arXiv subjects

Matt Landreman

Publications and source records attributed to Matt Landreman.

At least 19 recordsLinked to original sources

arXiv2026

Runaway Electrons in Stellarators: Unlikely or Unavoidable?

Generation of relativistic runaway electrons has historically not been considered a possible problem in stellarators, but this may not hold in reactor-scale stellarators despite the lack of an externally driven plasma current. The magnitude of the plasma current governs the exponential generation of runaways, and even if there is no externally driven plasma current, the bootstrap current could be considerable in reactor-relevant stellarators. In this paper, we present a pilot study on the generation of runaway electrons in stellarator temperature collapse scenarios. To reliably study runaway electrons in stellarators, we implemented a stellarator plasma model in the runaway electron simulation tool DREAM. The model is used to explore when runaway electrons can be generated with regard to combinations of initial plasma current, temperature decay time scale, and post-decay temperature. Special consideration is given to runaway generation through avalanche multiplication in stellarators, and how it compares to tokamaks. We find that significant runaway electron generation is possible also in stellarators, and demonstrate under which conditions it could be a concern. However, our findings support the conception that runaway electrons will be less of a concern in reactor-scale stellarators compared to tokamaks.

physics.plasm-ph↗

arXiv2026

yancc: A GPU-accelerated, differentiable solver for neoclassical transport in tokamaks and stellarators

We present yancc, a new GPU-accelerated solver for the drift kinetic equation that computes neoclassical transport fluxes, flows, and currents in tokamaks and stellarators. The drift kinetic equation is challenging to solve numerically due to strong advection-dominance, recirculating flows, internal boundary layers, severe anisotropy, and high dimensionality. The code solves both the full four-dimensional drift kinetic equation (retaining speed-dependent collisions, energy scattering, and full interspecies coupling), and the reduced monoenergetic form. The discretization combines a Maxwell polynomial collocation grid in speed with finite differences in pitch angle and the flux surface coordinates, using a modified upwind stencil designed to improve diagonal dominance for multigrid efficiency. The resulting linear system is solved with a multigrid-preconditioned Krylov method. Built in JAX, yancc is fully differentiable, enabling gradient-based optimization and adjoint sensitivity analysis. Benchmarks against MONKES and SFINCS show agreement within 1\% across a range of collisionalities, geometries, and multi-species configurations. yancc achieves roughly an order of magnitude speedup over SFINCS on a per-scan basis while using an order of magnitude less memory, with runtime remaining nearly flat across the full range of collisionality. The combination of speed, low memory footprint, and differentiability makes yancc well suited for integration into stellarator optimization workflows, uncertainty quantification, and profile prediction.

physics.plasm-ph↗

arXiv2026

Bayesian optimization of stellarator alpha-particle confinement using data-informed parameter spaces and dimensionality reduction

Modern stellarators are typically designed by optimizing the shape of the plasma boundary surface, with the parameters taken to be Fourier amplitudes. Many promising optimization algorithms such as Bayesian methods require bound constraints on the parameters and are most efficient when each parameter is scaled similarly to the others. With the typical Fourier parameterization, it is unclear how to set these bounds: wide constraints lead to self-intersecting boundaries and frequent failures of the MHD equilibrium calculation, while tight bound constraints limit expressiveness. To address these issues, here we propose two new parameter spaces for stellarator optimization. Both begin with a dataset of existing stellarator boundaries. In the first approach, a quantile transformation is applied to each Fourier degree of freedom, mapping the data distribution to a uniform distribution on the unit interval. In the second approach, principal component analysis (PCA) is applied to points on the boundaries, followed by a quantile transformation. For both approaches, the transformed variables become the degrees of freedom, naturally bounded to [0, 1]. The PCA method has the additional benefit of dimensionality reduction, with high expressiveness for a small number of parameters. The methods are demonstrated via Bayesian optimization for good alpha-particle confinement with guiding-center tracing inside the optimization loop, using asynchronous parallelization. These optimizations yield stellarator configurations with excellent fast-particle confinement in fields that can be far from quasisymmetric or quasi-isodynamic.

