesting an electron internal transport barrier (ITB) near the ECH heating location. Detailed profile analysis and equilibrium reconstructions suggest that the formation of these ITBs are correlated with off-axis values of the safety factor q being near 1. Furthermore, the ECH driven H-mode discharges demonstrate more rapid electron heating rate near the ECH deposition location than L-mode discharges with higher auxiliary ECH heating power. Additional modeling attributes this difference to the modification of electron heat transport in the core at the L-H transition, which also sustains the off-axis electron temperature peaks.


Introduction
Plasma transport dictates the degree of plasma confinement in tokamaks, and thus is a critical factor in achieving fusion power [1].In order to improve plasma confinement and increase fusion gain, high confinement modes (H-modes) [2], which are characterized by a pedestal region with reduced plasma transport near the plasma edge, have been explored and utilized.
Due to the strong dependence of energy confinement and fusion performance on pedestal parameters [3], many studies have been dedicated to the investigation of pedestal transport.On the other hand, the need for better understanding of transport mechanisms in the core remains.One of these mechanisms is the change in heat, momentum or particle transport induced by auxiliary heating such as electron cyclotron heating (ECH).Previous experiments performed on the Rijnhuizen Tokamak Project (RTP) tokamak with dominant off-axis ECH observed significantly hollow T e profile [4,5].These unusual T e profiles periodically form sharp ears, i.e., prominent off-axis maxima with large T e gradients on both sides of the peak.In addition, a recent study in the Large Helical Device (LHD) stellarator has observed quasi-steady-state hollow T e profiles when heating with off-axis ECH [6].These experimental results highlight a change in core plasma transport during the application of off-axis ECH.
Regarding the phenomenon observed on the RTP tokamak, previous modelings have linked electron thermal diffusivity χ e to safety factor q and suggested that the hollow T e profiles form when ECH is deposited precisely on top of an internal transport barrier (ITB) [7] located near a low order rational q surface [5,8,9,10].Further simulation effort confirmed the presence of negative convective heat flux in the core, which sustains the observed hollow profiles [11,12].An outward heat convection that sustains the hollow T e profile is also observed in the LHD experiment [6], but is not linked to the rotational transform profiles.While some questions regarding hollow T e profiles have been answered for the L-mode case, similar phenomena and modification of core plasma transport in ECH dominant H-mode discharges have not been closely examined.
A dedicated experiment was performed on DIII-D to study steady state hollow T e profiles with sharp gradient changes in H-mode discharges.Transport analysis highlights the presence of a region with reduced plasma transport, which is the characteristic of an ITB, near the plasma core during off-axis T e peaking.Simulation efforts using a linear transport model also indicate a difference in core heat transport between L-mode and H-mode discharges.The present work aims to provide quantitative experimental data in order to promote theoretical investigation into the formation and stability of these unusual profiles.The experimental setup and results for this dedicated experiment are presented in section 2. Comparisons with the transport model is shown in section 3. Finally, a conclusion will be given in section 4.

Dedicated experiment
A dedicated experiment was performed on the DIII-D tokamak to study the unusual off-axis electron temperature peaks observed in ECH dominant Hmode discharges (see figure 1(a)).Previous studies [13,14] on electron energy transport during off-axis ECH experiments were performed in L-mode.This experiment focuses on the ELM-free phase after a purely ECH-driven L to H-mode transition (figure 2).The plasma is in a lower single null configuration with elongation κ = 1.8 and average triangularity δ ∼ 0.5.The line averaged electron density is low during the initial ohmic phase, ne ≈ 1.9 × 10 19 m −3 .The toroidal magnetic field is set to B t = 1.8 T with plasma current I P = 0.75 MA, the major radius is R 0 = 1.68 m, and the minor radius is a = 0.61 m.The resulting safety factor is q 95 ∼ 6.7, and the normalized plasma pressure is β N ∼ 1.1 after H-mode transition.Five gyrotrons were used to launch 2.8 MW of ECH power at 110 GHz with X-mode polarization.In some discharges, one gyrotron was modulated, resulting in the ECH power cycling between 2.1 MW and 2.7 MW.While the neutral beam injection (NBI) heating power was not zero, only short 10 ms NBI "blips" every 100 ms were used for diagnostic purposes.These short pulses did not provide substantial heating or alter the plasma states significantly.
The radial n e and T e profiles are measured with Thomson scattering [15] every 12.5 ms.T e is also measured with an electron cyclotron emission (ECE) radiometer [16] at a higher time resolution every 0.2 ms.The carbon impurity ion temperature, density and toroidal rotation velocity are measured with charge exchange recombination (CER) spectroscopy [17].The ion parameters are also calculated using linear interand extrapolation of the available CER measurements.The TORAY-GA ray-tracing code [18] was used to determine the ECH power deposition profiles and deposition location ρ dep (normalized flux coordinate).Equilibrium reconstructions are created with the EFIT code [19] utilizing external magnetics data and kinetic profile constraints from TRANSP modeling [20,21].Internal motional Stark effect (MSE) [22] data is not always included as a constraint since the measurement is only available during NBI diagnostic "blips".The safety factor q profiles are then obtained from these reconstructions.

