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Pellet-Size Scaling of Quasi-Steady-State Plasma Performance in Wendelstein 7-X

This paper analyzes 2024–2025 Wendelstein 7-X experiments to reveal that larger hydrogen ice pellets enhance quasi-steady-state plasma performance by depositing particles deeper into the core to suppress turbulence, a phenomenon that exceeds neutral-gas-shielding model predictions due to significant inward transport of the pellet cloud.

Original authors: Keisuke Fujii, Edgardo Villalobos Granados, Maryam Huck, Jürgen Baldzuhn, Naoki Tamura, Steven Meitner, Larry Baylor, Golo Fuchert, Kai Jakob Brunner, Jens Knauer, Ekkehard Pasch, Jannik Wagner, Bart

Published 2026-09-17

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CC BY 4.0

Original authors: Keisuke Fujii, Edgardo Villalobos Granados, Maryam Huck, Jürgen Baldzuhn, Naoki Tamura, Steven Meitner, Larry Baylor, Golo Fuchert, Kai Jakob Brunner, Jens Knauer, Ekkehard Pasch, Jannik Wagner, Bart Lomanowski, W7-X 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

To understand the challenge of building a fusion reactor, imagine trying to keep a star contained within a bottle. The goal is to squeeze hydrogen atoms together so tightly that they fuse, releasing vast amounts of energy. To do this, scientists use powerful magnetic fields to trap superheated gas, known as plasma, inside a donut-shaped chamber. The secret to making this process efficient lies in how the fuel is distributed. If the fuel is spread evenly, the reaction is weak. But if the fuel is concentrated in the very center, the plasma becomes much hotter and more stable, allowing the fusion reaction to thrive. The difficulty is that simply blowing gas into the edge of the chamber does not reach the core; the gas gets stuck near the walls. To solve this, researchers shoot tiny, frozen pellets of hydrogen deep into the heart of the plasma, delivering fuel exactly where it is needed.

For years, scientists at the Wendelstein 7-X facility in Germany have been testing a continuous system that fires these frozen pellets to sustain high-performance plasmas. The idea is that by depositing fuel deep inside, they can create a steep density gradient—a sharp change in how crowded the particles are from the edge to the center. This steep gradient acts like a shield, suppressing the turbulence that usually cools the plasma and causes it to lose energy. However, the researchers noticed a limit to this method. After firing many pellets in a row, the plasma would stop getting better, no matter how many more pellets were added. It seemed to hit a ceiling. A recent study published in 2026 investigated why this saturation happens and discovered a simple, yet powerful, variable that had been overlooked: the size of the pellets themselves.

The researchers analyzed data from experiments conducted in 2024 and 2025, where the continuous pellet injector was used to fuel long-duration plasma shots. During these runs, the size of the frozen hydrogen pellets varied unintentionally due to the mechanics of the injector. This accidental variation provided a unique opportunity to see how different pellet sizes affected the plasma's performance. The team looked at hundreds of injection events, tracking how the plasma responded when hit by small pellets versus larger ones. They measured the stored energy of the plasma, which serves as a direct indicator of how well the magnetic bottle is holding the heat, and they mapped exactly where the fuel from each pellet ended up inside the chamber.

The results revealed a clear and positive relationship between the size of the pellet and the success of the plasma. When the plasma was already hot and energetic, injecting a small pellet often failed to improve the situation. In these cases, the small pellet would ablate, or evaporate, too quickly, depositing its fuel near the outer edge of the plasma rather than reaching the core. This edge-deposited fuel did not create the necessary steep density gradient, and in some cases, it actually disrupted the existing balance, causing the plasma's performance to drop. However, when a larger pellet was used, the outcome was different. The larger mass of frozen hydrogen could survive the journey through the hot outer layers and penetrate much deeper into the plasma. This deeper delivery created a sharper density gradient in the core, which suppressed turbulence and allowed the plasma to store significantly more energy.

The study found that the maximum performance a plasma could sustain was not a fixed limit but depended on the size of the fuel being injected. By using a statistical analysis of the injection events, the team determined that the steady-state energy of the plasma scales with the size of the pellet. Specifically, they found that larger pellets could sustain plasmas with much higher stored energy levels than smaller ones. This suggests that the saturation observed in previous experiments was not a fundamental barrier to fusion, but rather a consequence of using pellets that were too small to reach the deep core once the plasma became dense and hot. The larger pellets simply had the momentum and mass to push through the shielding effect of the surrounding plasma and deliver fuel to the center.

A surprising finding emerged when the researchers compared their observations with the standard physics models used to predict how deep a pellet would travel. The prevailing model, known as the neutral-gas-shielding model, assumes that as a pellet melts, the gas it releases forms a cloud that shields the remaining solid ice from the heat, allowing it to travel further. While the model correctly predicted that larger pellets would go deeper, it significantly underestimated just how deep they actually went in the Wendelstein 7-X experiments. The fuel from the pellets was found to penetrate much further inward than the model suggested. This discrepancy indicates that once the fuel is released, it does not just sit where it lands; it is actively transported inward by the plasma itself. This rapid inward movement of the fuel cloud helps concentrate the density in the core even more than the pellet's initial penetration would suggest.

