H-mode pedestal improvements with neon injection in DIII-D

Effects of neon level on the pedestal and confinement improvements are studied at two constant heating powers (3 and 6 MW). In each heating power case, two discharges are presented showing that the neon effects on the pedestal and confinement improvements are reproducible. For these two discharges, the only difference is the neon injection rate.

Figure 2 shows the time evolution of the 3 MW discharges 166615 (black lines) and 166616 (red lines) from 1200 to 5400 ms. These time evolution parameters include the neutral beam heating power, neon injection rate, neon density at ${\psi _N} \sim 0.9$, line-averaged density, plasma stored energy, global normalized beta, energy confinement enhancement factor ${H_{98y,2}}$, pedestal electron density, pedestal electron temperature, pedestal electron pressure, divertor Dα signal, which is used to monitor ELM instabilities, and electron temperature near the lower outer strike point, which is measured by the divertor Thomson scattering system [48]. The pedestal electron parameters were obtained by the method described in section 2. For the discharge 166615 with neon injection rate of 25% duty cycle at 0.5 Torr.l s⁻¹, the plasma almost immediately responded to the neon injection, which began at 2 s. Figure 2(c) shows the build-up of neon density at ${\psi _N} \sim 0.9$ after 2 s. It decreased due to the ELM bursts and re-built up during the inter-ELM phases. In this discharge, from 2.0 to 3.29 s, the line averaged density increased by ∼35%–45% and the plasma stored energy increased up to ∼35%, the global normalized beta increased from 1.5 to around 1.9, and the ELM frequency was significantly reduced. During the inter-ELM phase, the pedestal electron density increased by ∼60%, while the pedestal electron temperature quickly saturated to a value a little smaller than the value before neon injection. Consequently, the pedestal electron pressure had an increasing trend during the inter-ELM phase similar to the pedestal electron density. The blue and green lines in figure 2(h) show the electron contributions from neon and carbon at the pedestal top for the discharge 166615 and 166616 respectively. They can account for a lot (not all) of the increase in the pedestal electron density-about 50%. In addition, the impurity injection often decreases the ELM frequency so the pedestal density could build up higher. This physics does not require a change in source, just longer period between ELMs. During this inter-ELM phase, the ${H_{98y,2}}$ factor also increased by up to ∼25%. After 3.29 s, the plasma dropped back to the L-mode confinement regime following an ELM for 250 milliseconds, and then went back to the high confinement regime. As for the discharge 166616 with lower neon injection rate of 25% duty cycle at 0.15TL/s, the plasma very moderately responded to the neon injection from 2 to 3 s, but when there was enough neon in the plasma after 3 s, the pedestal electron density and other parameters exhibited a similarly increasing trend to the discharge 166615 as shown in figures 2(d)–(k). Note that in these two discharges, the electron temperature near the lower outer strike point was around 10–35 eV before and after neon injection as shown in figure 2(l). This indicates that the lower outer divertor was still in the attached state [49].

Figure 3 illustrates the effects of neon injection on the profiles in the pedestal region in a typical 3 MW discharge 166616. The profiles are obtained by the method described in the section 2. The red, blue and green profiles use the data from the last 20% of the inter-ELM period in an overall time window of 500–600 ms duration near 1765 ms, 2650 ms and 3615 ms respectively. The detailed time windows for each of the time points are highlighted by the same color band in figure 2. These time windows which were chosen based on the pedestal and ELM characteristics look approximately stationary. This rule applies in all the profiles analysis in this paper.

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As described above the plasma responded to the neon injection very moderately in the first 1000 ms duration (2–3 s) after neon injection in discharge 166616, the profiles near 2650 ms (blue lines) in the pedestal region of this discharge show a moderate change in figure 3. In this period (2–3 s), compared to the profiles before neon injection (red lines), the pedestal electron and ion temperature did not show obvious changes, the pedestal electron and ion density increased by a small amount, and as a result, the pedestal electron, ion and total pressure increased by a small amount. In the later time near 3165 ms after neon injection, the pedestal profiles (green lines) showed a strong change compared to the profiles before neon injection (also see figure 2). The pedestal height of the electron density increased by a factor of ∼1.6 and its width also increased. At this time, the pedestal electron temperature decreased by a small amount. Consequently, the pedestal electron pressure increased by a factor of ∼1.5. Notably, the neon did not dilute the carbon impurity concentration which increased by a factor of ∼1.4 as shown in figure 3(c). The deuterium and total ion density also increased significantly as shown in figure 3(b). The ion temperature profile decreased by a small amount and became flatter in the pedestal region; as a result, the pedestal deuterium and total ion pressure increased. Combining all of these profiles changes, the pedestal total pressure profile became higher and wider near 3165 ms after neon injection as shown in figure 3(i).

