Experimental characterization of turbulence properties in negative triangularity DIII-D plasmas

Core-edge integration remains a topic of extensive research and optimization in the design of a future fusion power plant [1]. Designs reliant on H-mode confinement require high heat fluxes across the separatrix to maintain H-mode access, causing high heat loads on the divertor. Additionally, large transient heat loads from Edge Localized Modes (ELMs) scale unfavorably with device size [2]. Many concepts exist to avoid, mitigate, or suppress ELMs, often sacrificing confinement or lacking robustness [3–5]. Negative Triangularity (NT) was first identified on TCV as an ELM-free operating mode with good confinement [6]. Triangularity is defined using $[R_0- R_{\max(z)}]/ r$ where R₀ is the major radius of the magnetic axis, r is the minor radius of the flux surface, and $R_{\max(z)}$ is the major radius at a vertical extrema of the flux surface. This can be expressed in terms of either the upper ($\delta_{\text{upper}}$) or lower ($\delta_{\text{lower}}$) vertical extrema individually as their average $\delta_{\text{avg}}$. NT modifies the edge infinite-n ballooning limits, preventing access to H-mode and providing a uniquely robust ELM-free operating space [7, 8]. In positive triangularity, two regions of ballooning stability are possible with strong H-mode pedestals associated with access to the second region of ballooning stability with stronger pressure gradients [9]. In shaping sweeps, infinite-n ballooning stability boundaries were calculated for self-consistent equilibria confirming that below a critical value of triangularity ($\delta\lesssim-0.15$) second stability access is prevented in NT shapes [10, 11]. The resulting plasmas exhibit a distinct ELM-free edge transport condition referred to as the NT-edge [7, 12]. Additionally, finite-n interchange MHD modes have been observed, which are expected to limit the NT-edge pressure gradients [13]. NT plasmas on DIII-D have demonstrated high performance with high confinement factor ($H_{98}\gtrsim 1$), normalized plasma pressure ($\beta_N \gt 2.5$), and Greenwald fraction ($f_{\text{GW}}\gtrsim1$), while retaining an ELM-free edge [8]. Confinement properties in NT plasmas have been shown to be comparable to H-mode operation, in part due to the mitigation of turbulent transport in NT tokamak plasmas [6, 14].

Turbulent transport is typically dominated by ion-scale drift-wave turbulence in fusion plasmas. These drift-wave instabilities can cause radial correlations large compared to the ion gyroradius that enhance the transport of heat and particles from the plasma. Trapped Electron Mode (TEM) turbulence, a prominent instability in DIII-D discharges, is theorized to experience a stabilizing effect from NT via a number of both linear and nonlinear mechanisms [15]. The collisionless branch of the TEM arises from resonance between the toroidal precession frequency of trapped electrons and electrostatic drift waves [16]. The toroidal precession frequency is dependant on the geometry so its resonance is sensitive to stronger NT, resulting in greater energy coupling for deeply trapped particles and less coupling for barely trapped ones. Gyro-kinetic simulations of heat flux contributions for differing pitch angles show increased heat flux from the most deeply trapped particles, but significant decreases from a broader range of barely trapped particles [17]. The turbulence arising from deeply trapped particles exhibits fluctuations with increased binormal wavenumber (k_y), where binormal refers to the direction orthogonal to both the field line and the flux gradient. NT configurations are also expected to have lower available thermal energy in TEM-resonant bounce-averaged drifts in the core of elongated plasmas. This energy is also shown to be available over a larger range of binormal wavenumbers [18].

Linear gyrokinetic simulations of TEMs predict lower growth rates and larger binormal wavenumbers for the modes which contribute most to transport [6]. Therefore, from a mixing length argument, lower heat diffusivity is expected as $(\chi \sim \gamma/{ \lt k^{2}_{y} \gt })$, where χ is the heat diffusivity and γ is the turbulence linear growth rate [17]. Additionally, a reduced trapped particle fraction is expected as the aspect ratio on the outboard midplane is increased. The increased Shafranov shift observed in NT also increases the penetration of elongation, which is known to stabilize TEMs [19]. These linear effects are significant but insufficient to fully explain the strong reduction in TEMs observed in experiments, indicating nonlinear effects. Nonlinear gyrokinetic simulations have been able to match the experimentally observed reduced heat flux levels in the edge, although the matching degrades toward the core necessitating further investigation of the nonlinear mechanisms [17].

