arXiv subjects

Rogerio Jorge

Publications and source records attributed to Rogerio Jorge.

18 recordsLinked to original sources

arXiv2026

Polaris: a flexible stellarator demonstration experiment with simple modular coils

We present the design, construction, and first plasma experiments of Polaris, a new small-scale stellarator experiment (major radius R ~ 0.4 m) located at the Swiss Plasma Center. Polaris consists of a relatively large vacuum vessel (~0.5 m^3) predominantly made of glass windows and inside which different sets of magnetic coils can be installed. A first modular coil configuration has been designed with six identical, circular, water-cooled copper coils toroidally arranged in an optimal way so that they generate a large volume of magnetic surfaces and rotational transform in vacuum (iota ~ 0.3). The total current in each coil goes up to ~ 5 kA, producing a magnetic field on-axis of B ~ 0.03 T. An RF antenna specifically designed to operate in vacuum delivers up to 2.5 kW of power to produce plasma via inductive coupling and electron-impact ionization. We present the engineering solutions adopted for the design of Polaris and illustrate the great experimental flexibility it enables. Time-averaged values and fluctuations of plasma density, electron temperature, and floating potential are measured at various toroidal locations, providing insights into the plasma equilibrium, electrostatic turbulence, and associated transport. The glass vacuum chamber of Polaris additionally provides unprecedented optical access to the entire plasma volume. With its original, flexible design, Polaris is a 'stellarator fish-tank', allowing interchangeable coil sets and exploration of various magnetic configurations. Furthermore, its low-temperature, low-density, high-neutral-pressure plasmas are relevant to stellarator edge physics, making Polaris a first-of-kind testbed for the fundamental investigation of stellarator edge-relevant physics.

physics.plasm-ph↗

arXiv2026

Compact quasiaxisymmetric stellarators, a near axisymmetric theory

We develop a theory of ridges in compact stellarators with quasiaxisymmetry (QA). The equilibrium with finite plasma currents and pressure is modeled by ideal magnetohydrostatics (MHS). Field lines are collimated near sharp ridges, much like X-points, making ridges attractive to divertor designs without the requirement of a rational rotational transform at the divertor. However, unlike X-points, which must cover the entire torus an integer number of times, sharp ridges are typically localized in certain parts of the flux surfaces. Motivated by recent work (Henneberg and Plunk, Phys. Rev. Research 6, L022052) on compact hybrid devices, we develop a perturbative treatment of nearly axisymmetric quasisymmetric devices by expanding in the deviation from perfect axisymmetry. As a result, we can analytically describe the key features of compact QA devices, such as the tendency for ridges to be localized on the inboard side, where the Gaussian curvature is typically negative, and the field strength is maximum. We provide comprehensive numerical evidence in support of our analytical theory.

physics.plasm-ph↗

arXiv2026

Optical analogy for stellarators: Ridges as caustics and coils as singularities

A common feature of most numerically optimized stellarator geometries is the presence of sharp ridges on outer flux surfaces, irrespective of the rotational transform. Despite their importance, an analytical theory for their existence has been lacking. In this work, we demonstrate that ridges are not artifacts but mathematical necessities. We develop such a theory for devices with quasisymmetry (QS). We demonstrate that QS exhibits close connections with the theory of geometrical optics, following Parker's ``optical analogy" (E.N. Parker, Geophys. Astrophys. Fluid Dyn, 1989). By mapping vacuum QS to the eikonal equation of geometrical optics, we derive the conditions for ridge formation, identified as field line caustics where magnetic field lines focus. Furthermore, we prove a geometric theorem for stellarator coil design: both ridges and filamentary coils must lie on the zero-determinant manifold of the magnetic gradient tensor. This topological constraint unifies the description of plasma ridges and external coils, providing a precise criterion for identifying valid coil locations and explaining the efficacy of the magnetic gradient lengthscale (J. Kappel et al., Plasma Phys. Control. Fusion, 2024) as a coil optimization parameter. We demonstrate that as the device becomes more compact, sharp ridges naturally form on the inboard side in quasiaxisymmetry. We support our analytical theory with extensive numerical evidence.

physics.plasm-ph↗

arXiv2026

Stochastic single-stage stellarator optimization using fixed-boundary equilibria

In this paper, single-stage stellarator optimization is combined with stochastic coil optimization to improve the robustness of the stellarator as compared to deterministic methods. The plasma boundary, solved with an MHD solver in fixed-boundary mode, is linked to a set of randomly perturbed coils via the squared flux. The optimizer avoids sharp local minima and can reach improved configurations. Two different configurations obtained with our method, one quasi-axisymmetric and one quasi-helically symmetric, are compared against both the standard stochastic stage II method and the single-stage method. The new configurations shown here yield improved squared flux, quasisymmetry, and particle loss following a posteriori perturbation of the coils.

physics.plasm-ph↗

arXiv2026

Designing A Buildable Optimized Stellarator to Confine Electron-Positron Plasmas

In this paper, the design of the the plasma equilibrium and superconducting coils for the Electrons and Positrons in an Optimized Stellarator EPOS experiment is presented. With newly developed stellarator optimization tools, including single-stage and stochastic optimization, as well as HTS strain, this work demonstrates that it is possible to achieve key metrics for the buildability and confinement properties of the device. In particular, satisfactory quality of quasisymmetry and stellarator robustness is designed, and engineering requirements are met for eight different candidates. A feasibility study is presented that optimizes multiple candidates for different plasma major radii and coil currents, as well as the best EPOS candidate to date.

