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At least 19 records
All sourcesNASA NTRSDOE OSTI
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 OSTI2024

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. ( Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

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 OSTI2023

Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry

We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The method is based on a bilevel optimization problem, where the outer coil optimization is constrained by a set of inner least squares optimization problems whose solutions describe magnetic surfaces. The outer optimization objective targets coils that generate a field with nested magnetic surfaces and good quasi-symmetry. The inner optimization problems identify magnetic surfaces when they exist, and approximate surfaces in the presence of magnetic islands or chaos. We show that this formulation can be used to heal islands and chaos, thus producing coils that result in magnetic fields with precise quasi-symmetry. We show that the method can be initialized with coils from the traditional two-stage coil design process, as well as coils from a near-axis expansion optimization. We present a numerical example where island chains are healed and quasi-symmetry is optimized up to surfaces with aspect ratio 6. Another numerical example illustrates that the aspect ratio of nested flux surfaces with optimized quasi-symmetry can be decreased from 6 to approximately 4. In conclusion, the last example shows that our approach is robust and a cold-start using coils from a near-axis expansion optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Electromagnetic coil optimization for reduced Lorentz forces

Abstract The reduction of magnetic forces on electromagnetic coils is an important consideration in the design of high-field devices such as the stellarator or tokamak. Unfortunately, these forces may be too time-consuming to evaluate by conventional finite element modeling within an optimization loop. Although mutual forces can be computed rapidly by approximating large-bore coils as infinitely thin, this approximation does not hold for self-forces as it leads to an unphysical divergence. Recently, a novel reduced model for the self-field, self-force, and self-inductance of electromagnetic coils based on filamentary models was rigorously derived and demonstrated to be highly accurate and numerically efficient to evaluate (Hurwitz et al 2024 IEEE Trans. Magn. 60 7001614). In this paper, we present an implementation of the reduced self-force model employing automatic differentiation within the simsopt stellarator design software and use it in derivative-based coil optimization for a quasi-axisymmetric stellarator. We show that it is possible to significantly reduce point-wise forces throughout the coils, though this comes with trade-offs to fast particle losses and the minimum distance between coils and the plasma surface. The trade-off between magnetic forces and coil-surface distance is mediated by the minimum coil–coil distance for coils near the inboard side of the ‘bean’ cross-section of the plasma. The relationship between forces and fast particle losses is mediated by the normal field error. Coil forces can be lowered to a threshold with minimal deterioration to losses. Importantly, the magnet optimization approach here can be used also for tokamaks, other fusion concepts, and applications outside of fusion.

Hurwitz, Siena (ORCID:0000000166599659)↗
DOE OSTI2022

Stellarator coil optimization supporting multiple magnetic configurations

Abstract We present a technique that can be used to design stellarators with a high degree of experimental flexibility. For our purposes, flexibility is defined by the range of values the rotational transform can take on the magnetic axis of the vacuum field while maintaining satisfactory quasisymmetry. We show that accounting for configuration flexibility during the modular coil design improves flexibility beyond that attained by previous methods. Careful placement of planar control coils and the incorporation of an integrability objective enhance the quasisymmetry and nested flux surface volume of each configuration. We show that it is possible to achieve flexibility, quasisymmetry, and nested flux surface volume to reasonable degrees with a relatively simple coil set through an NCSX-like example. This example coil design is optimized to achieve three rotational transform targets and nested flux surface volumes in each magnetic configuration larger than the NCSX design plasma volume. Our work suggests that there is a tradeoff between flexibility, quasisymmetry, and volume of nested flux surfaces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasisymmetry

We propose a new method to compute magnetic surfaces that are parametrized in Boozer coordinates for vacuum magnetic fields. We also propose a measure for quasisymmetry on the computed surfaces and use it to design coils that generate a magnetic field that is quasisymmetric on those surfaces. The rotational transform of the field and complexity measures for the coils are also controlled in the design problem. Using an adjoint approach, we are able to obtain analytic derivatives for this optimization problem, yielding an efficient gradient-based algorithm. Starting from an initial coil set that presents nested magnetic surfaces for a large fraction of the volume, our method converges rapidly to coil systems generating fields with excellent quasisymmetry and low particle losses. In particular for low complexity coils, we are able to significantly improve the performance compared with coils obtained from the standard two-stage approach, e.g. reduce losses of fusion-produced alpha particles born at half-radius from $17.7\,\%$ to $6.6\,\%$ . We also demonstrate 16-coil configurations with alpha loss ${<}1\,\%$ and neoclassical transport magnitude $\epsilon _{\text {eff}}^{3/2}$ less than approximately $5\times 10^{-9}$ .

