2025 Simons Collaboration on Hidden Symmetries and Fusion Energy Annual Meeting

Josh Burby
University of Texas at Austin

The non-perturbative adiabatic invariant is all you need

Developing reduced models for highly-oscillatory dynamical systems traditionally proceeds by applying asymptotic averaging methods. However, the quality of asymptotic averaging degrades as timescale separation decreases. In studying a classical application of asymptotic averaging methods, charged particles moving in a strong inhomogeneous magnetic field, we identified a regime of marginal timescale separation where asymptotic averaging fails quantitatively in spite of strong indications that a good averaged model ought to exist. We developed a non-perturbative, data-driven averaging method for the marginal regime and found the resulting non-perturbative averaged model significantly outperforms asymptotic averaging, even when accounting for corrections from higher-order averaging. I will explain the method in general and in the charged particle context.
 

Eduardo Rodriguez
IPP Max Planck Institute – Greifswald

Understanding quasi-isodynamicity

Quasi-isodynamicity (QI) is a property of magnetic field-plasma systems that enables the confinement of particle orbits necessary to undergo thermonuclear fusion. The class of QI stellarators, as an alternative to quasisymmetric ones, is garnering ever increasing interest due to its distinct advantages. However, this class is more complex, requiring additional effort to understand the broad implications of QI on the design of stellarator devices.

This presentation aims to explore the nature of QI fields from a fundamental perspective, focusing on how the defining characteristics of QI influence magnetic field properties. By doing so, we provide a broader understanding of how various aspects of the system are interconnected. In particular, we will identify which properties are easily achievable and which ones present challenges. While much of the discussion will be framed in general terms based on robust physical principles, many statements become rigorously true in the context of the near-axis description of the field, which we shall carry along through the discussion.

This talk will also go beyond purely theoretical considerations, applying the developed concepts — particularly those from the near-axis model — to a more practical context. We present a systematic survey of the space of QI stellarators grounded in recent advancements in their near-axis theory. These developments enable us to assess such things as neoclassical transport within the near-axis framework, and offer a rapid method for designing MHD-stable fields with minimal plasma boundary shaping.
 

Max Ruth
University of Texas at Austin

Regularization and Convergence of the Near-Axis Expansion

Through the course of the Simons collaboration, the near-axis expansion has become a ubiquitous technology for efficiently investigating stellarator configurations. The benefits of the near-axis expansion include its speed, ease of use, and simple expressions for quasisymmetry. In this talk, we analyze the near-axis expansion from a numerical point of view. We show that the vacuum near-axis expansion can be proven to converge when properly regularized. On the other hand, we find that no reasonable conditions can be given on the input to guarantee convergence in the unregularized case. We confirm this by demonstrating the convergence with real coil fields. These tests further suggest a link between the radius of convergence and the axis-coil distance, akin to the L-grad-B metric.
 

Georgia Acton
University of Oxford

Full Flux Surface of Gyrokinetic Code, stella

In the current landscape of gyrokinetic modelling, there exists a need for codes that can efficiently capture turbulent phenomena in complex magnetic geometries. As the fusion community progresses toward more sophisticated devices, such as stellarators and advanced tokamaks, the demand for reliable simulation tools grows. Our code aims to provide a robust algorithm for investigating turbulence under varied magnetic geometries, ultimately contributing to a more comprehensive understanding of plasma behaviour and improved design of future fusion reactors.

Our code leverages a pseudo-spectral method that preserves spectral accuracy in the perpendicular direction while employing an implicit algorithm to effectively model dynamics along the magnetic field. This approach not only retains spectral accuracy in perpendicular derivatives and gyro-averages but also captures fast parallel dynamics.

Here we present the full flux surface version of stella, which incorporates an iterative-implicit treatment that offers fully-implicit and mixed implicit-explicit options. This approach allows for larger time steps in the simulation of kinetic electron behaviour, significantly enhancing computational efficiency compared with fully explicit codes, and ultimately aims to reduce the computational cost of electrostatic turbulent simulations with kinetic electron effects.

To demonstrate the effectiveness of the new approach, we will present a comparative analysis of flux-tube simulations against the full flux version of stella, using both adiabatic and kinetic electrons. The hope is this tool will contribute to ongoing discussions regarding the effects of zonal modes in three-dimensional geometries and contribute to future advancements in turbulence modelling within the fusion research community.

