Decoupling of peeling and ballooning thresholds for pedestal stability and reduction in ELM frequency via enhanced turbulence with edge electron cyclotron heating in DIII-D

The edge localized mode (ELM) frequency (f ELM) decreased by 63% when electron cyclotron heating (ECH) deposition location is shifted from ρ = 0.4 to ρ = 0.8 in DIII-D discharges where the power ratio between neutral beam injection (NBI) and ECH (P NBI/P ECH) is kept at ∼1. The performance of the pedestal in the ECH heated case is compared with a pure NBI reference discharge while keeping the total input power constant. All these discharges are performed at balanced input torque conditions. Furthermore, in the pure NBI discharge a strong decoupling of the peeling–ballooning (PB) thresholds is observed. The PB decoupling is preserved when the ECH is deposited at ρ = 0.8 and P NBI/P ECH ∼ 1, while the thresholds manifest a closed stability boundary when the ECH is deposited at ρ = 0.4. The inter-ELM pedestal recovery time is considerably larger for the ECH at ρ = 0.8 case. Increased pedestal turbulence is observed in beam emission spectroscopy (BES), Doppler backscattering and magnetic diagnostics for the ECH at the ρ = 0.8 case. Strong growth of a TEM-like mode is observed in BES and the mode growth is correlated with the decrease in f ELM. In view of these observations, the increased pedestal turbulence seems to be the plausible reason behind the delayed pedestal recovery following an ELM event in the ECH at ρ = 0.8 case, and the preservation of PB decoupling through temperature pedestal profile widening. TRANSP interpretative simulations show that the ECH at the ρ = 0.8 case is more susceptible to ITG/TEM turbulence.

The edge localized mode (ELM) frequency (f ELM ) decreased by 63% when electron cyclotron heating (ECH) deposition location is shifted from ρ = 0.4 to ρ = 0.8 in DIII-D discharges where the power ratio between neutral beam injection (NBI) and ECH (P NBI /P ECH ) is kept at ∼1.The performance of the pedestal in the ECH heated case is compared with a pure NBI reference discharge while keeping the total input power constant.All these discharges are performed at balanced input torque conditions.Furthermore, in the pure NBI discharge a strong decoupling of the peeling-ballooning (PB) thresholds is observed.The PB decoupling is preserved when the ECH is deposited at ρ = 0.8 and P NBI /P ECH ∼ 1, while the thresholds manifest a closed stability boundary when the ECH is deposited at ρ = 0.4.The inter-ELM pedestal recovery time is considerably larger for the ECH at ρ = 0.8 case.Increased pedestal turbulence is observed in beam emission spectroscopy (BES), Doppler backscattering and magnetic diagnostics for the ECH at the ρ = 0.8 case.Strong growth of a TEM-like mode is observed in BES and the mode growth is correlated with the decrease in f ELM .In view of these observations, the increased pedestal turbulence seems to be the plausible reason behind the delayed pedestal recovery following an ELM event in the ECH at ρ = 0.8 case, and the preservation of PB decoupling

Introduction
With the advent of high-temperature superconductors, it has been predicted that a 5 m, 10 T machine can generate 2.5 GW of power in steady state conditions [1].This is an estimate considering the plasma performance achieved by existing tokamaks.Any attempt to build a more compact fusion reactor requires an improvement in the energy confinement time.Thus, apart from the improvement of magnet technology, compact power plants need substantial improvement in confinement and, hence, this issue demands an immediate attention.
The issue of enhanced confinement is being addressed nowadays by developing the Super-H mode regime in tokamaks [2,3].A brief context of the Super-H mode is worth mentioning here to help understand the accessibility towards higher confinement.The EPED model [4][5][6], developed to predict the pedestal height and width in H-mode plasmas, hypothesizes the constraints for pedestal build-up towards the onset of an edge localized mode (ELM) event.The edge transport barrier in the outer few per cent of the confined plasma is the pedestal [2] and the ELMs are intermittent instabilities causing periodic and transient loss of energy and particles across the edge region of the confined plasma.The two-fold constraints in EPED prescribe that the pedestal growth is limited by: (i) the non-local peeling-ballooning (PB) modes of low to intermediate toroidal mode number and (ii) the local kinetic ballooning modes (KBMs).In other words, the EPED model can be thought of as a tool for solving two numerical equations for two unknowns like the height and width of the pedestal.The Super-H mode regime is predicted by EPED when multiple solutions are achieved, where the low-pressure solution refers to the conventional H-mode and the highpressure solution refers to the Super-H mode regime featuring higher pedestal height and width compared to the conventional H-mode [2].
Analysis of the pedestal stability using the ELITE code [7] shows the instability threshold in terms of a normalized pressure gradient, α (∝dp PED /dρ, ρ being the normalized plasma radius), and the pedestal current density J PED .Instabilities, manifested as ELMs, can be triggered by either increasing α (i.e., the ballooning branch) or J PED (i.e. the kink-peeling branch).The Super-H mode is accessed by strong plasma shaping and increasing the pressure gradient with collisionality along the kink-peeling branch.Strong shaping leads to a partial decoupling of the current-driven and pressure-driven instabilities, leading to a 'nose' in the typical α-J PED stability diagram, which is strongly amplified when the KBM constraint is also applied, as in the EPED model [2].
So far, the accessibility conditions for higher confinement and Super-H modes have been hypothesized and achieved experimentally [4].However, the role of pedestal turbulence in either facilitating or inhibiting the decoupling of the PB thresholds in the α-J PED stability diagram has not been addressed in detail.Further, to the best of our knowledge, the effect of decoupling on the ELM frequency via turbulence or vice versa has not been addressed so far.Under the standard H-mode scenario, the ELM frequency increases with density as the operating point rolls clockwise towards the ballooning branch of the stability diagram with increased collisionality and decreased bootstrap current, which contributes to the majority of J PED .On the other hand, a reduction in ELM frequency with an increase in density is observed in high-power DND discharges in DIII-D due to the decoupling of the peeling and ballooning branch limits and the absence of the ballooning branch limit altogether in the α-J PED stability space [8].
Delving further into the ELM frequency dependence, it has been observed earlier that the ELM frequency can be increased [9] or decreased [10] by electron cyclotron heating (ECH), depending on the heating mix (neutral beam injection (NBI) vs ECH), in DIII-D.The ELM frequency increased from 15 Hz to 59 Hz when 1.8 MW of core ECH (at ρ = 0.5) is added to 2.3 MW NBI heated discharge in DIII-D [9].It is concluded that additional ECH in the NBI heated discharge leads to the suppression of TEM-scale and increase in ITG-scale density fluctuations, respectively.In another experiment in DIII-D, it has been observed that the ELM frequency decreased by 40% in ECH (at ρ = 0.2) dominated plasmas compared to pure NBI plasmas under the same total input power conditions [10].It is summarized that an enhanced gradient of the electron temperature (∇T e ) excites the micro tearing mode (MTM)-like and/or TEM-like modes and hence increases turbulence-driven transport, thus resulting in delayed pedestal gradient recovery (mainly ∇T e ) following an ELM event, thereby reducing ELM frequency in ECH dominated discharges.In TCV, the ELM frequency has been observed to increase by a factor of 2 and the energy loss per ELM to reduce by the same factor when ECH deposition is shifted from the core to the pedestal region while keeping the total input power constant [11].Further, when ECH is applied at the edge of AUG plasmas, pedestal gradients relax, and ELM frequency increased without any appreciable change in the MHD stability boundary [12].Increased ELM frequency and a random mix of ELM sizes were also observed in KSTAR [13] when 0.4 MW of NBI power is replaced by 0.4 MW of core (presumably) ECH, thus keeping the total input power (1.5 MW) constant.Hence, the dependence of the ELM frequency on the ECH power level and deposition radius has been observed in several machines and some attempts were made to understand the varied ELM response from the turbulence and transport point of view, but the understanding is far from complete.In this work, two separate ECH power deposition locations, like ρ = 0.4 and 0.8, are considered on a shot-to-shot basis.The ECH power deposition profiles for the ρ = 0.4 and 0.8 depositions are shown in figure 1.Also, the heating mix ratio (P NBI /P ECH ) varies from 2 to 1.The results are compared with the pure NBI reference case.Note that the total power input is kept constant in all cases and the total torque input is kept at zero.By doing so, we try to address the following questions: (i) can we gain further control over the ELM frequency by changing the ECH deposition location and the heating mix ratio (P NBI vs P ECH )? and (ii) What is the role of turbulence-driven transport in determining the observed change in the ELM frequency and how does the turbulence affect the stability space?Finally, (iii) How does the turbulence interlink the change in the pedestal profiles, ELM frequency and the change in the stability space?
The paper is organized as follows: the experimental setup and variation in the plasma profiles in the pure NBI and ECH substituted discharges are introduced in section 2. Peeling ballooning stability of these different heating mix scenarios are shown in section 3.In sections 4 and 5 the inter-ELM recovery of the pedestal and the pedestal turbulence observed in magnetic probes, beam emission spectroscopy (BES) and Doppler backscattering (DBS) diagnostics are discussed, respectively.Transport scenarios are investigated with TRANSP simulations in section 6.Finally, the results are summarized and discussed in section 7.

