arXiv subjects

Joaquim Loizu

Publications and source records attributed to Joaquim Loizu.

10 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

The Diocotron Instability in the Trapped Electrons Experiment T-REX and its Relevance to Electron Clouds in Gyrotron Guns

Gyrotrons are essential for electron cyclotron resonance heating (ECRH) in fusion reactors, making their efficient operation crucial for fusion energy. Past experiments revealed instability issues due to trapped electrons in the magnetron injection gun (MIG) region, causing undesired currents and operational failures. To address this, tight manufacturing tolerances are required for the MIG geometry~\cite{pago2}. We present findings of the TRapped Electrons eXperiment (T-REX) at the Swiss Plasma Center, designed to understand electron cloud physics in gyrotron MIGs. T-REX replicates MIG geometries, electric and magnetic fields, and is supported by the 3D FENNECS code. The setup includes two coaxial electrodes in a vacuum chamber atop a superconducting magnet; a central electrode is biased to negative DC voltages and an outer one is grounded, creating a radial electric field up to 2 MV/m and an axial magnetic field B < 0.31 T. Initial discrepancies between experiments and simulations were linked to the diocotron instability, leading to FENNECS being upgraded to 3D and a dedicated set of diagnostics for T-REX. This instability causes the electron cloud to collapse and reform at a frequency depending on plasma conditions. Within this article, time-resolved current measurements on the outer electrode and top flange are presented. Further, a fast current probe array installed at the top flange is detailed. Measurements highlight rotating structures in the electron cloud resulting from the diocotron instability. Simulations show remarkable agreement with experiments, especially regarding the cloud's build-up/collapse frequency, and the rotation frequency and direction of the modes. These results improve our understanding of non-neutral plasmas in environments mimicking a real gyrotron MIG, paving the way for better gyrotron reliability.

physics.plasm-ph↗

arXiv2025

Sawtooth crash in tokamak as a sequence of Multi-region Relaxed MHD equilibria

This study examines the sawtooth crash phenomenon in tokamak plasmas by modelling it as a sequence of Multi-region Relaxed Magnetohydrodynamic (MRxMHD) equilibria. Using the Stepped-Pressure Equilibrium Code (SPEC), we constructed a series of equilibria representing intermediate states during the sawtooth crash, with progressively increasing reconnection regions. Numerical results demonstrated that the system prefers the lower energy non-axisymmetric equilibria with islands and is eventually back to an axisymmetric state, capturing key features of the reconnection process. Comparisons with the nonlinear MHD code M3D-C1 showed remarkable agreement on the field-line topology, the safety factor, and the current profile. However, the simplified MRxMHD model does not resolve the detailed structure of the current sheet. Despite this limitation, MRxMHD offers an insightful approach and a complementary perspective to initial-value MHD simulations.

physics.plasm-ph↗

arXiv2025

Turnstile area as a measure for chaotic transport in magnetic confinement fusion devices

We analyze stochasticity in the magnetic fields of magnetic confinement fusion reactors by calculating the lobe areas of turnstiles - a method developed for characterizing transport into and out of resonance zones in Hamiltonian dynamical systems. We develop an efficient algorithm based on an action principle to calculate this quantity directly from the magnetic field, including stellarator magnetic fields which are sourced by a complicated set of three-dimensional coils. In the analyzed devices, the turnstile area on the inboard (plasma-facing) manifolds is much smaller than the turnstile area on the outboard (wall-facing) manifolds. The application of the turnstile area calculation for the design of future reactors will be discussed.

physics.plasm-ph↗

arXiv2024

Design and First Tests of the Trapped Electrons Experiment T-REX

Gyrotrons are essential for electron cyclotron resonance heating (ECRH) in fusion reactors, making efficient operation crucial for advancing fusion energy. Past experiments revealed instability issues due to trapped electrons in the magnetron injection gun (MIG) region, causing undesired currents and operational failures. To address this, tight manufacturing tolerances are required for the MIG geometry [1]. We present initial findings of the TRapped Electrons eXperiment (T-REX) developed at the Swiss Plasma Center, designed to understand the physics of electron clouds in gyrotron MIGs. T-REX replicates MIG geometries, as well as their typical electric and magnetic fields, and it is supported by 2D Particle-in-Cell (PIC) simulations with the FENNECS code [2, 3]. The setup includes two coaxial electrodes in a vacuum chamber atop a superconducting magnet, with a central electrode biased to negative DC voltages and an outer one at ground, creating a radial electric field (1 to 2 MV/M) and an axial magnetic field (B < 0.4 T). This setup mimics Penning-Malmberg traps. We present the experimental device and first findings on current distribution and also qualitative comparison with FENNECS simulations [4]. Planned diagnostics include optical emission spectroscopy, phosphor screen imaging, Streak camera imaging, and potentially electric field distribution via the Stark effect. This research aims to enhance gyrotron performance and reliability in fusion energy systems.