physics.plasm-ph↗

arXiv2026

FIRM3D: Fast ion reduced models in 3D

The dynamics of energetic particle (EP) species, born from fusion reactions or plasma heating schemes, are critical for predicting the behavior of magnetic confinement fusion experiments and future fusion reactors. Because energetic particles are largely collisionless, the orbits of Monte Carlo samples drawn from a given distribution function can be efficiently integrated in prescribed electromagnetic fields. In addition to the static magneto-hydrodynamic (MHD) equilibrium fields produced by the electromagnetic coils of a fusion device, MHD waves can be excited by -- and resonantly transport -- energetic particle populations. FIRM3D is an open-source Python/C++/CUDA software suite for modeling energetic particle dynamics in 3D magnetic fields, available at https://github.com/ColumbiaStellaratorTheory/firm3d. The core guiding-center integration routines grew out of SIMSOPT (Landreman et al., 2021), but have been extended to include additional physics and diagnostics not typically required in the stellarator optimization context. This standalone framework enables focused development of energetic particle physics capabilities with minimal dependencies, making it accessible to the broader stellarator and plasma physics community. Components of FIRM3D include interfaces with MHD equilibrium and wave stability software (BOOZ_XFORM, AE3D, FAR3D); CPU and GPU parallelized integration of the guiding center orbit equation, with symplectic and Runge-Kutta integrator options; and orbit visualization and transport diagnostics, including Poincare maps, orbit classification, and weighted Birkhoff averaging.

physics.plasm-ph↗

arXiv2026

How Does The Magnetic Gradient Scale Length Influence Complexity of Filamentary Coils in Stellarators?

The distance between the last closed flux surface (LCFS) and the nearest electromagnetic coils is a dominating factor in the cost, size, and engineering difficulty of stellarators. The smallest magnetic gradient scale length on the LCFS - denoted L_gradB - has been shown to be a good proxy for minimum coil-surface distance in optimizations of a current potential on a winding surface, such as through the REGCOIL method. However, it has not been shown the same is true for filament coils, or that the magnetic gradient scale length is an effective objective function in optimization. In this paper, we explore examples in which min(L_gradB) is correlated with the minimum coil-surface distance for filament coils. First, we analyze a subset of the single-stage-optimized equilibria from the QUASR dataset [Giuliani et al. JPP (2024)]. We find that the majority of configurations have min(L_gradB) located nearby the point of closest coil-surface distance. Second, we optimize quasihelically symmetric equilibria to have improved min(L_gradB), and optimize coils via a continuation method. We then traced alpha particles to test confinement. Finally, we compare min(L_gradB) to the minimum coil-surface distance with filament coils optimized for a set of finite beta equilibria with random boundary shapes. For all datasets, we find that min(L_gradB) is correlated with both the minimum coil-surface and coil-coil distances if sufficient coil length is allowed. Even when there is a trade-off with proxies for confinement, optimizing for improved min(L_gradB) can result in better confinement in the presence of coils, up to a point. This is because - when holding coil-coil distance constant - equilibria with lower min(L_gradB) have a larger normal field error dominated by coil ripple causing particle loss. Both can be reduced by increasing coil-surface distance for equilibria with a high min(L_gradB).

physics.plasm-ph↗

arXiv2025

Direct Optimization of Fast-Ion Confinement in Stellarators

Confining energetic ions such as alpha particles is a prime concern in the design of stellarators. However, directly measuring alpha confinement through numerical simulation of guiding-center trajectories has been considered to be too computationally expensive and noisy to include in the design loop, and instead has been most often used only as a tool to assess stellarator designs post hoc. In its place, proxy metrics, simplified measures of confinement, have often been used to design configurations because they are computationally more tractable and have been shown to be effective. Despite the success of proxies, it is unclear what is being sacrificed by using them to design the device rather than relying on direct trajectory calculations. In this study, we optimize stellarator designs for improved alpha particle confinement without the use of proxy metrics. In particular, we numerically optimize an objective function that measures alpha particle losses by simulating alpha particle trajectories. While this method is computationally expensive, we find that it can be used successfully to generate configurations with low losses.