Antoine Baillod
Columbia University

Design and Optimization of the Columbia Stellarator eXperiment

The Columbia Stellarator eXperiment (CSX), currently in the design phase at Columbia University, aims to investigate quasi-axisymmetric plasmas at a small aspect ratio and validate recent advancements in stellarator theory, optimization, and technology. CSX is designed to test key theoretical predictions, including plasma flow damping, magnetohydrodynamic (MHD) stability, and trapped particle confinement. The magnetic field is generated by two circular planar poloidal field (PF) coils and two shaped interlinked (IL) coils, with potential additional coils to enhance shaping and flexibility. The PF coils and vacuum vessel are repurposed from the former Columbia Non-Neutral Torus (CNT) experiment, while the IL coils will be fabricated in-house using non-insulated high-temperature superconducting (HTS) tapes. These coils undergo shape and strain optimization to achieve the desired plasma configuration while meeting engineering constraints. A major challenge in CSX’s design is finding a plasma shape that satisfies physics objectives while being realizable with a limited number of coils. The constrained coil set restricts the range of achievable plasma shapes, making the traditional two-stage stellarator optimization approach impractical. Instead, we employ novel single-stage

optimization techniques, where plasma and coils are optimized concurrently. While this increases problem complexity, it enables the discovery of configurations that satisfy both engineering and physics requirements. We compare two single-stage optimization methodologies and explore their application to CSX’s design, aiming to identify configurations that generate a plasma regime suitable for the experiment’s objectives. A set of promising configurations is then selected and further refined using a multi-filament model that accounts for the finite thickness of the coils. Finally, the robustness and sensitivity to manufacturing and installation errors are assessed for some noteworthy configurations. The shape gradients of key metrics and the performance degradation under random coil perturbations are evaluated. Our results underscore the feasibility of the CSX design and provide critical insights that will inform the coil engineering.
 

Alan Kaptanoglu
New York University

Recent advances in stellarator coil optimization

We will review recent work in the field of stellarator coil optimization, including adding strains, forces, and torques, as well as new methodologies based on voxels, dipole arrays, passive arrays, and more.
 

Chris Smiet
École Polytechnique Fédérale de Lausanne

Turnstiles and topological index in fusion reactor divertors

A divertor often exploits the topology of ‘x’-points –– hyperbolic fixed points in the Poincaré map of the magnetic field line trajectories –– to create diversion of field lines and increase the separation between the plasma and wall. Around these x-points the magnetic field can appear chaotic, and trajectories in the Poincaré map do not trace out neat surfaces, but appear randomly distributed. Despite appearing chaotic, field line flow is deterministic, and the amount of field lines that pass through a given boundary can be precisely quantified. In particular, an important quantity for analyzing chaotic transport in Hamiltonian systems is the so-called turnstile, which dictates the exchange of magnetic flux between two well separated regions of space, and whose area quantifies the efficiency with which this exchange happens.

In this talk, we present a numerical algorithm that can evaluate the turnstile area directly from a stellarator coil solution, and which is efficiently calculated using an action principle by Meiss. We also explore how the magnetic topology (i.e. the location and interactions between fixed points) and the magnetic chaos can be controlled in the edge of fusion reactors.

Using this tool, we explore select configurations from the QUASR database which exhibit novel divertor topologies where transport to the wall is mediated through interacting turnstiles. Furthermore, we show that in a low-iota configuration of W7-X, the turnstile mechanism causes intricate features in connection length plots used to analyze divertor heat loads. Finally, we present the first results of optimizations on W7-X and other configurations where fixed-point topology and stochasticity in the divertor region is controlled.
 

Eve Stenson
Max Planck Institute for Plasma Physics

Optimization & engineering for EPOS

Electron-positron plasmas are the quintessential “pair plasmas” (comprising positively and negatively charged particles of equal mass), and a moderately high-field, tabletop-sized stellarator (with ~2-ton axis and ~10-liter confinement volume) is an attractive option for laboratory trapping of these plasmas in the low-temperature (eV or less), strongly magnetized (r_L << λ_D ) regime. This will facilitate experimental comparisons to theoretical and computational predictions of plasma phenomena in these unusually symmetric systems. In turn, positrons and e+e- pair plasma offer a sensitive probe of confinement properties and hence a validation of modern stellarator optimization (e.g., more robust construction tolerances and a high degree of quasisymmetry). The mission of EPOS (Electrons and Positrons in an Optimized Stellarator), part of the APEX (A Positron-Electron eXperiment) Collaboration, is thus to unite and advance these two plasma physics frontiers.