The profiles of normalized current density ${j_{\text{N}}}$ and normalized pressure gradient α in the pedestal region, which are important in determining the peeling-ballooning stability, are shown in figures 3( j ) and 3(l). The α and ${j_{\text{N}}}$ are defined as follows [15],

$$\begin{align} \alpha & = \frac{{{R_0}{B_{{T_0}}}/f}}{{\left\langle {R_0^2/{R^2}} \right\rangle }}{R_0}{q^2}\frac{{\sqrt {V/(2{\pi ^2}{R_0})} }}{\rho }\frac{{\partial \beta }}{{\partial \rho }},\nonumber\\[6pt] \beta & = \frac{p}{{B_{{T_0}}^2/2{\mu _0}}},\nonumber\\[6pt] f & = R{B_{T,}}{\rm{ }}\rho = \sqrt {{\Phi _T}/(\pi {B_{{T_0}}})}. \end{align} \tag{ 1 }$$

where R is the major radius, ${B_{\text{T}}}$ is the toroidal field, ${R_0}{B_{{T_0}}}$ are values at the geometric plasma centre, $\left\langle {} \right\rangle$ represents a flux surface average, $V$ is the plasma volume, $p$ is the pressure, and ${\Phi _T}$ is the toroidal flux within a magnetic surface.

$$\begin{align} {j_N} &= ({j_{{\text{PB}}}} + j_{{\text{PB}}}^{{\text{SEP}}})/(2{I_{\text{P}}}/A), \nonumber\\ {j_{{\text{PB}}}} &\equiv \frac{f}{{{R_0}}}\left\langle {\frac{{\mathop J\limits^ \to \cdot \mathop B\limits^ \to }}{{{B^2}}}} \right\rangle {\text{ = }}\frac{f}{{{R_0}}}\left\langle {\frac{{{j_{PS}}}}{B}} \right\rangle + \frac{{{{(f/{R_0})}^2}}}{{\left\langle {{B^2}} \right\rangle }}{j_\parallel } \nonumber\\ &{\text{ = }} - \left[ {{R_0}\frac{{\partial p}}{{\partial \psi }}{{\left(\frac{f}{{{R_0}}}\right)}^2}\left\langle {\frac{1}{{{B^2}}}} \right\rangle + \frac{f}{{{\mu _0}{R_0}}}\frac{{\partial f}}{{\partial \psi }}} \right], \\ {j_{PS}} &= f\frac{{\partial p}}{{\partial \psi }}\left( {\frac{B}{{\left\langle {{B^2}} \right\rangle }} - \frac{1}{B}} \right),{\text{ }}{j_\parallel } = \frac{{\left\langle {\mathop J\limits^ \to \cdot \mathop B\limits^ \to } \right\rangle }}{{f/{R_0}}},\nonumber \end{align} \tag{ 2 }$$

${j_{{\text{PB}}}}$ is the current density important for PBM stability [33, 50] which includes contributions from the flux surface average parallel current ${j_\parallel }$ and the Pfirsh-Schluter current, ${j_{PS}}$, $j_{{\text{PB}}}^{{\text{SEP}}}$ is ${j_{{\text{PB}}}}$ at the separatrix. The normalized current density ${j_N}$ is the average of ${j_{{\text{PB}}}}$ and $j_{{\text{PB}}}^{{\text{SEP}}}$ which is then normalized to the total plasma current density. The neoclassical bootstrap current in the pedestal is the dominant term in ${j_\parallel }$ that is also shown in figure 3(j). ${j_{{\text{PB}}}}$ is self-consistently calculated in a 'kinetic' equilibrium constructed with the EFIT code [42].

Based on the above information, the peeling-ballooning mode (PBM) stability analysis was performed with the ELITE code [33] for the three time points of figure 3 as shown in figure 4. The X and Y axes in figure 4 represent peak values of normalized pressure gradient, α, and normalized current density, ${j_N}$, in the pedestal region. The stability boundary for each time point is determined by the ratio of growth rate to diamagnetic stabilization term on the grid, and then tracing the contour for which this ratio is 1 [15]. The form of the diamagnetic stabilization term used in this paper is derived from BOUT++ calculations described in reference [7]. The experimental operating points are computed from the 'kinetic' profiles as depicted in figure 3. If the operating points of the discharges are above or to the right of the stability boundary, the discharges are predicted to be unstable. The stability boundaries are only computed in the region near the operating points and are expected to extend to regions of lower α and ${j_N}$. As shown in figure 4, these three operating points, which use the data from the last 20% of the ELM cycle, are all at the instability threshold within the experimental uncertainties consistent with the peeling-ballooning theory predictions.

