Data-driven approach to model the influence of magnetic geometry in the confinement of fusion devices R. Laia, R. Jorge, G. Abreu Nuclear Fusion, 2026 Designing a fusion energy device to produce as much energy as possible requires balancing numerous physics constraints and metrics. In stellarators, the geometry is very flexible and involves a large number of free parameters. These can be optimized to achieve good performance. One of the main optimization targets is omnigenity, that is, the confinement of alpha particles stemming from the fusion reactions. In this work, two classes of omnigenous stellarators are studied, namely quasisymmetric and quasi-isodynamic stellarators. The goal is to determine the influence of the geometry on omnigenity, which can lead to greater insight into the design space of stellarators. For this purpose, a database of stellarator configurations with two field periods and a single dominant mode is created and analyzed for correlations, pair-wise distributions, and dimensionality reduction using a supervised autoencoder framework. Then, a classification model is trained on this database to predict the convergence of numerical solvers. Finally, two regression models, LightGBM and its probabilistic version, LightGBM LSS, as well as a feed-forward neural network, are trained to predict quasisymmetry and quasi-isodynamiticity and find the design parameters that most influence omnigenity.
Summary of the 5th IAEA technical meeting on fusion data processing, validation and analysis (FDPVA) M. Xu, D. Mazon, M. Barbarino, W. Biel, R.M. Churchill, et al. Nuclear Fusion, 2026 The purpose of the 5th International Atomic Energy Agency technical meeting on fusion data processing, validation and analysis (FDPVA) (Ghent University, Ghent, Belgium, 12–15 June 2023) was to provide a platform during which a set of topics relevant to FDPVA were discussed with the view of meeting the needs of next step fusion devices such as ITER. The validation and analysis of experimental data obtained from diagnostics used to characterize fusion plasmas are crucial for a knowledge-based understanding of the physical processes governing the dynamics of these plasmas. This paper presents the recent progress and achievements in the domain of plasma diagnostics data analysis and synthetic diagnostics reported at the meeting, including concept description of new devices; fusion databases; integrated data analysis; inverse problems; uncertainty propagation, verification and validation; probabilistic methods and machine learning. The relevant results underline trends observed in the current major fusion confinement devices.
High-order magnetic near-axis expansion: ill-posedness and regularisation Maximilian Ruth, Rogerio Jorge, David Bindel Journal of Plasma Physics, 2025 When analysing stellarator configurations, it is common to perform an asymptotic expansion about the magnetic axis. This so-called near-axis expansion is convenient for the same reason asymptotic expansions often are, namely, it reduces the dimension of the problem. This leads to convenient and quickly computed expressions of physical quantities, such as quasisymmetry and stability criteria, which can be used to gain further insight. However, it has been repeatedly found that the expansion diverges at high orders in the distance from axis, limiting the physics the expansion can describe. In this paper, we show that the near-axis expansion diverges in vacuum due to ill-posedness and that it can be regularised to improve its convergence. Then, using realistic stellarator coil sets, we demonstrate numerical convergence of the vacuum magnetic field and flux surfaces to the true values as the order increases. We numerically find that the regularisation improves the solutions of the near-axis expansion under perturbation, and we demonstrate that the radius of convergence of the vacuum near-axis expansion is correlated with the distance from the axis to the coils.
Near-axis description of stellarator-symmetric quasi-isodynamic stellarators to second order E. Rodríguez, G.G. Plunk, R. Jorge Journal of Plasma Physics, 2025 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, applying the second-order omnigeneity conditions derived in Rodríguez & Plunk (2023), to make explicit construction of equilibrium 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.
Using deep learning to design high aspect ratio fusion devices P. Curvo, D.R. Ferreira, R. Jorge Journal of Plasma Physics, 2025 The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator optimization where non-axisymmetric magnetic fields with a large parameter space are optimized to satisfy certain performance criteria. However, optimization is still required to find configurations with properties such as low elongation, high rotational transform, finite beta and good fast particle confinement. In this work, we train a machine learning model to construct configurations with favourable confinement properties by finding a solution to the inverse design problem, that is, obtaining a set of model input parameters for given desired properties. Since the solution of the inverse problem is non-unique, a probabilistic approach, based on mixture density networks, is used. It is shown that optimized configurations can be generated reliably using this method.
Electron root optimisation for stellarator reactor designs E. Lascas Neto, R. Jorge, C.D. Beidler, J. Lion Journal of Plasma Physics, 2025 In this work, we propose a method for optimising stellarator devices to favour the presence of an electron root solution of the radial electric field. Such a solution can help avoid heavy impurity accumulation, improve neoclassical thermal ion confinement and helium ash exhaust, and possibly reduce turbulence. This study shows that an optimisation for such a root is possible in quasi-isodynamic stellarators. Examples are shown for both vacuum and finite plasma pressure configurations.