Observation of off-axis electron temperature peaks in ECH heated H-mode discharges
When the ECH is applied at 1300 ms near ρ dep ∼ 0.4, an L-H transition occurs within 50 ms, indicated by the drop in D α emission intensity in figure 2(b).Figure 2(c) shows the evolution of electron temperature measured by ECE near the magnetic axis (ρ ∼ 0.05), near the peak (ρ ∼ 0.3), and by Thomson scattering on top of the pedestal (ρ ∼ 0.85).The first 10 ms diagnostic NBI pulse is injected 200 ms (300 ms in some discharges) after ECH application to avoid the effect of NBI heating on plasma states.The T i profile (figure 1(c)) is centrally peaked at this time.The T e ratio between off-axis peak and core ( Te(ρ∼0. 3) Te(ρ∼0.05) ) as well as T e ratio between core and pedestal (log 10 Te(ρ∼0.05)Te(ρ∼0.85) ) are shown in figure 2(d).When ECH is turned on, electron temperature grows faster near ρ dep than inside ρ ∼ 0.23, which is the approximate sawtooth inversion radius observed by ECE during the ohmic phase.Consequently, the ratio between off-axis peak and core in figure 2(d) quickly increases and becomes larger than unity, indicating the presence of an off-axis electron temperature peak.The line-averaged electron density (figure 2(b)) increases on a time scale similar to the core electron temperature.Both electron temperature and density reach equilibrium approximately 250 ms after ECH turns on.The T e ratio between off-axis peak and core (figure 2(d)) also decreases below unity around this time.The T e ratio between core and pedestal initial drops due to the formation of T e pedestal, then remains relatively constant afterwards.In figure 2(c), we observe similar T e growth rates at the core (ρ ∼ 0.05) and on top of the pedestal (ρ ∼ 0.85) while T e growth rate near the off-axis peak (ρ ∼ 0.3) is much higher.This difference suggests that the growth of the off-axis T e peak is not caused by the formation of the pedestal alone.
Since high power radio-frequency (RF) heating can produce non-maxwellian electron distribution functions (f e ) that distort the ECE signal near the ECH deposition location [23,24], it is fair to ask if the off-axis peaks observed in figure 1(a) could be caused by non-thermal high energy electrons created by the applied ECH.To confirm the thermal nature of the ECE electron temperature measurements, we compare the experimental data from ECE and Thomson scattering.Figure 3 shows the electron temperature measured by ECE and Thomson scattering at a time slice when the off-axis T e peak is observed.In this example, Thomson scattering observes an off-axis peak around the same ρ value with similar magnitude as the ECE data.T e from Thomson scattering and ECE also match on both sides of the peak.In addition, the electron temperature peak is clearly observed on both sides of the magnetic axis with roughly symmetrical location and magnitude in figure 1(a).If f e were non-Maxwellian, it would generally be expected to exhibit a strong asymmetry in ECE-Te profile measurements [23].Since no asymmetry is observed, and there is  good agreement with Thomson scattering, the electron distribution function is presumed to be Maxwellian.
T e (keV)  and the high field side (HFS) of the magnetic axis, respectively.At t − 35 ms, before the ECH is applied, we can see an electron temperature profile peaked inside ρ = 0.1.Approximately 20 ms after the ECH is applied, the previously mentioned off-axis electron temperature peak can be observed.Figure 4 shows that the largest change in electron temperature after ECH turns on happens around ρ = 0.3 while T e change is smaller inside ρ = 0.2; T e then continues to grow over the entire radial profile until approximately t+100 ms, when the peak T e starts to saturate and remains relatively stationary for the next ∼ 60 ms; T e inside ρ = 0.2 continues to grow.It should be noted that the location of off-axis T e peak (ρ ∼ 0.3) is different from the ECH deposition location ρ dep ∼ 0.4.This behavior is different from the RTP [4] and LHD [6] experiments, where the off-axis T e peaks coincide with ρ dep .
The plasma enters a grassy ELM phase at around t + 160 ms, and T e near ρ = 0.3 starts to gradually decay.At t + 225 ms, before the first major ELM event at t+227 ms, the off-axis peak is still observed in figure 1(a).It is worth-noting that the 3 outermost ECE channels on the LFS are experiencing density cutoff, so the ECE measurements outside ρ = 0.3 at t + 225 ms in figure 1(a) are likely lower than the actual T e values.After the ELM event at t + 227 ms, the T e profile becomes flattened inside ρ = 0.3 and the off-axis peaks are no longer clearly visible.Nevertheless, the off-axis T e peak lasts ≈ 200 ms, which is much longer than the electron energy confinement time τ Ee ≈ 60 ms.
Figure 5 shows the time history of experimental parameters for a discharge with intermittent H-mode transition.In this rare case, the plasma briefly transitioned back into L-mode between 1395 ms and 1415 ms.The D α emission intensity in figure 5(b) shows a major event at approximately 1400 ms; the calculated H 98y2 factor, which is the normalized energy confinement time with respect to the τ E,98y2 scaling [3], also decreases to 0.4 in figure 5(d), which is lower than during the ohmic phase.As the discharge back transitions to L-mode, the growing off-axis peak quickly disappears; in figure 5(c) and figure 5(d), we can see that T e near ρ ∼ 0.3 quickly decreases below T e inside the core and their ratio becomes less than unity between the two vertical dotted lines.Immediately after H-mode is recovered around 1415 ms, T e near ρ ∼ 0.3 increases and the off-axis peak is observed until the ELM event at 1550 ms.It should also be noted that this discharge first entered H-mode at a later time (∼ 1350 ms) than the discharge shown in Fig. 2 (∼ 1330 ms).Due to these delays, the diagnostic NBI injection at 1500 ms is able to measure T i when the off-axis T e peak is fully developed (figure 1(c), red circles).There is no obvious difference compared to the T i profile (figure 1(c), black squares) when the off-axis T e peak is decaying.

