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

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, $n_{e}<sup>\mathrm{ped}$, and the separatrix density, $n_{e}<sup>\mathrm{sep}$ with main chamber neutral measurements. $n_{e}<sup>\mathrm{ped}$ 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 $n_{e}<sup>\mathrm{ped}$. The Saarelma-Connor pedestal density prediction model is validated for ELMy H-modes up to $$n_{e}^\mathrm{ped} = 2.0 \times 10<sup>{20}$$ m$<sup>{-3}$. An additional transport channel driven by resistive ballooning modes (RBM), $D_\mathrm{RBM}$, scaling directly with $α<em>{t}$ and inversely with $k</em>\mathrm{RBM}<sup>{2}\hat{q}_\mathrm{cyl}$ is shown to improve the prediction for EDA H-modes, finding good model agreement up to $$n_{e}^\mathrm{ped} = 3.0 \times 10<sup>{20}$$ m$<sup>{-3}$. EPED scans in $n_{e}<sup>\mathrm{ped}$ are then performed at three values of $n_{e}<sup>\mathrm{sep}/n_{e}<sup>\mathrm{ped}$. Increasing this ratio moves the peeling-ballooning branch transition to lower $n_{e}<sup>\mathrm{ped}$, increasing $p<sup>\mathrm{ped}$ 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 $n_{e}<sup>\mathrm{ped}$ by approximately 20%.

• The paper shows that pedestal density is source-controlled in ELMy H-modes but becomes transport-limited in EDA, with the separatrix-to-pedestal density ratio rising from about 0.4 to 0.8.
• The study combines Thomson scattering, PCI spectroscopy, KN1D neutral modeling, and pedestal codes, finding that an added RBM transport channel reproduces C-Mod densities up to 3 × 10²⁰ m⁻³.
• The paper finds that some EDA pedestals exceed EPED predictions and that RBM transport reduces the projected high-density SPARC pedestal from 6.5 × 10²⁰ to 5.1 × 10²⁰ m⁻³.
• How does the ELMy-to-EDA transition alter the balance between neutral fueling, particle transport, and pedestal density regulation?
• What experimental measurements could distinguish reduced neutral penetration from enhanced resistive-ballooning transport in EDA plasmas?
• Why do some EDA pedestals exceed EPED peeling–ballooning predictions, and what role might resistive MHD effects play?
• How reliable are RBM-based pedestal transport scalings when extrapolated from Alcator C-Mod to SPARC operating conditions?
• Find recent papers about EDA H-mode pedestal transport and resistive-ballooning turbulence.

Overview and motivation

This paper presents an integrated experimental and modeling study of the transition between the Type-I ELMy H-mode and the enhanced D$_\alpha$ (EDA) H-mode on Alcator C-Mod, using a dedicated run day in a non-standard lower-single-null shape ($I_P = 0.9$ MA, $B_t = 5.6$ T) where the L-mode programmed density was systematically reduced. As fueling was lowered, discharges moved from EDA to large-ELM H-modes and finally to small-ELM H-modes at low collisionality. The work builds directly on prior separatrix operational space (SepOS) analysis of the same dataset (2603.16515) and pursues three objectives: characterizing pedestal response to neutral sources across regimes; tracking the quasi-coherent mode (QCM) through the transition; and validating/extending predictive pedestal models (Saarelma–Connor density model, EPED) before applying them to SPARC scenarios.

Pedestal profiles and neutral influence

Pedestal quantities are extracted with modified mtanh fits (with 30% ELM-cycle filtering for pedestal-top values), while separatrix location and near-SOL gradients use exponential decay fits anchored by two-point-model $T_e^\mathrm{sep}$. In the pedestal operational space, many discharges cluster near an isobar of $p_e^\mathrm{ped} \approx 12$ kPa, but EDA and ELMy plasmas reach similar pressure through different means: high $n_e^\mathrm{ped}$ versus high $T_e^\mathrm{ped}$. A collisionality boundary near $\nu^* = 1.5$ at the pedestal top organizes the data better than a pressure boundary.

The central experimental result concerns sensitivity of $n_e^\mathrm{ped}$ to the outer midplane neutral pressure $p_0^\mathrm{OMP}$, which crosses $I_P = 0.9$0 mTorr at the ELMy–EDA transition. For ELMy discharges ($I_P = 0.9$1 mTorr), $I_P = 0.9$2 varies strongly with source, spanning $I_P = 0.9$3, and $I_P = 0.9$4 scales approximately linearly with $I_P = 0.9$5 — a diffusive-like picture. In the EDA regime, this breaks down: $I_P = 0.9$6 continues rising up to and above $I_P = 0.9$7, while $I_P = 0.9$8 saturates near $I_P = 0.9$9 and even decreases slightly toward $B_t = 5.6$0 mTorr. The ratio $B_t = 5.6$1 rises from roughly 0.4 (ELMy) toward 0.8 (high-density EDA), reflecting profile flattening and outward shift rather than a simple gradient reduction. The authors caution that without local ionization measurements they cannot fully separate transport effects from reduced neutral penetration, though they argue the saturation is most plausibly a transport effect consistent with earlier Ly$B_t = 5.6$2 measurements.

