Wide-Pedestal QH-Mode ELM Predictor

• The paper presents a deep learning diagnostic that predicts breakthrough ELMs in wide-pedestal QH-mode plasmas using combined stability and transport models.
• It leverages high-fidelity nonlinear MHD simulations and a Deep Survival Machine approach, achieving strong predictive metrics (C-index ≈ 0.82, AUC₁₀₀ₘₛ ≈ 0.87).
• The integrated control system employs real-time actuator logic to reduce breakup ELM rates by up to 50% while improving energy confinement without compromising core performance.

A wide-pedestal quiescent H-mode (WPQH) edge-localized mode (ELM) predictor is a diagnostic, modeling, and real-time control tool designed to anticipate the rare “breakthrough” ELMs that may occur in advanced tokamak regimes where the edge pedestal is broad, the mean ELM frequency is low, and the standard ELM-triggering physics is suppressed or altered. The predictor concept originated as a means to assure robust ELM avoidance and maximize confinement in regimes where first-principles theory, nonlinear simulations, and empirical data all point to a multifactor operational boundary and complex, temporally evolving precursors for ELM events.

1. Physical and Operational Background

Quiescent H-mode (QH-mode) is a magnetically confined plasma regime in which enhanced edge transport provided by long-lived, saturated edge harmonic oscillations (EHO) prevents the formation of large-scale, type-I ELMs. The "wide-pedestal" variant (WPQH) is characterized by a broader-than-standard edge pressure pedestal that increases global energy confinement. In QH-mode, the pressure gradient and bootstrap-driven current profile approach (but remain just below) the peeling–ballooning instability threshold. However, in WPQH, sporadic, large ELMs may still occur if the pedestal width becomes insufficient relative to pressure, breaching the operational boundary for stability or turbulent transport saturation (Meier et al., 2023).

These breakthrough ELMs can damage plasma-facing components and degrade performance, and because their occurrence is rare (∼1 Hz or lower) and statistically hard to model, predictive, high-fidelity real-time detection and control are required for next-generation plasma regimes (Rothstein et al., 11 Nov 2025).

2. Theoretical Predictors: Stability and Transport Models

Multiple physics-based frameworks inform WPQH ELM prediction:

• Peeling–ballooning stability: The classical model tracks edge current density ⟨j⟩, pressure gradient (α parameter), and the edge safety factor (q₉₅). Stability diagrams demarcate the ELM onset surface in (α,⟨j⟩) space, with empirical fits of the stability boundary, e.g.

$$\alpha_{\rm crit}(\langle j\rangle) \approx 1.5 - 0.8\;\Bigl(\langle j\rangle/10^6\Bigr)$$

(Meier et al., 2023).

• Transport-limited pedestal models: The electron-temperature-gradient (ETG) and kinetic-ballooning-mode (KBM) frameworks yield analytic relations for the pedestal width (Δₚₑd) versus top-pedestal poloidal beta (β_θ,ped), with critical exponents depending strongly on the partitioning of pedestal pressure between density and temperature. For a stiff ETG regime,

$$\Delta_{\rm ped} \simeq C_{\rm ETG} \beta_{\theta,\rm ped}^{\gamma_{\rm ETG}}, \;\; \gamma_{\rm ETG}\simeq2$$

while ideal-MHD KBM scalings yield $\gamma_{\rm KBM} \approx 4/3$ (Parisi et al., 14 May 2025).

• Second (“shear”) constraint: Shear flow, especially the local $E \times B$ shearing rate $\gamma_{E \times B}$, is required to self-limit pedestal growth and yield a stable intersection with the transport-critical (TCP) curve at a point lying strictly “under” the ELM limit, enabling true QH operation. This leads to a predictive “ELM avoidance” criterion: the intersection of the TCP (ETG/KBM) and shear lines defines the operational WPQH window (Parisi et al., 14 May 2025).
• Kinetic and global MHD effects: The EPED3 model integrates reduced gyro-fluid kinetic ballooning boundaries with global ideal-MHD constraints (using tools such as GFS and ELITE) to realistically set the allowable pedestal width and pressure, with model coefficients tuned directly to experiment, yielding improved agreement for DIII-D and spherical tokamak plasmas (Tzanis et al., 15 Sep 2025).

3. Simulation-Derived Triggers and Key Variables

High-fidelity nonlinear MHD simulations provide quantitative diagnostics for WPQH onset and ELM termination:

• Sustained QH-mode: Identified when the equilibrium (α,⟨j⟩) remains just below the peeling boundary, the EHO spectrum is dominated by low n (especially n=1), and the edge safety factor q₉₅ drifts toward one of several discrete attractors. Saturation corresponds to $γ_1(q_*) \to 0$ (growth rate of dominant mode vanishes) (Meier et al., 2023).
• ELM onset: Occurs as pedestal-top density $n_{\rm ped}$ exceeds a critical value (e.g., $$n_{\rm ped,crit} \approx 4.7 \times 10^{19}~\mathrm{m}^{-3}$$ for ASDEX Upgrade), and/or as the Er well shallows such that MHD modes are no longer stabilized. The system may exhibit limit cycle oscillations (LCOs) in (∇p,Er) as it approaches the ELM boundary.
• Transport fingerprints: Saturated EHO/n=1 activity increases edge heat and particle fluxes by measurable factors (heat: +30%, particle: +3.5%), reflected in increased effective χ_eff and D_eff at the pedestal.
• Main diagnostic variables: n_ped, Er well, edge gradients (∇p, J_φ), q₉₅ evolution, mode spectral content, and MHD stability proxies (Meier et al., 2023).

