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Empirical impact of near-separatrix plasma and neutral transport on the pedestal in the transition between EDA and ELMy H-modes on Alcator C-Mod

T0 review · 4 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The pedestal density of the ELM-free EDA H-mode is set by resistive-ballooning-mode particle transport, not by neutral fueling.

desk verdict A careful C-Mod study that plausibly extends pedestal density prediction to EDA H-modes, but the new RBM transport channel rests on a boundary condition that could be absorbing a neutral-source error. read the letter →

arxiv 2603.16515 v2 pith:TAHQBQF2 submitted 2026-03-17 physics.plasm-ph

M.A. Miller , J.W. Hughes , S. Saarelma , T. Eich , J. Dunsmore , J. Han , P. Manz , J.W. Connor
show 11 more authors
G.R. Tynan A.E. Hubbard A. Ho T. Body D. Silvagni O. Grover S. Mordijck E.M. Edlund B. LaBombard M. Wigram A. Cavallaro
This is my paper · ORCID
classification physics.plasm-ph
keywords pedestaldensityEDAH-modeELMyresistiveballooningmodeparticletransportneutralfuelingquasi-coherentSPARCprediction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using a set of Alcator C-Mod discharges that cross the ELMy-to-EDA H-mode transition, the paper argues that the two regimes are governed by different density-control mechanisms. In the ELMy H-mode, the pedestal density climbs with neutral pressure and responds to fueling; in the EDA H-mode, it saturates and becomes insensitive to the neutral source, implying that a turbulent transport channel limits the density gradient. The paper identifies that channel as resistive ballooning mode (RBM) transport and shows that adding a diffusion term D_RBM, scaling with the collisionality parameter α_t and inversely with k_RBM^2 q_cyl, lets a recent pedestal-density prediction model reproduce EDA pedestals up to 3×10^20 m^-3. If correct, this would mean that in high-density, ELM-free regimes the pedestal density is transport-limited, not fueling-limited, a result with direct consequences for designing ELM-free operation in next-step devices such as SPARC.

What carries the argument

The load-bearing object is the RBM particle-diffusion coefficient D_RBM added to the pedestal transport sum D_ped = D_neo + D_KBM + D_TG + D_RBM. Two forms are tested: D_RBM = C_RBM α_t^a with a≈1.2, and D_RBM = C_k/(k_RBM^2 qhat_cyl), where α_t is a collisionality-like turbulence drive parameter, k_RBM is the characteristic resistive-ballooning wavenumber from the two-fluid model, and qhat_cyl is the cylindrical safety factor. This term provides the extra outward particle flux that clamps the density gradient at high density; the neutral boundary is supplied by a kinetic neutral simulation mapping the measured wall neutral pressure to the separatrix neutral density.

What would settle it

Measure the actual neutral ionization source in the pedestal (for example, with Ly-alpha emission or a calibrated neutral-density diagnostic) across the ELMy-to-EDA transition and compare it with the model's assumed source. If the separatrix neutral density is lower than the mapped value by enough to remove the overprediction, then D_RBM as added is an artifact; if the neutral source matches, the RBM transport channel is required. A gas-puff modulation experiment that varies neutral pressure while holding the separatrix density fixed could separate source effects from transport effects directl

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Extended reading notes

Core claim

The central claim is that the pedestal density in the high-density EDA H-mode is set by RBM-driven particle transport, not by neutral fueling. Experimentally, n_ped rises with neutral pressure in ELMy H-modes but saturates and becomes insensitive to the neutral source in EDAs, even as n_sep continues to grow. Fluctuation spectra show the quasi-coherent mode (QCM) strengthening across the transition, then saturating and weakening at the highest densities, while broadband fluctuation levels keep rising. The paper adds an RBM diffusivity D_RBM (either C_RBM α_t^a or C_k/(k_RBM^2 qhat_cyl)) to the pedestal transport sum and shows it reproduces EDA pedestals up to 3×10^20 m^-3. EPED scans at n_se

Load-bearing premise

The need for the extra RBM transport channel rests on the neutral boundary mapping from the kinetic neutral simulation, n_sep0[10^15 m^-3] = 38.5 p_OMP0[mTorr] with the assumption T_e=T_i; if the neutral source is overestimated, D_RBM may be compensating for a boundary-condition error rather than representing a real transport channel.