physics.plasm-ph↗

arXiv2025

JAX-in-Cell: A Differentiable Particle-in-Cell Code for Plasma Physics Applications

JAX-in-Cell is a fully electromagnetic, multispecies, and relativistic 1D3V Particle-in-Cell (PIC) framework implemented entirely in JAX. It provides a modern, Python-based alternative to traditional PIC frameworks. It leverages Just-In-Time compilation and automatic vectorization to achieve the performance of traditional compiled codes on CPUs, GPUs, and TPUs. The resulting framework bridges the gap between educational scripts and production codes, providing a testbed for differentiable physics and AI integration that enables end-to-end gradient-based optimization. The code solves the Vlasov-Maxwell system on a staggered Yee lattice with either periodic, reflective, or absorbing boundary conditions, allowing both an explicit Boris solver and an implicit Crank-Nicolson method via Picard iteration to ensure energy conservation. Here, we detail the numerical methods employed, validate against standard benchmarks, and showcase the use of its auto-differentiation capabilities.

physics.plasm-ph↗

arXiv2025

Control of a Uniformly Magnetized Plasma with External Electric Fields

Stabilizing plasma dynamics through externally applied electric and magnetic fields is a fundamental control problem. We study this question for a plasma evolving under a uniform external magnetic field. Although the governing dynamics are nonlinear, a linear analysis based on the Laplace-Fourier transform yields actionable insight. In particular, by controlling the location of the roots of the dispersion relation, we propose a general control strategy that restores stability, with the free-streaming solution recovered as a special case. Numerical experiments for Gaussian equilibria and for the Dory-Guest-Harris instability show that the proposed control suppresses the unstable modes and stabilizes the dynamics, in agreement with our theoretical predictions.

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

The High-Order Magnetic Near-Axis Expansion: Ill-Posedness and Regularization

When analyzing 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 regularized 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 regularization 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.

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

An asymptotic Grad-Shafranov equation for quasisymmetric stellarators

A first-order model is derived for quasisymmetric stellarators where the vacuum field due to coils is dominant, but plasma-current-induced terms are not negligible and can contribute to magnetic differential equations, with $\beta$ of the order of the ratio of induced to vacuum fields. Under these assumptions, it is proven that the aspect ratio must be large and a simple expression can be obtained for the lowest-order vacuum field. The first-order correction, which involves both vacuum and current-driven fields, is governed by a Grad-Shafranov equation and the requirement that flux surfaces exist. These two equations are not always consistent, and so this model is generally overconstrained, but special solutions exist that satisfy both equations simultaneously. One family of such solutions are the first-order near-axis solutions. Thus, the first-order near-axis model is a subset of the model presented here. Several other solutions outside the scope of the near-axis model are also found. A case study comparing one such solution to a VMEC-generated solution shows good agreement.

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↗

arXiv2022

Constructing precisely quasi-isodynamic magnetic fields

We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with only one field period. We examine the properties of these newfound quasi-isodynamic configurations, including their bootstrap currents, particle confinement, and available energy for trapped-electron driven turbulence, as well as the degree to which they change when a finite pressure profile is added. We finally discuss the differences between the magnetic axes of the optimized solutions and their respective initial conditions, and conclude with the prospects for future quasi-isodynamic optimization.

physics.plasm-ph↗

arXiv2022

Direct construction of stellarator-symmetric quasi-isodynamic magnetic configurations

We develop the formalism of the first order near-axis expansion of the MHD equilibrium equations described in Garren & Boozer (1991), Plunk et al. (2019) and Plunk et al. (2021), for the case of a quasi-isodynamic, N-field period, stellarator symmetric, single-well magnetic field equilibrium. The importance of the magnetic axis shape is investigated, and we conclude that control of the curvature and torsion is crucial to obtain omnigenous configurations with finite aspect ratio and low effective ripple, especially for a higher number of field periods. For this reason a method is derived to construct classes of axis shapes with favourable curvature and torsion. Solutions are presented, including a three-field-period configuration constructed at an aspect ratio of A=20, with a maximum elongation of e=3.2 and an effective ripple under 1%, which demonstrates that high elongation is not a necessary feature of QI stellarators.

physics.plasm-ph↗

arXiv2020

The On-Axis Magnetic Well and Mercier's Criterion for Arbitrary Stellarator Geometries

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

physics.plasm-ph↗

arXiv2020

Magnetic well and Mercier stability of stellarators near the magnetic axis

We have recently demonstrated that by expanding in small distance from the magnetic axis compared to the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the inverse expansion in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene, & Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

physics.plasm-ph↗

arXiv2016

Plasma Turbulence in the Scrape-off Layer of the ISTTOK Tokamak

The properties of plasma turbulence in a poloidally limited scrape-off layer (SOL) are addressed, with focus on ISTTOK, a large aspect ratio tokamak with a circular cross section. Theoretical investigations based on the drift-reduced Braginskii equations are carried out through linear calculations and non-linear simulations, in two- and three-dimensional geometries. The linear instabilities driving turbulence and the mechanisms that set the amplitude of turbulence as well as the SOL width are identified. A clear asymmetry is shown to exist between the low-field and the high-field sides of the machine. A comparison between experimental measurements and simulation results is presented.

physics.plasm-ph↗

arXiv2014

Indefinite theta functions and black hole partition functions

We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions.

hep-th↗