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From 1765 ms to 3615 ms, with increasing neon level in the plasma, the ballooning stability threshold increased by a small amount which let the plasma reach a higher α value. The normalized pressure gradient, α, profile at 3615 ms also was wider than the other two time points (see figure 3(l)). Since α is proportional to the ${q^2}$ as shown in equation (1) (where $q$ is the safety factor), the shift of the peak α inward to a region of lower q results in a further significant improvement of pressure gradient in real space after neon injection as shown in figure 3(k). Note that, although the ballooning stability boundary increased after neon injection in figure 4, the peeling stability boundary was not changed after neon injection. This may be due to the relatively low neon injection level in discharge 166616. For approximately 3.3 times higher neon injection rate in discharge 166615, the peeling stability boundary was reduced after neon injection, and the ballooning stability boundary was also increased as shown in figure 5. The operating points, based on the data from the last 20% of the ELM cycle, were in the stable region. More studies on discharge 166615 will be discussed in later sections.

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Effects of neon level on pedestal and confinement are also studied in the 6 MW discharges. The time evolution of the 6 MW discharges 166612 (black lines) and 166613 (red lines) from 1200–5400 ms is shown in figure 6. These waveforms represent the same parameters as described in figure 2. For the discharge 166613 with neon injection rate (50% duty cycle at 0.5 Torr.l s⁻¹), in which the neon injection began at 2 s, but the waveform was partially overlaid by the waveform from discharge 166612 (black), the plasma parameters after neon injection gradually changed and began to show big changes around 3.8 s. Figure 6(c) shows the gradually build up of the neon density at ${\psi _N} \sim 0.9$ after 2 s. From 2 to 3.8 s, the line averaged density gradually increased up to ∼55%, the plasma stored energy increased up to ∼15% and the global normalized beta increased from 2.0 to around 2.25. The ${H_{98y,2}}$ factor slightly increased by ∼7%. In this period, the ELM frequency gradually decreased as indicated by divertor Dα signals as shown in figure 6(k). In a general trend, the pedestal electron density gradually increased up to ∼55%, the pedestal electron temperature gradually decreased by ∼30% and pedestal electron pressure gradually increased by ∼20%. From 3.8 to 4.4 s, although the pedestal electron density increased during the ELM cycle, the pedestal electron temperature generally dropped; as a result, pedestal electron pressure only increased by a small amount. The plasma stored energy and confinement factor during this period showed a slight drop. The electron contributions from neon and carbon at the pedestal top increased from < 30% (at 2 s) to > 50% (at 4.5 s) as shown in figure 6(h). In the discharge 166612 (black) with a lower neon injection rate (25% duty cycle at 0.5 Torr.l s⁻¹), in which the neon injection also began at 2 s, all the parameters shown in figure 6 had a similar trend compared to 166613 from 1.2 to 4.0 s. Perhaps due to the lower neon injection level in discharge 166612, the pedestal parameters response to the neon injection is more moderate than in the discharge 166613 during this period. After 4 s, the discharge 166612 lost some heating power and the plasma confinement decreased probably due to the beginning of a significant n = 2 core MHD mode at 4.1 s (not shown here). As shown in figure 6(l), in these two discharges, the electron temperature near the lower outer strike point was around 15–40 eV before neon injection. After neon injection, the electron temperature near the lower outer strike point began to show a clear decrease after 2.5 s during the inter-ELM phases as indicated by the green line with $T_{\text{e}}^{{\text{DIV}}}{\text{ = }}5{\text{ eV}}$. But there were also many time points in which the electron temperature was still higher than 5 eV during the inter-ELM phases. The lower outer divertor was close to the detached state during the inter-ELM phases after neon injection. This has little influence on the pedestal studies in this paper.

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Figure 7 illustrates the profile changes before (red lines) and after (blue, green and magenta lines) neon injection in a typical 6 MW discharge 166613. All of these four color profiles use the data from the last 20% of the inter-ELM period in an overall time window of 400–500 ms duration near 1765 ms (red lines), 2765 ms (blue lines), 3465 ms (green lines) and 4165 ms (magenta lines) respectively. And the detailed time windows for each of the time points are highlighted by the same color band in figure 6.

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As the gradual evolution trend of the discharge 166613 depicted in figure 6, the gradual increasing trend of profiles after neon injection are also exhibited in figure 7. After neon injection, the pedestal electron density gradually increased up to a factor of ∼2.2 near 4165 ms, the pedestal electron temperature gradually decreased by ∼30% near 4165 ms, as a result, the pedestal electron pressure followed the trend of electron density and gradually increased by a factor of ∼1.6 near 4165 ms. As shown in figure 7(c), from 1765 ms to 3465 ms, the neon injection did not dilute the carbon concentration but increased its concentration by a factor of ∼1.4 near 3465 ms. Near 4165 ms, the neon showed some dilution effect as the carbon concentration was reduced but it was still higher than the value before neon injection. The increase in carbon concentration with neon injection in these and the 3 MW cases is likely the result of the decrease in ELM frequency as ELMs are known to be effective at flushing medium Z impurities [51–54]. And as shown in figure 7(b), the total ion density and deuterium density increased with time. Following the gradual decrease of the pedestal ion temperature after the start of neon injection, a larger decrease of ∼25% was observed at 4165 ms. The ion density increase dominated resulting in the pedestal deuterium and total ion pressure increasing with neon injection as shown in figure 7(h). Combining all of these profiles changes, the pedestal total pressure increased by a factor ∼1.35 by 4165 ms.

