How turbulence spreading improves power handling in quiescent high confinement fusion plasmas

The study addresses a critical challenge for ITER and future fusion reactors: managing divertor target heat loads while maintaining high core confinement. The heat flux width λq is predicted to be very narrow by heuristic drift (HD) and Eich scaling, potentially leading to unacceptably high peak heat loads. The HD model, which neglects scrape-off-layer (SOL) turbulence due to expected E×B shear stabilization, predicts λq ≈ 2ρi (∼1–2 mm for ITER). However, advanced simulations (XGC and BOUT++) suggest broader λq driven by edge turbulence. The research question is whether and how pedestal turbulence spreads into the linearly stable SOL to broaden λq, and what turbulence characteristics control this process. The paper focuses on quiescent H-mode (QH-mode) plasmas on DIII-D, which exhibit high confinement without ELMs, to isolate and analyze the role of pedestal turbulence in determining divertor heat flux width.

Prior work includes the Eich empirical scaling and Goldston's heuristic drift model explaining narrow inter-ELM λq in H-mode. Gyrokinetic and two-fluid simulations (XGC, BOUT++) predicted broader λq near marginal pedestal stability due to turbulence, but the mechanisms for SOL turbulence production and impact on λq remained unclear. Theoretical models proposed turbulence spreading across the separatrix as a mechanism for SOL broadening, with experimental indications on devices such as LHD. The paper builds on these by directly linking pedestal turbulence characteristics (e.g., PBM vs DAW), turbulence intensity flux across the separatrix, and downstream λq in QH-mode plasmas.

- Experimental platform: DIII-D tokamak (R=1.67 m, a=0.67 m, Bt up to 2.2 T). QH-mode discharges without ELMs were used. - Diagnostics: - Beam Emission Spectroscopy (BES): 64 channels in an 8×8 grid imaging ~7×9 cm at the outboard midplane, 1 MHz sampling, resolving k < 3 cm⁻¹, to measure density fluctuation spectra and radial envelopes across pedestal and into SOL. - Divertor Langmuir Probes: Dome-type tips (6 mm diameter, 1 mm height, ~1.5 cm spacing), operated at 1 kHz sweep; strike-point sweeps used to obtain radially resolved heat flux; median filtering and MAD for error bars. - Infrared Thermography (IRTV): 12 kHz, ~2 mm/pixel; THEODOR used to infer perpendicular heat flux and map to parallel heat flux, with spreading factor S up to 1.5 mm for fitting. - Observables and analysis: - Characterization of pedestal turbulence bands: low-frequency ion-diamagnetic-direction (IDD) mode (10–200 kHz, broadly extending to SOL) and high-frequency electron-diamagnetic-direction (EDD) mode (60–200 kHz, localized at upper pedestal). Poloidal wavenumber sign used to distinguish propagation direction in lab frame. - Divertor heat flux width λq measured via Langmuir probes and IRTV, compared to Eich scaling and multi-machine regressions; correlation with BES-measured edge turbulence amplitude near separatrix. - Numerical modeling: - BOUT++ six-field two-fluid model (Braginskii-based) with carbon impurity, electromagnetic, domain ψN=0.85–1.10 spanning pedestal and SOL; grid: nr=256, nθ=64, nφ=64 in a field-aligned mesh; toroidal modes n=5,10,...,80; implicit PVODE time-stepping to saturation; realistic Spitzer-Härm resistivity; sheath boundary conditions at divertor targets; Neumann boundaries for densities, temperatures, vorticity, and parallel velocity; zero-Laplacian for A∥; flux-limited parallel heat conduction. - Equilibrium and fields: Profiles from EFIT reconstruction; E_r profile from CER-based momentum balance kept realistic; diamagnetic E_r retained; Reynolds-stress-driven zonal flows omitted. - Linear stability analysis to distinguish peeling-ballooning modes (PBM, low–intermediate n, extended into SOL) vs drift Alfvén waves (DAW, high n, localized at upper pedestal). Determined ncrit≈30 separating PBM from DAW. - Parameter scans as numerical experiments to modulate turbulence composition and spreading: - Pedestal ion/electron temperature scaling Fi, Fe (0.6–1.8) inside separatrix while keeping SOL profiles fixed (linearly stable SOL), to vary PBM and DAW drive separately. - SOL E_r scans to vary separatrix E×B shear (≈3–7 MRad/s) while holding pedestal E_r fixed, to assess suppression of spreading. - Computation of turbulence intensity flux across the separatrix Γturb = ⟨(δp/P)² δv_r c_s⟩ (flux-surface and time averages), pressure perturbation skewness (ξ), and radial turbulence e-folding scale δl at the outboard midplane. - Comparative framework: λq normalized to Eich scaling to assess turbulence-driven broadening and threshold behavior.