Operating conditions
In this paper, low-power (∼3 MW), type-I ELMing, H-mode discharges in the ITER of similar shape [14] (ISS) in DIII-D are investigated.For the ECH power and deposition location scans, at 3000 ms of the discharge, the NBI power is decreased from 3 MW to 2.1 MW and ∼1 MW of ECH power is injected.Further, at 4000 ms, the NBI power is further decreased to ∼1.5 MW and ECH power is increased to ∼1.5 MW (figures 2(a) and (b)).Thus, there are two distinct phases in the ECH discharges, one from 3000 to 4000 ms where the ratio of NBI to ECH power, P NBI /P ECH is ∼2 and then from 4000 to 5000 ms, where P NBI /P ECH is ∼1.It is worth mentioning here that DIII-D is an elaborate ECH system involving several gyrotrons.These gyrotrons operate at 110 and 117.5 GHz [15].Note that NBI is optimized for core deposition.Here, black represents the NBI reference discharge while the discharges with ECH deposition locations at ρ = 0.4 and 0.8 are shown in red and blue, respectively.The total injected power in all of these discharges is kept constant at ∼3 MW.The ECH deposition location is varied between ρ = 0.4 and 0.8 in a dischargeto-discharge basis.The power deposition profile (referred to in figure 1) for the ECH discharges is calculated with TORAY [10,16].Hence, the ECH is deposited either at the core (ρ = 0.4) or more towards the edge (ρ = 0.8).Here, three representative discharges from the data set will be discussed.Discharge #184429 is representative of the pure NBI reference discharge, while discharges #184437 and #184431 are representative discharges for the core and edge ECH cases, respectively.Figures 2(a) and (b) show the time evolution of the NBI and ECH power levels in the three representative discharges.The line-averaged density n e ave in the quasi-stationary phase of the pure NBI reference discharge is at 4.8 × 10 19 m −3 .In the ECH case n e ave is at ∼3.6 × 10 19 m −3 during the ECH phase due to the density pump-out [10,17,18].
Plasma current I p , toroidal magnetic field B T and hence q 95 is kept constant and are these discharges at 1 MA, 2 T and 6 respectively.The normalized plasma pressure, β N (= βaB T /I p , a being the minor radius and β being the ratio of the plasma pressure to the magnetic pressure, expressed as a percentage) is ∼1.4 in the pure NBI discharge, while it is ∼1.0 and ∼0.9 for the core and edge ECH discharges.These discharges are intended to operate with balanced input torque.However, the pure NBI and the low ECH power phases have a total input torque of 0.5 Nm while the high ECH power phases have a total input torque ∼0 Nm.
A multi-chord, multi-pulse Thomson scattering (TS) system is used to measure the profiles of electron density n e and electron temperature T e along a vertical chord in the machine [19].Pedestal measurements are made in the upper part of the vessel, which has a high density of chord views to provide good resolution of the n e and T e profiles.An upgrade of the system in 2012 provides improved measurements in this region, including a spatial separation of chords of about 6 mm with a measurement spot size of less than 5 mm [20].In the outer midplane, the measurement spot size projects to about 3 mm (due to the smaller spacing of flux surfaces at the midplane than at the top of the machine).
For purposes of profile-fitting, multiple Thomson pulses are obtained during the phase of the discharge with steady operating conditions.Conditional averaging is used to obtain composite n e and T e profiles from multiple Thomson pulses during this phase to improve the statistics of the profile fits [21].The conditional averaging uses data from the last 20%-30% of the inter-ELM phases in order to best represent pedestal parameters just prior to an ELM crash.
The pedestal structural parameters of height and width for both n e and T e are obtained with a modified hyperbolic tangent (tanh) fit of the pedestal and near pedestal regions [22].The function used for this fit consists of a tanh to model the pedestal, a line with finite slope to model the region onboard the pedestal and a constant line to model the region outside the pedestal.As shown in [22], the pedestal height is the sum of the offset of the constant (background) term plus the vertical extent of the tanh function.The pedestal width is also obtained from the fit parameter and represents the width of the region of high gradients in the profile.The fitting process uses standard propagation of errors from individual Thomson measurements to compute error bars on the pedestal height and width parameters.Statistical error bars of individual Thomson measurements are obtained from the one standard deviation of noise due to electronics, photons, and detectors [19].Due to the combination of system design that produces high signal throughput with low background signal, comprehensive calibration techniques and the use of multiple Thomson profiles for the signal profile fit, the error bars of the fit parameters are , typically, quite small.
The time evolution of the pedestal parameters like the height and width for n e , T e and p e are shown in figures 2(c)-(h).The statistical errors in the pedestal parameters are obtained by propagation of errors from the measurement errors in the input TS data.The error percentages for these discharges are n e PED ∼ 2%-3%, T e PED ∼ 4%-6%, p e PED ∼ 4%-6%, n e WID ∼ 8%-19%, T e WID ∼ 10%-14% and p e WID ∼ 6%-10% respectively.The widths of n e , T e and p e are smooth using a moving average filter spanning over 30 ms.Some excursions in the width data are observed, especially in the case of ECH at ρ = 0.8 (blue) in the 3000-4000 ms phase, probably due to the high ELM frequency in this phase.Widths of n e , T e and p e appear to be highest in the case of the scenario when ECH is at ρ = 0.8 and P NBI /P ECH is ∼1 (blue trace).Electron collisionality at the pedestal top for the pure NBI discharge is 1.6, while that of both ECH discharges is 0.85.

ELM frequency variation
A wide variation in ELM frequency (f ELM ) is observed in these different phases of the heating mix (NBI vs. ECH) and ECH deposition locations.The ELMs can be observed in the Dα traces as shown in figures 2(i)-(k).Table 1 shows the variation of f ELM as a function of the heating mix and ECH deposition location.
In a pure NBI discharge, f ELM is 50 Hz.In the case of ECH deposition at ρ = 0.8, the phase with P NBI /P ECH ∼ 2 shows f ELM as 67 Hz, while for the phase with P NBI /P ECH ∼ 1 shows f ELM as 27 Hz.On the other hand, in the case of ECH /n GW ∼ 0.76, n GW being the Greenwald density limit = I p /πa 2 , a being the minor radius), low electron collisionality at the pedestal top (ν e * ∼ 0.85) and lower single null plasmas (type-II ELMs) are not expected for ECH discharges either [23][24][25].
In our earlier study with a further core deposition of ECH at ρ = 0.2, under balanced torque conditions, it has been observed that f ELM decreased by 40% and ELM spacing becomes more regular in time when heating is changed from pure NBI to predominantly ECH (P NBI /P ECH ∼ 0.33) in ISS plasmas [10].There also, the total input power is almost constant in the pure NBI and ECH dominated discharges.Note that in this recent experiment, we can achieve a condition of P NBI /P ECH ∼ 1 at most for both the ρ = 0.4 and at ρ = 0.8 ECH depositions respectively and could not dominate the heating mix with ECH, as done earlier.Henceforth, the pure NBI reference case, as well as the two ECH cases in the P NBI /P ECH ∼ 1 phases will be discussed in detail with occasional references to the P NBI /P ECH ∼ 2 phases.This is because in the P NBI /P ECH ∼ 1 phase the highest ECH power available is applied and the effect of mixing P NBI and P ECH is the most pronounced.