The peeling-ballooning stability analysis was also performed with the ELITE code for the 4 time points of figure 7 as shown in figure 8. The PBM stability boundary and operating points were computed as described for the 3 MW discharge. The operating points at time 1765, 2765 and 4165 ms were either above the stability threshold or at the stability boundary within the experimental uncertainties. The operating point at 3465 ms had the biggest deviation from the PBM stability boundary and will be discussed more in section 3.4. From 1765 to 3465 ms, after neon injection, the ballooning stability boundary was extended and peeling stability boundary showed a slight decrease. This helped the plasma to reach higher pressure gradient as shown in figures 8 and 7(k). At time 4165 ms, there was more neon injected into the plasma as shown in figure 7(c). Both the peeling stability boundary and ballooning stability boundaries were reduced. The plasma reached relatively smaller normalized pressure gradient at 4165 ms than the value at 3465 ms as shown in figure 8. Compared to the ballooning stability limit before neon injection at 1765 ms, the ballooning stability limit at 4165 ms was still improved.

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Two discharges with the same settings including the neon injection rate (25% duty cycle at 0.5 Torr.l s⁻¹) from 2 to 4 s, but only different heating powers (3 MW and 6 MW) are compared in figure 9. The waveforms represent the same parameters as described in figure 2. As shown in figure 9(b), the neon was injected at 2 s. The neon density at ${\psi _N} \sim 0.9$ in both 3 and 6 MW discharges (see figure 9(c)) generally reached a similar value, but the evolution of the neon density was quite different due to the different ELM behaviors. Before neon injection, the 3 MW discharge 166615 (red lines) had higher line-averaged density but lower plasma stored energy than the 6 MW discharge 166612 (black lines). The global normalized beta of the 3 MW discharge was smaller than the 6 MW discharge. And these two discharges had similar plasma confinement factors as depicted by the ${H_{98y,2}}$ in figure 9(g) before neon injection. Before neon injection, the 3 MW discharge had higher pedestal electron density and lower pedestal temperature than the 6 MW discharge. Consequently, these two discharges had similar pedestal electron pressure. The 3 MW discharge also had lower ELM frequency than the 6 MW discharge before neon injection as indicated by the divertor Dα signals in figure 9(k). After neon injection, the plasma in 3 MW discharge responded to the neon injection much quicker and stronger than the 6 MW discharge. In the 3 MW discharge, the plasma stored energy increased by up to ∼35% in the enhanced confinement phase, while in the 6 MW discharge, the plasma stored energy gradually increased by up to ∼20%. At this neon injection rate, the 3 MW discharge returned to L-mode between 3310 and 3360 ms as shown in figures 9(d)–(k), while the 6 MW discharge reached an approximately stationary neon enhanced confinement phase from 3400 ms to 3800 ms. As shown in figure 9(a), the 6 MW discharge later lost some heating power, the lost confinement probably mostly due to the beginning of the core MHD mode which is not shown here. As shown in figure 9(l), at the same neon injection rate, the electron temperature near the lower outer strike point did not show a very clear decrease in the 3 MW discharge and the lower outer divertor was still in the attached state. While in the 6 MW discharge, the electron temperature near the lower outer strike point showed a clear decrease after 2.5 s, the lower outer divertor was close to the detached state as also mentioned in section 3.1.

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The profiles from these two discharges are compared before and after neon injection as shown in figures 10 and 11. Before neon injection as shown in figure 10, the profiles of the 3 MW (red) and 6 MW (blue) discharges near 1765 ms both used the data from the last 20% of the inter-ELM phase in the time window from 1500 to 2000 ms, which were highlighted with the red dashed rectangle and red color band respectively in figure 9. The 3 MW discharge 166615 had higher pedestal electron and total ion density profiles but lower pedestal electron and ion temperature profiles than the 6 MW discharge 166612. The carbon concentration and effective charge profiles in the 3 MW discharge were also higher, possibly due to the lower ELM frequency, than the profiles in the 6 MW discharge. But the 3 and 6 MW discharge had the similar electron, ion and total pressure profiles in the pedestal gradient region as shown in figures 10(g)–(i).

