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Divertor topology and vacuum vessel design for stellarators

This paper introduces a novel optimization framework that jointly designs modular coils and vacuum vessels for stellarators, enabling the first realization of precise snowflake divertors alongside standard X-point and null configurations for next-generation prototypes.

Original authors: Andrew Giuliani, Raffael Wendlinger, Misha Padidar, Robert Davies, Shibabrat Naik, Calvin Lowe, Georg Harrer

Published 2026-07-30

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CC BY 4.0

Original authors: Andrew Giuliani, Raffael Wendlinger, Misha Padidar, Robert Davies, Shibabrat Naik, Calvin Lowe, Georg Harrer

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

Imagine trying to cook a meal inside a pot that is constantly trying to boil over. In the world of fusion energy, scientists are trying to build a "star in a jar" to create limitless clean power. The challenge is that the super-hot fuel, a soup of charged particles called plasma, is so energetic it wants to escape in every direction. If it touches the walls of the container, it cools down instantly and stops the reaction, or worse, it melts the container. To solve this, scientists use powerful magnetic fields to levitate the plasma in the middle of a vacuum chamber, keeping it from touching the sides. But even with magnetic cages, some particles inevitably drift to the edge. To keep the star alive, we need a way to catch these escaping particles and let them out safely without damaging the machine. This is where the "divertor" comes in: a specialized exhaust system that acts like a funnel, guiding the heat and waste particles away from the main star and onto a reinforced plate where they can be cooled and pumped away.

For decades, scientists have been perfecting these exhaust systems for doughnut-shaped machines called tokamaks. However, there is another type of machine, the stellarator, which looks more like a twisted, knotted pretzel. Stellarators are incredibly promising because they can run continuously without the risk of sudden shutdowns, but designing their exhaust systems has been like trying to solve a puzzle in the dark. The magnetic fields in these twisted machines are complex, and figuring out exactly where the "exhaust pipes" should be, and how to build a container (vacuum vessel) that fits around them without getting in the way, has been a massive headache. If the container is too close, the magnets might crash into it; if it's too far, the machine becomes inefficient. Until now, there hasn't been a reliable way to design the exhaust and the container together as a single, harmonious unit.

This paper introduces a new set of digital tools that finally allows scientists to design the exhaust system and the container of a stellarator at the same time. Think of it as a master architect who can simultaneously design the shape of a house, the placement of its windows, and the layout of its plumbing, ensuring everything fits perfectly without any pipes bursting through the walls. The authors developed a clever mathematical method to find the exact "dead ends" in the magnetic field where particles get trapped and guided out. They call these dead ends "fixed points," and they can be shaped into different types of exhaust funnels, from simple single exits to complex, six-legged "snowflake" patterns that spread the heat out even more effectively.

The team's big breakthrough is that they figured out how to make the computer "see" the distance between these invisible magnetic funnels and the physical walls of the machine. They created a family of container shapes that are easy for the computer to measure, allowing the design software to nudge the walls and the magnets until they are perfectly spaced. Using these new algorithms, the researchers successfully designed several new stellarator concepts, including the first-ever precise "snowflake" divertor for this type of machine. In their simulations, they showed that they could create a machine with a "quasi-axisymmetric" shape (which helps the plasma stay stable) that also has a highly efficient exhaust system and a vacuum vessel that fits snugly around it. They didn't just guess; they ran the numbers and showed that these designs work mathematically, offering a blueprint for a next-generation prototype called "STAR Lite." This work suggests that we are getting much closer to building stellarators that are not only stable but also practical to build and operate.

Technical Summary: Divertor Topology and Vacuum Vessel Design for Stellarators

Problem Statement
The divertor is a critical component for exhausting heat and particles in both tokamaks and stellarators. While tokamak divertor design is a mature field with established topologies (single-null, double-null, snowflake), stellarator divertor design has historically lagged, often relying on "island divertors" or indirect optimization of the edge magnetic field. Existing methods for stellarator optimization struggle to directly control the position and type of magnetic fixed points (elliptic, hyperbolic, or parabolic) required for advanced divertor configurations. Furthermore, designing a vacuum vessel that is compatible with these complex edge topologies and modular coils, while maintaining necessary clearances, presents a significant geometric and computational challenge. There is a need for a unified framework that can jointly optimize modular coils, divertor fixed points, and the vacuum vessel geometry to realize a wide range of magnetic topologies, including those previously unattainable in stellarators.