L-mode comparison
The experiment is also performed in L-mode for comparison.In these discharges, the lower triangularity is increased from 0.5 to 0.6, and the average electron density ne during the ohmic phase is decreased from 1.9 × 10 19 m −3 to 1.4 × 10 19 m −3 .These changes raise the L-H threshold, causing the discharge to remain in L-mode with up to 2.8 MW of ECH power.Figure 6 shows a pair of L-mode discharges with 1.5 and 2.8 MW of ECH heating power.In both cases, electron density remains the same after ECH switch-on.No off-axis peak is observed during the low power L-mode discharge; the ratio in figure 6(e) stays less than unity.It is worth-noting that an hollow T e profile is observed in the high power L-mode discharge.However, the electron heating rate near ρ dep is slower than that in H-mode discharges with lower auxiliary ECH power.No central T e cooling was observed during the formation of hollow T e profiles (Fig. 6(d)), which is a marked difference from previous RTP experiments [4].Power balance analysis from ONETWO [25] also shows that heat transfer from electrons to ions does not increase after ECH switch-on.As a result, the hollow T e profile is not due to additional energy sink near the magnetic axis.
In figure 6(d) we can see that T e near ρ dep grows larger than T e in the core.The ratio between the two is shown in figure 6(f) and becomes greater than unity at around 1235 ms until 1320 ms.Near the off-axis T e peak, the normalized electron collisionality ν * e ≪ 1 and is comparable to the ν * e in the H-mode discharges.However, this off-axis peak is much less prominent and persists for less time than its counterpart in Hmode discharges; as in figure 2(d), the ratio increases to approximately 1.5 and is greater than unity for more than 200 ms.The difference in off-axis T e peak evolution between L-mode and H-mode discharges with similar ν * e suggests that collisionality is unlikely the driving force of core transport changes.
It should be noted that we observe a brief L-H transition in L-mode discharges with more than 2 MW of ECH during this campaign.For example, the discharge shown in Fig. 6(b) briefly entered H-mode around 1285 ms, indicated by the oscillation in D α emission intensity (see figure 6(b)).This transition caused a quick rise in T e near ρ dep ∼ 0.40 (figure 6(d)) at the same time and extended the duration of off-axis peak shown in Fig. 6