Recent linear gyrokinetic analysis predict Ion Temperature Gradient (ITG) modes to have decreased linear growth rates for the low-k modes ($k_{y} \rho_s \lt 0.5$), where ρ_s is the ion gyro-radius calculated from the sound speed [20]. The modes with the lowest wavenumber are expected to dominate transport by mixing length arguments. Some nonlinear gyro-kinetic simulations of ITG modes also predict lower heat fluxes in NT configurations [21]. The heat flux in nonlinear simulations of NT was confirmed to be localized to lower-k ITG modes ($k_{y} \rho_s \lt 0.5$) [21]. The theoretical understanding of the behavior of ITG turbulence in NT plasmas is less well established, with results showing varying levels of stabilization [22, 23]. The identification of a potential physical mechanism of ITG stabilization in NT is still an open research question.

Nonlinear saturation mechanisms are also predicted to be sensitive to changes in triangularity. Specifically, E × B shearing rates are increased off the midplane and reduced on the midplane. Increased neoclassical zonal flow screening is predicted to increase zonal flow damping and reduce turbulence shearing rates [24]. This has been observed as reductions in zonal flow magnitude with increases in the magnitude of triangularity in nonlinear gyrokinetic simulations of ITG turbulence [21]. Geodesic Acoustic Modes (GAMs), however, are predicted to experience reduced damping and exhibit lower frequency, allowing for more effective turbulence saturation [20]. Changes to the nonlinear saturation mechanisms can alter the magnitude and spectral spread of experimentally observed modes as measured via fluctuation diagnostics.

Measurements using Correlation Electron Cyclotron Emission (CECE) in TCV confirmed lower fluctuation levels and shorter radial correlation lengths for $\rho = 0.45-0.85$ in NT plasmas [25]. The fluctuations were stabilized by collisionality and destabilized by the ratio of electron temperature to ion temperature ($T_e/T_i$), indicative of TEM turbulence [26]. Previous NT experiments on DIII-D were run with inner wall limited plasmas with up to 13 MW of heating power and limited L-mode edge conditions [14, 27]. High normalized plasma pressure was achieved ($\beta_N = 2.7$) with high levels of confinement ($H_{98,y2}\simeq1.2$) exhibiting increased stored energy and less power degradation when compared to the ITER-89P scaling. In linear gyrokinetic analysis using experimental profiles, both TEM and ITG turbulence seem to play prominant roles in the ion-scale turbulence in the core with ITG turbulence dominating at low-k ($k_{y}\rho_s \lt 0.3$) in some discharges [27, 28]. Additionally, nonlinear gyrokinetic simulations have been shown to reliably reproduce the experimentally derived heat and particle fluxes in the core region [28]. Using BES, CECE, and Phase Contrast Imaging diagnostics, matching discharges with positive and NT were confirmed to show a reduction in NT in ion-scale turbulence amplitude of 10-30% in the region $\rho = 0.65-85$ [27]. This was accompanied by a 20%–30% increase in confinement particularly reducing the electron heat diffusivity. Studies of the diverted NT-edge on a larger scale, higher power tokamak allow the nature of the H-mode inhibition physics to be studied. To validate NT TEM and ITG theory and understand mode characteristics, further study on the 2D nature of the turbulence is needed with diverted edge conditions.

1.1. Experimental methods

To study the effect of triangularity directly on turbulence, injected neutral beam power was held constant while shaping was scanned in DIII-D discharge 194371, with the parameters at the extrema shown in table 1 where $T_{\text{inj}}$ is the injected beam torque, ρ is the toroidal flux coordinate normalized to the flux at the separatrix, and q₉₅ is the safety factor at ρ = 0.95. The divertor X-point location was held constant, and the upper triangularity was scanned from −0.12 to −0.38, with lower triangularities held between +0.10 and +0.12 as shown in figure 1(c). Keeping the X-point location fixed limits the changes in fueling, strikepoint conditioning and pumping effectiveness throughout the shaping scan. At 1.4 MW of injected beam power, the plasma accessed H-mode at $\delta_{\text{avg}}\gtrsim-0.11$. At $\delta_{\text{avg}}\sim -0.11$ the plasma exhibited Limit Cycle Oscillations (LCO) [34], and at $\delta_{\text{avg}}\sim -0.13$ the NT-edge was fully ELM-free. The time trace of the triangularity scan is shown in figure 2(a) and the extrema of the shapes are shown in figure 1(c). BES is positioned on the outboard midplane measuring from $\rho = 0.87-1.08$ as shown by the blue box in figure 1(c). The edge D-alpha light shows the ELM-free nature of the NT-edge (blue phase in figure 2(c)), as well as decreased ELM amplitude and increased ELM frequency as the triangularity is decreased in the sweep. Normalized plasma pressure (β_N), a proxy for plasma performance, is degraded by ${\sim}15\%$ with stronger NT as shown in figure 2(b). However, no sharp change in β_N is seen across the H-mode to NT-edge transition. As shown in figures 1(a) and (b), the NT-edge phase shows a decreased electron density accompanying an increased core electron temperature as measured by the Thomson scattering diagnostic keeping β_N in a comparable range [35]. This is characteristic of NT, which exhibits lower edge pressure but good energy confinement [11]. This β_N dependency on δ is not ubiquitous across all triangularity scans, with some scans showing little or no dependence. However, the analysis of this discharge will focus on the region measured with the BES diagnostic.