Editorial extensions

If this is right

  • The density-pedestal model, extended with D_RBM, is validated for ELMy H-modes up to 2×10^20 m^-3 and for EDA H-modes up to 3×10^20 m^-3, extending the model's range to non-ELMing, high-density regimes.
  • In EDA H-modes, n_ped is essentially fixed by turbulent transport, so gas fueling cannot be used to raise pedestal density; density must be controlled through edge transport or plasma shape.
  • EPED scans show that rising n_sep/n_ped shifts the peeling-ballooning transition to lower n_ped, so a high separatrix-to-pedestal ratio (typical of EDA) makes pedestal pressure ballooning-limited at lower density.
  • For SPARC, including RBM transport lowers n_ped by about 20% and weakens the density gradient near the separatrix in the high-density EDA/QCE-like scenario, changing the expected edge profile for power handling and ELM avoidance.
  • The observed saturation of the QCM amplitude at high n_ped, while broadband fluctuations keep rising, points to additional turbulence beyond the QCM contributing to transport near the density limit.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the α_t/k_RBM^2 q scaling for D_RBM is universal, pedestal models for other high-density, ELM-free regimes (for example, the quasi-continuous exhaust regime on other tokamaks) may need the same term; this is testable with existing databases.
  • The neutral-boundary uncertainty could be reduced by comparing the kinetic neutral simulation's mapping to direct Ly-alpha measurements of the ionization source; such a test would either strengthen or remove the case for a separate RBM transport channel.
  • The prediction that n_ped approaches n_sep at high density in SPARC suggests that pedestal performance and divertor protection become coupled through the same RBM transport; if true, optimizing the separatrix density may be the shared lever for both.
  • The weakening of the QCM just before the density limit hints that the RBM channel may replace, rather than merely supplement, the kinetic ballooning mode; a fluid turbulence simulation resolving both instabilities could identify which one is active.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. This paper analyzes a set of Alcator C-Mod discharges spanning ELMy and EDA H-modes, using high-resolution Thomson scattering profiles and PCI fluctuation measurements. The authors show that the pedestal density is insensitive to neutral fueling in the EDA regime, while it is fueling-sensitive in the ELMy regime. They validate the Saarelma-Connor pedestal density prediction model on this dataset and find that the model overpredicts the EDA pedestal density at high density. To correct this, they add an ad hoc resistive-ballooning-mode (RBM) particle transport channel, D_RBM, with two alternative forms scaling with α_t and with 1/(k_RBM^2 q_cyl), and report improved agreement up to n_ped = 3×10^20 m^-3. They also perform EPED scans at different n_sep/n_ped ratios, compare to experiment, and make initial SPARC pedestal density predictions for an ELMy and an EDA/QCE-like scenario, finding that D_RBM lowers the predicted SPARC pedestal density by about 20%.

Significance. If the central claim holds, this paper would extend the validated range of a predictive pedestal density model into high-density, ELM-free regimes relevant to ITER and SPARC, and would identify RBM-driven particle transport as the mechanism setting the pedestal density in EDA/QCE H-modes. The manuscript has several concrete strengths: it uses a well-characterized C-Mod dataset with two independent Thomson-scattering fitting approaches; it tracks the QCM amplitude systematically across regimes; it validates the Saarelma-Connor model on a new device and regime; and it is transparent about the model's free parameters and limitations. The EPED scans at fixed n_sep/n_ped are a useful sensitivity study. However, the evidence for the new D_RBM channel is not yet independent of the neutral-boundary model used to infer the separatrix neutral density, and several transport coefficients are hand-tuned. As a result, the main claim is plausible but not fully established.