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After neon injection as shown in figure 11, the profiles (red) of the 3 MW discharge 166615 near 2805 ms used the data from the last 20% of the inter-ELM phase in the time window from 2500–3100 ms which was highlighted with the blue dashed rectangle in figure 9. For comparing the profiles at the similar neon injection level, the profiles (blue) of the 6 MW discharge 166612 near 2850 ms used the data from the similar ELM averaging (only data from the last 20% of the inter-ELM phase was used) time window to the 3 MW discharge as highlighted with blue color band in the figure 9. As depicted in figure 11, the 3 MW discharge had higher pedestal electron and total ion density profiles but lower pedestal electron and ion temperature profiles than the 6 MW discharge, which was similar to the case before neon injection. Although the carbon concentration and neon concentration profiles between the two discharges were similar (figure 11(c)), since the 3 MW discharge had much higher electron density profile (figure 11(a)), the carbon and neon densities (not shown here) of 3 MW discharge were actually higher than the 6 MW discharge. As a result, the 6 MW discharge had a little higher effective charge profile than the 3 MW discharge. And similar to the case before neon injection, the 3 and 6 MW discharges had similar pedestal ion and total pressure profiles in the pedestal gradient region. At this time, the 6 MW discharge had higher normalized current density than the 3 MW discharge which is similar to case before neon injection, but the 6 MW discharge had a little lower peak values of normalized pressure gradient than the 3 MW discharge. The location of peak normalized pressure gradient of the 6 MW discharge moved a little outward compared to the one of 3 MW discharge as shown in figure 11(l).

A later ELM averaging time window from 3500 to 4000 ms in the 6 MW discharge 166612, in which the plasma was in the final enhanced confinement phase, was chosen for the profiles (green) analysis as highlighted with green color band in figure 9. These profiles (green) from the 6 MW discharge are compared to the profiles (red) from the final enhanced confinement phase in the 3 MW discharge 166615 in figure 11. The comparison is similar to the case before neon injection and the case with similar injection level as described above: the 3 MW discharge (red) achieved higher pedestal electron and total ion density profiles but lower pedestal electron and ion temperature profiles than the 6 MW discharge (green) in the final enhanced confinement phase. The neon concentration profile from the final enhanced confinement phase in the 6 MW discharge (green) was higher than the one in the 3 MW discharge (red) as shown in figure 11(c). As illustrated in figures 11(g)–(i), the pedestal electron, ion and total pressure gradient regions in the 6 MW discharge were closer to the separatrix than the 3 MW discharge, but the pedestal pressure heights were not lower than the 3 MW discharge. As a result, the peak normalized current density and pressure gradient in the 6 MW discharge were much larger than the values in the 3 MW discharge, and their locations shifted outward to be closer to the separatrix than in the 3 MW discharge as depicted in figures 11( j) and (l).

The peeling-ballooning stability analysis was examined using the profiles from figures 10 and 11 to study the effects of heating power on the neon seeded discharges. The peeling-ballooning stability boundary and operating points were computed in the same way as described in section 3.1. As illustrated in figure 12(a), before neon injection, the operating points representing the data from the last 20% of the inter-ELM phase for both 3 and 6 MW discharges were inside and close to the PBM stability boundary which is consistent with the peeling-ballooning theory predictions. The 3 MW discharge (red) had the similar peeling stability boundary to the 6 MW discharge (blue) but broader ballooning stability boundary than the 6 MW discharge. The operating points between 3 and 6 MW discharges did not show a significant difference.

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As illustrated in figure 12(b), after neon injection, at a similar neon injection level in the enhanced confinement phase, the 3 MW discharge (red) again had a broader ballooning stability boundary than the 6 MW discharge (blue) but lower peeling stability boundary than the 6 MW discharge. Both of the operating points were also inside and close to the PBM stability boundary. The 3 MW discharge reached slightly lower normalized current density and higher normalized pressure gradient, but the overall difference was not large. As described in the previous profile analysis, at the final enhanced confinement phase in the 6 MW discharge, the plasma achieved much larger peak values of normalized current density and normalized pressure gradient (see figures 11(j) and (l)) than the one at the final enhanced confinement phase in the 3 MW discharge which was also shown by the operating point (green) in figure 12(b). At this time, the peeling stability boundary of the 6 MW discharge (green) was lower than the one in the early neon injection time (blue) but the ballooning boundary was increased. The PBM stability boundary (green) from the final enhanced confinement phase in the 6 MW discharge was similar to the PBM stability boundary in the 3 MW discharge, but its operating point (green) was quite far outside the boundary in the unstable region. This case will be discussed more in the section 3.4.