Superradiance of rotating cohomogeneity-1 black holes: Scalar case Rogério Jorge, Ednilton S. de Oliveira, Jorge V. Rocha 14th Marcel Grossman Meeting on Recent Developments in Theoretical and Experimental General Relativity Astrophysics and Relativistic Field Theories Proceedings, 2018
Ray tracing in weakly turbulent, randomly fluctuating media: A quasilinear approach 45th Eps Conference on Plasma Physics Eps 2018, 2018
Optical analogy for stellarators: Ridges as caustics and coils as singularities W Sengupta, S Buller, R Jorge, J Kappel, A Brown, R Nies, PF Gil, ... arXiv preprint arXiv:2605.21814 , 2026 2026
Control of a Uniformly Magnetized Plasma with External Electric Fields: P. Chen et al. P Chen, R Jorge, Q Li, Y Yue Journal of Statistical Physics 193 (4), 40 , 2026 2026
Stochastic single-stage stellarator optimization using fixed-boundary equilibria PF Gil, J Smoniewski, R Jorge, P Huslage, EV Stenson arXiv preprint arXiv:2603.11699 , 2026 2026
Designing A Buildable Optimized Stellarator to Confine Electron-Positron Plasmas PF Gil, J Smoniewski, P Huslage, R Jorge, T Thun, E Buglione-Ceresa, ... arXiv preprint arXiv:2603.11737 , 2026 2026 Citations: 1
Summary of the 5th IAEA technical meeting on fusion data processing, validation and analysis (FDPVA) M Xu, D Mazon, M Barbarino, W Biel, RM Churchill, R Fischer, K Fujii, ... Nuclear Fusion 66 (1), 017002 , 2026 2026 Citations: 2
Data-driven approach to model the influence of magnetic geometry in the confinement of fusion devices R Laia, R Jorge, G Abreu Nuclear Fusion 66 (1), 016034 , 2026 2026 Citations: 2
JAX-in-Cell: A Differentiable Particle-in-Cell Code for Plasma Physics Applications L Ma, R Jorge, H Lu, A Tran, C Woolford arXiv preprint arXiv:2512.12160 , 2025 2025
An analytical approach to modeling the effect of magnetic permeable materials on the magnetic fields produced by coils D Seidita, R Jorge DPP 2025 , 2025 2025
Relation Between Magnetic Geometry and Stellarator Confinement using Data-Driven Methods R Jorge, R Laia, G Abreu DPP 2025 , 2025 2025
Stellarator Techniques to Optimize 3D Mirrors for Improved MHD Stability and Reduced Particle Drift D Patch, R Jorge, T Qian DPP 2025 , 2025 2025
Learning reduced models for collisionless shocks JPF Biu, DD Carvalho, P Alves, R Jorge, F Fiuza DPP 2025 , 2025 2025
Axisymmetric coil winding surfaces for non-axisymmetric fusion devices J Biu, R Jorge Fundamental Plasma Physics, 100098 , 2025 2025
The shear Alfvén continuum of quasisymmetric stellarators EJ Paul, A Hyder, E Rodríguez, R Jorge, A Knyazev Journal of Plasma Physics 91 (4), E101 , 2025 2025 Citations: 4
High-order magnetic near-axis expansion: ill-posedness and regularisation M Ruth, R Jorge, D Bindel Journal of Plasma Physics 91 (3), E73 , 2025 2025 Citations: 4
Stellaris: A high-field quasi-isodynamic stellarator for a prototypical fusion power plant J Lion, JC Anglès, L Bonauer, AB Navarro, SAC Ceron, R Davies, ... Fusion Engineering and Design 214, 114868 , 2025 2025 Citations: 67
Near-axis description of stellarator-symmetric quasi-isodynamic stellarators to second order E Rodriguez, GG Plunk, R Jorge Journal of Plasma Physics 91 (2), E44 , 2025 2025 Citations: 10
The shear Alfvén continuum of quasisymmetric stellarators. Part 1. Perturbation theory EJ Paul, A Hyder, E Rodríguez, R Jorge, A Knyazev arXiv e-prints, arXiv: 2503.03711 , 2025 2025
Using deep learning to design high aspect ratio fusion devices P Curvo, DR Ferreira, R Jorge Journal of Plasma Physics 91 (1), E38 , 2025 2025 Citations: 5
Electron root optimisation for stellarator reactor designs EL Neto, R Jorge, CD Beidler, J Lion Journal of Plasma Physics 91 (1), E24 , 2025 2025 Citations: 6
High order free boundary MHD equilibria in DESC R Conlin, J Schilling, DW Dudt, D Panici, R Jorge, E Kolemen arXiv preprint arXiv:2412.05680 , 2024 2024 Citations: 2
