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First step toward multi machine ELM energy scalings and extrapolations to SPARC and ITER

This paper analyzes a multi-machine database to demonstrate that while neoclassical collisionality fails to universally predict ELM energy losses, a new turbulence-based scaling for small/QCE ELMs and a revised regression for type-I ELMs provide more accurate projections for future reactors like SPARC and ITER.

Original authors: R. Perillo, A. Redl, T. Eich, C. J. Lasnier, A. Nelson, R. Rizkallah, D. Silvagni, A. Stagni, J. A. Boedo, A. McLean, P. Traverso, N. Vianello, the DIII-D team, JET contributors, the ASDEX Upgrade tea

Published 2026-08-24

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CC BY 4.0

Original authors: R. Perillo, A. Redl, T. Eich, C. J. Lasnier, A. Nelson, R. Rizkallah, D. Silvagni, A. Stagni, J. A. Boedo, A. McLean, P. Traverso, N. Vianello, the DIII-D team, JET contributors, the ASDEX Upgrade team, the TCV team, the EUROfusion Tokamak Exploitation team

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside the heart of a fusion reactor, where temperatures soar far beyond the surface of the sun, plasma is held in a magnetic cage. To generate power, this superheated gas must be kept stable and confined for long periods. However, the edge of this plasma is a turbulent frontier. It frequently erupts in sudden, violent bursts known as edge localized modes. Think of these bursts like a pressure valve on a steam engine that opens and slams shut; they are necessary to flush out impurities that would otherwise cool the core, but they also hurl massive amounts of energy and particles against the reactor's inner walls. If these bursts are too strong, they can melt or erode the tiles lining the reactor, threatening the machine's very survival. As scientists design the next generation of fusion devices, such as the massive ITER project under construction in France and the smaller, high-performance SPARC prototype, a critical question remains: will these future machines be able to handle these eruptions without destroying themselves?

A team of researchers from universities and laboratories across the United States and Europe has taken a major step toward answering this question by analyzing data from seven different tokamak machines. Their work challenges an old assumption about how to predict the size of these energy bursts. For years, scientists relied on a specific model that suggested the energy lost during an eruption depended on how often electrons in the plasma collided with one another near the top of the magnetic cage. The researchers tested this model against a vast collection of new data and found it failed to predict the behavior of the most dangerous, large-scale eruptions, as well as a different, more frequent type of smaller burst that is crucial for future reactors. The old model simply could not capture the physics of these high-density scenarios, leaving a gap in our ability to forecast how future machines will perform.

To fill this gap, the team performed a fresh analysis, separating the data into two distinct categories: the large, infrequent eruptions and the small, rapid-fire bursts. For the large eruptions, they developed a new way to estimate the energy loss based on the density of the plasma and the shape of the magnetic cage. When they applied this new calculation to the projected conditions for SPARC and ITER, the results were sobering. The model predicts that under standard operating conditions, these future machines would experience energy losses of 4.5% and 12% of their total stored energy, respectively. Such high percentages would likely be intolerable for the delicate materials lining the reactor walls, suggesting that operating these machines with large, standard eruptions could lead to rapid damage.

The story changes, however, when the researchers looked at the smaller, high-frequency bursts. These events, often called quasi-continuous exhaust, occur when the plasma is pushed to very high densities. The team discovered that the behavior of these smaller bursts is not governed by conditions at the top of the plasma cage, but rather by the turbulence at the very edge where the plasma meets the vacuum. By measuring a specific parameter related to this edge turbulence, they found a clear pattern: as the turbulence increases, the energy lost in each burst drops dramatically, while the frequency of the bursts rises. This means the reactor releases its energy in a steady, manageable stream rather than in violent, damaging spikes.

Using this new understanding, the researchers projected how these small bursts would behave in future reactors. For the SPARC machine, if it can maintain the right high-density conditions, the energy loss per burst is predicted to be around 1%, a level that the reactor walls could likely withstand. For ITER, a high-fueling scenario could similarly reduce the energy loss to about 1.2%. The study suggests that if these future machines can be tuned to operate in this high-density, small-burst regime, they could avoid the catastrophic wall damage associated with larger eruptions. While these projections are based on the best available data and require further testing to confirm their accuracy, the findings offer a promising roadmap. They indicate that by carefully controlling the turbulence at the plasma's edge, scientists may be able to keep the most powerful fusion reactors on Earth safe and operational for the long haul.

Technical Summary: First Step Toward Multi-Machine ELM Energy Scalings and Extrapolations to SPARC and ITER

Problem Statement
Edge Localized Modes (ELMs) are plasma instabilities inherent to High-Confinement Mode (H-mode) operations. While they help flush impurities, unmitigated Type-I ELMs pose a severe threat to the integrity of divertor targets in future fusion reactors like SPARC and ITER due to excessive peak energy fluence. Current projections for unmitigated Type-I ELMs in ITER exceed the melting limits of tungsten monoblocks. While "small" or "Quasi-Continuous Exhaust" (QCE) ELM regimes offer a potential solution characterized by lower energy losses and higher frequencies, a robust scaling law for their energy loss ( $\Delta E_{ELM}/W_{plasma}$ ) has not yet been established. Furthermore, existing models, such as the Loarte scaling based on pedestal-top neoclassical electron collisionality ( $\nu^*_{e,neo}$ ), have been shown to inadequately describe Type-I ELMs in peeling-ballooning-limited regimes and fail to capture the physics of small ELMs.