major comments (4)
  1. [4.2 / Appendix A / Eqs. (12)-(14)] The conclusion that an RBM-driven transport channel is required in EDA H-modes is load-bearing and rests on the KN1D boundary mapping n_sep0[10^15 m^-3] = 38.5 p_OMP0[mTorr]. The paper itself states 'Two possibilities exist – either the neutral source is overestimated or the plasma transport is underestimated.' The present analysis does not resolve this ambiguity: the mapping is fit to moving-average profiles from the same dataset, assumes T_e=T_i (flagged in Appendix A), uses a linear fit in Fig. A3 despite visible saturation at high p_OMP0, and applies a limiter-shadow density that may overestimate particle content. If n_sep0 is overestimated for EDA points, the standard model may already match the high-density data. Please provide sensitivity tests (e.g., T_i/T_e variation, limiter density variation, alternative neutral model) or independent neutral-density constraints to show D_RBM i
  2. [4.1, Eq. (9) and Fig. 9] The improved transport settings use C_KBM=0.01 and α_crit=3, whereas α_crit=2 was found suitable for other devices. The motivation for α_crit=3 from an average separatrix α_c=2.6 is suggestive but not a derivation; α_crit is a free parameter for the KBM onset inside the pedestal. Fig. 14 shows that lowering α_crit to 2 changes SPARC n_ped by roughly 15%, so the model is sensitive. Please report a systematic parameter scan (C_KBM, α_crit, (D/χ)_TG) with a quantitative goodness-of-fit metric and uncertainty estimates; otherwise the claimed validation is vulnerable to overfitting.
  3. [3.1 / Fig. 6 and Fig. 10] The fluctuation data do not currently corroborate the D_RBM term where it matters most. The QCM amplitude B saturates and weakens for n_ped > 2.5×10^20 m^-3 (Fig. 6, right), yet D_RBM is largest at the highest n_ped. The background amplitude A continues to grow, but A is not directly linked to the radial particle transport coefficient D_RBM. Please either connect the fluctuation measurements quantitatively to the proposed transport channel (e.g., through a mixing-length estimate) or temper the claim that the RBM channel is independently supported by the PCI data.
  4. [6, Fig. 16] The SPARC high-density predictions use very crude inputs—T_EDA = 0.5 T_PRD, n_EDA = 1.5 n_PRD, and ad hoc width adjustments—and the result is highly sensitive to the choice of n_sep0 and whether D_RBM is included (n_ped ranges from 5.1 to 8.8×10^20 m^-3 across the explored settings). The statement that the predictions are 'consistent with assumptions used in previous EPED modeling' should be qualified with these sensitivities; as it stands, the SPARC section is illustrative rather than predictive.
minor comments (4)
  1. [Fig. A3] The linear fit n_sep0 = 38.5 p_OMP0 appears to be strongly influenced by the highest-pressure point, and the text notes a possible saturation. Show residuals and fit uncertainty, or use a saturating form and justify the linear choice.
  2. [Eq. (14)] Define all symbols (k_RBM, q_cyl) and give units. Currently C_k_RBM is given only numerically, and the physical dimensions of the expression are not stated.
  3. [Section 2.2] The transition at p_OMP0 ≈ 0.1 mTorr is central to the regime classification. Provide an uncertainty estimate for the pressure measurement and for how the transition value is determined.
  4. [Section 4.2] The sentence 'C_RBM = 0.039, taken empirically from the dataset in [33]' is ambiguous—was the coefficient calibrated on the same run day or on an independent dataset? Please clarify to avoid circularity concerns.

Circularity Check

3 steps flagged · score 6.0 of 10

EDA 'prediction' is substantially in-sample: model settings, KN1D boundary, and D_RBM constants all come from the same C-Mod dataset/self-cited analyses.

  1. fitted input called prediction [Section 4.1, Eqs. (7)-(10), Fig. 9 (left)]
    "Lowering (D/χ)_TG to 0.05, adding weak KBM-driven transport with C_KBM = 0.01, and using a slightly higher value of α_crit = 3 than the value of α_crit = 2 found most suitable for other devices gives the results shown with turquoise squares."