(f).
A similar behavior can be observed during the intermittent H-mode discharge shown in figure 5.In figure 5(c), we can clearly see an increase in the T e growth rate near ρ ∼ 0.33 after the first L-H transition around 1350 ms while the rate of increase of T e near the magnetic axis (ρ ∼ 0.05) remains the same.This change in T e response only has a delay time of a few milliseconds or less compared to the drop in D α emission intensity, which indicates that there is a fast reduction in local transport.From these observations, we hypothesize that the growth of the off-axis T e peak is the result of local transport changes in the core after the L-H transition at the edge.Qualitatively, this suggests that the prominence and extended lifetime of the off-axis peak is related to L-H transition.

Observation of internal transport barrier
The sustained steep electron temperature gradient ∇T e on both sides of the off-axis peak is a signature of reduced electron heat transport and suggests that an ITB has formed in the region.To confirm the presence of the ITB, we compare changes of T e profile induced by perturbations before and after the off-axis peak disappears.Since the time scale of these changes is faster than the acquisition rate of Thomson scattering measurements, this section focuses on the experimental T e data from the ECE radiometer.Two types of perturbative heat pulses are analyzed: cold pulses induced by ELM events and modulated ECH (MECH).Figure 7 shows the impact of ELM event on T e profiles (a) with and (b) without the off-axis peak.In figure 7(a), notice that the T e profile inside ρ ∼ 0.35 at 1350 ms remains the same as 1343 ms, before the ELM event.From 1350 to 1360 ms, only T e between ρ ∼ 0.3 and 0.4 has visibly decreased.It is evident that there is a delay in T e drop approaching the T e peak at ρ ∼ 0.3.Compare figure 7(b) with figure 7(a): ECE channels outside ρ ∼ 0.3 in figure 7(b) show similar T e reduction during the ELM event without any visible delay.This observation suggests that the cold pulse caused by the ELM event is damped as it propagates through the region with high ∇T e .Qualitatively, this supports the existence of an ITB in the region surrounding the off-axis T e peak.
It is possible to quantitatively infer the presence of this ITB from ECE T e data in discharges with MECH.One discharge with MECH is shown in figure 2. In this example, the MECH is deposited off-axis near ρ ∼ 0.3 and varies slightly during the shot due to electron density evolution.The gyrotron is modulated at 100 Hz as a square wave with 50% duty cycle (∆t = 10 ms).The applied MECH periodically provides a localized heat deposition to electrons, creating an oscillation in T e without affecting n e .The T e time traces are analyzed with standard fast Fourier transform (FFT) techniques, and we can observe the propagation of the heat pulses.
Figure 8 shows the extracted amplitude (A) and phase lag (ϕ) profiles of the heat pulse at the modulation frequency (f = 100 Hz).The signal to noise ratio for FFT profiles at higher harmonics is much lower than the first harmonic, and the amplitude profiles do not show clear peaks.Nevertheless, we can compare the first harmonic FFT profiles during different time intervals of the same discharge.The first FFT time interval (1313 − 1383 ms), during which the off-axis T e peak is present, is limited to 7 modulation cycles to avoid the effect of drifting ECE channel (figure 8  ms) of 10 cycles is used when the plasma is in steady state and T e is peaked inside the core (figure 8(b)).
In figures 8(a) and 8(b), the FFT amplitude is the highest and the phase is the lowest at the same position, which agrees with the calculated MECH deposition location.This confirms the estimated MECH deposition profiles calculated with TORAY-GA.Moreover, it allows us to assess that there is no significant heat convection in this region.In the presence of strong heat convection, which was observed in previous RTP results [26,12], the first harmonic amplitude peak will shift inward or outward relative to the MECH deposition location.In contrast, the amplitude and phase profiles shown in figure 8 have characteristics of diffusive transport: the amplitude decreases and phase increases away from the deposition location.
In cylindrical geometry, the heat pulse diffusivity χ HP e can be calculated using the amplitude A and phase ϕ with [27]: where ω = 2πf , and r is the minor radius of the measurement location.ϕ ′ and A ′ /A are estimated at ρ ∼ 0.2 by linearly interpolating ϕ and ln(A) around the location of interest.The fitted diffusivities at ρ ∼ 0.2 are 0.16 ± 0.03 m 2 /s when the off-axis T e peak is present (figure 8(a)) and 2.5 ± 0.8 m 2 /s at the later time without the off-axis T e peak (figure 8(b)).
Although the exact values of the diffusion coefficient are uncertain, comparison between the two time intervals accurately determines the relative magnitude of diffusion coefficients.Figure 8(a) shows a sharp drop in A and rise in ϕ on both sides of the off-axis T e peak, which matches the regions with high ∇T e in figure 1(a).The heat pulse becomes strongly damped when it propagates through the ITB.There is also a discontinuity in the A and ϕ slopes near the foot of the off-axis T e peak at ρ ∼ 0.2.In contrast, figure 8(b) shows a different behavior: after an initial A drop and ϕ rise, the slopes of A and ϕ profiles are less steep than those in figure 8(a) and have no clear discontinuity.This indicates that, when the off-axis T e peak is present, there is a region with reduced heat diffusivity between ρ = 0.2 and 0.4, which is consistent with the existence of an ITB.