- Edge turbulence structure: Two bands observed by BES in QH-mode pedestals. IDD mode has larger amplitude, peaks near separatrix (ψ≈1.0) and extends into SOL; EDD mode peaks at upper pedestal (ψ≈0.93) and is localized with little SOL penetration. - Linear stability (BOUT++): PBM dominates n=5–30 with radial extension from pedestal to SOL; DAW dominates n>ncrit≈30 localized at upper pedestal, consistent with observed IDD (PBM-like) and EDD (DAW-like) bands. - Role of modes in λq: Scaling pedestal Ti (Fi) increases PBM growth and broadens λq markedly; scaling Te (Fe) primarily affects DAW and has weak impact on λq, indicating DAW does not directly broaden λq via spreading. - Turbulence spreading mechanism: Nonlinear simulations show turbulence generated around ψN≈0.96–0.97 spreads both inward and outward. Zero-crossings of turbulence intensity flux and skewness align near the generation region. Large positive skewness (ξ>2) in the SOL indicates blob-dominated outward spreading. - E×B shear effect: Increasing separatrix E×B shearing rate (~3–7 MRad/s) reduces SOL skewness (from ~0.7 to ~0.3), decreases turbulence intensity flux across the separatrix, and narrows λq accordingly, demonstrating shear suppression of spreading. - Threshold in turbulence intensity flux: The ratio λq/λq,Eich remains near unity for weak Γturb; λq exceeds Eich scaling when Γturb surpasses a threshold Γcrit ≈ 1.0×10^11 (units consistent with m²/s² after normalization), with λq increasing monotonically with Γturb beyond this threshold. - Scaling with turbulence scale length: The upstream SOL turbulence e-folding scale δl at the midplane increases with stronger pedestal drive (e.g., higher Fi), and λq scales approximately linearly with δl, indicating the SOL mixing length set by spreading controls the downstream heat flux width. - Experimental correlations: In QH-mode discharges, λq broadens as separatrix turbulence amplitude (BES-measured IDD δη/n) increases, and overall λq decreases with increasing poloidal magnetic field Bp, consistent with multi-machine trends but with turbulence-induced deviations from Eich scaling.

The findings directly link pedestal turbulence characteristics to divertor heat flux width via turbulence spreading across the separatrix. PBM-like, ion-directed broadband modes that radially extend from the pedestal top into the SOL effectively transport turbulence intensity into the otherwise linearly stable SOL, increasing the SOL mixing length and broadening λq beyond neoclassical and heuristic drift predictions. In contrast, DAW-like, electron-directed turbulence localized at the upper pedestal does not significantly contribute to λq broadening due to minimal spreading into the SOL. The observed threshold in Γturb reflects a regime transition where neoclassical drifts dominate cross-field SOL transport at low turbulence levels, while turbulent mixing governs when spreading is strong. E×B shear at the separatrix modulates this coupling by suppressing spreading, reducing skewness and Γturb, and narrowing λq. These insights provide a physics basis for controlling heat flux widths in high-confinement, ELM-free scenarios, suggesting that maintaining a turbulent pedestal (specifically PBM-like activity) can enable broader λq while preserving core confinement, aiding core–edge integration targets for ITER.

This work demonstrates that pedestal turbulence spreading is the key mechanism broadening the divertor heat flux width in QH-mode plasmas on DIII-D. Experimentally, λq increases with separatrix turbulence amplitude, and simulations show that PBM (IDD-like) turbulence spreads into the SOL, increasing the SOL mixing length and λq, while DAW (EDD-like) turbulence remains localized and has weak effect on λq. A separatrix E×B shear increase suppresses spreading, reducing skewness and Γturb and narrowing λq. A threshold in turbulence intensity flux across the separatrix (Γcrit ~ 1×10^11 in normalized units) marks the onset of turbulence-dominated SOL transport, beyond which λq grows with Γturb. The upstream turbulence scale length δl correlates linearly with downstream λq, reinforcing a mixing-length picture. These results establish the pedestal–SOL coupling physics and support the strategy of leveraging controlled pedestal turbulence to achieve broader heat flux widths compatible with power handling in future devices. Future research should include kinetic turbulence (e.g., TEM, MTM), self-consistent flux-driven core–edge coupling, and systematic optimization of trade-offs between pedestal performance and boundary heat flux handling for ITER and beyond.

- Modeling employs a reduced two-fluid (six-field) BOUT++ framework without kinetic effects; trapped electron modes and micro-tearing modes are not included and could contribute to spreading and λq broadening. - Reynolds-stress-driven zonal flows are omitted; only diamagnetic E_r is retained, potentially affecting turbulence regulation and spreading. - Parameter scans keep SOL profiles fixed and linearly stable, which isolates pedestal-driven spreading but may under-represent feedbacks from SOL profile evolution. - Sheath boundary conditions and flux-limited parallel transport are simplified representations that may impact quantitative λq predictions. - Experimental λq fitting includes a spreading factor constraint (S ≤ 1.5 mm) and diagnostic resolution limits (IRTV ~2 mm/pixel) which can affect inferred widths. - Results are based on DIII-D QH-mode conditions; generalizability to other regimes/devices requires further validation. - The study notes absence of self-consistent core-driven flux and full core–edge coupling in current modeling, which may influence pedestal–SOL interactions.