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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Flexible Stellarator Physics Facility

We propose to build a Flexible Stellarator Physics Facility to explore promising regions of the vast parameter space of disruption-free stellarator solutions for Fusion Pilot Plants (FPPs). The FESAC Long Range Plan recognized the quasi-symmetric stellarator as “the leading US approach to developing disruption-free, low-recirculating-power fusion configurations”. To deliver the ambitious Decadal Vision for Commercial Fusion Energy, we must establish a persuasive stellarator program in parallel to the tokamak one: the stellarator will prove to be a better path to a reactor if theoretical predictions are confirmed and novel optimization techniques and strategies work as desired. Since the release of the Long Range Plan in 2020, stellarators have arguably made the most significant advances of all fusion concepts. Groundbreaking results from W7-X demonstrated low neoclassical transport and the successful operation of the island divertor. Advances in theory and modeling now allow us to minimize turbulent transport, to achieve equilibria with precise quasisymmetry, to reduce neoclassical transport and fast ion loss to levels far below what has been previously achieved, and to minimize the effect of coil manufacturing errors. If realized, these advances will lead to cost-effective stellarator designs with confinement comparable to tokamaks but without the fundamental challenges of disruptions and current drive.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Global stellarator coil optimization with quadratic constraints and objectives

Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvements in conditioning, regularization, sparsity, and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10$ 2 x faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL’s effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Improved stellarator permanent magnet designs through combined discrete and continuous optimizations

A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for stellarator plasma confinement, such problems have tens of thousands of degrees of freedom whose solutions, for practical reasons, should be constrained to discrete spaces. We perform a direct comparison between two algorithms that have been developed previously for this purpose, and demonstrate that composite procedures that apply both algorithms in sequence can produce substantially improved results. One approach uses a continuous, quasi-Newton procedure to optimize the dipole moments of a set of magnets and then projects the solution onto a discrete space. The second uses an inherently discrete greedy optimization procedure that has been enhanced and generalized for this work. Further, the approaches are both applied to design arrays cubic rare-Earth permanent magnets to confine a quasi-axisymmetric plasma with a magnetic field on axis of 0.5 T. The first approach tends to find solutions with higher field accuracy, whereas the second can find solutions with substantially (up to 30%) fewer magnets. When the approaches are combined, they can obtain solutions with magnet quantities comparable to the second approach while matching the field accuracy of the first.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Robustness of quasi-symmetry along parametric boundary variation

Quasi-symmetry is a guiding principle to modern stellarator optimization for improved plasma confinement. However, the robustness of optimized configurations, which can be crucial for maintaining performance under diverse engineering constraints and practical limitations, has received relatively little attention. Here, in this work, we present various case studies on this robustness, by investigating variations in 1/ v neoclassical transport when plasma configurations are smoothly altered across distinct optimized targets. These targets, optimized from different families—quasi-axisymmetric, quasi-helical, and quasi-isodynamic—are approximately matched in major radius as part of a flexible stellarator design. Our study shows that an optimized target does not always represent a local minimum in transport and that the robustness of a local minimum when present can vary significantly. Furthermore, there are configurations which belong to no established families but have transport levels as low as those of optimized targets. These results highlight the importance of conducting extended searches with key parametric variations around optimized configurations, to ensure its robustness as well as flexibility if desired.

neoclassical transport↗
DOE OSTI2020

Estimation of 14 MeV neutron rate from triton burn-up in future W7-X deuterium plasma campaigns

Fast ion confinement is of major importance for the ignition of a burning fusion plasma. In future deuterium plasma campaigns of the Wendelstein 7-X stellarator, W7-X, the amount of triton burn-up is one possible measure for fast ion confinement. A well-established technique to observe triton burn-up is the 14 MeV neutron rate. In this paper, it is estimated whether an existing scintillating fibre neutron detector is also suited to measure triton burn-up in W7-X with sufficient accuracy. In this work, an estimation is presented, which can be applied to any tokamak or stellarator design and is one-dimensional in the minor radius. The inputs are profiles of density, temperature, and differential volume element as well as the triton slowing-down time. The estimation calculates the thermal deuteron fusion rate and the associated deuteron-triton fusion rate; thus, the triton burn-up generated 14 MeV neutron rate. It neither takes triton diffusion nor explicit losses into account. This thermally generated fusion rate is compared to the neutral beam injection heating induced beam-plasma fusion rate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Computing material volume fractions on a superimposed mesh as applied to Monte Carlo particle transport simulations