Initial comparison with transport model
Motivated by observations in the previous section, we analyze the experimental result using a linear transport modeling code.This simulation effort aims to derive radial diffusivity χ e and convection velocity v e profiles that would reproduce the off-axis T e peaks and quantify transport changes driven by ECH application.
The code is constructed to solve the timedependent electron thermal diffusion equation in cylindrical coordinates.q e and S e denote the electron thermal flux and net input power to electron.
Radial S e profiles are obtained using power balance calculations by ONETWO and TORAY-GA, which account for Ohmic and ECH input power, radiated loss and electron-ion energy exchange.In this simulation, n e is assumed to be constant and only T e is simulated over time.The electron thermal flux q e can be described using a simple model −q e = n e χ e ∇T e + v e n e T e where χ e and v e denote the electron heat diffusivity and electron heat convection velocity.Based on experimental observations presented in section 2.1, we divide the simulation into three phases: ohmic phase, ECH pre H-mode phase and ECH Hmode phase.In the ohmic phase, we assume v e = 0 and reproduce the steady-state ohmic T e profile using a purely diffusive model.After the ECH is turned on, we invoke a heat pinch inside the core.Based on previous RTP modeling works [10,12] and the observation that radiated loss is much smaller than the Ohmic heating power density (figure 9), we expect the existence of an outward heat convection inside the off-axis T e peak.In addition, the inward shift of T e maximum relative to ρ dep suggests that heat convection is inward around ρ dep .Thus, to model the heat pinch and simulate the effect of convection, we use two parameters v 1 and v 2 ohm P rad #137481 Figure 9.Time evolution of Ohmic heating power density P ohm and radiated loss P rad calculated with TRANSP near the magnetic axis at ρ = 0.21 in an H-mode discharge.The vertical dashed line indicate the time ECH is turned on (1300 ms).
to create v e input profiles of the form: ρ c is chosen to be at the foot the off-axis peaks, and the rest of the v e profile is generated using linear interpolation.The χ e profile is also changed in response to the application of ECH.In the ECH pre H-mode phase, T e starts from the Ohmic profile, grows over the radial profile, and forms the initial offaxis T e peak.35 ms after the ECH is switched on, the simulation enters the ECH H-mode phase.In the third phase, we continue from the pre H-mode offaxis peaked profile and recreate the experimentally observed T e profile evolution.Both the χ e and v e profiles are modified at L-H transition.
To mimic the effect of ECH, S e profiles are assumed to be constant except at the start of ECH application.
This simplification reduces the free parameters to three χ e profiles and two v e profiles.Using S e , χ e and v e profiles as inputs, the code solves Eq. 2 numerically using the Crank-Nicolson method to derive the T e profiles.The χ e and v e profile inputs are then optimized to minimize the difference between simulated T e profile and the experimental one.