Quasi-coherent fluctuation evolution

PCI spectra are fit with a triple piecewise power law plus Gaussian, allowing the same fitting routine to be applied across regimes. The Gaussian amplitude $B_t = 5.6$3 grows nearly linearly with density in the ELMy regime ($B_t = 5.6$4), jumps sharply at the transition ($B_t = 5.6$5), then saturates or weakens at the highest densities ($B_t = 5.6$6), possibly signaling approach to a density limit where non-coherent turbulence dominates.

Plotted against dimensionless parameters evaluated at the separatrix, no single parameter unambiguously controls $B_t = 5.6$7, but strong growth occurs at critical values $B_t = 5.6$8, $B_t = 5.6$9, and especially as $T_e^\mathrm{sep}$0 — consistent with the picture that the QCM emerges when RBM-driven fluctuations acquire electromagnetic character via drift-Alfvén wave coupling. The mid-pedestal product $T_e^\mathrm{sep}$1 similarly marks the transition. Notably, the background fluctuation amplitude $T_e^\mathrm{sep}$2 behaves differently: it stays flat in ELMy phases, increases almost linearly with $T_e^\mathrm{sep}$3 and $T_e^\mathrm{sep}$4 upon entering EDA (rolling over only above $T_e^\mathrm{sep}$5), and keeps growing even after the QCM saturates. This suggests that at high density additional filamentary or broadband transport coexists with, or supplants, the QCM.

Validation and extension of the Saarelma–Connor density model

The standalone Saarelma–Connor model couples a Groebner–Mahdavi-type two-fluid neutral penetration model to a reduced turbulent/neoclassical transport model ($T_e^\mathrm{sep}$6). Its validation here extends the model's tested range to densities up to three times higher than previous devices (JET, MAST-U, AUG). With settings tuned to C-Mod ($T_e^\mathrm{sep}$7, $T_e^\mathrm{sep}$8, $T_e^\mathrm{sep}$9), predictions agree well with experiment for ELMy H-modes up to $p_e^\mathrm{ped} \approx 12$0. Sensitivity studies show that changing the fixed neutral boundary condition from $p_e^\mathrm{ped} \approx 12$1 to $p_e^\mathrm{ped} \approx 12$2 alters predictions by ~50% at low density but only ~20% at high density, consistent with shorter neutral penetration lengths in opaque pedestals.

KN1D kinetic neutral simulations parameterize $p_e^\mathrm{ped} \approx 12$3 against the measured wall pressure, yielding the linear relation $p_e^\mathrm{ped} \approx 12$4. With this boundary condition the model begins overpredicting $p_e^\mathrm{ped} \approx 12$5 as the EDA transition is approached. The paper attributes this to missing resistive-ballooning-mode (RBM) particle transport and adds a fourth channel:

$p_e^\mathrm{ped} \approx 12$6

Two empirical forms are tested: $p_e^\mathrm{ped} \approx 12$7 (consistent with analytic RBM scalings) and $p_e^\mathrm{ped} \approx 12$8. Both reduce overpredicted EDA densities from ~$p_e^\mathrm{ped} \approx 12$9 down to ~$n_e^\mathrm{ped}$0, achieving good agreement up to $n_e^\mathrm{ped}$1, though each form slightly degrades moderate-density accuracy. An important assumption is that these mid-pedestal/separatrix-derived expressions apply throughout the pedestal and lack an onset threshold; the authors acknowledge that a critical-$n_e^\mathrm{ped}$2 trigger may be more physical.

EPED scans and deviations in the EDA

EPED 1.0 scans over $n_e^\mathrm{ped}$3 at fixed $n_e^\mathrm{ped}$4, 0.6, 0.8 reveal that increasing this ratio shifts the peeling-to-ballooning branch transition ($n_e^\mathrm{ped}$5) to lower density, raises $n_e^\mathrm{ped}$6 on the peeling branch, and lowers it on the ballooning branch. At the highest densities relevant to C-Mod, solutions converge toward $n_e^\mathrm{ped}$7 kPa independent of the ratio.