physics.plasm-ph↗

arXiv2025

Efficient calculation of magnetic fields from ferromagnetic materials near strong electromagnets, and application to stellarator coil optimization

In fusion reactor design, steels under consideration for the blanket are ferromagnetic, so the steel's effect on the plasma physics must be examined. For efficient calculation of these fields, we can exploit the fact that the magnetic material gives a small perturbation relative to the fields from the electromagnetic coils and plasma. Moreover the magnetization is saturated due to the strong fields in typical fusion systems. These approximations significantly reduce the nonlinearity of the problem, so the magnetic materials can be described by an array of point dipoles of known magnitude, oriented in the direction of the coil and plasma field. The approach is verified by comparison to finite-element calculations with commercial software and shown to be accurate. As no linear or nonlinear solve is required, only evaluation of Biot-Savart-type integrals, the method here is significantly simpler to implement than other methods, and extremely fast. The method is compatible with arbitrary CAD geometry, and also allows rapid computation of the magnetic forces. We demonstrate adding the ferromagnetic effects to free-boundary MHD equilibrium calculations, assessing the effect on plasma properties such as confinement and stability. Moreover, it is straightforward to differentiate through the model to get the derivative of the field with respect to the electromagnet parameters. We thereby demonstrate gradient-based coil optimization for a quasi-isodynamic stellarator in which the field contribution from a ferromagnetic blanket is included. Even a significant steel volume is found to have little impact on the plasma physics properties, with the main effects being a slight destabilization of ballooning modes and a radial shift of the edge islands due to decrease in rotational transform. Both issues are corrected by minor reoptimization of the coil shapes to account for the field from the steel.

physics.plasm-ph↗

arXiv2025

Machine-learning Closure for Vlasov-Poisson Dynamics in Fourier-Hermite Space

Accurate reduced models of turbulence are desirable to facilitate the optimization of magnetic-confinement fusion reactor designs. As a first step toward higher-dimensional turbulence applications, we use reservoir computing, a machine-learning (ML) architecture, to develop a closure model for a limiting case of electrostatic gyrokinetics. We implement a pseudo-spectral Eulerian code to solve the one-dimensional Vlasov-Poisson system on a basis of Fourier modes in configuration space and Hermite polynomials in velocity space. When cast onto the Hermite basis, the Vlasov equation becomes an infinitely coupled hierarchy of fluid moments, presenting a closure problem. We exploit the locality of interactions in the Hermite representation to introduce an ML closure model of the small-scale dynamics in velocity space. In the linear limit, when the kinetic Fourier-Hermite solver is augmented with the reservoir closure, the closure permits a reduction of the velocity resolution, with a relative error within two percent for the Hermite moment where the reservoir closes the hierarchy. In the strongly-nonlinear regime, the ML closure model more accurately resolves the low-order Fourier and Hermite spectra when compared to a naïve closure by truncation and reduces the required velocity resolution by a factor of sixteen.

physics.plasm-ph↗

arXiv2025

Exponential Spectral Scaling: Robust and Efficient Stellarator Boundary Optimization via Mode-Dependent Scaling