Modeling results
The simulated and experimental T e profiles are shown in figure 10. Figure 11 shows the associated χ e and v e input profiles that reproduce the off-axis T e peak evolution in an H-mode discharge.Although this simulation effort recreates the experimental profile, it should be noted that this model has i!" # I$%& '( #137503 Figure 10.Optimized results of linear simulation.Experimental (symbols) and simulated (solid lines) Te profiles for H-mode discharge 137503 during ohmic phase (blue squares), during ECH pre H-mode phase (green circles), and after L-H transition (red diamonds and black crosses).ECH is turned on at 1300 ms.L-H transition occurs at approximately 1335 ms.Safety factor q profile during off-axis peaking is also shown (dashed line).
many simplifications and free parameters to uniquely determine the transport coefficients.
In figure 11(a), we observe a depression in χ e profile around ρ ∼ 0.3 during ohmic and ECH phases.The location of this χ e well during the ohmic phase agrees with the approximate sawtooth inversion radius (ρ ∼ 0.23) observed by ECE, suggesting that it is near the q = 1 surface.The χ e depression deepens after ECH turns on, and becomes widened after L-H transition.
In figure 11(b), we observe an inward convection on the outside of the T e peak and an outward convection on the inside of the T e peak.
The negative v e represents outward heat convection.This indicates that the convective component in equation 3 is transporting heat towards the T e peak against the T e gradient.The inward convection near ρ dep also shifts the T e peak towards the magnetic axis, creating a mismatch between the off-axis T e peak and ρ dep .After L-H transition, the inward convection near ρ dep is reduced while the outward convection near ρ c is slightly increased.This change in net heat convection can be caused by the reduction of inward heat pinch component, the increase of outward convection, or a combination of both.However, we currently do not have enough evidence to distinguish the two mechanisms from each other.Figures 10 and 11(a) show the q profiles obtained from EFIT equilibrium reconstructed with kinetic pressure and current constraints.In figure 11(a), we observe the q = 1 surface near the inside foot of the ITB and a flattened q profile with value close to 6/5 near the outside edge of the ITB. Figure 12 shows the time evolution of T e measured by 5 ECE channels inside ρ = 0.3 during off-axis T e peaking.T e crashes are observed inside ρ = 0.1 and inverted sawtooth oscillations are observed at ρ ∼ 0.22.Since T e profile is flat inside ρ = 0.2, the sawtooth oscillation amplitude is below the ECE noise level for channels located between ρ = 0.1 and ρ = 0.2.Nonetheless, this observation confirms the existence of q = 1 surface near ρ ∼ 0.2 during off-axis T e peaking.
Previous modeling efforts on off-axis T e peaks in the RTP tokamak have found similar thermal barrier around a low order rational q surface when using a qcomb model, in which the χ e profile is a function of q and consists of a series of χ e wells centered around low order rational q values [8].It should be noted that the location of off-axis T e peak coincide with ρ dep and a low order rational q surface in the RTP cases.In contrast, the off-axis peaks are shifted inward relative to ρ dep in this study.This suggests that the ITB observed in Hmode discharge may not be characterized with a single q value; the enhanced ITB is likely a collection of two or more ITBs centered around different low order rational q surfaces between q = 1 and q = 2. Unfortunately, internal MSE data is not available as a constraint during these time slices, and the q profiles shown have large uncertainty.It is alternatively possible for q to be around 1 between ρ ∼ 0.2 and ρ ∼ 0.4, which means the ITB corresponds to a single low order rational value q = 1.However, TORAY calculation shows that ECH is deposited at ρ dep ∼ 0.4, and the current drive is localized between ρ ∼ 0.3 and ρ ∼ 0.5.This observation led us to incline towards the first hypothesis since we do not expect the q profile to be strongly modified between ρ ∼ 0.2 and ρ ∼ 0.3 without significant current drive.Provisionally, we hypothesize that the presence of low-order rational q surfaces and flattening of q profile inside ρ dep during L-H transition leads to the observed core transport changes in ECHdriven H-mode discharges.
It is noteworthy that χ e at ρ ∼ 0.2 is comparable to the value extracted using FFT analysis in section 2.3.The consistency of transport coefficient provides some confidence in the capability of this simulation.Although this model does not include many aspects of ITB physics, it allows us to qualitatively access formation of off-axis T e peaks and provides further evidence that the experimentally observed off-axis T e peaks are caused by the presence of ITB and an outward heat convection inside the core.off-axis peak.After the L-H transition, the off-axis T e peak continues to grow and T e gradient is strongly negative between ρ = 0.2 and ρ = 0.3.In the L-mode discharge, the off-axis T e peak stop growing and −∇T e changes from negative towards positive.