    The three parameters altered here are 'user-supplied' free parameters of the Saarelma-Connor model. They are changed until the prediction matches the C-Mod dataset, and the same settings are then called 'validation' and used for the EDA predictions. Thus the agreement in Fig. 9/10 is not an out-of-sample test of the model: the model's transport coefficients were selected on the same n_ped data being predicted.

  2. fitted input called prediction [Section 4.2 / Appendix A (n_sep0 = 38.5 p_OMP0)]
    "This is done by running 10 KN1D simulations using characteristic plasma profiles at 10 different logarithmically-spaced values of p OMP 0 that span this dataset. The resulting fit is given by n sep 0 [10^15 m^-3] = 38.5 p OMP 0 [mTorr]."

    The characteristic plasma profiles used to build the KN1D boundary are moving averages of the same experimental profiles (including pedestal-top values) that the model is later compared against. The boundary condition is therefore derived from the very data whose n_ped the model claims to predict. Because the paper itself states 'Two possibilities exist – either the neutral source is overestimated or the plasma transport is underestimated', agreement obtained with this boundary cannot uniquely establish the missing transport.

1 more flagged steps
  1. self citation load bearing [Section 4.2, Eqs. (13)-(14), Fig. 10 (right)]
    "Solid red squares use the same expression from Equation 13, with C αt RBM = 0.039, taken empirically from the dataset in [33]. Open red squares in the right plot use the expression from Equation 14, with C k RBM = 0.086, taken from the dataset in [8]."

    The central EDA result is the addition of D_RBM, but its two forms are not derived here: the constants are empirical fits from the authors' prior C-Mod studies, and [8] is the same run-day/dataset whose classification this paper follows. The 'good agreement' with EDA n_ped then partly re-imports the transport already contained in those fitted constants. Because [65] (the source of the k_RBM/q_cyl scaling) is a submitted self-citation, the loop is not externally checkable.

full rationale

Three in-sample/self-cited inputs support the paper's central EDA claim: (1) user-supplied transport parameters are adjusted on the C-Mod dataset before 'validation'; (2) the KN1D n_sep0 boundary is constructed from moving averages of the same experimental profiles; (3) D_RBM constants are empirical fits from earlier C-Mod papers by the same authors, including [8] on the same run day. The paper explicitly concedes that an overestimated neutral source is an alternative to missing transport, so the RBM channel is underdetermined. This is not a purely definitional circularity — the Saarelma-Connor model was developed on JET and the neutral/plasma integration is nontrivial, and the ELMy validation with fixed n_sep0=1e15 retains independent content. But the 'good agreement' up to 3e20 for EDA is substantially a calibrated reproduction, not a first-principles prediction. EPED comparisons and SPARC projections are not part of this circular loop.

Assumptions & free parameters 7 free parameters · 9 assumptions · 0 invented entities

The central validation is built on several user-supplied transport coefficients and an in-sample boundary-condition mapping; the RBM term's coefficients come from earlier C-Mod analyses. The EPED comparison inherits the empirical width-height constant and ELITE stability. No new physical entities are introduced.