Pedestal profiles
In this section, the average pedestal profiles in the 70%-99% of the ELM cycle are discussed.With the pure NBI reference case being purely ion heated and the ECH being responsible for direct electron heating, one can expect a variation in the profiles of the electron and ion parameters in the pure NBI and NBI + ECH phases of the discharges.Figure 3 shows the pedestal profiles of the electron and ion parameters.The n e profile and its gradient (∇n e ) at the pedestal are shown in figure 3(a).The width of the n e pedestal is similar for the pure NBI and the edge ECH cases.However, the n e pedestal for the core ECH case is narrower.The dotted lines show the ∇n e plots for the three cases.The maxima of the ∇n e for the pure NBI and core ECH is similar while ∇n e of the edge ECH case is smaller.However, ∇n e for the pure NBI and the edge ECH cases are higher as compared to the core ECH case from the pedestal top and beyond the maximum gradient region towards the pedestal foot.Essentially, ∇n e is higher for the pure NBI and edge ECH cases from ρ = 0.92 ∼ 0.97 for the pure NBI and edge ECH cases as compared to the core ECH case, as shown by the shaded bar, and ∇n e is higher for the core ECH case only at a narrow radial extent towards the foot of the pedestal.
The solid and broken lines in figure 3(b) show the T e and ∇T e profiles respectively.Again, the T e profile is wider for the edge ECH case.Also, ∇T e is highest for the core ECH, but at a narrow region in the lower half of the pedestal.∇T e is, in fact, highest for the edge ECH case from the pedestal top and beyond the maximum gradient region (ψ = 0.92 ∼ 0.97), as shown by the shaded bar.The T i profiles do not show any appreciable difference as shown in figure 3(c).Wider pedestal of the n e and T e profiles for the edge ECH case is also reflected in the p e profile as shown in figure 3(d).Even though the ECH case is expected to be of lower n e and higher T e , and, hence, lower electron collisionality, and the bootstrap current density at the edge does not show much of a difference (figure 3(e)).Figure 3(f ) shows the T e /T i profiles.As expected, T e /T i is higher for the two ECH cases as compared to the pure NBI case.
There is a difference in the E r profile for the NBI case in terms of the E r well value and radial position as compared to the ECH cases, as shown in figure 3(g).Furthermore, the E r well is significantly shallower for the edge ECH case compared to the core ECH case.The E × B rotation (ω E ) is shown in figure 3(h).The absolute value of ω E and hence E × B rotation shear is the highest in the core ECH case.Hence, these observations lead to the hypothesis that the gradients being stronger in the edge ECH case for the majority of the pedestal width and the E × B shear being weaker for the edge ECH case, higher levels of pedestal turbulence are expected for the edge ECH case.We will verify this hypothesis later in sections 5 and 6 of the paper while investigating the turbulence and transport dynamics.

ELM frequency and energy loss per ELM
In this section we will discuss the energy loss per ELM observed in the experiments and its possible relationship with f ELM .Figure 4 shows the ELM-synchronized [10,26,27] evolution of the stored energy (W MHD ), calculated from the fast EFIT reconstructions in the 4200-5200 ms range for the P NBI /P ECH ∼ 1 phase with ECH at the core (red) and at the edge (blue) respectively.Note that we do not use the diamagnetic loop for fast stored energy estimation.This is because (i) it is outside the vessel conducting wall and so has a poor time response, (ii) it is compensated by a Rogowski measure of the toroidal field coil current which has a noise level larger than the ELM effect.Instead, we perform fast EFIT reconstructions using internal magnetic probes and flux loops on a 500 µs time scale.The equilibrium is recovered from an ELM on an MHD time scale which is a few tens of µs.The magnetic measurements used for the fast equilibrium reconstruction have 5 µs sampling but are smoothed over 50 µs.Typically, some transients, lasting around 100 µs, are seen in the stored energy that is likely associated with the equilibrium relaxation, but these are ignored in, for example, the ELM energy loss estimates.The recovery time of the stored energy between ELMs is , typically, much longer than the equilibrium relaxation time, usually at least tens of ms.
The ELM synchronization procedure involves the detection of ELMs in the Dα amplitude beyond a user-defined threshold.For ELMs larger than ∼20% of the largest ELMs in the Dα amplitude that are detected this threshold is identical for pure NBI as well as ECH substituted discharges.The threshold detection is demonstrated in figure 4(a) of [10].Data on the time series of the respective quantities (say W MHD in this case) for which the ELM-synchronized analysis is being performed is truncated on the left-hand side of the ith ELM peak to the left-hand side of the (i + 1)th ELM peak when the Dα amplitude goes above the threshold value.The time evolution of the respective quantities in the inter-ELM period is synchronized with the ELM-maxima for each ELM and then stacked together for all the ELMs in one composite time window.The ∆t = 0 ms in the time evolution of the pedestal parameters (figure 4) signifies the ELM maxima in the Dα trace.Hence, the time evolution of each of the concerned parameters is essentially constructed from all the ELMs, above the threshold and the corresponding inter-ELM periods for the selected time window.
The energy loss per ELM (∆W MHD ) is 0.012 MJ and 0.031 MJ for the core and edge ECH cases respectively.This makes ∆W MHD /W MHD 0.03 and 0.08 for the core and edge ECH cases respectively.It has been shown earlier in the ASDEX Upgrade that the higher the pedestal energy, the higher the ∆W MHD and hence the lower the f ELM (refer to figure 3 in [28]).However, in our case, the higher W MHD in the core ECH case (even though the difference is <10%) leads to lower ∆W MHD compared to the edge ECH case.
It has been shown earlier in the ASDEX Upgrade that the duration of the pedestal recovery phase, and hence f ELM depends inversely on the energy loss per ELM for type-1 ELMs, and this relation holds for a wide range of parameters and is independent of plasma triangularity [29].This relationship is further emphasized, and it is shown that increased triangularity leads to lower f ELM and larger energy loss per ELM [28].Howeverin this case, the error bars in f ELM are quite large and, hence, it posits the situation that even though the inverse relationship holds in general, for a given energy loss per ELM, a wide range of f ELM is possible.For example, refer to figure 5 of [28].It shows that for an energy loss of ∼7 kJ per ELM, f ELM can vary between ∼100 and 260 Hz.Similarly, for an energy loss of ∼3 kJ per ELM, f ELM can vary between ∼200 and 320 Hz.
Based on this inverse relationship, a 'leaky hosepipe model' is used to predict the energy loss per ELM [30].It can be seen in figure 6(b) of [30] that even though a straight-line relationship can be roughly recovered between the energy loss per ELM as predicted by the model and as observed in the JET experiments, there is a significant spread in the data.As an example, for the model with predicted loss of ∼0.7 MJ, experimental loss of ∼0.2-0.9MJ is observed.Further, in DIII-D, it has also been observed that the energy loss per ELM does not vary significantly with heating power even with an increase in f ELM [31].Hence, albeit with an overall inverse relationship, the energy loss per ELM might not serve as a necessary and sufficient condition for deciding f ELM .So, the question prevails like once a set of pedestal parameters are reached for a given set of operating conditions, what decides the f ELM and/or the ∆W MHD in the first place?More precisely, why does the core ECH case, sitting at a higher W MHD not produce even larger ELMs, compared to the edge ECH case, and thereby for larger ∆W MHD and lower f ELM ?Note that variation of ∆W MHD with n e ped or collisionality, as discussed in [32] is excluded in this section, as n e ped , T e ped and collisionality are not significantly different in the core and edge ECH cases.
Another important consideration is at what point in time is the inter-ELM evolution, an ELM onset is triggered?As per the PB model, an ELM is triggered as the destabilization of PB instabilities when the pedestal pressure gradient or edge current density reach a critical threshold [33].However, in several tokamaks like the ASDEX Upgrade, Alcator C-Mod, DIII-D and JET, it has been observed that ELMs are not triggered immediately even though the pedestal pressure gradient has reached the threshold level for ELMs and continues in a long metastable state prior to the eventual ELM onset [12,27,30,[34][35][36][37].In this context, it has been shown further in DIII-D that inter-ELM turbulence plays a critical role in deciding the length of the inter-ELM period [10,27,35] and hence f ELM .Hence, it is important to investigate the inter-ELM turbulence evolution and then try to ascertain how that could affect pedestal recovery and f ELM .
Before analysing the inter-ELM pedestal recovery and turbulence, it is worthwhile to investigate the PB stability of these cases.This is important as f ELM might depend on the operating point being either closer to the peeling or the ballooning threshold.