Stellarator boundary optimization faces a fundamental numerical challenge: the extreme disparity between low- and high-mode amplitudes creates an optimization landscape in which direct full-spectrum approaches typically converge to poor local minima. Traditionally, this challenge has been addressed through a computationally expensive, multi-step Fourier continuation, in which low Fourier modes are optimized first, followed by the gradual incorporation of higher modes. We present Exponential Spectral Scaling (ESS), a technique that applies a mode-dependent exponential scaling factor to each Fourier mode. Our primary implementation uses the $L_{\infty}$ norm to determine the scaling pattern, creating a square spectral decay profile that effectively reduces the dynamic range of optimization variables from $10^{6}$--$10^{7}$ to $10^{2}$--$10^{3}$. This scaling aligns with the natural spectral decay of physically meaningful configurations and enables direct single-step optimization using the full spectrum of boundary Fourier modes. ESS eliminates arbitrary staging decisions and reduces computation time by a factor of $2$ to $5$ in benchmark cases. In addition to accelerating optimization, ESS improves robustness, reducing sensitivity to initial conditions and increasing confidence in avoiding local optima. We demonstrate the effectiveness of ESS across both quasi-axisymmetric (QA) and quasi-helically symmetric (QH) configurations, using two distinct optimization toolkits: SIMSOPT and DESC.

physics.plasm-ph↗

arXiv2025

Surface Current Optimization and Coil-Cutting Algorithms for Stage-Two Stellarator Optimization

Stellarator optimization often takes a two-stage approach, where in the first stage the boundary is varied in order to optimize for some physics metrics, while in the second stage the boundary is kept fixed and coils are sought to generate a magnetic field that can recreate the desired stellarator. Past literature dealing with this stage lacks details on the coil cutting procedure and the mathematical and physical properties of the surface current potential which dictates it. In this work, some basic physical quantities of the surface current and how they relate to the parameters in the current potential are presented, and supported for the first time by explicit mathematical derivations. Additionally, the details of how to account for the presence of an external field in the surface current algorithm are explicitly presented. These relations underpin the procedure of discretizing the surface current into coils. Finally, the conventionally-used algorithm for discretizing the surface current into coils is detailed, along with an example coil optimization for both a modular and a helical coilset. The algorithm is implemented in the \texttt{DESC} code, with both modular and helical coil capabilities, where it is available for use in stellarator coil design.

physics.plasm-ph↗

arXiv2025

How does ion temperature gradient turbulence depend on magnetic geometry? Insights from data and machine learning

Magnetic geometry has a significant effect on the level of turbulent transport in fusion plasmas. Here, we model and analyze this dependence using multiple machine learning methods and a dataset of > 200,000 nonlinear simulations of ion-temperature-gradient turbulence in diverse non-axisymmetric geometries. The dataset is generated using a large collection of both optimized and randomly generated stellarator equilibria. At fixed gradients, the turbulent heat flux varies between geometries by several orders of magnitude. Trends are apparent among the configurations with particularly high or low heat flux. Regression and classification techniques from machine learning are then applied to extract patterns in the dataset. Due to a symmetry of the gyrokinetic equation, the heat flux and regressions thereof should be invariant to translations of the raw features in the parallel coordinate, similar to translation invariance in computer vision applications. Multiple regression models including convolutional neural networks (CNNs) and decision trees can achieve reasonable predictive power for the heat flux in held-out test configurations, with highest accuracy for the CNNs. Using Spearman correlation, sequential feature selection, and Shapley values to measure feature importance, it is consistently found that the most important geometric lever on the heat flux is the flux surface compression in regions of bad curvature. The second most important feature relates to the magnitude of geodesic curvature. These two features align remarkably with surrogates that have been proposed based on theory, while the methods here allow a natural extension to more features for increased accuracy. The dataset, released with this publication, may also be used to test other proposed surrogates, and we find many previously published proxies do correlate well with both the heat flux and stability boundary.

physics.plasm-ph↗

arXiv2025

Reactor-scale stellarators with force and torque minimized dipole coils

In this work, we utilize new coil objectives for stellarator optimization with autodifferentiation, including pointwise and net coil-coil forces and torques. We use these methods to perform the first large-scale optimization of planar dipole coil arrays, since arrays of small and geometrically simple coils have been proposed to partially produce the 3D magnetic fields for stellarators, generate advantageous magnetic field perturbations in tokamaks, and provide active, real-time control capabilities. We perform an ablation study to show that minimizing the orientation and location of each coil may be essential to get coil forces, coil torques, and field errors to tolerable levels. We conclude with solutions for three reactor-scale quasi-symmetric stellarators by jointly optimizing nonplanar TF coils and planar coil arrays.