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Table 1. Comparison of plasma parameters at extrema of the triangularity sweep.

Discharge Number (Times)	BT (T)	IP (MA)	$P_{\text{inj}}$(MW)	$T_{\text{inj}}$ (Nm)	q95	βN	$\delta_{\text{avg}}$	BES Location (ρ)
194371 (3300–3600 ms)	−2.01	0.89	1.37	0.00	4.34	0.87	−0.01	0.87–1.09
194371 (5000–5100 ms)	−2.01	0.89	1.37	0.00	4.30	0.69	−0.13	0.85–1.07

Charge Exchange Recombination (CER) spectroscopy can be used to measure the ion temperature, carbon density, toroidal rotation, and poloidal rotation [36, 37]. This allows the radial electric field to determined by solving the ion-force balance equation [38]. An identical shaping sweep to that shown in figure 2 is performed from $t = 1.2-3.2$ seconds in the same discharge with CER data. The radial electric field profile is shown in figure 3 for the scan of matching triangularity values. When $\delta_{\text{avg}}\unicode{x2A7E} -0.09$, the plasma enters H-mode with a 'well' of strong negative E_r observed inside the separatrix. The radial gradient of E_r is associated with the $V_{E\times B}$ shearing rate generally understood to be responsible for the suppression of low-k turbulence in the H-mode pedestal [38]. In the ELM-free phase with $\delta_{\text{avg}} = -0.13$, the E_r well is seen to be much weaker providing much lower $V_{E\times B}$ shear in the edge.

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Fluctuation amplitudes in the edge are observed to change across the scan of triangularity as shown in figure 4. The cross-power frequency spectrum between two poloidally separated BES channels is integrated over the frequency range of 30–300 kHz, where broadband turbulence fluctuations are dominant. The local intensity fluctuation magnitude is normalized to the time-averaged local beam emission intensity level using a DC-coupled low sample-rate BES signal. These normalized intensity fluctuation values are corrected using a linear factor dependent on local temperature, density, effective ion charge ($Z_{\text{eff}}$), and beam voltage to determine the density fluctuation amplitude [39]. The photon noise power is determined from the high-frequency portion of the frequency spectra where fluctuation amplitude is constant in frequency. This level is assumed constant across the spectrum and the inferred photon noise is subtracted. Turbulence in the H-mode and the LCO phases is compared for the inter-ELM periods to avoid ELM dynamics. Sharp increases in the edge D-alpha light are used to detect ELMs. The ELM itself and an additional 5% of the inter-ELM period before and after the ELM are excluded from the analysis. At less NT ($\delta_{\text{avg}} \gtrsim - 0.1$), type I ELMS are dominant. Depending on radius, the edge pressure can change by 15-35% during the inter-ELM period. At moderately low triangularity ($\delta_{\text{avg}} \gtrsim - 0.13$), LCOs and type III ELMs appear, where the edge pressure can be modulated by 25-50% during the LCO/ELM cycles. Broadband turbulence modes are observed with propagation in the electron diamagnetic direction, consistent with TEM-like turbulence as discussed later in this section. The fluctuation amplitude on the separatrix remains comparable; however, an increase of ${\sim}70\%$ is seen at $\rho\sim0.95$ in the NT-edge phase. This may be consistent with an observed decrease in the radial electric field (E_r) well depth and mean E × B shearing rate in the ELM-free NT-edge phase. The outer-core turbulence ($\rho\sim0.85$) is seen to decrease by ${\sim}50\%$ in the NT-edge phase. This could be indicative of the theorized TEM stabilization by NT.