Here, we present a newly implemented ray tracing algorithm in OpenMC for efficiently computing material volume fractions on superimposed meshes in complex geometries. By firing rays along each coordinate direction through the geometry, the approach accumulates track-length data in each mesh element, thereby determining the fractional composition of each material. Scaling studies on three different models—a random tetrahedra configuration, the Frascati Neutron Generator ITER dose rate benchmark, and a stellarator design—show excellent parallel performance, with nearly linear speedup on modern multi-threaded and distributed-memory systems. An analysis of the residual error relative to high-resolution reference solutions demonstrated that under optimal conditions it decreases as 1/R, where R is the number of rays fired, making it straightforward to achieve user-prescribed accuracy. This new functionality enables practical, mesh-based approaches for detailed nuclear analyses in production Monte Carlo workflows without resorting to expensive, fully conformal or unstructured meshing.

Monte Carlo↗
DOE OSTI2021

Combined plasma–coil optimization algorithms

Combined plasma–coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot–Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma–coil optimization algorithms, we emphasize the importance of the stability matrix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Gradient-based optimization of 3D MHD equilibria

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al. , J. Plasma Phys. , vol. 85, issue 2, 2019; Paul et al. , J. Plasma Phys. , vol. 86, issue 1, 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well and quasi-symmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ( ${\sim }50\text {--}500$ ) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

Physics↗
DOE OSTI2021

Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman, Nucl. Fusion , vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlak et al. , Nucl. Fusion , vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul, Nucl. Fusion , vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al. , Nucl. Fusion , vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson, Phys. Fluids , vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau, Phys. Plasmas , vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

Physics↗
DOE OSTI2023

The DESC stellarator code suite. Part 1. Quick and accurate equilibria computations

Three-dimensional equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two three-dimensional equilibrium codes: VMEC, which uses a steepest-descent algorithm to reach a minimum-energy plasma state, and DESC, which minimizes the magnetohydrodynamic (MHD) force error in real space directly. Accuracy as measured by satisfaction of MHD force balance is presented for each code, along with the computation time. It is shown that DESC is able to achieve more accurate solutions, especially near axis. The importance of higher-accuracy equilibria is shown in DESC's better agreement of stability metrics with asymptotic formulae. DESC's global Fourier–Zernike basis also yields solutions with analytic derivatives explicitly everywhere in the plasma volume, provides improved accuracy in the radial direction versus conventional finite differences and allows for exponential convergence. Further, DESC can compute a solution with the same accuracy as VMEC in order-of-magnitude less time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Resonant alpha particle loss in stellarators

Particle resonances in stellarators can produce islands in the space of passing particle orbits without the presence of an unstable Alfven mode, provided the period of the resonance matches the period of the equilibrium magnetic field. In this case, the equilibrium itself plays the role of a mode amplitude, and the islands appear on surfaces where the orbital helicity matches the field period. At low energy, these surfaces are given by the field line helicity, but at higher energy, cross field drift causes them to move. The resonances are also felt by trapped particles bouncing back and forth on surfaces with matching helicity. The periodic variation of B along these orbits produces local wells, giving loss due to drift while trapped in a well. Stellarator designs that have equilibrium-induced resonance islands exhibit anomalous alpha particle loss and are unsuitable for reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Inputs and Outputs for paper "The DESC stellarator code suite. Part 1. Quick and accurate equilibria computations"

Contains the DESC and VMEC input and output files used in the paper, as well as the plotting scripts used to create the figures in the paper (Current with the arXiv Mar 31 2022 version, https://arxiv.org/abs/2203.17173v1): 3D equilibrium codes are vital for stellarator design and operation, and high-accuracy equilibria are also necessary for stability studies. This paper details comparisons of two 3D equilibrium codes, VMEC, which uses a steepest-descent algorithm to reach a minimum-energy plasma state, and DESC, which minimizes the MHD force error in real space directly. Accuracy as measured by final plasma energy and satisfaction of MHD force balance, as well as other metrics, will be presented for each code, along with the computation time. It is shown that DESC is able to achieve more accurate solutions, especially near-axis. DESC's global Fourier-Zernike basis also yields the solution everywhere in the plasma volume, not just on discrete flux surfaces. Further, DESC can compute the same accuracy solution as VMEC in an order of magnitude less time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

A flexible and differentiable coil proxy for stellarator equilibrium optimization