Transport changes at L-H transition
In the simulation, changes to the χ e and v e input profiles at L-H transition are required to reproduce the experimental T e behavior.If no modification to the input profiles is made, the simulation fails to capture the growth of off-axis T e peak.The dashed line in Fig. 13(a) shows the simulated T e profile after evolving Eq. 2 for an additional 60 ms using the input profiles from the ECH pre H-mode phase.Even though these input profiles can reproduce the initial formation of off-axis T e peaks, the T e profile will relax to a monotonic one.This type of behavior is observed in L-mode discharges with off-axis peaks, as shown in Fig. 13(b).
These observations suggests that the sustainment of strongly negative T e gradient on the inside of the T e peaks can not be explained with the presence of outward heat convection alone.To reproduce the experimentally observed time evolution of T e peaks, either a transport change or additional electron heat flux is required inside the core after L-H transition.

Conclusion
In summary, unambiguous signatures of core electron heat transport barriers have been seen in DIII-D H-mode discharges triggered solely with electron cyclotron heating.This is clearly evidenced with observations of enduring hollow T e profiles and abrupt phase jumps in electron heat pulse analysis in these plasmas.
In addition, the difference in electron temperature evolution between L-mode and H-mode cases confirms that the transition to H-mode is a key part of sustaining the off-axis T e peaks.Comparison with a linear transport model suggests that there is a change in core electron heat transport during L-H transition.This observation is consistent with previous studies [28,29] that observe prompt transport change and confinement improvement in the plasma core at L-H transitions.The work has implications for future tokamak devices that intend to reach the H-mode state with ECH as the dominant auxiliary heating method.The exact mechanisms of ITB formation and transport change in this class of discharge remain unclear.
One potential trigger of ITB is the change in q profile.For example, integer q min crossing [30] and non-monotonic q profile [31] can both cause the onset of ITBs, but we are unable to validate this with experimental data due to the lack of MSE diagnostic measurements during L-H transition.Another likely cause of transport change is the flattening of electron density gradient and the reduction of associated density gradient driven turbulence during L-H transition.In the dedicated experiment, the core T e response to ECH changes extremely fast after L-H transition.These observations are consistent with the suppression of electron microinstabilities, leading to the improved confinement in the plasma core.This type of stabilization effect has been observed in simulation works of cold-pulse experiments [32].
Furthermore, the strongly negative T e gradient on both sides of the T e peaks can be explained with the presence of convective terms in electron thermal transport.This agrees with previous RTP and LHD results [4,12,6].However, it is uncertain whether the same mechanisms give rise to the convective countergradient transport.The RTP experiments were in Lmode with high density and ν * e ≃ 1, whereas ν * e ≪ 1 in DIII-D.The application of ECH in RTP also had a large impact on plasma current due to its relatively small size.In contrast, the LHD discharges were almost current-less with no significant current change due to ECH.
In the future, it would be good to obtain measurements of turbulent fluctuations in the apparent barrier region in the core that could verify cause and effect of the transport reduction; these were not available in the experiments presented here.Experiments in different parameter spaces and with on-axis ECH would also allow projections of this phenomenon's potential impact on ITER.Additionally, enhancements to turbulent transport modeling codes to be able handle non-standard profiles, like the ones seen in this research, would enable clarification of whether the barrier physics is related specifically to current or density profile physics.opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Figure 1 .
Figure 1.Samples of (a) Te profile measured by ECE, (b) ne profile measured by Thomson scattering, and (c) T i profiles measured by CER in off-axis ECH heated H-mode DIII-D discharges.The negative ρ values in (a) indicate the high field side of magnetic axis.T i profile for discharge 137487 in (c) is measured when strong off-axis Te peak is present.The steadystate ECH deposition profile (red dashed line, in a.u.) is also shown in (c).The experimental data clearly shows sustained off-axis peaking of Te after ECH is applied at t = 1300 ms close to ρ ∼ 0.4 on high field side.

Figure 2 . 137503 Figure 3 .
Figure 2. Time history plot of (a) injected neutral beam, ECH power and plasma current I P , (b) line averaged electron density ne and a Dα signal, (c) Te measured by ECE near the peak (red, ρ ∼ 0.3), at the core (blue, ρ ∼ 0.05), and by Thomson scattering on top of the pedestal (green, ρ ∼ 0.85), and (d) ratios of Te measurements in (c) for one of the H-mode discharges with modulated ECH.