The Simons HSFE collaboration and the SIMSOPT framework have been instrumental to addressing key optimization and engineering questions for EPOS. Despite its exotic target, these questions relate to those for fusion efforts in many ways. Milestones have included, for example: the calculation, fabrication, and successful tests of small (10-cm-scale), non-planar coils made from high-temperature superconducting (HTS) tape; implementation of single-stage, stochastic optimization, with the inclusion of HTS strain and finite-build coils, to produce highly quasisymmetric magnetic field configurations even when subjected to errors/uncertainties; and the integration of more device-specific needs, such as a “weave lane” for e+ injection from an external beam line. This talk will provide an overview of those results, the resulting design for the device, and the plans for building it in the coming year.

Participation in the meeting falls into the following four categories. An individual’s participation category is communicated via their letter of invitation.

The Simons Foundation will never ask for credit card information or require payment for registration to our events.

Group A – PIs and Speakers

Economy Class: For flights that are three hours or less to your destination, the maximum allowable class of service is Economy class.
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The foundation will arrange and pay for round-trip air or train travel to the conference as well as hotel accommodations and reimbursement of local expenses. Economy-class airfare will be booked for all flights.

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Individuals in Group C will not receive financial support, but are encouraged to enjoy all conference-hosted meals.

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Individuals in Group D will participate in the meeting remotely.

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Travel Deviations

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Overview

In-person participants will be reimbursed for meals and local expenses including ground transportation. Expenses should be submitted through the foundation’s online expense reimbursement platform after the meeting’s conclusion.

Expenses accrued as a result of meetings not directly related to the Simons Foundation-hosted meeting (a meeting held at another institution, for example) will not be reimbursed by the Simons Foundation and should be paid by other sources.

Below are key reimbursement takeaways; a full policy will be provided with the final logistics email circulated approximately 2 weeks prior to the meeting’s start.

Meals

The daily meal limit is $125; itemized receipts are required for expenses over $24 USD. The foundation DOES NOT provide a meal per diem and only reimburses actual meal expenses up the following amounts.

• Breakfast $20
• Lunch $30
• Dinner $75

Allowable Meal Expenses

• Meals taken on travel days (when you traveled by air or train).
• Meals not provided on a meeting day, dinner on Friday for example.
• Group dinners consisting of fellow meeting participants paid by a single person will be reimbursed up to $75 per person and the amount will count towards each individual’s $125 daily meal limit.

Unallowable Meal Expenses

• Meals taken outside those provided by the foundation (breakfast, lunch, breaks and/or dinner).
• Meals taken on days not associated with Simons Foundation-coordinated events.
• Minibar expenses.
• Meal expenses for a non-foundation guest.

• Ubers, Lyfts, taxis, etc., taken to and from restaurants in Manhattan.

  • Accommodations will be made for those with mobility restrictions.

Ground Transportation

Expenses for ground transportation will be reimbursed for travel days (i.e. traveling to/from the airport or train station) as well as subway and bus fares while in Manhattan are reimbursable.

Transportation to/from satellite meetings are not reimbursable.

Attendance

In-person participants and speakers are expected to attend all meeting days. Participants receiving hotel and travel support wishing to arrive on meeting days which conclude at 2:00 PM will be asked to attend remotely.

Entry & Building Access

Upon arrival, guests will be required to show their photo ID to enter the Simons Foundation and Flatiron Institute buildings. After checking-in at the meeting reception desk, guests will be able to show their meeting name badge to re-enter the building. If you forget your name badge, you will need to provide your photo ID.

The Simons Foundation and Flatiron Institute buildings are not considered “open campuses” and meeting participants will only have access to the spaces in which the meeting will take place. All other areas are off limits without prior approval.

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Guests & Children

Meeting participants are required to give 24 hour advance notice of any guests meeting them at the Simons Foundation either before or after the meeting. Outside guests are discouraged from joining meeting activities, including meals.

With the exception of Simons Foundation and Flatiron Institute staff, ad hoc meeting participants who did not receive a meeting invitation directly from the Simons Foundation are not permitted.

Children under the age of 18 are not permitted to attend meetings at the Simons Foundation. Furthermore, the Simons Foundation does not provide childcare facilities or support of any kind. Special accommodations will be made for nursing parents.

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