The measured pedestal widths in the neon injection experiment described in this paper are compared with the predicted widths from the EPED1.0 [34, 55] model in this section. The EPED model predicts the pedestal width and height in many tokamaks, such as DIII-D [7, 34, 55–57], JET [55, 58–60], AUG [60], JT-60 U [55, 61], generally within ∼20% deviation. This model combines two hypotheses to predict the pedestal height and width. The first hypothesis is that the maximum achievable pedestal height between ELMs is limited by finite-n peeling-ballooning MHD modes [62], and the second hypothesis is that the pedestal width (${\Delta _{{\psi _N}}}$) is constrained at all times by the nearly local kinetic ballooning modes giving the relationship ${\Delta _{{\psi _N}}} = \beta _{p,ped}^{1/2}G({\nu _*},\varepsilon ,\ldots)$, where ${\beta _{p,ped}}$ is the poloidal beta at the pedestal top and $G$ is a weakly varying function of aspect ratio ($\varepsilon$), collisionality (${\nu _*}$), and other dimensionless parameters, with value generally in the range 0.07–0.1 for the standard aspect ratio shaped tokamaks [7, 34].

The comparison between the experimental pedestal widths and the EPED1.0 scaling, ${\Delta _{{\psi _N}}} = {c_{{\text{EPED1}}}}\beta _{p,ped}^{1/2}$, in the neon injection experiment described in this paper is shown in figure 13, where ${c_{{\text{EPED1}}}} = 0.076$, the value derived by fitting to a set of DIII-D discharges without impurity seeding [34], is used in figures 13(a) and (b) and ${c_{{\text{EPED1}}}} = 0.089$, the value obtained expected based on theory [7], is used in figures 13(c) and (d). The measured pedestal width is the average of the ${T_{\text{e}}}$ and ${{\text{n}}_{\text{e}}}$ widths in normalized poloidal flux, ${\psi _N}$. All the ${T_{\text{e}}}$ and ${{\text{n}}_{\text{e}}}$experimental widths were taken from the corresponding profiles described in section 3.1 and 3.2. The triangles and stars in figure 13 represent the 6 MW discharges 166612 and 166613 respectively, and the circles and squares represent the 3 MW discharges 166615 and 166616 respectively. The colors used in figure 13 represent the time points that were mentioned in section 3.1 and 3.2. So the color red always represents the time before neon injection, and the colors blue, green, magenta represent the time after neon injection. In figure 13, the solid lines are unity lines, and the dashed lines show deviations of $\pm 20\%$ from unity. As shown in figure 13(a), the measured pedestal widths in some discharges exceed the EPED1.0 width scaling, ${\Delta _{{\psi _N}}} = 0.076\beta _{p,ped}^{1/2}$, by more than 20%. The measured pedestal widths in all the discharges before or after neon injection from the EPED1.0 width scaling, ${\Delta _{{\psi _N}}} = 0.089\beta _{p,ped}^{1/2}$, are within 20% deviation as shown in figure 13(c). The data area in figures 13(a) and (c) is also zoomed in and shown in figures 13(b) and (d), respectively for a clearer view.

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In this section, a possible explanation of the pedestal and confinement improvements in the neon injection experiment presented in this paper is proposed. As shown in section 3.1 and section 3.2, we found that not only could neon cross the separatrix and penetrate into the pedestal region but also it led to additional electron, carbon and deuterium density increase in the pedestal region, possibly related to decrease of ELM frequency. This significant increase in the pedestal density with a corresponding small reduction of the pedestal temperature helped to increase the pedestal pressure. The peeling-ballooning analysis in section 3.1 and section 3.2 showed that, in both 3 and 6 MW discharges, after neon injection, the ballooning stability boundary was generally extended to larger pressure gradient, while the peeling stability boundary only began to drop when the neon level was relatively high. The improved ballooning stability boundary allows the plasma to reach higher pressure as well as normalized pressure gradient. In combination with the core profile stiffness these pedestal effects could lead to the plasma stored energy and confinement improvement.

As mentioned in the section 3.1 and section 3.2, the operating points of discharge 166612 at time 3765 ms and discharge 166613 at time 3465 ms were computed to be in the MHD unstable zone and relatively far away from the peeling-ballooning stability boundary. These two operating points, representing the data from the last 20% of the inter-ELM period, should be close to the PBM stability boundary if the PBM is dominant in limiting pedestal height in this experiment.

In the following part of this section it will be shown that by modifying the effective diamagnetic frequency, which sets the peeling-ballooning mode growth rate threshold [7], to take into account impurity effects, the stability threshold can be brought into better agreement with the operating points. This in turn indicates that the impurity may help to improve pedestal pressure and confinement through increasing the effective ion diamagnetic frequency in the pedestal region extending ballooning stability boundary extension.