Figure 4 .
Figure 4. 2D plot of the fitted (versus ρ) electron temperature from 1205 ms to 1605 ms.The vertical dashed line indicate the time ECH is turned on (1300 ms).ECH is injected close to ρ ∼ 0.4.

Figure 1 (
Figure1(a) and 4 show the evolution of electron temperature profiles before and after the ECH is turned on at t = 1300 ms.The positive and negative ρ values in figure1(a) indicate the low field side (LFS) and the high field side (HFS) of the magnetic axis, respectively.At t − 35 ms, before the ECH is applied, we can see an electron temperature profile peaked inside ρ = 0.1.Approximately 20 ms after the ECH is applied, the previously mentioned off-axis electron temperature peak can be observed.Figure4shows that the largest change in electron temperature after ECH turns on happens around ρ = 0.3 while T e change is smaller inside ρ = 0.2; T e then continues to grow over the entire radial profile until approximately t+100 ms, when the peak T e starts to saturate and remains relatively stationary for the next ∼ 60 ms; T e inside ρ = 0.2 continues to grow.It should be noted that the location of off-axis T e peak (ρ ∼ 0.3) is different from the ECH deposition location ρ dep ∼ 0.4.This behavior is different from the RTP[4] and LHD[6] experiments, where the off-axis T e peaks coincide with ρ dep .The plasma enters a grassy ELM phase at around t + 160 ms, and T e near ρ = 0.3 starts to gradually decay.At t + 225 ms, before the first major ELM event at t+227 ms, the off-axis peak is still observed in figure1(a).It is worth-noting that the 3 outermost ECE channels on the LFS are experiencing density cutoff, so the ECE measurements outside ρ = 0.3 at t + 225 ms in figure1(a) are likely lower than the actual T e values.After the ELM event at t + 227 ms, the T e profile becomes flattened inside ρ = 0.3 and the off-axis peaks are no longer clearly visible.Nevertheless, the off-axis T e peak lasts ≈ 200 ms, which is much longer than the electron energy confinement time τ Ee ≈ 60 ms.Figure5shows the time history of experimental parameters for a discharge with intermittent H-mode transition.In this rare case, the plasma briefly

Figure 5 .
Figure 5.Time history plot of (a) injected neutral beam, ECH power and plasma current I P , b) line averaged electron density ne and a Dα signal, (c) Te measured by ECE near the peak (red, ρ ∼ 0.33) to Te at the core (blue, ρ ∼ 0.05), (d) ratio of the two Te measurements in (c) and the calculated H 98y2 confinement factor for the dithering H-mode discharge.This discharge briefly dropped out of H-mode inside the shaded region.

Figure 6 .
Figure 6.(a) and Time history plot of ECH power and a Dα signal for a pair of L-mode discharges with different ECH heating power.(c) and (d) Te measured by ECE channels close to the ECH deposition location (red, ρ ∼ 0.38) and inside the core (blue, ρ ∼ 0.05).(e) and (f) Ratio between the Te measurements in (c) and (d).

Figure 7 .
Figure 7. Radial Te profiles measured by ECE before (no symbol, black solid line), less than 5 ms after (circle, red dashed line) and more than 10 ms after (×, blue solid line) an ELM event (a) with and (b) without clear off-axis Te peak.The ELM events are at 1346 ms and 2517 ms.

Figure 8 .
Figure 8. Radial profile of first harmonic MECH amplitude (red triangles) and phase (blue circles) when (a) the off-axis Te peak is present (1313 − 1383 ms) and (b) after the off-axis peak has disappeared (3080−3180 ms).The solid black lines represent the linearly fits of φ and ln(A).The MECH deposition profiles calculated with TORAY are plotted in dashed lines.The change in MECH deposition location is due to electron density evolution.

Figure 13 Figure 11 .Figure 12 .
Figure 13  compares the evolution of T e profiles between H-mode and L-mode discharges after the formation of

Figure 13 .
Figure 13.Comparison of experimental Te profiles between (a) H-mode and (b) L-mode discharges at two times after the formation of off-axis Te peaks.In (a), the solid line is the simulation result during the ECH pre H-mode phase, and is the same as the one shown in figure 10.The dashed line is the simulation result at 1385 ms that uses the ECH pre H-mode χe and ve input profiles after L-H transition at approximately 1335 ms.