Methodology
The authors present a comprehensive numerical framework integrating three primary components:

Robust Fixed Point Computation: The paper introduces a spectral method to compute periodic-orbit fixed points of any type (elliptic, hyperbolic, or parabolic) within a vacuum magnetic field.
- For elliptic and hyperbolic points, the method solves a nonlinear root-finding problem using Newton's method with a Chebyshev collocation scheme.
- For parabolic points (where the Jacobian is singular or ill-conditioned), the authors augment the system of equations with additional constraints and degrees of freedom (specifically auxiliary poloidal field coils). This includes enforcing trace conditions ($Tr(M) = 2$) or full matrix constraints ( $M = I$ ) to stabilize the solver and allow for the computation of rank-1 and rank-0 parabolic fixed points (including snowflakes).
- The method provides exact derivatives of the fixed point positions with respect to design variables, enabling gradient-based optimization.
Parametric Vacuum Vessel Design: To couple divertor design with vessel geometry, the authors define parametric families of vacuum vessels for which signed distance functions (SDFs) can be computed efficiently.
- Canal Surfaces: Includes "pill pipe" vessels (envelopes of spheres along a rounded rectangle) and non-planar vessels with Fourier-series centerlines. These offer closed-form or 1D minimization SDFs.
- Piecewise Cylindrical (PC) Vessels: Vessels formed by sequences of mitred cylinders. The SDF requires solving a sequence of 1D minimizations but allows for complex, non-axisymmetric shapes.
- These SDFs are differentiable and used to enforce clearance constraints between coils, fixed points, and the vessel.
Joint Optimization Framework: The authors combine the fixed point solver and vessel SDFs into a single optimization loop.
- The optimization treats coil geometries, currents, and vacuum vessel parameters as degrees of freedom.
- Constraints enforce pairwise distances (coil-vessel, divertor-vessel, flux surface-vessel) and maintain the fixed point at a constant vertical position and distance from the vessel.
- The objective function targets quasi-axisymmetry (QA), rotational transform, magnetic well, and aspect ratio, while satisfying engineering constraints on coil curvature and current.

Key Contributions and Results

Numerical Stability: The paper demonstrates that the proposed spectral methods can robustly compute fixed points across bifurcation points, converting elliptic points to hyperbolic ones and healing "broken" snowflakes, all while maintaining a well-conditioned Jacobian.
Diverse Divertor Topologies: Using the framework, the authors generate stellarator designs featuring:
- Standard single-null and double-null X-point divertors.
- Parabolic single-null divertors.
- Snowflake Divertors: For the first time, the authors demonstrate that precise, non-axisymmetric snowflake divertors (rank-0 parabolic fixed points with six legs) can be achieved in a stellarator.
Integrated Design: The framework successfully produces quasi-axisymmetric stellarator designs (candidates for a "STAR Lite" prototype) that simultaneously satisfy core performance metrics (quasisymmetry, magnetic well) and complex edge topologies with compatible vacuum vessels.
Visualization: The paper presents five distinct device configurations (Figure 1) illustrating the variety of achievable topologies, including Poincaré sections showing stable/unstable manifolds and connection lengths.

Significance and Claims
The paper claims to provide the first demonstration of precise snowflake divertors in stellarators, expanding the range of exhaust strategies available to stellarator design beyond island divertors. By treating the vacuum vessel geometry as a degree of freedom and utilizing efficient signed distance functions, the authors enable a "joint optimization" approach that ensures physical compatibility between the magnetic field, the divertor plates, and the vessel structure. The work suggests that incorporating divertor design early in the optimization cycle is feasible and likely beneficial for the commercial viability of future fusion power plants. The authors position these designs as candidates for a next-generation "STAR Lite" prototype, aiming to leverage the flexibility of non-axisymmetric fields to realize advanced divertor configurations previously limited to tokamaks.

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