Peeling ballooning stability
As stated in section 2, the reference NBI discharge is a standard ELMing H-mode discharge in the ISS configuration.However, ELITE [7] analysis revealed that the peeling and ballooning thresholds are widely decoupled in this discharge.Figure 5 shows the PB stability for this discharge in the quasistationary phase.It is observed that the critical pressure gradient for ballooning is increased resulting in the decoupling of the peeling and ballooning thresholds.Such decoupling was observed earlier in DIII-D DND discharges [38] but with a significantly higher power (∼15 MW).The stability channel opens up due to decoupling and has provided the opportunity to achieve much higher pedestal pressure, like the Super-H mode regime [4], by carefully navigating through the channel.It is also shown that the decoupling increased by several factors such as (i) widening of the electron density pedestal, (ii) increasing q 95 , (iii) reducing d r sep towards zero and (iv) increasing power which seems to act through an increase in the ion diamagnetic stabilization level [38].
For a better understanding of the reason behind the decoupling in our NBI reference discharge, we compare this discharge with another standard ELMing H-mode discharge (#170868).Figure 5 shows the comparison of the stability for these two discharges.A detailed description of how the ELITE calculations are performed is given in [21].The stability boundary is determined by the ratio of the growth rate to the diamagnetic stabilization term on the grid of the normalized pedestal pressure gradient (α) and normalized pedestal current density (j N ), and then tracing the contour for which this ratio is 1 [21,39].The form of the diamagnetic stabilization derived from BOUT++ calculations, as discussed in [6,21], is used in this paper.Pedestal turbulence and transport of this discharge is well documented [9].Unlike the #184429 discharge, the #170868 discharge features a closed PB boundary, as shown in figure 5.There could be several reasons behind this difference in stability.Discharge #184429 (discharge #170868) features higher q 95 = 6 (=5), higher injected power, P inj = 3.2 MW (=2.2 MW), lower collisionality at the pedestal, ν e * ∼ 1.5 (∼1.9), lower injected torque T inj = 0.5 Nm (=2.2 Nm) and higher pedestal electron temperature T e ped ∼ 520 eV (∼420 eV) and hence pedestal electron pressure p e ped .There is a variation in the shape as well, as shown in figure 5. Line-averaged electron density, pedestal electron density n e ped and pedestal widths of electron density, temperature, pressure and plasma current are similar in these two discharges.
We present a comparison of the stability of the reference NBI discharge (figure 6(a)) with the core and edge ECH cases for the P NBI /P ECH ∼ 1 phase.Stability of the P NBI /P ECH ∼ 2 phase for both core and edge ECH discharges is also shown in figures 6(b) and (d) to show the progressive evolution of the stability as the heating mix is varied.For the core ECH case, there is a close stable PB boundary (figure 6(c)), while for the edge ECH case, the boundary is still marginally open (figure 6(e).Further, for both the pure NBI and the core ECH cases, the operating point is very close to the peeling boundary while for the edge ECH case, it is more deeply seated in the stable region.Note that the d r sep , q 95 and total power inputs in these three cases are similar.The main differences are in the n e ped and T e ped heights and widths.Since there is a difference in the n e ped and T e ped heights and widths among the three cases, we now intend to scan the pedestal height and widths of the pure NBI discharge to gain further insight into the decoupling of the PB boundaries.This scan can reveal the role of the pedestal profiles behind the preservation of the decoupling of the PB boundaries in the edge ECH case, as we move from the pure NBI case, while the decoupling is not preserved in the core ECH case.All the scans are done in the VARYPED module [40] starting with the kinetic EFIT [41,42] while keeping the total stored energy constant.In the first scan, the pedestal heights are kept unchanged and the n e ped width is varied.T e ped height and width remain unchanged.Figure 7(a) shows the variation in the stability boundaries and the corresponding n e ped and T e ped profiles in the onset.The n e ped and T e ped profiles of the core and edge ECH discharges are also shown with broken lines for reference.Contrary to Petrie's findings [38], it is observed that as the n e ped width is reduced progressively (0.01-0.03 in the normalized flux coordinate ψ), the decoupling increases.
Next, the T e ped width is scanned (0.02-0.04 in ψ) and n e ped height and width are kept unchanged.In this case, no appreciable change in the decoupling is observed with the steepening of the T e ped (figure 7(b)).The third and fourth scans are similar to the first two scans except that the n e ped height is scaled down and the T e ped height is scaled up to match those of the ECH discharges.The results obtained with the n e ped width scan (0.02-0.04 in ψ) with the scaled n e ped and T e ped emphasize the earlier observation that the channel to achieve higher pedestal pressure is more likely to open at steeper n e ped (figure 7(c)).However, the channel tends to close with a reduction in the T e ped width (0.01-0.05 in ψ; figure 7(d)).Hence, these scans reveal that for the core ECH case, the pedestal profile steepens and even though the reduction in the n e ped width would have helped to preserve the decoupling, the reduction in the T e ped width has pushed the decoupling to disappear.On the other hand, both the n e ped and T e ped widths are higher and as a combined result, the decoupling is preserved in the edge ECH case.Hence, the observations suggest that wider pedestal temperatures at lower pedestal densities and higher pedestal temperatures seem to be the main factors behind the preservation of decoupling in the edge ECH case.

Inter-ELM pedestal recovery
To understand the reason behind the decreased f ELM in the edge ECH case, ELM synchronized analysis [10,26,27] of the pedestal parameters is performed.The ELM synchronization analysis is described in section 2.4 earlier.First, we would like to present the ELM synchronized analysis of the pedestal electron density height, width, and maximum gradient, obtained from the high time resolution profile reflectometer [43] data (figures 8(a)-(c)).
The height of the density pedestal is higher than expected in a pure NBI discharge.For the core ECH case, the drop in the density pedestal height is smaller as compared to that for the edge ECH case.A smaller drop may facilitate quicker recovery.Also, the density pedestal height takes much longer for the edge ECH case to recover to the pre-ELM level.This is also true for the pedestal density gradient.Furthermore, the drop in the pedestal density gradient is for the edge ECH case.However, there is not much difference in the pedestal density width evolution in these three cases.
The inter-ELM recovery of the pedestal is further studied with the TS diagnostic [20].Figure 9 left-hand panels show the ELM synchronized analysis of n e ped , T e ped and p e ped for the core (red) and edge (blue) ECH cases.Data is taken from hyperbolic tangent (tanh) fits of the TS data and from a time window of 1200 ms (4200-5400 ms).According to the f ELM for these two ECH cases, the core ECH case comprises 82 and the edge ECH comprises 35 ELM cycles respectively.For the core ECH case, n e ped is slightly lower than the pre-ELM value as compared to the edge ECH case.Inter-ELM recovery from the n e ped to the pre-ELM level for the core ECH case is much faster in ∼15 ms, while the n e ped recovery takes ∼35 ms for the edge ECH case.A strong T e ped crash and ∼35 ms recovery are observed in the edge ECH case, while the T e ped crash is negligibly small for the core ECH.In accordance with the n e ped and T e ped crashes and recoveries, p e ped recoveries to the respective pre-ELM levels are also ∼15 ms and ∼35 ms for the core and edge ECH cases, respectively.Gradient recoveries of these pedestal parameters also show the same trend.∇n e ped , ∇n e ped and ∇T e ped recovers within ∼15 ms for the core ECH case, while it takes ∼35 ms for the edge ECH case (figure 9 right panels).Recovery of ∇T e ped for the edge ECH case is, however, not clearly discernable from the TS data for the edge ECH case.