physics.plasm-ph↗

arXiv2024

Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach

We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al. 2020; Loizu & Bonfiglio 2023), we make use of SPEC (Hudson et al. 2012), an equilibrium solver based on the variational principle of the Multi-Region relaxed MHD, featuring stepped pressure profiles and arbitrary magnetic topology. We work in slab geometry and employ a simple bootstrap current model $J_\textrm{bs} = C \nabla p$ to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter $Δ'$ and the bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHD code (Huang & Bhattacharjee 2016) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical Modified Rutherford Equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and neoclassical tearing modes, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current

physics.plasm-ph↗

arXiv2024

Efficient single-stage optimization of islands in finite-$β$ stellarator equilibria

We present the first single-stage optimization of islands in finite-$β$ stellarator equilibria. Stellarator optimization is traditionally performed as a two-stage process; in the first stage, an optimal equilibrium is calculated which balances a set of competing constraints, and in the second stage a set of coils is found that supports said equilibrium. Stage one is generally performed using a representation for the equilibrium that assumes nestedness of flux surfaces, even though this is not warranted and occasionally undesired. The second stage optimization of coils is never perfect, and the mismatch leads to worse performing equilibria, and further deteriorates if additional constraints such as force minimization, coil torsion or port access are included. The higher fidelity of single-stage optimization is especially important for the optimization of islands as these are incredibly sensitive to changes in the field. In this paper we demonstrate an optimization scheme capable of optimizing islands in finite $β$ stellarator equilibria directly from coils. We furthermore develop and demonstrate a method to reduce the dimensionality of the single-stage optimization problem to that of the first stage in the two-stage approach.

physics.plasm-ph↗

arXiv2024

Constructing nested coordinates inside strongly shaped toroids using an action principle

A new approach for constructing polar-like boundary-conforming coordinates inside a toroid with strongly shaped cross-sections is presented. A coordinate mapping is obtained through a variational approach, which involves identifying extremal points of a proposed action in the mapping space from [0, 2π] x [0, 2π] x [0, 1] to a toroidal domain in R3. This approach employs an action built on the squared Jacobian and radial length. Extensive testing is conducted on general toroidal boundaries using a global Fourier-Zernike basis via action minimization. The results demonstrate successful coordinate construction capable of accurately describing strongly shaped toroidal domains. The coordinate construction is successfully applied to the computation of 3D MHD equilibria in the GVEC code where the use of traditional coordinate construction by interpolation from the boundary failed.

physics.plasm-ph↗

arXiv2024

Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces and a continuous rotational transform. These currents have two components: a surface current (Dirac $δ$-function in flux surface labeling) that prevents the formation of magnetic islands and an algebraically divergent Pfirsch--Schlüter current density when a pressure gradient is present across the rational surface. At flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch--Schlüter current density scaling as $J\sim1/Δι$, where $Δι$ is the difference of the rotational transform relative to the rational surface. If the distance $s$ between flux surfaces is proportional to $Δι$, the scaling relation $J\sim1/Δι\sim1/s$ will lead to a paradox that the Pfirsch--Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm\textendash Kulsrud\textendash Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch--Schlüter current density but also the diamagnetic current density are divergent as $\sim1/Δι$. However, due to the formation of a Dirac $δ$-function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with $s\sim(Δι)^{2}$. Consequently, the singular current density $J\sim1/\sqrt{s}$, making the total current finite, thus resolving the paradox.

physics.plasm-ph↗

arXiv2023

Numerical study of $δ$-function current sheets arising from resonant magnetic perturbations

General three-dimensional toroidal ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces are susceptible to forming singular current sheets when resonant perturbations are applied. The presence of singular current sheets indicates that, in the presence of non-zero resistivity, magnetic reconnection will ensue, leading to the formation of magnetic islands and potentially regions of stochastic field lines when islands overlap. Numerically resolving singular current sheets in the ideal MHD limit has been a significant challenge. This work presents numerical solutions of the Hahm-Kulsrud-Taylor (HKT) problem, which is a prototype for resonant singular current sheet formation. The HKT problem is solved by two codes: a Grad-Shafranov (GS) solver and the SPEC code. The GS solver has built-in nested flux surfaces with prescribed magnetic fluxes. The SPEC code implements multi-region relaxed magnetohydrodynamics (MRxMHD), where the solution relaxes to a Taylor state in each region while maintaining force balance across the interfaces between regions. As the number of regions increases, the MRxMHD solution approaches the ideal MHD solution assuming a continuum of nested flux surfaces. We demonstrate excellent agreement between the numerical solutions obtained from the two codes through a thorough convergence study.

physics.plasm-ph↗