free parameters (7)
  • (D/χ)_TG = 0.05 or 0.5
    Ratio of particle to thermal transport from TG modes; user-supplied, varied to improve model agreement (Section 4.1, Figure 9).
  • C_KBM = 0.01
    Magnitude of KBM-driven particle transport; user-supplied, with 0 used in one configuration (Eq. 9, Section 4.1).
  • α_crit = 3
    Critical normalized pressure gradient for KBM onset; set to 3 for C-Mod, compared to 2 on other devices, to improve fit (Section 4.1).
  • C_RBM (α_t form) = 0.039
    Coefficient in D_RBM = C_RBM α_t^1.2, taken from earlier C-Mod database [33] (Eq. 13, Section 4.2).
  • C_k_RBM = 0.086
    Coefficient in D_RBM = C_k_RBM / (k_RBM^2 q_cyl), taken from earlier C-Mod dataset [8] (Eq. 14, Section 4.2).
  • n_sep0 mapping coefficient = 38.5 (10^15 m^-3 per mTorr)
    Linear fit to 10 KN1D runs using characteristic profiles constructed from the same dataset; sets the neutral boundary condition (Appendix A, Figure A3).
  • EPED width-height constant C = 0.076
    Empirical proportionality in Δp = C sqrt(β_p^ped), calibrated on multi-machine pedestal data including C-Mod; inherited as an input in the EPED scans (Appendix B).
assumptions (9)
  • domain assumption Reduced two-fluid neutral transport model (Eqs. 4–6) accurately captures neutral penetration in the pedestal.
    The Saarelma-Connor model rests on this adapted Groebner-Mahdavi neutral model (Section 4.1).
  • domain assumption Pedestal particle transport is the sum of neoclassical, KBM, TG, and RBM channels with the given functional forms.
    Equations 7 and 12 postulate this additivity and the specific scalings of each channel; no full transport model is used (Section 4.1).
  • domain assumption EPED width-height scaling Δp = C sqrt(β_p^ped) with C=0.076 describes KBM-limited pedestals in these discharges.
    Used as the KBM constraint in EPED scans (Appendix B).
  • domain assumption Peeling-ballooning stability computed with ELITE determines the pedestal height/width for Type-I ELMy H-modes.
    This is the second EPED constraint, used for the scans and comparisons (Appendix B).
  • domain assumption Two-point model with Spitzer-Härm heat transport locates the separatrix and provides T_sep.
    Used for separatrix identification and profile fitting (Section 2).
  • domain assumption T_e = T_i is assumed in KN1D simulations and for total pressure estimates.
    Stated in Appendix A: 'an assumption that can and should likely be relaxed at low n_e'.
  • domain assumption The PCI spectral fit function H(f)=P(f)+N(f) (Eqs. 1–3) adequately separates QCM amplitude B from background fluctuations.
    The fluctuation analysis in Section 3 relies on this assumed spectral shape; no independent validation of the fit is provided.
  • domain assumption p_OMP0 is a valid proxy for volumetric ionization rate S_ion and cross-field particle flux Γ⊥.
    Stated in Section 2.2; the mapping among p_OMP0, S_ion, and Γ⊥ is not directly measured.
  • ad hoc to paper For the SPARC high-density scenario, crude profile scalings (T_EDA = ½ T_PRD, n_EDA = 1.5 n_PRD, width adjustments) are adequate inputs.
    Section 6 explicitly calls these 'very crude approximations' used because no core transport predictions exist for the high-density scenario.

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Pith. "Pith review of Empirical impact of near-separatrix plasma and neutral transport on the pedestal in the transition between EDA and ELMy H-modes on Alcator C-Mod." pith.science (2026). https://pith.science/paper/TAHQBQF2

@misc{pith2026260316515,
  author       = {Pith},
  title        = {Pith review of: Empirical impact of near-separatrix plasma and neutral transport on the pedestal in the transition between EDA and ELMy H-modes on Alcator C-Mod},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TAHQBQF2}},
  note         = {Machine review of arXiv:2603.16515}
}
abstract