The implications of this discovery are straightforward and practical for the future of fusion energy. The study confirms that the size of the fuel pellet is not just a detail of the injection system but a critical control parameter for the performance of the entire reactor. By using larger pellets, scientists can push the plasma to higher energy levels and maintain a more stable, high-performance state for longer periods. The researchers suggest that if they were to inject even larger pellets than those used in these experiments, they might be able to break through the current performance ceiling entirely. This insight shifts the focus from simply trying to inject more fuel to optimizing the size of the fuel to ensure it reaches the heart of the reaction. The work provides a clear path forward for improving the efficiency of stellarator reactors, bringing the dream of a clean, limitless energy source one step closer to reality.

Technical Summary: Pellet-Size Scaling of Quasi-Steady-State Plasma Performance in Wendelstein 7-X

Problem Statement
Efficient core particle fueling is a critical requirement for reactor-relevant magnetically confined plasmas. In large fusion devices like the Wendelstein 7-X (W7-X) stellarator, gas puffing primarily supplies particles near the plasma boundary, often failing to sustain the peaked density profiles necessary for high-performance operation. While cryogenic hydrogen pellet injection offers a direct mechanism for core fueling by penetrating flux surfaces before ablation, the performance improvements it provides are not indefinite. Previous observations indicate that after multiple injections, plasma performance saturates. Furthermore, during the 2024 (OP2.2) and 2025 (OP2.3) experimental campaigns, the continuous pellet fueling system (CPFS) exhibited unintentional variations in pellet size. This paper addresses the need to understand how these variations in pellet size influence the quasi-steady-state plasma performance and the underlying physical mechanisms governing particle deposition and transport.

Methodology
The study utilizes data from continuous pellet injection experiments conducted in W7-X during the OP2.2 and OP2.3 campaigns. The analysis focuses on a specific subset of injection events satisfying strict criteria: steady electron cyclotron resonance heating (ECRH) power between 5 and 6 MW, no neutral-beam injection, injection intervals greater than 0.3 seconds, and operation in the high-ι (FTM) magnetic configuration.

Key diagnostics include:

Diamagnetic loops: To measure plasma stored energy ( $W_{dia}$ ) as a proxy for confinement performance.
Thomson scattering: To measure spatial profiles of electron temperature ( $T_e$ ) and density ( $n_e$ ) at approximately 100 Hz.
Microwave cavity signals: To estimate the size ( $N_{pellet}$ ) of each injected hydrogen ice pellet.

The authors define specific metrics to characterize the plasma response:

Deposition position ( $r_{deposit}$ ): The mean radial position of the pellet-induced density increase.
Density gradient change ( $\Delta L_n^{-1}$ ): The difference in the logarithmic density gradient before and immediately after injection.
Net stored energy gain ( $\Delta W_{dia}^+$ ): The increase in $W_{dia}$ from the post-injection minimum to the subsequent maximum before the next injection.

A statistical analysis was performed on these injection events to correlate $r_{deposit}$ , $\Delta L_n^{-1}$ , and $\Delta W_{dia}^+$ with the pre-injection stored energy ( $W_{dia}$ ) and pellet size ( $N_{pellet}$ ). Additionally, the measured deposition depths were compared against the Neutral-Gas-Shielding (NGS) model predictions.

Key Results

Dependence on Plasma State: There is a clear dependence of the deposition position on the pre-injection stored energy. In plasmas with higher $W_{dia}$ (which generally correspond to higher core density and temperature), pellets ablate more quickly, resulting in particle deposition at larger radii (further outward). Consequently, the ability of a pellet to increase the density gradient and stored energy diminishes as $W_{dia}$ increases, leading to performance saturation.
Dependence on Pellet Size: For plasmas with high stored energy ( $W_{dia} > 0.8$ MJ), larger pellets penetrate significantly deeper into the plasma. This deeper penetration generates steeper density gradients and results in a larger net gain in stored energy ( $\Delta W_{dia}^+$ ).
Quasi-Steady-State Scaling: By analyzing the boundary where $\Delta W_{dia}^+ = 0$ (the point where pellet injection neither improves nor degrades performance), the authors performed a logistic regression. This revealed a power-law relationship for the quasi-steady-state stored energy: $W_{dia} \propto N_{pellet}^{0.68 \pm 0.10}$ . This indicates that injecting larger pellets can sustain plasmas with higher stored energy levels.
Discrepancy with NGS Model: When comparing the measured normalized fueling depth $(a_0 - r_{deposit})/a_0$ with the NGS model prediction, the experimental data shows significantly deeper penetration than the model predicts. The measured depth exhibits a weaker dependence on electron temperature and a stronger dependence on electron density than the NGS scaling suggests.

Significance and Claims
The paper establishes that pellet size is not merely a fueling parameter but a control parameter for the sustainable performance level of W7-X plasmas. The positive correlation between pellet size and quasi-steady-state stored energy suggests that the saturation of performance in current experiments is partly due to the use of smaller pellets that cannot penetrate deeply enough into high-performance plasmas to suppress ion-temperature-gradient (ITG) turbulence effectively.

The authors claim that the observed deeper-than-predicted penetration implies significant inward transport of the pellet cloud (plasmoid) following ablation, a phenomenon not fully captured by the standard NGS model. While the qualitative trends align with pellet-ablation physics (where higher plasma density/temperature reduces penetration and larger pellets increase it), the quantitative discrepancy highlights the importance of rapid inward transport mechanisms.

The study concludes that the injection of even larger pellets could further improve plasma performance in W7-X. However, the authors remain modest regarding the specific mechanisms driving the inward transport, noting that a detailed analysis of plasmoid drift is left for future work. The primary contribution is the statistical identification of the pellet-size scaling law for quasi-steady-state performance and the identification of the gap between measured deposition depths and current theoretical models.

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