Comparison with experiment yields a differentiated picture. Large-ELM discharges near $n_e^\mathrm{ped}$8 match the EPED ballooning-branch prediction reasonably well, confirming prior interpretive modeling. Small-ELM low-collisionality discharges fall well below all predicted heights, implying their pedestals are not peeling-ballooning limited — despite resembling I-mode-like temperature-dominated profiles, they retain density pedestals and favorable-drift H-mode characteristics. Most strikingly, EDA discharges split into two populations: many sit below the EPED prediction, but a non-negligible number exceed it, contradicting the expectation from earlier ELITE work that EDAs always lie far inside the PB boundary. Probing the KBM width-height scaling shows that most discharges follow $n_e^\mathrm{ped}$9, but at high $T_e^\mathrm{ped}$0 there is clear deviation toward wider-than-KBM-limited pedestals, implicating a resistively driven broadening mechanism analogous to SepOS gradient widening on AUG, C-Mod, and EAST. Whether RBMs supplant or supplement KBMs, or whether non-ideal visco-resistive MHD effects suffice, remains open; CASTOR3D and GRILLIX simulations are proposed to resolve it.

SPARC pedestal density predictions

Using SepOS-projected boundaries for the PRD parameters ($T_e^\mathrm{ped}$1 T, $T_e^\mathrm{ped}$2 MA), two operating points are modeled: the PRD itself ($T_e^\mathrm{ped}$3, Type-I ELMy space) and a proposed high-density point ($T_e^\mathrm{ped}$4, in EDA/QCE space beyond the projected ELMy disappearance boundaries). For the PRD, the extended Saarelma–Connor model predicts $T_e^\mathrm{ped}$5, broadly consistent with earlier EPED inputs; raising $T_e^\mathrm{ped}$6 to $T_e^\mathrm{ped}$7 pushes this to $T_e^\mathrm{ped}$8. Transport decomposition shows $T_e^\mathrm{ped}$9 dominates inside the pedestal due to the large $\nu^* = 1.5$0 factor at high field, while $\nu^* = 1.5$1 is negligibly small — yet reducing neoclassical transport tenfold raises the prediction only slightly, whereas lowering $\nu^* = 1.5$2 from 3 to 2 lowers it to $\nu^* = 1.5$3. Identifying the true KBM onset threshold is therefore as consequential as the transport magnitude.

For the high-density scenario, standard settings predict $\nu^* = 1.5$4, exceeding $\nu^* = 1.5$5 with the higher neutral boundary — above Greenwald. Self-consistent inclusion of the RBM channel, active primarily near the separatrix where $\nu^* = 1.5$6 peaks, cuts the prediction to $\nu^* = 1.5$7, about a 20% reduction relative to the no-RBM case, yielding $\nu^* = 1.5$8, within the range observed for C-Mod EDAs. The authors note the possible benefit of a relatively flat density pedestal for avoiding excessive core radiative dilution, while acknowledging uncertainty about whether the applied RBM form over- or underestimates transport at SPARC temperatures.

Limitations and open questions

Several caveats bear directly on the results. The dataset comes from a single run day in a non-standard shape with warm cryopump, limiting generality; ELM filtering choices, absence of Ly$\nu^* = 1.5$9 ionization measurements, and use of $n_e^\mathrm{ped}$0 as a proxy for both $n_e^\mathrm{ped}$1 and $n_e^\mathrm{ped}$2 leave the fueling-versus-transport decomposition partly ambiguous. KN1D is 1D and assumes full recycling and $n_e^\mathrm{ped}$3, and the far-SOL plasma behind the limiter is poorly diagnosed. The RBM transport forms carry empirically fitted coefficients and no onset criterion, and the assumption of uniform applicability across the pedestal is unverified. The EPED comparison is explicitly not a validation exercise, and the finding that some EDAs exceed the EPED height challenges the universality of the KBM-PBM framework for non-Type-I regimes. Whether the EDA/QCE can exist at the high pedestal temperatures of burning-plasma-class devices remains unresolved, and the SPARC high-density prediction depends on crude extrapolations of pedestal widths and core profiles from C-Mod trends.

Conclusion

By combining a controlled ELMy–EDA density scan with high-resolution Thomson scattering, PCI fluctuation spectroscopy, KN1D neutral modeling, and predictive pedestal codes, the paper establishes that pedestal density regulation changes character abruptly at the ELMy–EDA transition: source-controlled in the ELMy regime, transport-limited in the EDA. The Saarelma–Connor model, augmented with an RBM-driven particle channel scaling with $n_e^\mathrm{ped}$4 or $n_e^\mathrm{ped}$5, reproduces C-Mod pedestals up to $n_e^\mathrm{ped}$6 and materially revises SPARC high-density projections downward. The divergent behavior of EDAs relative to EPED expectations, and the coexistence of QCM saturation with growing background turbulence at the highest densities, identify the interplay of local separatrix turbulence conditions with global pedestal stability as the key open problem for predicting Type-I-ELM-free operation.