Physics↗
DOE OSTI2026

Minimizing the Electromechanical Stresses in Poloidal Field Coils by Optimizing their Numbers and Locations using FREDA Framework

Poloidal field (PF) and central solenoid (CS) coils play a crucial role in sustaining the equilibrium and preserving the shape of highly confined tokamak plasmas. Ensuring that PF coil current and mechanical stress stay within superconducting and structural limitations is an important check in the design assessment. Minimizing the PF coil currents and mechanical stresses influences reliability, cost, and performance. A free-boundary MHD equilibrium code—FreeGS is employed within the fusion reactor design and assessment (FREDA) whole facility modeling (WFM) framework to construct the plasma equilibrium based on the configuration and currents in the PF coils. Here, we present the capability of the FreeGS code to minimize the currents, forces, and electromagnetic stresses on the PF coils by optimizing their number, sizes, structures, and locations while maintaining an MHD stable plasma configuration with a large confinement factor. The workflow is initialized with a configuration of plasma parameters and coils’ locations from the 0-D tokamak build systems code in the FREDA framework. Then, FreeGS is called to calculate the initial equilibrium at the minimum total current in PF coils. Thereafter, FreeGS’s internal optimizer minimizes the currents and hoop and central forces on the PF coils while maintaining the reference equilibrium. Finally, the input configuration is updated with the optimized parameters for equilibria over the ramp-up phase of a burning-plasma operation. FREDA’s whole facility optimization capability, which includes all magnetic field coil systems, blanket, vacuum vessel (VV), first wall, divertor, etc., is under development and out of the scope for this study.

Hassan, Ehab [ORNL] (ORCID:0000000181060301)↗
DOE OSTI2021

Constrained stellarator coil curvature optimization with FOCUS

Finding less complicated coils that have adequately low field errors is a crucial step in stellarator development. One coil metric that is of high importance is the maximum curvature of the coil centreline, or coil single filament. Conductors cannot be bent below some threshold minimum radius of curvature. High coil curvatures can cause strains to exceed acceptable levels, especially in superconducting coils. We investigate three ways to optimize coil curvature and find that applying penalty functions to the coil curvature solves for coils that have a constrained maximum curvature and low field error. Penalty functions are implemented in FOCUS and coil solutions optimized for an HSX-like ‘plasma boundary’ are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Single-stage gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry

Here we present a new coil design paradigm for magnetic confinement in stellarators. Our approach directly optimizes coil shapes and coil currents to produce a vacuum quasi-symmetric magnetic field with a target rotational transform on the magnetic axis. This approach differs from the traditional two-stage approach in which first a magnetic configuration with desirable physics properties is found, and then coils to approximately realize this magnetic configuration are designed. The proposed single-stage approach allows us to find a compromise between confinement and engineering requirements, i.e., find easy-to-build coils with good confinement properties. Using forward and adjoint sensitivities, we derive derivatives of the physical quantities in the objective, which is constrained by a nonlinear periodic differential equation. In two numerical examples, we compare different gradient-based descent algorithms and find that incorporating approximate second-order derivative information through a quasi-Newton method is crucial for convergence. We also explore the optimization landscape in the neighborhood of a minimizer and find many directions in which the objective is mostly flat, indicating ample freedom to find simple and thus easy-to-build coils.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Improved performance of stellarator coil design optimization

Following up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a Wendelstein 7-X test case. This is done by increasing the sample size and applying fully three-dimensional perturbations, but most importantly, by changing the design sequence in which the optimization targets are applied: optimization for field error is conducted first, with coil shape penalties only added to the objective function at a later step in the design process. A robust, feasible coil configuration with a local maximum field error of 3.66 % and an average field error of 0.95 % is achieved here, as compared to a maximum local field error of 6.08 % and average field error of 1.56 % found in our earlier work. These new results are compared to those found without stochastic optimization using the FOCUS and ONSET suites. The relationship between local minima in the optimization space and coil shape penalties is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Localizing resonant magnetic perturbations for edge localized mode control in KSTAR

An external 3D magnetic perturbation typically drives a resonant response at the rational surfaces from the core to the edge of tokamak plasmas, due to strong mode coupling and amplification. In this paper, we present a method to isolate the edge from core resonant fields using the ideal perturbed equilibrium code and to design an edge-localized resonant magnetic perturbation (RMP) for effective edge localized mode (ELM) control. A robust feature of the edge-localized RMP is the curtailed response to the field at the low-field-side (LFS) midplane, as opposed to typical RMPs which strongly resonate with the LFS fields. This emphasizes the importance of off-midplane coils to improve ELM control without provoking a large core response that could lead to devastating instabilities. The conceptual design of new ELM control coils based on the edge-localized RMP in KSTAR shows how this new insight can be utilized to enhance the efficiency of our ELM suppression capabilities. Simple window-pane coils matching the edge-localized resonant mode structure substantially expand in the ELM suppression window beyond the existing coil. Further optimization using the flexible optimized coils using space-curves code leads to additional enhancement in the edge-localized control.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Single-stage stellarator optimization: combining coils with fixed boundary equilibria