4. Data-Driven Real-Time Predictors: The Deep Survival Machine Approach

The WPQH-ELM predictor deployed on DIII-D is implemented as a Deep Survival Machine (DSM) neural network within the PACMAN (Prediction And Control using MAchiNe learning) AI control architecture (Rothstein et al., 11 Nov 2025). Key attributes:

• Inputs: Edge and core diagnostics (BES, CO₂ interferometry, ECE, Dα, actuator waveforms, rt-EFIT scalars) are ingested as short-window (10–20 ms) time-series.
• Feature engineering: Hand-crafted features include maximal Tₑ gradient and calculated peeling proxies (pedestal height minus core pressure over width).
• Architecture: DSM parameterizes the ELM inter-arrival hazard function h(t|x) as a mixture of learned, input-dependent parametric kernels and outputs the probability of ELM occurrence in a specified future window (e.g., 100 ms).
• Learning paradigm: Negative log-likelihood loss with censoring, L² regularization, 10% dropout, and an MLP sub-network for each kernel/weight branch.
• Training: Approximately 70 WPQH pulses from 10+ years of DIII-D, with explicit annotation of breakthrough ELM times. Data is split by shot (60% train, 20% validate, 20% test). Key performance metrics: C-index ≈ 0.82, AUC₁₀₀ₘₛ ≈ 0.87, precision at 20% FPR ≈ 65%, TPR at 10% FPR ≈ 75%, missed ELMs <15% (Rothstein et al., 11 Nov 2025).

5. Control Integration and Actuator Logic

In operation, the DSM runs at a 2 ms cycle and sub-millisecond inference latency within PACMAN. Its real-time output, $p_{\rm ELM}(\Delta T |\mathbf{x})$, is passed to a finite-state controller that implements simple threshold logic for actuator commands:

• $p_{\rm ELM} > 0.3$: increment gas puff
• $p_{\rm ELM} > 0.5$: ramp RMP coil current
• $p_{\rm ELM} > 0.7$: reduce NBI power

Actuator requests are relayed via PACMAN’s output block, which arbitrates and safety-limits all device commands. Missing or outlier inputs trigger predictor suppression to prevent erroneous actuation (Rothstein et al., 11 Nov 2025).

6. Experimental Validation and Key Results

A dedicated WPQH campaign on DIII-D (shots 215000–215040) demonstrated the DSM predictor/controller sequence:

• Closed-loop operation reduced breakthrough ELM rate by 50%—e.g., from 0.06 Hz to 0.03 Hz average.
• Global energy confinement time τ_E improved by ≈5% against standard ELMy H-mode scaling.
• No significant drop in stored energy or core temperature.
• The predictor provided advance alarms (∼80–120 ms before ELM), giving actuators sufficient time to respond.

Selected experimental results:

Shot	Open-loop ELM rate (Hz)	Closed-loop ELM rate (Hz)	Δτ_E/τ_E (%)
215005	0.08	0.03	+4.8
215012	0.05	0.02	+5.5
215027	0.07	0.04	+4.2

False negatives (ELMs not predicted) were typically associated with shots exhibiting extremely low turbulence, motivating future inclusion of additional fast turbulence diagnostics (Rothstein et al., 11 Nov 2025).

7. Limitations and Future Directions

Principal current limitations include:

• Modest false-alarm rate (~10%), which increases actuator cycling
• Residual missed ELMs in low-turbulence regimes
• Model history depth is limited to 10–20 ms; no recurrent or temporal-convolutional memory

Suggested improvements:

• Integrate longer time-history using recurrent or convolutional architectures
• Incorporate online retraining or Bayesian updating for nonstationary pedestal conditions
• Couple the predictor more tightly to advanced (e.g., RL-based) actuators for optimized ELM suppression and confinement maximization

This suggests that future WPQH-ELM predictors will integrate first-principles transport/stability criteria, machine-learned hazard estimation, and closed-loop actuator optimization for improved performance, aiming for generalized, adaptive, and portable ELM avoidance strategies across devices and operating scenarios (Rothstein et al., 11 Nov 2025, Parisi et al., 14 May 2025, Meier et al., 2023).

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Key sources: (Rothstein et al., 11 Nov 2025, Parisi et al., 14 May 2025, Tzanis et al., 15 Sep 2025, Meier et al., 2023)