arXiv subjects

Eduardo Rodriguez

Publications and source records attributed to Eduardo Rodriguez.

At least 19 recordsLinked to original sources

arXiv2026

Estimating coil features from an equilibrium

We present an explicit theoretical framework for constructing artificial modular coils for vacuum stellarator fields based solely on equilibrium properties, achieved through the formulation of a current potential defined on flux surfaces. Contours of constant Boozer toroidal angle can be directly interpreted as proxy coils, and so we demonstrate that key measures of coil complexity (particularly coil non-planarity) are strongly governed by local magnetic field properties. This approach shows promise as predictor for more realistic coil configurations, providing both a pathway towards deeper understanding of equilibrium-coil relationships and a potential practical proxy for coil design.

physics.plasm-ph↗

arXiv2026

Near-axis quasi-isodynamic database

In this work, we investigate the landscape of quasi-isodynamic stellarators using the near-axis expansion of the magnetic field. Building on recent theoretical developments, we construct a database of more than 800,000 stable, approximately quasi-isodynamic vacuum magnetic configurations. These configurations span a range of field period numbers and other geometric control parameters, including the magnetic axis shape and plasma elongation. To evaluate each configuration, we use a broad set of measures, including effective ripple, sensitivity of the Shafranov shift to changes in plasma beta, the prevalence of maximum-J trapped particles, and the Rosenbluth-Hinton residual, among others. This enables an exhaustive, thorough and quantitative characterization of the database. Statistical analysis and modern machine learning techniques are then employed to find correlations, and identify key descriptors and heuristics to help understand tendencies that govern the behaviour of numerical optimization. The database provides baseline configurations for further studies, and to serve as tailored initial conditions for optimization. With this work we initiate a long term program to complete a systematic exploration of quasi-isodynamic stellarator design space.

physics.plasm-ph↗

arXiv2025

Quantum Fourier Transform Based Kernel for Solar Irrandiance Forecasting

This study proposes a Quantum Fourier Transform (QFT)-enhanced quantum kernel for short-term time-series forecasting. Each signal is windowed, amplitude-encoded, transformed by a QFT, then passed through a protective rotation layer to avoid the QFT/QFT adjoint cancellation; the resulting kernel is used in kernel ridge regression (KRR). Exogenous predictors are incorporated by convexly fusing feature-specific kernels. On multi-station solar irradiance data across Koppen climate classes, the proposed kernel consistently improves median R2 and nRMSE over reference classical RBF and polynomials kernels, while also reducing bias (nMBE); complementary MAE/ERMAX analyses indicate tighter average errors with remaining headroom under sharp transients. For both quantum and classical models, the only tuned quantities are the feature-mixing weights and the KRR ridge alpha; classical hyperparameters (gamma, r, d) are fixed, with the same validation set size for all models. Experiments are conducted on a noiseless simulator (5 qubits; window length L=32). Limitations and ablations are discussed, and paths toward NISQ execution are outlined.

stat.ML↗

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

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

Near-axis measures of quasi-isodynamic configurations

We present a number of measures and techniques to characterise and effectively construct quasi-isodynamic stellarators within the near-axis framework, without the need to resort to the computation of global equilibria. These include measures of the reliability of the model (including aspect-ratio limits and the appearance of ripple wells), quantification of omnigeneity through $ε_\mathrm{eff}$, measure and construction of MHD stabilised fields, and the sensitivity of the field to the pressure gradient. The paper presents, discusses and gives examples of all of these, for which expansions to second order are crucial. This opens the door to the exploration of how key underlying choices of the field design govern the interaction of desired properties (``trade-offs''), and provides a practical toolkit to perform efficient optimisation directly within the space of near-axis QI configurations.

physics.plasm-ph↗

arXiv2024

Near-axis description of stellarator-symmetric quasi-isodynamic stellarators to second order

The near-axis description of optimised stellarators, at second order in the expansion, provides important information about the field, both of physical and practical importance for stellarator optimisation. It however remains relatively underdeveloped for an important class of such stellarators, called quasi-isodynamic (QI). In this paper we develop the theoretical and numerical framework for the construction of such solutions. We find that the case of QI stellarators calls for the careful treatment of continuity, smoothness and periodicity of the various functions involved, especially for so-called half-helicity fields, which feature prominently in existing QI designs. The numerical implementation of necessary elements is described, and several examples are constructed and quantitatively verified in detail. This work establishes a basis for further systematic exploration of the space of QI stellarators, and the development of both theoretical and practical tools to facilitate effective optimisation of QI stellarators.