Methodology
The authors constructed a multi-machine database comprising seven tokamaks (DIII-D, JET, ASDEX Upgrade, TCV, HL-2A, COMPASS, and MAST) with a wide range of normalized ELM energy losses (0.5% to 14%). The study distinguishes between "large" Type-I ELMs ( $\Delta E_{ELM}/W_{plasma} > 2\%$ ) and "small" ELMs ( $\Delta E_{ELM}/W_{plasma} < 2\%$ ).

Key methodological steps included:

Evaluation of Existing Models: The Loarte scaling was tested against the multi-machine dataset, specifically examining its applicability to elevated- $q_{95}$ Type-I and small ELM regimes.
Regression Analysis: Least-squares regression was performed on Type-I ELMs using pedestal-top parameters (temperature $T_e$ , density $n_e$ , major radius $R_{maj}$ , and elongation $\kappa$ ).
Separatrix Analysis: For small ELMs, the study shifted focus from the pedestal top to the separatrix region. A turbulence control parameter at the separatrix ( $\alpha_t$ ) was utilized to characterize the transition between regimes.
Stability and Modeling: The ELITE code was used to analyze pedestal stability boundaries, while the Eich model was employed to compare experimental peak parallel energy fluence against theoretical predictions.
Extrapolation: Derived scalings were applied to nominal scenarios for SPARC and the ITER D-T Q=10 scenario.

Key Contributions and Results

Limitations of Pedestal-Top Collisionality: The study confirms that the normalized neoclassical electron collisionality at the pedestal top ( $\nu^*_{e,neo}$ ) does not adequately order $\Delta E_{ELM}/W_{plasma}$ for peeling-ballooning-limited Type-I ELMs or ballooning-limited small ELMs. The correlation is weak ( $R^2 \approx 0.02-0.05$ ).
Type-I ELM Scaling: A new empirical scaling was derived specifically for Type-I ELMs ( $\Delta E_{ELM}/W_{plasma} > 2\%$ ):
$\frac{\Delta E_{ELM}}{W_{plasma}} [\%] = 6.8 \cdot T_{e,ped}^{0.03} \cdot n_{e,ped}^{-0.4} \cdot \kappa^{-0.4} \cdot R_{maj}^{0.0}$
Extrapolating this to SPARC yields a loss of ~4.5%, and to ITER (Q=10) yields ~12%. The authors note these values are likely intolerable for divertor survivability.
Small ELM Physics and Scaling: The study identifies that small/QCE ELMs are governed by conditions near the separatrix rather than the pedestal top. The transition from Type-I to small ELMs occurs at a separatrix turbulence parameter $\alpha_t \approx 0.35$ $α_{t} \approx 0.35$ .
- As $\alpha_t$ increases, the pedestal moves toward a ballooning-limited boundary, the toroidal mode number increases (from $n \sim 10$ to $n \sim 20-25$ ), and ELM frequency rises exponentially ( $f_{ELM} = 46 e^{0.035 \cdot \alpha_t}$ ).
- A new scaling for small ELMs was proposed:
  $\frac{\Delta E_{ELM}}{W_{plasma}} [\%] = 1.6 \cdot e^{-\alpha_t / 2}$
Extrapolations to Future Devices:
- SPARC (QCE regime): With $\alpha_t = 0.86$ , the scaling predicts $\Delta E_{ELM}/W_{plasma} \approx 1.0\%$ and $f_{ELM} \approx 320$ Hz.
- ITER (Baseline vs. High-fueling): The baseline scenario ( $n_{e,sep}=4.9 \times 10^{19} \text{m}^{-3}$ ) yields $\alpha_t = 0.23$ , which falls below the transition threshold ( $\alpha_t > \sim 0.35$ ) and does not predict a small ELM regime. However, high-fueling scenarios with $n_{e,sep}$ up to $8.3 \times 10^{19} \text{m}^{-3}$ result in $\alpha_t = 0.64$ . In this high-fueling case, the scaling predicts $\Delta E_{ELM}/W_{plasma} \approx 1.2\%$ and $f_{ELM} \approx 200$ Hz.
- The authors note that if $\alpha_t > 1$ is achieved, losses could fall below 1%.

Significance and Claims
The paper presents an initial step toward establishing multi-machine energy scalings for reactor-relevant scenarios. Its primary significance lies in the identification of two distinct ELM classes requiring separate scaling laws:

Type-I ELMs: Scaled by pedestal-top parameters and plasma shape, predicting high energy losses for future devices.
Small/QCE ELMs: Scaled by separatrix turbulence parameters ( $\alpha_t$ ), predicting significantly lower energy losses (1–1.2%) that are favorable for divertor survivability.

The authors explicitly state that these results represent a "first step" and that the small ELM-fitted results are an initial attempt. They emphasize that future analysis on broader datasets, including dedicated separatrix analysis from other machines (JET, Alcator C-MOD, MAST-U), is necessary to improve the accuracy of these projections. The study does not claim these scalings are definitive for all future scenarios but rather provides a framework for projecting ELM energy losses based on the specific operational regime (Type-I vs. Small/QCE).

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