Balancing plasma performance and coil cost is a significant challenge when designing a stellarator power plant. Most current stellarator designs are produced through two-stage optimization: stage-1 for the equilibrium and stage-2 for a coil design that reproduces its magnetic configuration. Because few proxies connect both stages, two-stage optimization can produce plasmas that have high-quality physical properties but overly complex coils. In recent years, single-stage optimization has increasingly been used to optimize the plasma and coils simultaneously in order to improve the plasma–coil balance. However, all existing single-stage tools are specialized for filament coils, cannot model coil systems containing permanent magnets or dipole arrays, and continue to be challenged by numerical problems. The quasi-single-stage optimization finds a middle ground by integrating a coil optimization subproblem into stage-1 optimization. We present a flexible, differentiable coil complexity proxy based on the newly developed QUADCOIL coil optimization code. QUADCOIL is fast and can target realistic coil metrics and constraints that are unavailable to codes with comparable speed. We demonstrate the effectiveness and flexibility of the QUADCOIL proxy by presenting two QSS optimization studies. The first study produces a permanent magnet solution for the MUSE stellarator with 34% fewer magnets than previous solutions. The second study produces a coil solution for the ARIES-CS stellarator with 30% reductions in both peak and root-mean-square force.

Fu, Lanke [Princeton Plasma Physics Laboratory (PP↗
DOE OSTI2025

A framework for discrete optimization of stellarator coils

Designing magnets for three-dimensional plasma confinement is a key task for advancing the stellarator as a fusion reactor concept. Stellarator magnets must produce an accurate field while leaving adequate room for other components and being reasonably simple to construct and assemble. In this paper, a framework for coil design and optimization is introduced that enables the attainment of sparse magnet solutions with arbitrary restrictions on where coils may be located. The solution space is formulated as a 'wireframe' consisting of a mesh of interconnected wire segments enclosing the plasma. Two methods are developed for optimizing the current distribution on a wireframe: Regularized Constrained Least Squares, which uses a linear least-squares approach to optimize the currents in each segment, and Greedy Stellarator Coil Optimization, a fully discrete procedure in which loops of current are added to the mesh one by one to achieve the desired magnetic field on the plasma boundary. Examples are presented of solutions obtainable with each method, some of which achieve high field accuracy while obeying spatial constraints that permit easy assembly.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Stellarators as a fast path to fusion

Herein this paper is focused on three points: (1) overcoming obstacles to tokamak power plants may require a configuration modification as large as that of a stellarator. (2) The demonstrated reliability of the computational design of stellarators should change fusion strategy. (3) Deployment of carbon-free energy sources is mandated by the thirty-year doubling of carbon dioxide emissions. Carbon-free energy options must be developed and fully deployed within a few doubling times. Unit size and cost of electricity are only relevant in comparison to alternative worldwide energy solutions. Intermittency, site specificity, waste management, and nuclear proliferation make fusion attractive as the basis for a carbon-free energy system compared to the alternatives. Nonetheless, fusion is not an option for deployment until a power plant has successfully operated. A critical element in a minimal time and risk program is the use of computational design as opposed to just extrapolation. Only the stellarator has an empirical demonstration of the reliable computational design through large changes in configuration properties and scale. The computational design of stellarators should proceed while the inventions necessary for a more tokamak-like power plant are sought. The cost of computational design is extremely small, but adequate time is required for the development of ideas that maximize attractiveness and minimize risk. Rapid power-plant construction without many intermediate steps may seem risky, but the price is small compared to the cost of trillions of dollars for each year's delay in addressing carbon-dioxide emissions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Magnetic mesh generation and field line reconstruction for scrape-off layer and divertor modeling in stellarators

The design of divertor targets and baffles for optimal heat and particle exhaust from magnetically confined fusion plasmas requires a combination of fast, low-fidelity models (such as EMC3-Lite (Feng 2022 Plasma Phys. Control. Fusion 64 125012)) for scoping studies and high-fidelity ones (such as EMC3-EIRENE (Feng et al 2014 Contrib. Plasma Phys. 54 426–31)) for verification. Both of those approaches benefit from a magnetic flux tube mesh for fast interpolation and mapping of field line segments (Feng et al 2005 Phys. Plasmas 12 052505). A new automated mesh generator for unstructured quadrilateral flux tubes with adaptive refinement is presented and integrated into FLARE (Frerichs 2024 Nucl. Fusion 64 106034). For HSX with an extended first wall, it is found that several layers of flux tubes can span the entire half field period before splitting is required. This is an advantage over the traditional setup of the EMC3-EIRENE mesh where careful construction of several sub- domains is required already for the much tighter present first wall. In particular, there is no longer the need to manually construct a suitable outer boundary for the mesh. The divide and conquer paradigm with unstructured mesh layout offers a powerful alternative for fast head load approximation that is suitable for integration into optimization workflows. Further examples for W7-X and CTH demonstrate the versatile application range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