physics.plasm-ph↗

arXiv2024

The zonal-flow residual does not tend to zero in the limit of small mirror ratio

The intensity of the turbulence in tokamaks and stellarators depends on its ability to excite and sustain zonal flows. Insight into this physics may be gained by studying the ''residual'', i.e. the late-time linear response of the system to an initial perturbation. We investigate this zonal-flow residual in the limit of a small magnetic mirror ratio, where we find that the typical quadratic approximation to RH (Rosenbluth & Hinton, 1998) breaks down. Barely passing particles are in this limit central in determining the resulting level of the residual, which we estimate analytically. The role played by the population with large orbit width provides valuable physical insight into the response of the residual beyond this limit. Applying this result to tokamak, quasi-symmetric and quasi-isodynamic equilibria, using a near-axis approximation, we identify the effect to be more relevant (although small) in the core of quasi-axisymmetric fields, where the residual is smallest. The analysis in the paper also clarifies the relationship between the residual and the geodesic acoustic mode, whose typical theoretical set-ups are similar.

physics.plasm-ph↗

arXiv2024

The Kinetic Ion-Temperature-Gradient-driven instability and its localisation

We construct a description of Ion Temperature Gradient (ITG) driven localised linear modes which retains both wave-particle and magnetic drift resonant effects while capturing the field-line dependence of the electrostatic potential. We exploit the smallness of the magnetic drift and the strong localisation of the mode to resolve the problem with a polynomial-gaussian expansion in the field-following co-ordinate. A simple semi-analytical formula for the spectrum of the mode is shown to capture long wavelength Landau damping, ion-scale Larmor radius stabilization, weakening of Larmor radius effects at short-wavelengths and magnetic-drift resonant stabilisation. These elements lead to linear spectra with multiple maxima as observed in gyrokinetic simulations in stellarators. Connections to the transition to extended eigenfunctions and those localized by less unfavourable curvature regions (hopping solutions) are also made. The model provides a clear qualitative framework with which to interpret numerically simulated ITG modes linear spectra with realistic geometries, despite its limitations for exact quantitative predictions.

physics.plasm-ph↗

arXiv2023

Constructing the space of quasisymmetric stellarators

A simplified view of the space of optimised stellarators has the potential to guide and aid the design efforts of magnetic confinement configurations suitable for future fusion reactors. We present one such view for the class of quasisymmetric stellarators based on their approximate description near their centre (magnetic axis). The result is a space that captures existing designs and presents new ones, providing a common framework to study them. Such a simplified construction offers a basic topological approach, guided by certain theoretical and physical choices, which this paper presents in detail.

physics.plasm-ph↗

arXiv2023

Higher order theory of quasi-isodynamicity near the magnetic axis of stellarators

The condition of quasi-isodynamicity is derived to second order in the distance from the magnetic axis. We do so using a formulation of omnigenity that explicitly requires the balance between the radial particle drifts at opposite bounce points of a magnetic well. This is a physically intuitive alternative to the integrated condition involving distances between bounce points, used in previous works. We investigate the appearance of topological defects in the magnetic field strength (``puddles''). A hallmark of quasi-isodynamic fields, the curved contour of minimum field strength, is found to be inextricably linked to these defects. Our results pave the way to constructing solutions that satisfy omnigenity to a higher degree of precision, and also to simultaneously consider other physical properties, like shaping and stability.

physics.plasm-ph↗

arXiv2023

MHD stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators

How much does the cross-section of a toroidal magnetic field configuration tell us about its MHD stability? It is generally believed that positive triangularity (typically leading to bean-shaped cross-sections with their indentation on the inboard side in stellarators) contributes positively to MHD stability. In this paper, we explore the basis of this statement within a near-axis description for axisymmetric and quasisymmetric magnetic configurations. In agreement with the existing literature, we show that positive triangularity stabilises vertically elongated tokamaks. In quasisymmetric stellarators, the toroidal asymmetry of flux surfaces modifies this relation. The behaviour of stellarator-symmetric, quasisymmetric stellarators can still be described in terms of the shape of one of their up-down symmetric cross-sections. However, we show that for a sample of quasisymmetric configurations, the positive-bean-shaped cross-sections do not contribute positively to stability. Unlike in the axisymmetric case, we also learn that finite $β$ can improve stability even without magnetic shear.