physics.plasm-ph↗

arXiv2025

Optimization of passive superconductors for shaping stellarator magnetic fields

We consider the novel problem of optimizing a large set of passive superconducting coils (PSCs) with currents induced by a background magnetic field rather than power supplies. In the nuclear fusion literature, such coils have been proposed to partially produce the 3D magnetic fields for stellarators and provide passive stabilization. We perform the first optimizations of PSC arrays with respect to the orientation, shape, and location of each coil, jointly minimized with the background fields. We conclude by generating passive coil array solutions for four stellarators.

physics.plasm-ph↗

arXiv2024

Electromagnetic coil optimization for reduced Lorentz forces

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. 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.

physics.plasm-ph↗

arXiv2024

Optimization of Nonlinear Turbulence in Stellarators

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC. Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasisymmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles.

physics.plasm-ph↗

arXiv2024

A family of quasi-axisymmetric stellarators with varied rotational transform

We apply a continuation method to recently optimized stellarator equilibria with excellent quasi-axisymmetry (QA) to generate new equilibria with a wide range of rotational transform profiles. Using these equilibria, we investigate how the rotational transform affects fast-particle confinement, the maximum coil-plasma distance, the maximum growth rate in linear gyrokinetic ion-temperature gradient (ITG) simulations, and the ion heat flux in corresponding nonlinear simulations. We find values of two-term quasisymmetry error comparable to or lower than the similar Landreman-Paul (Phys. Rev. Lett. 128, 035001) configuration for values of the mean rotational transform $\barι$ between $0.12$ and $0.75$. The fast-particle confinement improves with $\barι$ until $\barι = 0.73$, at which point the degradation in quasisymmetry outweighs the benefits of further increasing $\barι$. The required coil-plasma distance only varies by about $\pm 10\%$ for the configurations under consideration, and is between $2.8\,\mathrm{m}$ to $3.3\,\mathrm{m}$ when the configuration is scaled up to reactor size. The maximum growth rate from linear gyrokinetic simulations increases with $\barι$, but also shifts towards higher $k_y$ values. The maximum linear growth rate is sensitive to the choice of flux tube at rational $ι$, but this can be compensated for by taking the maximum over several flux tubes. The corresponding ion heat fluxes from nonlinear simulations display a non-monotonic relation to $ι$. Sufficiently large positive shear is destabilizing. This is reflected both in linear growth rates and nonlinear heat fluxes.

physics.plasm-ph↗

arXiv2023

Coil Optimization for Quasi-helically Symmetric Stellarator Configurations

Filament-based coil optimizations are performed for several quasihelical stellarator configurations, notably the one from [M. Landreman, E. Paul, PRL 128, 035001, 2022], demonstrating that precise quasihelical 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 MeV on the flux surface with 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 about 0.15 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 quasihelical configuration with 5% volume-averaged plasma beta from [M. Landreman, S. Buller, M. Drevlak, PoP 29, 082501, 2022], 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 about 5.5% of alpha particles launched at s=0.5.

physics.plasm-ph↗

arXiv2023

Grad-Shafranov equilibria via data-free physics informed neural networks

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad-Shafranov equation by using Physics-Informed Neural Networks (PINNs). For PINNs, we optimize neural networks by directly minimizing the residual of the PDE as a loss function. We show that PINNs can accurately and effectively solve the Grad-Shafranov equation with several different boundary conditions. We also explore the parameter space by varying the size of the model, the learning rate, and boundary conditions to map various trade-offs such as between reconstruction error and computational speed. Additionally, we introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity in order to handle a broader range of plasma scenarios within a single network. Parametrized PINNs could be used in future work to solve inverse problems such as shape optimization.

physics.plasm-ph↗