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Using a poloidal array of 8 BES channels on the separatrix ($\rho\sim0.98-1.02$), the cross-phase spectra can be used to estimate the power density spectrum as a function of frequency and poloidal wavenumber [40]. The resulting spectra are averaged over the array of poloidal pairs. The frequency-wavenumber spectra can be used to investigate mixed-mode behavior with improved wavenumber resolution compared to spatial Fourier analysis. The spectra are shown for the separatrix location as this is where the turbulence is strongest, however the mode characteristics are similar for $\rho \gtrsim 0.93$. The triangularity is scanned in time and the resulting change in the turbulence fluctuation power density spectrum is shown in figure 5. In this example, positive poloidal wavenumbers (k_θ) refers to the electron diamagnetic direction in the lab frame. To determine the mode direction in the plasma frame, the plasma flow velocity must be subtracted. The binormal plasma velocity arises predominantly from the E × B velocity ($V_{E\times B}$), which can be determined from CER spectroscopy. The measured plasma velocity is plotted in figure 5 as a white line whose slope is $V_{E\times B}$. Spectral power density above the $V_{E\times B}$ line propagates in the electron-diamagnetic direction in the plasma frame and spectral density below the line propagates in the ion-diamagnetic direction.

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The details of the turbulence spectral density across the triangularity sweep reveal mixed mode behavior in the H-mode phases. At weak triangularity ($\delta_{\text{avg}} = -0.01$), three modes can be observed. Two modes are observed below 70 kHz with low turbulence phase velocity in the plasma frame and a high-frequency mode is seen propagating in the electron diamagnetic direction (above the $V_{E\times B}$ line). The lower frequency modes are weaker at stronger triangularity and can no longer be seen at $\delta_{\text{avg}} = -0.09$. At stronger values of NT across the LCO and NT-edge phases, the mode propagating in the electron diamagnetic direction broadens and decreases in frequency and wavenumber, gaining similar characteristics to those seen in a strong triangularity case ($\delta_{\text{avg}} = -0.52$) in discharge 193775 described in table 2.

Table 2. Comparison of overview plasma parameters for discharges 193921 and 193775.

Discharge Number (Times)	BT (T)	IP (MA)	$P_{\text{inj}}$(MW)	$T_{\text{inj}}$ (Nm)	q95	βN	$\delta_{\text{avg}}$	BES Location (ρ)
193921 (3330–4200 ms)	−2.06	0.79	5.0	4.87	3.39	2.28	−0.51	0.65–0.83
193775 (3150–3450 ms)	−2.06	0.79	5.81	4.97	3.36	2.36	−0.52	0.82–1.05

Integrating the spectral density over frequency yields the poloidal wavenumber (k_θ) spectrum of the turbulence as shown in figure 6. The turbulence intensity peaks around $k_{\theta}\sim0.25$ rad cm⁻¹ in the H-mode phase ($\delta_{\text{avg}} = -0.09$). In the NT-edge, the wavenumber spectrum is broader than the similar H-mode, with higher spectral power at larger k_θ as predicted by theory [17]. The low wavenumber turbulence ($k_{\theta} \lt 0.25$) is additionally seen to increase in the ELM-free NT-edge phase. This could be due to the reduced shear from the mean radial electric field in the NT-edge as compared to the H-mode. Additionally, this could be influenced by the proposed effect of triangularity on nonlinear saturation mechanisms such as GAMs or zonal flows [20, 24]. As triangularity is swept toward stronger NT, fluctuation amplitudes are reduced at ρ < 0.9, low-velocity turbulence edge modes are suppressed, and modes propagating in the electron diamagnetic direction broaden in wavenumber space.

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Discharge 193775 was identified as a well-diagnosed, representative discharge with strong NT ($\delta_{\text{avg}}\sim-0.52$) and higher plasma pressure ($\beta_N \simeq$ 2.2) with good CER and BES data, enabling a detailed study. BES is positioned on the outboard midplane in this discharge ($\rho\sim0.82-1.05$). In its 8x8 configuration, BES has a radial extent in any given discharge of ${\sim}7$ cm, so to compare core and edge turbulence, two discharges with different radial BES locations must be found with similar conditions. Discharge 193921 was identified as a plasma with similar parameters outlined in table 2, and a BES location measuring the outer-core ($\rho\sim0.65-0.83$). The two discharges additionally have comparable kinetic profiles and plasma shapes as shown in figure 7. Matching discharge parameters in this manner allows local turbulence behavior with matched characteristics to be compared over a larger radial range.