Turbulence
Following the pedestal recovery analysis, which agrees well with the variation in f ELM in the three representative cases, we will now investigate the pedestal turbulence in density and magnetics fluctuation diagnostics.The turbulence analysis will help us to understand the reason behind the variation in pedestal recovery time and f ELM in the three representative cases.Let us first start the turbulence analysis with low wavenumber (k θ ρ s ∼ 0.03) local density fluctuations measured by the BES diagnostic [44].Figure 10 shows the cross power (a), (c), (e) and cross phase (b), (d), (f ) of channels at three locations at the pedestal.Figures 10(a) and (b) represent the top of the pedestal (ρ = 0.92, refer to figure (1)), figures 10(c) and (d) represent the upper half of the pedestal, while figures 10(e) and (f ) represent the maximum gradient region of the pedestal.These plots are in the phase of the ECH discharges when P NBI /P ECH ∼ 2. In the cross-power plots, there is no quasi-coherent activity at the top of the pedestal.However, there is a quasi-coherent mode at ∼300 kHz in the maximum gradient region (figures 10(c) and (e)).It is worth mentioning here that quasi-coherent modes are generally observed as a narrowband and well-defined frequency [10,27,[45][46][47][48].They appear as a band of increased amplitude in the frequency spectrogram.This convention is followed while presenting the quasi-coherent activity in this paper.The quasi-coherent mode is strongest when the ECH is towards the edge and weakest in the reference NBI discharge.Further, in the maximum gradient region, two counter-propagating quasicoherent modes are observed (figure 10(f )), one rotating in the ion direction at ∼50 kHz and the other rotating in the electron direction ∼300 kHz.Here the positive cross phase represents the ion direction, and the negative cross-phase frequency represents the electron direction respectively in the lab-frame.Unfortunately, BES data is not available in the phase of the ECH discharges when P NBI /P ECH ∼ 1.This is because the NBI power is decreased in this part of the discharge and the specific beam required for BES is switched off as we cannot sacrifice the beams required for the charge exchange recombination measurements.
However, we have another discharge of #179494 where ECH is applied with a power ratio P NBI /P ECH ∼ 1, towards the edge, similar to discharge #184431, and in this case BES measurements are prioritized.Up to 3.5 s in this discharge is the pure NBI phase while ECH is applied at 3.5 s and NBI power is decreased to keep the total input power roughly constant as in the case of discharge #184431.Figure 11 shows the crosspower and cross-phase of the NBI phase and the ECH phase of this discharge.It is observed that the quasi-coherent mode at ∼300 kHz, propagating in the electron direction, is much stronger in the ECH phase compared to the pure NBI phase.
BES measurements can help localize the observed modes.To localize the quasi-coherent mode at ∼300 kHz radially, in figure 12(a) we plot the percentage intensity fluctuations (δI/I) of three adjacent channels, filtered with a 200-400 kHz band pass filter for the edge ECH phase of the #179494 discharge.Here, channel #44 is at the pedestal top while channels #45 and #46 are at the vicinity of the maximum gradient region of the pedestal.Intensity fluctuations are observed to increase following the ECH injection at 3.5 s, represented by a broken vertical black line, only in the maximum gradient region (figure 12(a)).Another observation is that the fluctuations do not increase instantaneously following the ECH injection, but start to increase after a certain delay of ∼100 ms, shown by the shaded blue bar.Note that the ELM behaviour (figure 12(b)) also takes that much time (∼100 ms) to change  from the randomly spaced high frequency bursts in the pure NBI phase to the uniformly spaced low frequency ELMs in the P NBI /P ECH ∼ 1 phase.This conformal delay in the increase in the mode amplitude and change in ELM behaviour following the ECH injection, which indicates that the mode at ∼300 kHz might play a vital role in changing the ELM frequency following the ECH injection.It is also evident from figures 10(e) and 11 that the mode needs to be strong enough to play a role in reducing the ELM frequency as the weak mode activity does not seem to affect the ELM frequency in the P NBI /P ECH ∼ 2 phase in both the core and edge ECH cases.
Moving forwards with the density fluctuation, let us now investigate the intermediate wavenumber density fluctuations measured by the DBS diagnostic [49].The DBS diagnostics are used to measure density fluctuations (ñ) in the pedestal in purely NBI heated, core ECH and edge ECH discharges, respectively.The measured ñ has k θ ρ s ∼ 0.15 − 0.86 where k θ is the perpendicular fluctuation wavenumber and ρ s is the ion Larmour radius assuming T e ∼ = T i .The RMS values of ñ is estimated by integrating the turbulence intensity over the Doppler shifted part of the spectrum.
ELM synchronized calculations in the inter-ELM period are done to understand the difference in turbulence behaviour in purely NBI heated discharges as well as while replacing beam power with ECH power deposition either at the edge (ρ ∼ 0.8) or at the core (ρ ∼ 0.4).The relative changes in ñ RMS values are compared for the same DBS channel for these three cases and cannot be compared among different radial locations for the same discharge.
It can be noted here that the spatial positions of the DBS channels are always a careful consideration when analysing the DBS data.Spatial positions of the DBS channels are always calculated from the profile reflectometry data (density profile at high time resolution) and the ray tracing code GENRAY [50].In this case, for the pure NBI discharge (figure 13), the maximum variation in ρ, following the ELM crash to the saturated phase of the inter-ELM period is 0.01.Also, the spatial locations for all channels reach their nominal locations in the saturated part of the inter-ELM cycle within 3 ms from the ELM crash.Hence, data from the ELM crash (where the x-axis is 0) up to the first 3 ms can be ignored due to channel position movement resulting from the density profile variation.After that, the data is perfectly real as per the nominal spatial locations of the respective channels.Hence, we put in a transparent mask on the inter-ELM evolution shown in figure 13 from 0 ms to 3 ms.
Similarly, for the case with P NBI /P ECH ∼ 2, and ECH at ρ = 0.4 (figures 14(a)-(c)) we need a 2 ms mask and the maximum location variation within the masked period is again 0.01 ρ for all the channels.For the case with P NBI /P ECH ∼ 1, and ECH at ρ = 0.4 (figures 14(d)-(f ), we need a mask of 3 ms and the location variation for the innermost and outermost channels that are 0.03 and 0.01 rho, respectively, within this first 3 ms.
For the case with P NBI /P ECH ∼ 2, and ECH at ρ = 0.8 (figures 15(a)-(c) we need a 4 ms mask and the location variation for the innermost and outermost channels are 0.03 and 0.02 rho, respectively, within this first 4 ms or the case with P NBI /P ECH ∼ 1, and ECH at ρ = 0.8 (figures 15(d)-(f )) we need a 4 ms mask and the location variation for the innermost and outermost channels are 0.03 and 0.01 rhos respectively within this first 4 ms.
It can be further noted here that the data from these masked periods are not being discussed in this paper, but the data from the final saturated phase of the ELM cycles are compared.These masked periods are also calculated from several ELM cycles in a given operation scenario.Figures 13(a)-(c) show the ELM synchronized ñ RMS values at three different pedestal localized radial locations in a time window of 3000-5000 ms for a pure NBI discharge.There are no appreciable differences in the turbulence level at the different parts of the pedestal.Figures 14(a)-(c) show the differences in ELM synchronized ñ RMS values at three different pedestal localized radial locations at 3700 ms with P NBI /P ECH ∼ 2 power ratio and at 4600 ms (figures 14(d)-(f )) with P NBI /P ECH ∼ 1 power ratio and ECH at ρ ∼ 0.4.Again, no appreciable change can be observed in the ñ RMS values in the core ECH deposition case when the ECH power replaces the NBI beam power at all pedestal locations (pedestal top, maximum gradient, and pedestal foot regions), as compared to the pure NBI case.Further, the ñ RMS values do not change either when more NBI power is replaced by the ECH power (P NBI /P ECH = 1 power ratio) in the core ECH deposition case.
Figures 15(a)-(c) show the differences in ELM synchronized ñ RMS values at three different pedestal localized radial locations at 3700 ms, with P NBI /P ECH ∼ 2 power ratio, and at 4600 ms with P NBI /P ECH ∼ 1 power ratio and ECH at ρ ∼ 0.8.With P NBI /P ECH ∼ 2 power ratio, the turbulence level decreases slightly as compared to the pure NBI and the core ECH cases.However, it can be seen clearly that the ñ RMS values increase at all pedestal locations (top, max.gradient, and pedestal foot regions) by ∼100% when more NBI power is replaced by edge ECH deposition (P NBI /P ECH ∼ 1 power ratio).
As a final fluctuation diagnostic, we will now discuss the magnetic spectrograms recorded with a fast magnetics pickup coil in DIII-D.Figure 16 shows the magnetic spectrograms for the three cases like the pure NBI (a), P NBI /P ECH ∼ 1 case with ECH at the core (b, ρ = 0.4) and for the P NBI /P ECH ∼ 1 case with ECH at the edge (c, ρ = 0.8).Two characteristic features are common in all three cases.There are several coherent and/or quasi-coherent modes in the low frequency range (20-150 kHz).These quasi-coherent modes appear as harmonics in the range of 40-45, 80-90 and 120-130 kHz range (refer to figure 16(b) where these harmonics are clearly visible).These harmonics resemble the edge harmonic oscillation (EHO)-like fluctuations observed earlier in DIII-D [51][52][53][54].Hence, these fluctuations will be termed as EHO-like in the rest of the paper.Figures 16(d)-(f ) show the cross-correlation power between the fast magnetic signal and three channels of BES in the edge ECH case, where the top, middle and bottom panels represent the pedestal top, maximum gradient and foot respectively.We find a correlation between the magnetic fluctuations and the BES signal in the maximum gradient region at frequencies <150 kHz, showing that these modes are most likely localized in the steep gradient region.Then, there is a broadband feature comprising one or more than one mode in the higher frequency range (250-400 kHz).Magnetic fluctuations in the range of 200-400 kHz have been characterized as MTM-like in DIII-D [55,56].Correlations between the BES signal in the steep gradient region and the magnetic fluctuations are also observed at ∼300 kHz (figures 16(d)-(f )).Thus, the high frequency (200-400 kHz) fluctuations could be a mix of MTMlike and TEM-like fluctuations and localized in the maximum gradient region.Even though TEM is usually electrostatic, the possibility of the 200-400 kHz fluctuations being TEM-like is not ruled out as both BES and DBS observe a growth of TEMscale fluctuations in this range of frequency.Note that the cross-power amplitude decreases as we move away in either direction from the maximum gradient region.These two frequency zones are marked as zones 1 (low frequency) and 2 (higher frequency) in figure 16.Apart from that, there is a strong coherent mode in the low frequency zone (zone 1) of the edge ECH case (figure 16(c)) that chirps up in frequency and saturates before either disappearing completely or getting considerably weaker at halfway through the inter-ELM period.
The inter-ELM evolution of the mode activities in these frequency zones is studied in the ELM-synchronized way [10].Evolution of the average amplitudes in the respective frequency zones and in the time window 4200-5000 ms is shown in figure 17.Note that several ELM cycles are included in this analysis depending upon the f ELM for these respective cases.It is very difficult to separate out the strong frequency chirping mode in the edge ECH case.However, we try to show the evolution of this mode by averaging the amplitude in the 52-100 kHz range only for the edge ECH case separately (shown in green).Zones 1 and 2 are colour-coded as per the colours marked (magenta and black) in figure 15.For the modes in zone 1, and for the pure NBI and core ECH cases, the amplitude grows stronger right after the ELM crash and then stays almost saturated for a while and then finally drops off before the ELM crash.In the case of edge ECH, however, the amplitude grows after the ELM crash at a much slower rate and peaks at almost the end of the ELM cycle and then drops down before the ELM crash.The ELM-synchronized analysis for the frequency chirping coherent mode done for this case specifically, shows the same behaviour as the entire zone 1 taken collectively as a whole (edge ECH case inset).Another observation here is that the standard deviation, shown by the shaded area in these plots, grows wider towards the end of the ELM cycle, both for zone 1 as a whole and for frequency chirping coherent modes separately.The reason, most probably, is due to several overlapping mode activities in this region.
The inter-ELM evolution of the higher frequency MTM/TEM-like broadband fluctuations shows a complementary behaviour to that of the EHO-like modes.In both the pure NBI and the core ECH cases, there is a sharp drop in the broadband fluctuation amplitude following the ELM crash and then a steady recovery along the ELM cycle.Just before the ELM crash there was a sharp rise in the broadband amplitude.In the case of the edge ECH case, similar evolution of the broadband fluctuations is observed except that the recovery in amplitude is much more gradual along the longer inter-ELM period and there is a more subtle increase at the end.
If the low frequency fluctuations are indeed the same as the EHO observed in the QH-mode, they are expected to drive main particle transport as reported earlier [52].On the other hand, if the broadband fluctuations are MTM-like, then they might be contributing towards electron heat transport mainly and have minimal contribution towards particle transport [56,57].Hence, one can expect that the particle transport mechanisms are stronger in the first half of the ELM cycle while heat transport is stronger in the latter half of the inter-ELM phase.Further, in this case, both the EHO-like and MTM-like fluctuations are localized to the maximum gradient region of the pedestal [51,56].
In view of these transport mechanisms, one might ask the question 'why is n e ped recovering strongly while the particle transport mechanisms are the strongest?'To answer this, it can be noted that the particle/neutral source is either at the edge, during the first few ms following the ELM crash [58] or the core and not the pedestal itself.On the other hand, the fluctuations, which are local to the pedestal, are modulating the recovery rate.As a result, the pedestal will tend to recover at a relatively slower rate if the particle transport mechanisms are stronger and vice versa.
To summarize the observed turbulence, note that in figures 10(c) and (e), turbulence increased for both the cases where ECH deposition is at ρ = 0.4 and ρ = 0.8 respectively.However, the increase in the turbulence cross power is higher in the edge ECH case (ECH at ρ = 0.8) compared to the core ECH case (ECH at ρ = 0.4).Alsoin this case, P NBI /P ECH ∼ 2. In other words, the ECH power fraction of the total power is low.In figure 11, we have shown only the ECH deposition at ρ = 0.8 cases, compared to the pure NBI case.However in figure 11, P NBI /P ECH ∼ 1. Figure 11 shows that the increased turbulence seen in figure 10 for the ECH deposition at ρ = 0.8 cases is strongly amplified when the ECH power fraction is increased.Further, referring to the observations from DBS diagnostic in figures 13-15 it is clear that turbulence increased much more strongly in the ECH deposition at ρ = 0.8 cases, whereas the change in turbulence level is not that significant for the ECH deposition at ρ = 0.4 cases.Magnetic fluctuations also show that the low-frequency EHO-like modes grow much faster in the ECH deposition at ρ = 0.8 cases, compared to the ECH deposition at ρ = 0.4 case (refer to figure 17 core and edge ECH magenta plots).Finally, in figure 12, it is shown clearly that the decrease in f ELM and the increase in density turbulence observed in BES are well correlated.We infer that the increased turbulence could be the reason for enhanced transport and hence larger time required for the pedestal to recover from an ELM crash in the ECH deposition at ρ = 0.8 cases, compared to the ECH deposition at ρ = 0.4 cases.Eventually, this could lead to lower ELM frequencies for the ECH deposition at ρ = 0.8 cases.