MOST CITED SCHOLAR PUBLICATIONS
Lawson criterion for ignition exceeded in an inertial fusion experiment H Abu-Shawareb, R Acree, P Adams, J Adams, B Addis, R Aden, P Adrian, ... Physical review letters 129 (7), 075001 , 2022 2022 Citations: 626
Achievement of target gain larger than unity in an inertial fusion experiment H Abu-Shawareb, R Acree, P Adams, J Adams, B Addis, R Aden, P Adrian, ... Physical review letters 132 (6), 065102 , 2024 2024 Citations: 497
SIMSOPT: a flexible framework for stellarator optimization M Landreman, B Medasani, F Wechsung, A Giuliani, R Jorge, C Zhu Journal of Open Source Software 6 (65), 3525 , 2021 2021 Citations: 157
Constructing precisely quasi-isodynamic magnetic fields AG Goodman, KC Mata, SA Henneberg, R Jorge, M Landreman, ... Journal of Plasma Physics 89 (5), 905890504 , 2023 2023 Citations: 80
Stellaris: A high-field quasi-isodynamic stellarator for a prototypical fusion power plant J Lion, JC Anglès, L Bonauer, AB Navarro, SAC Ceron, R Davies, ... Fusion Engineering and Design 214, 114868 , 2025 2025 Citations: 67
Greybody factors for rotating black holes in higher dimensions R Jorge, ES de Oliveira, JV Rocha Classical Quantum Gravity 32, 065008 , 2015 2015 Citations: 54
Single-stage stellarator optimization: combining coils with fixed boundary equilibria R Jorge, A Goodman, M Landreman, J Rodrigues, F Wechsung Plasma Physics and Controlled Fusion 65 (7), 074003 , 2023 2023 Citations: 47
Magnetic well and Mercier stability of stellarators near the magnetic axis M Landreman, R Jorge Journal of Plasma Physics 86 (5), 905860510 , 2020 2020 Citations: 45
Direct construction of stellarator-symmetric quasi-isodynamic magnetic configurations KC Mata, GG Plunk, R Jorge Journal of Plasma Physics 88 (5), 905880503 , 2022 2022 Citations: 44
A single-field-period quasi-isodynamic stellarator R Jorge, GG Plunk, M Drevlak, M Landreman, JF Lobsien, KC Mata, ... Journal of Plasma Physics 88 (5), 175880504 , 2022 2022 Citations: 44
Near-Axis Expansion of Stellarator Equilibrium at Arbitrary Order in the Distance to the Axis R Jorge, W Sengupta, M Landreman Journal of Plasma Physics 86 (1), 905860106 , 2020 2020 Citations: 44
A gyrokinetic model for the plasma periphery of tokamak devices BJ Frei, R Jorge, P Ricci Journal of Plasma Physics 2 (86), 905860205 , 2020 2020 Citations: 42
A drift-kinetic analytical model for scrape-off layer plasma dynamics at arbitrary collisionality R Jorge, P Ricci, N Loureiro Journal of Plasma Physics 83 (6), 905830606 , 2017 2017 Citations: 41
Construction of Quasisymmetric Stellarators Using a Direct Coordinate Approach R Jorge, W Sengupta, M Landreman Nuclear Fusion 60 (7), 076021 , 2020 2020 Citations: 34
Optimization of nonlinear turbulence in stellarators P Kim, S Buller, R Conlin, W Dorland, DW Dudt, R Gaur, R Jorge, ... Journal of Plasma Physics 90 (2), 905900210 , 2024 2024 Citations: 27
Nonlinear Gyrokinetic Coulomb Collision Operator R Jorge, BJ Frei, P Ricci Journal of Plasma Physics 85 (6), 905850604 , 2019 2019 Citations: 25
The use of near-axis magnetic fields for stellarator turbulence simulations R Jorge, M Landreman Plasma Physics and Controlled Fusion 63 (1), 014001 , 2021 2021 Citations: 22
Theory of the Drift-Wave Instability at Arbitrary Collisionality R Jorge, P Ricci, NF Loureiro Physical Review Letters 121 (16), 165001 , 2018 2018 Citations: 20
Development of advanced linearized gyrokinetic collision operators using a moment approach BJ Frei, J Ball, ACD Hoffmann, R Jorge, P Ricci, L Stenger Journal of Plasma Physics 87 (5), 905870501 , 2021 2021 Citations: 18
Linear Theory of Electron-Plasma Waves at Arbitrary Collisionality R Jorge, P Ricci, S Brunner, S Gamba, V Konovets, NF Loureiro, ... Journal of Plasma Physics 85 (2), 905850211 , 2019 2019 Citations: 16