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Figure 8 shows the cross-power spectrum of poloidal pairs of BES channels. As no mixed-mode behavior is observed, the cross-power spectrum can be shown against frequency alone. At frequencies greater than 20 kHz, broadband spectra are observed indicative of turbulence activity. Below 20 kHz, strong MHD signatures are observed, the largest of which corresponds to a low toroidal mode number (n = 1) mode (f∼12.5 kHz), as confirmed by the magnetic spectra. Additionally, bursty edge modes ($n = -1$) unique to NT can be seen around 5 kHz as described in [41]. For discharge 193775, BES fluctuations are filtered from 20 kHz to 300 kHz to capture the spectral region where turbulence is dominant. Broadband fluctuations are also present below 20 kHz and these may be important for determining transport behavior. For discharge 193921, the common-mode signal dominates the spectral range below 40 kHz as identified by high coherence between channels with $\gt$6 cm of radial separation where the radial correlation length is ∼3 cm. The channels spanning $\rho = 0.65-0.84$ in discharge 193921 are therefore filtered from 40–300 kHz to preserve locality.

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Fluctuation amplitude profiles, shown in figure 9, are determined from the integrated cross-power frequency spectra for both discharges 193921 and 193775 for the outer-core ($\rho\sim0.65-0.83$) and the edge ($\rho\sim0.82-1.05$) respectively. The scatter of points at each radial location are from different poloidal pairs of channels each separated by 1.4 to 1.8 cm. Some poloidal variation exists within the BES measurement locations ranging from −4.8 to +6.6 cm relative to the outboard midplane. The fluctuation amplitudes peak at $\rho \sim 0.95$ and decrease in power toward the core. These amplitudes drop to very low levels ($\tilde{n}/n \lt 0.4\%$) inside of $\rho \sim 0.83$. Additionally, the amplitude is decreased at the separatrix, a feature distinct compared with positive triangularity L-mode plasmas, which typically peak in normalized amplitude at or near the separatrix [42, 43]. Notably this decrease of fluctuation amplitude at the separatrix is not observed in the ELM-free NT-edge case shown in figure 4. This could indicate a triangularity dependence of the behavior, where the effect may be more prominent in stronger NT however additional studies are required.

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In cases with long integration times and no mixed mode behavior, time-lag cross correlation techniques can be used to highlight the statistical structure of the turbulence. The time-lag cross correlation between two signals provides a power-weighted measure of turbulence behavior. Using the Hilbert transform, the envelope of the correlation function can be estimated allowing measurements of the group velocity, correlation length, and correlation time. Taking poloidal arrays of 8 channels, the time lag of the maximum in the correlation envelope is calculated for increasing channel spacing. The group velocity is determined from the linear fit of time lag as a function of channel spacing. This group velocity is in the lab frame. To determine mode velocity in the plasma frame, plasma flow velocity must be subtracted using CER as described previously. The turbulence group velocity in the lab frame as well as $V_{E\times B}$ are shown in figure 10(a). Subtracting $V_{E\times B}$ from the lab frame group velocity provides the turbulence group velocity in the plasma frame as seen in 10(b)). Modes propagating in the electron diamagnetic direction (negative velocity) consistent with TEM-like turbulence are observed outside of ρ > 0.83, as was also seen in the reduced NT shapes. As shown with the extended radial profile, modes propagating in the ion diamagnetic direction (positive velocity) consistent with ITG-like turbulence dominate the outer-core $(\rho = 0.65-0.83$). Additionally, the turbulence group velocity increases at the edge (ρ > 0.9) where pressure gradients are maximal. This is consistent with the drift wave velocity typically scaling with the diamagnetic velocity and therefore the pressure gradient [44].

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As the channel spacing increases, the correlation between any two given channels decreases according to the turbulence correlation length. Fitting the decay of the value of the correlation envelope at zero time-lag with channel spacing gives a measure of the correlation length. The poloidal correlation length is best fit using an exponential function while the radial correlation length is best fit using a Gaussian function [45]. As can be seen in figure 11, the core turbulence propagating in the ion diamagnetic direction is characterized by a radially-poloidally symmetric eddy structure with comparable poloidal and radial correlation lengths. The turbulence in the edge shows a poloidally extended asymmetry with long poloidal correlation lengths relative to the radial correlation lengths. The poloidal lengths for the electron mode increase monotonically toward the separatrix while the radial lengths remain constant. In contrast, the poloidal elongation is typically constant radially in positive triangularity L-modes discharges [43].