The transition between the ELMy H-mode and the EDA H-mode is studied on Alcator C-Mod using an experimental database and predictive pedestal models. High-resolution Thomson scattering measurements are used to compare the pedestal density, $n_{e}^\mathrm{ped}$, and the separatrix density, $n_{e}^\mathrm{sep}$ with main chamber neutral measurements. $n_{e}^\mathrm{ped}$ is sensitive to neutral sources only in the ELMy H-mode regime and not in the EDA H-mode regime. Density fluctuation spectra reveal that quasi-coherent structures become stronger at higher densities and more coherent in the EDA relative to the inter-ELM phases of ELMy H-modes, before weakening again at the highest values of $n_{e}^\mathrm{ped}$. The Saarelma-Connor pedestal density prediction model is validated for ELMy H-modes up to $n_{e}^\mathrm{ped} = 2.0 \times 10^{20}$ m$^{-3}$. An additional transport channel driven by resistive ballooning modes (RBM), $D_\mathrm{RBM}$, scaling directly with $\alpha_{t}$ and inversely with $k_\mathrm{RBM}^{2}\hat{q}_\mathrm{cyl}$ is shown to improve the prediction for EDA H-modes, finding good model agreement up to $n_{e}^\mathrm{ped} = 3.0 \times 10^{20}$ m$^{-3}$. EPED scans in $n_{e}^\mathrm{ped}$ are then performed at three values of $n_{e}^\mathrm{sep}/n_{e}^\mathrm{ped}$. Increasing this ratio moves the peeling-ballooning branch transition to lower $n_{e}^\mathrm{ped}$, increasing $p^\mathrm{ped}$ in the peeling branch and decreasing it in the ballooning branch. Agreement is found for large ELM H-modes. SPARC pedestal density predictions for an ELMy and an EDA/QCE-like H-mode are performed and found consistent with assumptions used in previous EPED modeling. Inclusion of $D_\mathrm{RBM}$ significantly weakens the density gradient near the separatrix, lowering $n_{e}^\mathrm{ped}$ by approximately 20%.

Figures

Figures reproduced from arXiv: 2603.16515 by the authors.

Figure 1
Figure 1. Operational space in terms of Te and ne at the separatrix (left) and pedestal top (right), showing discharges with small ELMs (light red squares), large ELMs (dark red squares), mixed EDA and ELMy (purple circles), and only EDA (blue diamonds). At left, dash-dotted black and purple lines show αt and βe contours at the separatrix from [8]. At right, the dashed black line shows the contour of constant collisionality, … view at source ↗
Figure 3
Figure 3. Dα emission as a function of time from beginning of time window, tmin, for selected discharges from [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. n sep e (top, left) and n ped e (bottom, left) plotted against p OMP 0 and p OMP 0 plotted against −∇n sep e (right) for discharges with small ELMs (light red squares), large ELMs (dark red squares), mixed EDA and ELMy (purple circles), and only EDA (blue diamonds). m−4 , an additional mechanism, driven at high ne as will be discussed below, impedes further build-up of density inside the separatrix, such that n ped … view at source ↗
Figures from the paper (13 more)
Figure 5
Figure 5. Figure 5: Fourier-transformed time series of line-averaged density [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Amplitude of Gaussian describing QC mode (top) and amplitude of background piecewise polynomials (bottom) as a [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Amplitude of Gaussian describing QC mode against [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Amplitude of Gaussian describing QCM as a function of [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Results of pedestal density prediction for ELMy-EDA dataset with different transport settings (left) and different [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Results of pedestal density prediction for ELMy-EDA dataset, using same settings as for solid turquoise squares from [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: The top two panels show the results of the [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 11
Figure 11. Figure 11: Total pedestal top pressure (top), pressure pedestal [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: Experimental ratio of ∆p to q β ped p against α sep t using the categorization in previous sections: discharges with small ELMs (light red squares), large ELMs (dark red squares), mixed EDA and ELMy (purple circles), and only EDA (blue diamonds). The dashed curve in g…
Figure 13
Figure 13. Figure 13: Projected boundaries for the separatrix operational [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]
Figure 14
Figure 14. Figure 14: Prediction of SPARC pedestal density profile for PRD scenario (left) and high-density H-mode (right), using standard [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]
Figure 15
Figure 15. Figure 15: Modeled D profile of density pedestal prediction of SPARC for PRD scenario (left) and high-density H-mode (right), showing total Dped in black, as well as Dneo, DKBM, DTG, and DRBM (not included in the total Dped for initial simulations) in shades of pink and purple. …
Figure 16
Figure 16. Figure 16: Comparison of prediction of SPARC density pedestal profile for PRD scenario (left) and high-density H-mode (right) [PITH_FULL_IMAGE:figures/full_fig_p020_16.png]

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Reviewed August 2, 2026 · model on record in the stance chip above.