Transport analysis
To begin with, we would like to compare the evolution of the baseline of the Dα signal.We consider the total neutral source at the edge to be similar in this discharge series as the fuelling and wall conditions are similar.Also, since we are considering differences in the Dα signal at least up to 10 ms from the ELM crash, thus direct ELM effects have dissipated.Under these considerations, one can expect the baseline of the Dα signal as an indication of the cross-field transport, especially particle transport [10,59].Figure 18 shows the ELM synchronized Dα signal for the pure NBI (black), edge ECH (P NBI /P ECH ∼ 1, blue) and core ECH (P NBI /P ECH ∼ 1, red) cases.Dα baseline is highest for #184431 (edge ECH) and takes the longest time to come down to pre-ELM values, while the lowest for #184437 (core ECH).Pure NBI cases remain in between these two ECH cases.This might indicate the highest cross-field transport in the edge ECH case and the lowest in the core ECH case is expected, and this observation is consistent with f ELM and pedestal recovery.
The main goal now is to identify the observed fluctuations in the core and edge ECH cases.The plausible candidates for the observed fluctuations and their role in particle and heat transport at the pedestal are further investigated with interpretive time-dependent transport analysis with TRANSP [60] to obtain the transport coefficients for use in the 'transport fingerprint' method [57].The heat and particle diffusivities  are calculated from the measured profiles in TRANSP in association with models for the neutral beam and ECH power deposition profiles (TORAY-GA, GENRAY and TORBEAM).Profiles are evaluated in a time window of 4200-5000 ms.
The transport coefficients from the TRANSP run for the edge ECH and core ECH discharges are shown in figure 19.The neutron rates obtained from TRANSP agree well with the experimental neutron rates.It is noted that the transport coefficients remain similar over the entire analysis time window.The electron particle diffusivity (D e ), the electron heat diffusivity (χ e ) and ion heat diffusivity (χ i ) are marked in figure 19.D e is observed to be ≪χ e and χ i ⩾ χ e in the pedestal.Hence, both ITG/TEM are the main possibilities in the pedestal for both these discharges.In this case, the ion heat diffusivity (χ i ) is higher in the edge ECH case, suggesting that the ITG mode might be stronger.This supports the BES observation of a strong ion mode in the lower frequency range (∼50 kHz) in the pedestal of the edge of the ECH discharge.Electron transport coefficients χ e and D e are similar in both the ECH cases.Another important observation here is that χ i is always higher than or equal to χ e .Hence, as per fingerprint [57] ratios, ETG and/or MTM might not be the major heat transport mechanisms for the ECH case and ITG/TEM-like modes are likely to be responsible for both heat and particle transport.
The inferred particle transport/heat transport coefficients depend on the particle source at the edge, and the uncertainty involved with the source at the edge can alter the 'transport fingerprint' picture completely.However, the uncertainty of the particle source at the edge was addressed earlier [10] by changing the particle confinement time (τ p ) in TRANSP runs from 50 ms to 1 s in steps of 50 ms, 100 ms, 200 ms, 500 ms and 1.0 s.With these variations in τ p and therefore edge particle source, the ratio of transport coefficients D e /χ e remains ≪1.

