arXiv subjects

Rory Conlin

Publications and source records attributed to Rory Conlin.

At least 19 recordsLinked to original sources

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

Deflation Techniques for Stellarator Equilibrium and Optimization

Stellarator optimization is a multi-objective, non-convex problem characterized by a complex objective landscape containing many local minima. The solution resulting from a single optimization is highly sensitive to factors such as the initial guess, objective weights, and the optimization method employed. However, merely varying these factors does not guarantee that a physically distinct minimum will be found; optimizations often fail to converge to good minima or simply return to the same or very similar local minima despite large-scale parameter scans. This paper presents a novel application of deflation methods to effectively explore this landscape. By modifying the objective function to penalize and "deflate" away already-found solutions, this technique encourages the optimizer towards attractive, distinct new minima while using a single initial guess and optimization setup. We provide a primer on deflation for nonlinear systems and non-convex optimization before applying it to non-axisymmetric equilibrium and stellarator optimization problems. Key results include the discovery of families of global equilibria with similar core characteristics and the convergence to helical core equilibria without prescient initial guesses. Furthermore, we demonstrate that augmenting stage-one stellarator and stage-two coil optimization with deflation constraints readily produces multiple high-quality, distinct solutions, establishing the method's efficacy and ease of use.

physics.plasm-ph↗

arXiv2025

Narrow Operator Models of Stellarator Equilibria in Fourier Zernike Basis

Numerical computation of the ideal Magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated Partial Differential Equations (PDEs) like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons (MLP) that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.

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

Improving ideal MHD equilibrium accuracy with physics-informed neural networks

We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global force residual across the volume in real space is then minimized with first order optimizers. Already,we observe competitive computational cost to arrive at the same minimum residuals computed by existing codes. With increased computational cost,lower minima of the residual are achieved by the neural networks,establishing a new lower bound for the force residual. We use minimally complex neural networks,and we expect significant improvements for solving not only single equilibria with neural networks,but also for computing neural network models valid over continuous distributions of equilibria.

cs.LG↗

arXiv2025

Extending near-axis equilibria in DESC

The near-axis description of optimised stellarator fields has proven to be a powerful tool both for design and understanding of this magnetic confinement concept. The description consists of an asymptotic model of the equilibrium in the distance from its centermost axis, and is thus only approximate. Any practical application therefore requires the eventual construction of a global equilibrium. This paper presents a novel way of constructing global equilibria using the \texttt{DESC} code that guarantees the correct asymptotic behaviour imposed by a given near-axis construction. The theoretical underpinnings of this construction are carefully presented, and benchmarking examples provided. This opens the door to an efficient coupling of the near-axis framework and that of global equilibria for future optimisation efforts.

physics.plasm-ph↗

arXiv2025

Numerical asymptotics of near-axis expansions of quasisymmetric magnetohydrostatic equilibria with anisotropic pressure

Quasisymmetry (QS) is a property of special magnetic configurations, where the magnetic field strength, but not necessarily the full vector field, has a direction of symmetry. QS leads to reduced neoclassical transport and thus can be a desirable property in stellarator design. The Garren-Boozer (GB) conundrum has been interpreted to mean that globally quasisymmetric magnetohydrostatic (MHS) equilibria, other than axisymmetric solutions, with isotropic pressure do not exist. When expanded as power series of an effective minor radius, the governing equations become overdetermined at the 3rd order. Despite this, recent optimization efforts have found numerical isotropic-pressure equilibria with nearly exact global QS. To reconcile these two perspectives, Rodriguez and Bhattacharjee (RB) showed that by introducing pressure anisotropy into the problem, one can overcome the GB conundrum. This formally enables the study of equilibria with exact, global QS. Building on RB's work, we present pyAQSC, the first code for solving the near-axis expansion (NAE) of anisotropic-pressure quasisymmetric equilibria to any order. As a demonstration, we present a 6th order, QA near-axis equilibrium with anisotropic pressure, and a convergence analysis. PyAQSC opens the door to the study of higher-order properties of equilibria with exact global QS. Like existing isotropic-pressure NAE codes, PyAQSC can accelerate stellarator optimization as an initial state tool. However, by optimizing for low pressure anisotropy in a space that allows anisotropy, pyAQSC may discover practical QS stellarator designs previously hard to access. We give results comparing the RB method with DESC equilibria with anisotropic pressure.