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NT offers a unique ELM-free approach to the core-edge integration problem in part through its impact on turbulent transport. In a sweep of triangularity ($\delta_{\text{avg}} = -0.01 \rightarrow -0.13$) with fixed power, turbulence fluctuation amplitudes are seen to increase locally by ${\sim}70\%$ at $\rho\sim0.95$ but decrease by ${\sim}50\%$ in the outer-core ρ < 0.9 when the H-mode is suppressed. Additionally, low-velocity edge modes below 70 kHz are suppressed with stronger triangularity, and the mode rotating in the electron diamagnetic direction becomes broader in wavenumber space. A plasma with strong NT ($\delta_{\text{avg}}\sim-0.5$) is shown to have low amplitude core turbulence and a reduction of fluctuations on the separatrix. ITG-like modes propagating in the ion diamagnetic direction are observed for $\rho\lesssim0.83$ and TEM-like modes propagating in the electron diamagnetic direction are seen for $\rho\gtrsim0.83$. The ITG-like modes have a radially-poloidally symmetric structure, while the TEM-like modes are poloidally extended towards the separatrix.

The modes in the edge of NT plasmas are consistent with TEM-like drift wave turbulence; however, other edge instabilities which also propagate in the electron diamagnetic direction include the Resistive Ballooning Mode and the Micro-Tearing Mode. These can also exhibit driftwave-like behavior, but both typically require significant collisionality ($\nu^* \unicode{x2A7E} 1$) for the instability to be observed [46, 47]. This condition can be achieved in the edge (ρ > 0.95) in various discharges, but it is not achieved in the outer-core ($\rho\sim0.85$) due to the increased local temperature. Since similar behavior is observed in the mode spectrum from $\rho \sim 0.85-1.05$, it suggests that a collisionless mode could be a dominant instability drive with TEM as a prime candidate.

In the scan of triangularity, the reduction of the TEM-like turbulence at ρ < 0.9 is indicative of the TEM suppression predicted by theory [15, 17] and shown in previous wall-limited experiments [27]. Additionally the wavenumber broadening observed is similar to the theoretical predictions for NT TEM turbulence [17, 18]. Similar to previous simulations, ITG-like turbulence was observed to be dominant at $\rho\lesssim0.83$ [28]. These fluctuations were of a similar amplitude to those observed in previous wall-limited cases [27]. Turbulence amplitude is observed to decrease toward the separatrix as compared to $\rho\sim0.95$ in the strong triangularity case as seen in figure 9. This hints at the thin local shear layer observed by the Doppler BackScatter (DBS) diagnostic described in [48]. The radially thin shear layer at the base of the NT-edge pedestal is observed to locally suppress the turbulence measured by the DBS system. The layer is smaller than the BES radial resolution ($\Delta R \lt 0.9$ cm), but the effect may be seen in the decrease in the measured local fluctuation amplitude on the separatrix.

This study opens up avenues for future work to investigate the more subtle nonlinear interaction of turbulence with GAMs or zonal flows using bi-coherence techniques. Additionally, the predicted poloidal variation of turbulence described in [24] could be studied with targeted sweeps of poloidal diagnostic location, by changing the focusing location of BES along the vertical extent of the viewed beam. The joint Probability Density Function of the radial and poloidal velocities measured by BES are predicted to distort according to local radial electric field shear. The poloidal variation of the radial electric field shear is predicted to be dependant on triangularity [24]. The measured turbulence in NT could also be used to validate existing gyro-kinetic codes using synthetic diagnostics. Linear gyrokinetic analysis could also aid in confirming the dominant plasma instability. The impact of NT on the generation of poloidal Reynolds stress necessary for an L-H transition could be investigated to elucidate the physical mechanism of H-mode inhibition. Additionally, targeted sweeps of triangularity from L-mode to the NT-edge could be performed to isolate the shaping effect from edge shear effects present in H-mode.

Special thanks to Shawn Simko for helpful discussions and assistance in editing this document. Many calculations presented in this work were completed in the OMFIT framework [49]. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Awards DE-FG02-08ER54999, DE-SC0022270, DE-SC0020287, and DE-FC02-04ER54698.

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

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.