Summary and discussions
The heating mix ratio between NBI and ECH (P NBI /P ECH ) and the ECH power deposition location are varied, and the results are investigated in comparison to a pure NBI reference discharge.In the α-J PED pedestal stability diagram the PB thresholds are decoupled in the pure NBI discharge, and the decoupling is preserved when P NBI /P ECH ∼ 1 and the ECH is deposited closer to the pedestal top.The decoupling is, however, lost when the ECH is deposited closer to the magnetic axis.Scans of the height and width of the pedestal n e and T e revealed that a wider temperature pedestal at lower pedestal density and higher pedestal temperature could be the main factor behind the preservation of the decoupling in the edge ECH case.In the core ECH case, even though the density pedestal is steeper, which favours the decoupling, the steeper the temperature pedestal facilitates the closure of the PB threshold decoupling.
With P NBI /P ECH ∼ 1, f ELM increases by ∼50% for ECH at ρ = 0.4, while f ELM decreases by ∼50% for ECH at ρ = 0.8 respectively, compared to the pure NBI discharge.This variation in f ELM is expected as the operating point is closer to the PB threshold rollover point, which is often referred to as the 'nose', in the core ECH case, while the operating point is comparatively deeply seated in the stable zone in the edge ECH case.
The role of turbulence is investigated with the BES, DBS and magnetic diagnostics.Increased turbulence is observed in the density fluctuations measured by both BES (low wavenumber) and DBS (intermediate wavenumber) diagnostics for the edge ECH case.In BES, a strong growth of a ∼300 kHz, electron direction mode at the pedestal is observed in the edge ECH case.Further, a counter propagating ion direction mode is also observed in the low-frequency range (∼50 kHz) for both core and edge ECH cases.Conformal delay between the ECH injection near the pedestal top, growth of the ∼300 kHz TEM-like mode and the change in ELM frequency suggest a vital role of the observed turbulence in setting the ELM frequency.However, the mode needs to be strong enough to affect the ELM frequency.Fast magnetic spectrograms show that the broadband turbulence in the 250-400 kHz frequency range weakens in the ECH discharges compared to the pure NBI discharge.Furthermore, the low frequency (<150 kHz) EHO-like quasi-coherent fluctuations are strongest along with the frequency chirping coherent mode in the edge ECH case.Thus, the increased turbulence in the edge ECH case could be the reason behind the delayed pedestal recovery following an ELM event.
Finally, the ratio of transport coefficients in the TRANSP analysis shows that ITG/TEM-like fluctuations are the most likely candidates for the observed fluctuations.Note that ITG/TEM-like fluctuations are susceptible to shear suppression.This might be the reason behind the observation of decreased fluctuation amplitude in the core ECH discharge where the E r well is deeper and E × B shear suppression is stronger.
The above observations can be summarized as showing that the gradients are higher for the edge ECH case for most of the pedestal, including the maximum gradient region, compared to the core ECH case.These higher gradients lead to higher turbulence and transport and widening of the pedestal inside.Widening of the T e pedestal profile helps to preserve the decoupling of the PB thresholds observed in the pure NBI reference discharge.This dependence of the PB thresholds has been confirmed by pedestal width scans in the ELITE analysis.Earlier, the dependence of the PB thresholds on the pedestal widths (n e and T e ) has been demonstrated for double null diverted discharge [38].Here, we performed a systematic scan to decipher the effect of the pedestal widths on the PB thresholds in ISS plasmas.As the PB thresholds tend to decouple with the edge ECH, the operating point is less susceptible to hit either of these two thresholds, hence lowering the ELM frequency.From the viewpoint of gradient recovery after an ELM crash, a reduction in the ELM frequency with edge ECH can be further perceived as the time required being longer for the pedestal to recover to the pre-ELM level to trigger a subsequent ELM event.In this case, the recovery time is prolonged in the edge ECH case due to increased turbulencedriven transport.

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.

Figure 1 .
Figure 1.ECH deposition profiles calculated with TORAY for the (a) ρ ∼ 0.4 and (b) ρ ∼ 0.8 deposition cases.Note that the ECH power absorbed is ∼1.5 MW in both of these cases.Broken vertical lines denote the position of the pedestal top in the representative discharges.Red, green and blue colors represent profiles for the three gyrotrons used in this experiment.