We introduce a novel approach for the simultaneous optimization of plasma physics and coil engineering objectives using fixed-boundary equilibria that is computationally efficient and applicable to a broad range of vacuum and finite plasma pressure scenarios. Our approach treats the plasma boundary and coil shapes as independently optimized variables, penalizing the mismatch between the two using a quadratic flux term in the objective function. Four use cases are presented to demonstrate the effectiveness of the approach, including simple and complex stellarator geometries. As shown here, this method outperforms previous two-stage approaches, achieving smaller plasma objective function values when coils are taken into account.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

ELM control optimization for various ITER scenarios based on linear and quasi-linear figures of merit

For the purpose of better understanding type-I edge localized mode (ELM) control in ITER with resonant magnetic perturbation (RMP) fields, the plasma response to RMP is computed by a resistive full magneto-hydrodynamic model in toroidal geometry. Five scenarios designed for ITER are considered, ranging from the pre-nuclear to nuclear phases. The plasma response to RMP is quantified by the plasma surface displacement near the X-point of the divertor plasma and at the outboard mid-plane. The optimal coil configurations between two high- Q deuterium-tritium (DT) scenarios (at the same plasma current of 15 MA and the same magnetic field of 5.3 T but different fusion gains, Q = 5 and 10) are predicted to be similar. For the other ITER scenarios with similar edge safety factor q 95 ~ 3 to that of the baseline scenario, the optimal coil phasing is also similar. The optimization results are different for a half-current full-field (7.5 MA/5.3 T) scenario, largely due to the difference in q 95 . The RMP coil currents are also optimized to tailor the core vs edge toroidal torques exerted by the 3D RMP fields on the plasma column. Torque optimization, with various objective functions proposed in the study, is useful for minimizing the side effects of RMP on the plasma core flow in ITER, while still maintaining the ELM control capability. Full utilization of three rows of ELM control coils in ITER is found to be essential to ensure both flexibility and robustness of ELM control, in terms of both linear and quasilinear plasma responses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Wire-coil insert optimization for high-heat-load/flux synchrotron components

Many synchrotron components require high levels of internal-flow, forced-convection heat transfer to minimize surface temperatures, thermal gradients, and thermally induced stress on high-power beam-interacting surfaces. Wire-coil inserts, physically similar to a common spring, are mechanically fitted inside of component cooling passages to optimize heat transfer performance. They are routinely used in Advanced Photon Source (APS) front end and beamline high-heat-load/flux components to significantly enhance convection heat transfer-up to 400% compared to plain open passages. This has the additional benefit of greatly reducing coolant flow requirements for these components. Using several cooling passage sizes, five different wire sizes, and a range of pitch values, an experimental investigation conducted at the APS has determined the average heat transfer coefficient and resulting pressure loss as a function of water flow rate for 65 different wire-coil inserts. Data from this study have been non-dimensionalized and generalized to yield relationships that can be used to determine the heat transfer performance and resulting pressure loss for any given wire-coil insert that may be used at the APS. Through data reduction, the wire-coil insert characteristic dimensions have also been optimized to yield the highest heat transfer enhancement while minimizing the coolant flow requirements. These generalized expressions for wirecoil inserts will be presented, and they can be used by scientists and engineers during the component design process to evaluate achievable heat transfer performance and associated pressure loss, aiding in the establishment of optimized operating parameters and cooling passage flow distribution schemes.

43 PARTICLE ACCELERATORS↗
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

A Field Enhancement Integration Design Featuring Misalignment Tolerance for Wireless EV Charging Using LCL Topology

This article proposes a magnetic integration design for EV wireless power transfer (WPT) systems, where the compensation and transmitting coils overlap one on top of the other to share the ferrite layer without any decoupling consideration. The magnetic field generated by both the compensation and transmitting coils are exploited to transfer power. To this end, a compensation method is proposed to enable magnetic field enhancement without any reactive power flow between the compensation and the transmitting coils, and to achieve input zero phase angle and constant current output. In addition, an efficient finite element analysis-based coil optimization algorithm is proposed to improve the coil misalignment tolerance on the horizontal plane, in which a reversely connected inner coil is used to stabilize the system output under misalignment conditions. Analytical and simulation results confirm transmission flux density enhancement and reduced leakage field characteristics of the proposed coil design. Finally, a scaled-down WPT prototype is built and tested to verify the performance and effectiveness of the design. The proposed design achieves 91.17% efficiency and misalignment tolerance up to 200 mm in any XY-direction while maintaining the power transfer and its efficiency. The results of this work provide insights into magnetic integration design of high-order compensation topologies featuring higher compactness, less ferrite usage, magnetic field enhancement, and misalignment tolerance for WPT systems.

42 ENGINEERING↗