arXiv subjects

Dario Panici

Publications and source records attributed to Dario Panici.

At least 19 recordsLinked to original sources

arXiv2026

Characterization of ELM Pacing via Vertical Jogs on DIII-D

Edge localized mode (ELM) pacing via vertical plasma oscillations or jogging has been successfully demonstrated on DIII-D. Rapid vertical movement of the plasma toward the X-point has been shown to effectively trigger ELMs. By vertically oscillating the plasma at a rate of 10 Hz, the ELM frequency increased from $\sim$5~Hz, the natural ELM frequency in similar DIII-D discharges, to 10~Hz. Downward jogs have been observed to trigger multiple ELMs in one cycle. ELMs triggered at higher than natural frequencies lead to smaller decreases in stored energy, from ~10\% to as little as below 1\%. As a consequence, the peak heat flux to the divertor has been observed to be reduced by a factor of $\sim$2. In addition, a reduction in the carbon impurity concentration has been observed. During downward jogs in the lower single null (LSN) configuration, the X-point movement is slower and smaller than the top of the plasma. As a result, a reduction in the plasma cross section and hence volume has been observed. To understand the mechanism of ELM triggering by jogging, a toy model of the edge toroidal current has been built and tested with DIII-D experiment data. The experimental data and model suggest that when the plasma moves down towards the X-point, a net positive toroidal current is locally induced in the edge region. ELITE stability analysis suggests that this current pushes the plasma state across the peeling side of the peeling-ballooning stability boundary into the unstable region triggering ELMs.

physics.plasm-ph↗

arXiv2026

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 $ε_{\mathrm{eff}}$ 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↗

arXiv2026

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 (PM) or dipole arrays, and continue to be challenged by numerical problems. The quasi-single-stage (QSS) 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 29% fewer magnets than previous solutions. The second study produces a coil solution for the ARIES-CS stellarator with 27% reductions in both peak and root-mean-square force.

physics.plasm-ph↗

arXiv2026

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↗

arXiv2026

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↗

arXiv2026

Optimizing stellarators with hidden symmetry

Stellarators confine fusion plasmas using three-dimensional magnetic fields composed of nested toroidal magnetic surfaces. In generic stellarators, trapped particles can drift across these surfaces and degrade plasma confinement. Certain topological properties of the magnetic field strength can suppress these drifts. However, conventional stellarator design approaches typically enforce restrictive constraints to realize such properties, thereby segmenting and limiting the accessible configuration space. In this work, we reformulate the conditions for efficient confinement as constraints on a homeomorphic straightening transformation of the field contours. Within this framework, the various families of stellarator magnetic fields optimized for plasma confinement arise naturally as specific realizations of a unified mapping. This new perspective provides a significantly more comprehensive description of viable stellarator configurations, enabling systematic exploration of trade-offs among confinement quality, geometric complexity, and engineering requirements. We illustrate this approach by presenting a highly compact stellarator design that nevertheless achieves plasma performance comparable to that of leading reactor-scale designs with much larger aspect ratios.

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

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↗

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

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↗

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

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-$β$ 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

Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared to unoptimised configurations. Though stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratio and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation, and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared to solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface; three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

physics.plasm-ph↗

arXiv2024

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↗

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↗

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↗

arXiv2023

The DESC Stellarator Code Suite Part II: Perturbation and continuation methods

A new perturbation and continuation method is presented for computing and analyzing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $F \equiv J \times B - \nabla p = 0$, and an efficient algorithm for computing solutions to 2nd and 3rd order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator, and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

physics.plasm-ph↗

arXiv2023

The DESC Stellarator Code Suite Part I: Quick and accurate equilibria computations

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 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 the solution 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 the same accuracy solution as VMEC in an order of magnitude less time.

physics.plasm-ph↗