Figure 2 .
Figure 2. Time evolution of (a), (b): the heating waveforms P NBI and P ECH ; (c)-(h): height and width of the electron density, temperature, and pressure of the pedestal, calculated from the tanh fits of the TS data; (i)-(k): Dα signal from filter scope showing the ELM bursts.The pure NBI case is shown in black, ECH case with deposition at ρ = 0.4 (core) is shown in red and ECH case with deposition at ρ = 0.8 (edge) is shown in blue.Time interval between the broken and solid vertical lines represents the P NBI /P ECH ∼ 2 phase while the time interval beyond the solid vertical line represents the P NBI /P ECH ∼ 2 phase.

Figure 4 .
Figure 4. ELM-synchronized evolution of the total stored energy in the inter-ELM period for the core ECH (at ρ = 0.4, red) and the edge ECH (at ρ = 0.8) cases.The shaded regions represent the (±) standard deviation for all the ELMs in the time window of 4200-5200 ms.

Figure 5 .
Figure 5. PB stability of the pure NBI reference discharge (#184429, black) compared with that of another standard ELMing H-mode discharge (#170868, red).PB decoupling is observed only in case of #184429.Shape of the two discharges are shown from EFIT reconstructions in the right.

Figure 6 .
Figure 6.Stability diagrams calculated with ELITE for all the five cases like pure NBI (a), P NBI /P ECH ∼ 2 (light red) and 1 (dark red) with ECH at ρ = 0.4 (b) and P NBI /P ECH ∼ 2 (light blue) and 1 (dark blue) with ECH at ρ = 0.8 (c).Decoupling of the PB boundaries are clearly visible in (a), while the decoupling is preserved in (c) with P NBI /P ECH ∼ 1 (dark blue).In the cases with ECH at ρ = 0.4 (b), decoupling of PB boundaries is not observed.

Figure 7 .
Figure 7. VARYPED scans for the pure NBI discharge, where the experimental ne and Te profiles are shown in black; (a): only ne ped width is decreased with the shift parameter, which translates into an outward shift of the pedestal top w.r.t. the flux coordinate ψ; (b) only Te ped width is decreased; (c): only ne ped width is decreased while scaling the ne ped and Te ped so that they match the edge ECH case; (d) only Te ped width is decreased while scaling the ne ped and Te ped so that they match the edge ECH case.The inset in each panel shows the ne ped and Te ped of the respective scans.Also, ne ped and Te ped of the edge (blue broken) and core (red broken) cases are shown for comparison.

Figure 8 .
Figure 8. (a)-(c): ELM synchronized inter-ELM evolution of ne pedestal height (×10 19 m −3 ), ne pedestal width (m) and ∇ne (×10 19 m −4 ) derived from profile reflectometer data.The pure NBI reference discharge is shown in black.Core and edge ECH cases in the P NBI /P ECH ∼ 1 phase are shown in red and blue respectively.

Figure 10 .
Figure 10.Cross power (top row) and cross phase (bottom row) of two poloidally separated BES channels (separation = 1.5 cm) at the top (a), (b), maximum gradient (c), (d) and towards the foot (e), (f ) of the pedestal for three cases, like the pure NBI (black), P NBI /P ECH ∼ 2 with ECH at ρ = 0.4 (red) and P NBI /P ECH ∼ 2 with ECH at ρ = 0.8 (blue).Cross power shows increase in quasi-coherent mode activity at ∼300 kHz with ECH and maximum for edge ECH.Also, counter propagating electron and ion direction mode can be seen in the lower half of the pedestal from the cross phase.

Figure 11 .
Figure 11.(a) Cross power and (b) cross phase of two BES channels at the maximum gradient region in the pure NBI phase (black) and the P NBI /P ECH ∼ 1 with ECH at the edge (blue).Strong growth of the quasi-coherent mode at the frequency of ∼300 kHz is observed in the ECH phase.Further, this mode is propagating in the electron direction (negative phase) along with a low frequency ion direction (positive phase) mode at ∼50-100 kHz.

Figure 12 .
Figure 12.(a) Percentage fluctuation (δI/I%) in three channels of the BES data are shown in red (towards pedestal foot), blue (maximum gradient) and black (towards pedestal top).δI/I increases strongly after a brief delay of ∼100 ms following ECH injection; (b) ELMs seen in the Dα filter scope signal.Here also a brief delay of ∼100 ms is seen before the ELM characteristics change.

Figure 13 .
Figure 13.Inter-ELM phase-averaged ñ RMS values estimated from DBS measurements at three different radial locations at ∼3700 ms with pure NBI heating only (a) close to the pedestal top at ρ ∼ 0.93, (b) close to the maximum electron pressure gradient location at ρ ∼ 0.95, and (c) close to the pedestal foot at ρ ∼ 0.97.Transparent black masks denote the period where the spatial locations of the channels are uncertain.

Figure 14 .
Figure 14.Inter-ELM phase-averaged ñ RMS values estimated from DBS measurements at three different radial locations at ∼3700 ms with 1 MW core ECH power (a) close to the pedestal top at ρ ∼ 0.93, (b) close to the maximum electron pressure gradient location at ρ ∼ 0.95, and (c) close to the pedestal foot at ρ ∼ 0.97.Corresponding plots at similar radial locations (ρ ∼ 0.925, 0.95, and 0.97) for 1.5 MW core ECH power are shown in (d)-(f ) respectively.Transparent red masks denote the period where the spatial locations of the channels are uncertain.

Figure 15 .
Figure 15.Inter-ELM phase-averaged ñ RMS values estimated from DBS measurements at three different radial locations at ∼3700 ms with 1 MW edge ECH power (a) close to the pedestal top at ρ ∼ 0.90, (b) close to the maximum electron pressure gradient location at ρ ∼ 0.925, and (c) close to the pedestal foot at ρ ∼ 0.96.Corresponding plots at similar radial locations (ρ ∼ 0.92, 0.94, and 0.967) for 1.5 MW edge ECH power are shown in (d)-(f ) respectively.Transparent blue masks denote the period where the spatial locations of the channels are uncertain.

Figure 16 .
Figure 16.Magnetic spectrograms for the pure NBI discharge (a); discharge #184429), for the P NBI /P ECH ∼ 1 case with ECH at the core (b); discharge #184437) and for the P NBI /P ECH ∼ 1 case with ECH at the edge (c); discharge #184431); the EHO-like low frequency (20-150 kHz) fluctuations are represented in zone 1, while the broadband high frequency fluctuations are represented in zone 2 for all three cases respectively.The frequency chirping coherent mode is shown in case (c); (d)-(f ): spectrograms of cross correlation power between the fast magnetic signal and 3 channels of BES in the edge ECH case, where the top, middle and bottom panels represent pedestal top, maximum gradient, and foot respectively.

Figure 17 .
Figure 17.ELM-synchronized analysis showing the inter-ELM evolution of the EHO-like and MTM-like modes in the magnetic spectrogram for the pure NBI discharge and the P NBI /P ECH ∼ 1 cases for the core and edge ECH depositions respectively.

Figure 18 .
Figure 18.ELM-synchronized amplitude evolution of the Dα signal recorded with filter scope.The shaded regions represent the (±) standard deviation of the data for all the ELMs in the analysis window.

Figure 19 .
Figure 19.Electron and ion heat (χe and χ i ) and electron particle (De) diffusivities in cm 2 s −1 in the pedestal for the edge ECH (left panel) and the core ECH (right panel) for the P NBI /P ECH ∼ 1 phase.Color bands represent variation among time instants in the analysis time window.

Table 1 .
Scan of heating mix (NBI vs. ECH), ECH deposition location and the corresponding ELM frequencies.
ELM regime is observed.Note that at low Greenwald fraction (n e ave