The formula for the diamagnetic frequency of different ions in CGS units is described by

$$\begin{align} {\omega _{ * Z}} &= \frac{{cn}}{{{\text{Ze}}{n_Z}}}\frac{{\partial {p_Z}}}{{\partial \psi }}\, \nonumber\\ &= \frac{{cn}}{{{\text{Ze}}{n_Z}}}\left(\frac{{\partial {n_Z}}}{{\partial \psi }}{T_i} + {n_Z}\frac{{\partial {T_i}}}{{\partial \psi }}\right), \end{align} \tag{ 3 }$$

where $Z$ is effective charge number, c is the speed of light in vacuum, $n$ is the toroidal mode number, e is the elementary charge, ${n_Z}$ is the ion density in which its effective charge number is $Z$, ${p_Z}$ is the ion pressure in which its effective charge number is Z, ${T_i}$ is the ion temperature assuming that different ions have the same ion temperature, and $\psi$ is the poloidal magnetic flux. The main ion in the experiment described in this paper is deuterium, and it is denoted by letter $D$. So deuterium diamagnetic frequency in CGS units is given by

$$\begin{equation}{\omega _{ * D}} = \frac{{cn}}{{{\text{e}}{n_D}}}\left(\frac{{\partial {n_D}}}{{\partial \psi }}{T_i} + {n_D}\frac{{\partial {T_i}}}{{\partial \psi }}\right).\end{equation} \tag{ 4 }$$

And the carbon and neon diamagnetic frequencies in CGS units are described respectively by

$$\begin{equation}{\omega _{ * C}} = \frac{{cn}}{{{\text{6e}}{n_C}}}\left(\frac{{\partial {n_C}}}{{\partial \psi }}{T_i} + {n_C}\frac{{\partial {T_i}}}{{\partial \psi }}\right){\text{ }}\end{equation} \tag{ 5 }$$

$$\begin{equation}{\omega _{ * Ne}} = \frac{{cn}}{{{\text{10e}}{n_{Ne}}}}\left(\frac{{\partial {n_{Ne}}}}{{\partial \psi }}{T_i} + {n_{Ne}}\frac{{\partial {T_i}}}{{\partial \psi }}\right).\end{equation} \tag{ 6 }$$

In the ELITE code, with the assumption that the total ion density (${n_i}$) equals the electron density (${n_e}$), the approximate total ion diamagnetic frequency (${\omega _{ * i}}$) is calculated with the equation,

$$\begin{align} {\omega _{ * i}} &= \frac{{cn}}{{{\text{e}}{n_i}}}\frac{{\partial {p_i}}}{{\partial \psi }}\, \nonumber\\ &= \frac{{cn}}{{{\text{e}}{n_e}}}\left(\frac{{\partial {n_e}}}{{\partial \psi }}{T_i} + {n_e}\frac{{\partial {T_i}}}{{\partial \psi }}\right). \end{align} \tag{ 7 }$$

All the diamagnetic frequency profiles of different ions in the pedestal region, as mentioned above, before and after neon injection in both 3 and 6 MW discharges are calculated with the experimental profiles and toroidal number n = 10 as illustrated in figure 14. Since every kind of ion diamagnetic frequency is proportional to toroidal number, the exact n number does not affect the comparison between different ion diamagnetic frequencies. The time points from each discharge used in the figure 14 are same as the time points that were used in section 3.2. The ${\omega _{ * e}}$ in figure 14 is used to represent the ELITE calculated total ion diamagnetic frequency (${\omega _{ * i}}$), and the ${\omega _{ * D,C}} = {\omega _{ * D}} + {\omega _{ * C}}$and ${\omega _{ * D,C,Ne}} = {\omega _{ * D}} + {\omega _{ * C}} + {\omega _{ * Ne}}$. As shown in figure 14, for both discharges before and after neon injection, the peak values of approximate total ion diamagnetic frequency (${\omega _{ * e}}$) (black curve) calculated by the ELITE code are close to the peak values of deuterium diamagnetic frequency (${\omega _{ * D}}$) (green curve). The peak values of ${\omega _{ * e}}$ are smaller than the peak values of ${\omega _{ * D,C}}$ and this is smaller than the peak values of ${\omega _{ * D,C,Ne}}$.

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In the following analysis, we use ${\omega _{ * D,C}}$ and ${\omega _{ * D,C,Ne}}$ as the approximate experimental total ion diamagnetic frequency before and after neon injection respectively. And its peak value in the pedestal region is denoted by ${\omega _{ * ,EXP}}$. The peak value of ELITE calculated total ion diamagnetic frequency (${\omega _{ * e}}$) is denoted by ${\omega _{ * ,ELITE}}$. The detailed comparison between ${\omega _{ * ,EXP}}$ and ${\omega _{ * ,ELITE}}$ at all the time points in the discharges studied in section 3.1 and section 3.2 are provided in figure 15. The symbols except the '$\times$' representing the discharges and the colors representing the time points have the same meaning as used in figure 13.