physics.plasm-ph↗

arXiv2022

Phases and phase-transitions in quasisymmetric configuration space

We explore the structure of the space of quasisymmetric configurations identifying them by their magnetic axes, described as 3D closed curves. We demonstrate that this topological perspective divides the space of all configurations into well-separated quasisymmetric phases. Each phase is characterized by the self-linking number (a topological invariant), defining different symmetry configurations (quasi-axisymmetry or quasi-helical symmetry). The phase-transition manifolds correspond to quasi-isodynamic configurations. By considering some models for closed curves (most notably torus unknots), general features associated with these phases are explored. Some general criteria are also built and leveraged to provide a simple way to describe existing quasisymmetric designs. This constitutes the first step in a program to identify quasisymmetric configurations with a reduced set of functions and parameters, to deepen understanding of configuration space, and offer an alternative approach to stellarator optimization that begins with the magnetic axis and builds outward.

physics.plasm-ph↗

arXiv2022

Connection between quasi-symmetric magnetic fields and anisotropic pressure equilibria in fusion plasmas

The stellarator as a concept of magnetic confinement fusion requires careful design to confine particles effectively. A design possibility is to equip the magnetic field with a property known as quasisymmetry. Though it is generally believed that a steady-state quasisymmetric equilibrium can only be exact locally (unless the system has a direction of continuous symmetry such as the tokamak), we suggest in this work that a change in the equilibrium paradigm can ameliorate this limitation. We demonstrate that there exists a deep physical connection between quasisymmetry and magnetostatic equilibria with anisotropic pressure, extending beyond the isotropic pressure equilibria commonly considered.

physics.plasm-ph↗

arXiv2021

Measures of quasisymmetry for stellarators

Quasisymmetric stellarators are an attractive class of optimised magnetic confinement configurations. The property of quasisymmetry (QS) is in practice limited to be approximate, and thus the construction requires measures that quantify the deviation from the exact property. In this paper we study three measure candidates used in the literature, placing the focus on their origin and the comparison of their forms. The analysis shows clearly the lack of universality in these measures. As these metrics do not directly correspond to any physical property (except when exactly QS), optimisation should employ additional physical metrics for guidance. Especially close to QS minima, treating QS metrics through inequality constraints so that additional physics metrics dominate optimisation is suggested. The impact of different quasisymmetric measures on optimisation is presented through an example.

physics.plasm-ph↗

arXiv2021

Generalized Boozer coordinates: a natural coordinate system for quasisymmetry

We prove the existence of a straight-field-line coordinate system we call generalized Boozer coordinates. This coordinate system exists for magnetic fields with nested toroidal flux surfaces} provided $ \oint\mathrm{d}l/B\:(\mathbf{j}\cdot\nablaψ)=0$, where symbols have their usual meaning, and the integral is taken along closed magnetic field lines. All quasisymmetric fields, regardless of their associated form of equilibria, must satisfy this condition. This coordinate system presents itself as a convenient form in which to describe general quasisymmetric configurations and their properties. Insight can be gained analytically into the difference between strong and weak forms of quasisymmetry, as well as axisymmetry, and the interaction of quasisymmetry with different forms of equilibria.

physics.plasm-ph↗

arXiv2021

A Prototype Compact Accelerator-based Neutron Source (CANS) for Canada

Canada's access to neutron beams for neutron scattering was significantly curtailed in 2018 with the closure of the National Research Universal (NRU) reactor in Chalk River, Ontario, Canada. New sources are needed for the long-term; otherwise, access will only become harder as the global supply shrinks. Compact Accelerator-based Neutron Sources (CANS) offer the possibility of an intense source of neutrons with a capital cost significantly lower than spallation sources. In this paper, we propose a CANS for Canada. The proposal is staged with the first stage offering a medium neutron-flux, linac-based approach for neutron scattering that is also coupled with a boron neutron capture therapy (BNCT) station and a positron emission tomography (PET) isotope station. The first stage will serve as a prototype for a second stage: a higher brightness, higher cost facility that could be viewed as a national centre for neutron applications.

physics.ins-det↗

arXiv2020

Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions. II. Circular axis stellarators

We apply the near-axis expansion method for quasisymmetric magnetic fields with anisotropic pressure (developed in the companion paper, Part I [E. Rodriguez, A. Bhattacharjee, arXiv:2008.04715 (2020)]) to construct numerical solutions to circular axis stellarators. The solutions are found to second order in the distance from the axis, not possible in the standard Garren-Boozer construction [D. A. Garren and A. H. Boozer, Physics of Fluids B: Plasma Physics, 2822 (1991)], which assumes magnetostatic equilibria with isotropic pressure. In the limit of zero anisotropy, it is shown that a subset of coefficients can be chosen to avoid the overdetermination problem.

physics.plasm-ph↗