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↗

arXiv2024

High Order Free Boundary MHD Equilibria in DESC

In this work we consider the free boundary inverse equilibrium problem for 3D ideal MHD. We review boundary conditions for both fixed and free boundary solutions and under what circumstances a sheet current may exist at the plasma-vacuum interface. We develop an efficient and accurate algorithm for computing the residual of these boundary conditions and use it to compute free boundary equilibria in the DESC code both in vacuum and at finite plasma beta, with and without sheet currents.

physics.plasm-ph↗

arXiv2024

Spectrally accurate, reverse-mode differentiable bounce-averaging algorithm and its applications

We present a fast, spectrally (exponentially) accurate, automatically differentiable bounce-averaging algorithm that is used to simplify kinetic models. Using this algorithm, implemented in the DESC stellarator optimisation suite, we can perform efficient optimisation of many objectives to improve stellarator performance, such as the effective ripple $\epsilon_{\mathrm{eff}}$ metric for the neoclassical transport coefficient in the low collisionality regime, energetic particle confinement, and turbulent transport. For the first time, we optimise a finite-beta stellarator to directly reduce neoclassical ripple transport using reverse-mode differentiation. This ensures the computational cost of differentiation is independent of the number of controllable parameters.

physics.plasm-ph↗

arXiv2024

Omnigenous stellarator equilibria with enhanced stability

To build an economically viable stellarator, it is essential to find a configuration that satisfies a set of favorable properties to achieve efficient steady-state nuclear fusion. One such property is omnigenity, which ensures confinement of trapped particles. After creating an omnigenous equilibrium, one must also ensure reduced transport resulting from kinetic and magnetohydrodynamic (MHD) instabilities. This study introduces and leverages the GPU-accelerated DESC optimization suite, which is used to design stable high-$\beta$ omnigenous equilibria, achieving Mercier, ideal ballooning, and enhanced kinetic ballooning stability. We explain the link between ideal and kinetic ballooning modes and discover stellarators with second stability, a regime of large pressure gradient where an equilibria becomes ideal ballooning stable.

physics.plasm-ph↗

arXiv2024

ZERNIPAX: A Fast and Accurate Zernike Polynomial Calculator in Python

Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently finite and smooth at the disc center (r=0), ensuring continuous differentiability along the axis. This property makes them particularly suitable for simulations, requiring no additional handling at the origin. We developed ZERNIPAX, an open-source Python package capable of utilizing CPU/GPUs, leveraging Google's JAX package and available on GitHub as well as the Python software repository PyPI. Our implementation of the recursion relation between Jacobi polynomials significantly improves computation time compared to alternative methods by use of parallel computing while still performing more accurately for high-mode numbers.

cs.PF↗

arXiv2024

Stellarator Optimization with Constraints

In this work we consider the problem of optimizing a stellarator subject to hard constraints on the design variables and physics properties of the equilibrium. We survey current numerical methods for handling these constraints, and summarize a number of methods from the wider optimization community that have not been used extensively for stellarator optimization thus far. We demonstrate the utility of new methods of constrained optimization by optimizing a QA stellarator for favorable physics properties while preventing strong shaping of the plasma boundary which can be difficult to create with external current sources.

physics.plasm-ph↗

arXiv2023

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↗

arXiv2023

Magnetic Fields with General Omnigenity

Omnigenity is a desirable property of toroidal magnetic fields that ensures confinement of trapped particles. Confining charged particles is a basic requirement for any fusion power plant design, but it can be difficult to satisfy with the non-axisymmetric magnetic fields used by the stellarator approach. Every ideal magnetohydrodynamic equilibrium previously found to approximate omnigenity has been either axisymmetric, quasi-symmetric or has poloidally closed contours of magnetic field strength $B$. However, general omnigenous equilibria are a much larger design space than these subsets. A new model is presented and employed in the DESC stellarator optimization suite to represent and discover the full parameter space of omnigenous equilibria. Although exact omnigenity aside from quasi-symmetry is impossible, these results reveal that excellent particle confinement can be achieved in practice. Examples far from quasi-symmetry with poloidally, helically and toroidally closed $B$ contours are attained with DESC and shown to have low neoclassical collisional transport and fast particle losses.

physics.plasm-ph↗

arXiv2022

Exploration via Planning for Information about the Optimal Trajectory

Many potential applications of reinforcement learning (RL) are stymied by the large numbers of samples required to learn an effective policy. This is especially true when applying RL to real-world control tasks, e.g. in the sciences or robotics, where executing a policy in the environment is costly. In popular RL algorithms, agents typically explore either by adding stochasticity to a reward-maximizing policy or by attempting to gather maximal information about environment dynamics without taking the given task into account. In this work, we develop a method that allows us to plan for exploration while taking both the task and the current knowledge about the dynamics into account. The key insight to our approach is to plan an action sequence that maximizes the expected information gain about the optimal trajectory for the task at hand. We demonstrate that our method learns strong policies with 2x fewer samples than strong exploration baselines and 200x fewer samples than model free methods on a diverse set of low-to-medium dimensional control tasks in both the open-loop and closed-loop control settings.

cs.LG↗