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As shown in figure 15, the ${\omega _{ * ,EXP}}$ (filled symbols) and ${\omega _{ * ,ELITE}}$ (open symbols) have the same evolution trend. For both 6 MW (figures 15(a) and (b)) and 3 MW (figure 15(d)) discharges, after neon injection, the peak values of total ion diamagnetic frequency were generally increased. When the neon level is relatively high enough, the peak values dropped as illustrated in figures 15(b) and (d). Note that in figure 15(a), the 6 MW discharge 166612 did not drop its peak values of total ion diamagnetic frequency, probably due to its relatively low neon injection rate (compared to the 6 MW discharge 166613) and high heating power (compared to the 3 MW discharge 166615). In contrast, in figure 15(c), the peak value of total ion diamagnetic frequency directly dropped after neon injection, probably due to the relatively high neon injection rate (which is the same as the value in the 6 MW discharge 166612 and larger than the value in the 3 MW discharge 166616) and its low heating power.

As depicted in figure 15, ${\omega _{ * ,EXP}}$ (filled symbols) is larger than ${\omega _{ * ,ELITE}}$ (open symbols) in both 3 and 6 MW discharges before and after neon injection. And the ratio of ${\omega _{ * ,EXP}}$ to ${\omega _{ * ,ELITE}}$ is in the range from 1.1 to 1.4 (see the '$\times$' symbols). Interestingly, the ratios of ${\omega _{ * ,EXP}}$ to ${\omega _{ * ,ELITE}}$ were larger with neon than without neon for both 3 and 6 MW discharges (see dash $\times$ lines). In figure 15(b), the ratios of ${\omega _{ * ,EXP}}$ to ${\omega _{ * ,ELITE}}$ began to drop after 2850 ms (in the discharge with highest neon injection rate), but they were still higher than the ratio before neon injection. Since the PBM growth rate threshold is determined by a model of diamagnetic stabilization [7], a larger value of ${\omega _{ * ,EXP}}$, comparing to the ${\omega _{ * ,ELITE}}$, suggests that the ELITE computed peeling-ballooning stability boundary might be improved in the discharges both before and after neon injection by using the approximate experimental total ion diamagnetic frequency (${\omega _{ * D,C}}$ and ${\omega _{ * D,C,Ne}}$, respectively) instead of the approximate total ion diamagnetic frequency in ELITE (${\omega _{ * e}}$). For qualitative studies, we approximate this effect by adjusting the critical value of the toroidal mode number (${n_{crit}}$) [7] to give the corresponding ratio of ${\omega _{ * ,EXP}}$ to ${\omega _{ * ,ELITE}}$. The ${n_{crit}}$ is the toroidal mode number of the transition point in the bilinear fit to the BOUT + + evaluated effective diamagnetic stabilization coefficient [7], which does not include the impurity effects and is used for determining the PBM growth rate threshold in section 3.1 and 3.2 in our paper. For convinence, we use a schematic diagram to demonstrate the effects of modifying ${n_{crit}}$ on the effective diamagnetic frequency calculation as shown in figure 16. Increasing ${n_{crit}}$ gives stronger stabilization for modes with toroidal mode numbers larger than the original ${n_{crit}}$ (see figure 16).

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Next, we examine the effect of including the contributions of impurities, i.e. carbon and neon to the total diamagnetic frequency on the PBM stability boundary for the 6 and 3 MW discharges respectively. For the 6 MW discharges, using the total diamagnetic frequency (including the contributions of impurities) to compute the instability threshold (see figures 17(c) and (d)) resulted in an increase in the ballooning branch instability threshold and little change in the kink-peeling threshold compared to the usual ELITE treatment (see figures 17(a) and (b)). Also the ballooning stability boundary after neon injection increased more than the one before neon injection. After the PBM stability boundary modification, the stability boundaries, especially at time 3765 ms in the discharge 166612 and at 3465 ms and 4165 ms in the discharge 166613, were closer to the experimental operating points.

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For the 3 MW discharges in figure 18, the instability threshold computed with the total diamagnetic frequency (including the contributions of impurities) affected the PBM stability boundary in the similar way to the 6 MW discharges. After the modification, the operating points in discharge 166616 with lower neon injection rate (compared to the discharge 166615) were still close to the stability boundary (see figures 18(b) and (d)). However, for the discharge 166615 with higher neon injection rate (compared to the discharge 166616), the operating points were inside the stability boundary and away from the ballooning stability boundary (see figures 18(a) and (c)). Since the data of operating points in the discharge 166615 were from the last 20% of the inter-ELM period, the operating point locations of discharge 166615 might be still reasonable.

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Further theoretical work and simulation with BOUT++ [63] or other codes are needed to justify using the total diamagnetic frequency (including the contributions of impurities) to compute the stability threshold. However, this modification quantitatively makes the PBM stability boundary more consistent with the experimental observations, especially for the 6 MW discharges. This also implies the possible role of impurities in enhancing the pedestal pressure and global confinement as described above.