arXiv subjects

Matthias Hoelzl

Publications and source records attributed to Matthias Hoelzl.

At least 19 recordsLinked to original sources

arXiv2026

Hybrid Kinetic-MHD Simulations of Drift-Orbit Effects on the Stability and Non-Linear Dynamics of Runaway Electron Beams

During tokamak disruptions, the Ohmic current may be replaced by a non-inductive runaway electron (RE) current, affecting resistive stability. Previous studies suggest that, in the linear phase, the presence of REs acts destabilizing for tearing modes (TM) compared to a scenario with Ohmic current. In the non-linear regime, this translates to larger saturation amplitudes. These results are based on the assumption of zero drift-orbit deviation from the magnetic flux surfaces corresponding to the low-energy limit. This work investigates the importance of this kinetic effect by studying the linear and non-linear TM dynamics in RE beams with different RE energies, providing a clear picture of finite-orbit-width (FOW) effects. We use a hybrid fluid-kinetic model in the 3D non-linear magnetohydrodynamic (MHD) code JOREK, treating REs kinetically with a full-f Monte Carlo approach in self-consistent interaction with the MHD mode dynamics. The study shows that the presence of REs modifies the characteristics of the instability in several ways. First, we find that the major-radial displacement of drift orbits from flux surfaces induces an $m=1$ perturbation to the equilibrium current, introducing additional mode coupling between $(m,n)$ instabilities and the $(m\pm1,n)$ sidebands. Second, we find that increasing RE energy has a stabilizing effect on the MHD modes because REs cannot support narrow current sheets on rational flux surfaces owing to the drift-orbit displacement. This counteracts the destabilizing effect that REs have on TMs in the low-energy limit. For the scenario investigated, the stabilizing effect dominates over the additional mode coupling, reducing the development of stochastic magnetic regions with increasing RE energy and thereby lowering radial particle transport. Overall, we find that FOW effects can substantially alter the MHD stability and non-linear dynamics of RE beams.

physics.plasm-ph↗

arXiv2026

Implementation and verification of the avalanche source in a 3D full-f particle-in-cell model of relativistic electrons for studies of tokamak disruptions

Disruptions threaten tokamak operation not only because of large in-vessel forces and thermal heat loads, but also because some electrons may be accelerated to relativistic energies. These so-called runaway electrons (REs) can multiply exponentially via knock-on collisions with thermal electrons. As the resulting RE avalanche is exponentially sensitive to the pre-disruption plasma current, multi-MA RE beams may form in large future devices, risking severe localized wall damage. Detailed understanding of RE beam formation and the particle phase-space distribution requires a self-consistent treatment of the RE avalanche and competing losses in the stochastic fields of MHD-active plasmas. Such simulations including the RE sources in 3D fields are needed to develop viable mitigation scenarios. For this, the 3D nonlinear MHD code JOREK includes a hybrid fluid-kinetic model, describing REs with a full-f relativistic particle-in-cell (PiC) approach using full-orbit or drift-kinetic descriptions. In this work, an energy and momentum conserving knock-on collision operator is implemented to enable accurate modeling of the RE phase-space dynamics in 3D electromagnetic fields. To make such novel high-fidelity simulations computationally viable, a resampling technique was also implemented to restrict the number of markers. The avalanche model is verified using analytical expressions from literature and applied to a JET-like termination scenario, demonstrating its applicability to realistic 3D MHD active scenarios. Future work on porting to accelerated high-performance computing systems will be needed to cross the long time scales involved, e.g., in periodic termination and re-avalanching that could occur in large devices like ITER.

physics.plasm-ph↗

arXiv2026

Mechanism Behind the Recombination Requirement for Benign Termination of Relativistic Electron Beams

We present a first-principles explanation of the recombination requirement for benign termination of relativistic electron (RE) beams in tokamaks. Kinetic modeling including neutrals shows that the injection of neutrals over a finite quantity window, together with recombination, increases bulk resistivity. Nonlinear MHD simulations using the JOREK code demonstrate that this preferentially amplifies edge tearing modes, producing a more stochastic edge magnetic field during RE deconfinement, resulting in a larger RE wetted area. We identify resistivity, not the free electron density, to govern access to benign termination. This provides the first broadly applicable and experimentally consistent picture of the MHD mechanisms behind the benign scenario, critical to its extrapolation to next-step devices.

physics.plasm-ph↗

arXiv2026

OpenMP GPU Acceleration and Portability of TRIMEG-C1 for Electromagnetic Gyrokinetic Simulations in Tokamak Plasmas

The Triangular mesh-based gyrokinetic code TRIMEG-C1 solves the gyrokinetic equations using the particle-in-cell scheme to simulate electromagnetic instabilities in tokamak plasmas. TRIMEG-C1 utilizes a high-order C1 finite element method, which captures the accurate physics with lower grid resolution than the C0 method. In this work, we focus on achieving a portable implementation on multiple graphics processing unit (GPU) architectures to accelerate the TRIMEG-C1 code for future physics studies. The OpenMP framework is chosen as the acceleration framework for GPU offloading on different hardware platforms, specifically, NVIDIA and AMD GPUs. The particle pushing procedure, as well as particle-to-grid operations have been adapted for GPU execution. A speedup of $\approx9$ for the particle pusher kernel is achieved on 2 AMD MI300A APUs (Accelerated Processing Unit) compared with 2 AMD 9754 CPUs. In addition, the efficiency of hybrid MPI-OpenMP offloading parallelization was assessed by oversubscribing GPU resources. The Ion Temperature Gradient (ITG) mode was simulated using the GPU implementation, and its correctness was verified by comparing the physics results in terms of the energy growth rate and the two-dimensional mode structures.

physics.plasm-ph↗

arXiv2026

Gyrokinetic global simulation of Alfvenic ion temperature gradient mode in reversed magnetic shear

In this work, a systematic study of electromagnetic instabilities driven by the temperature gradient in magnetically confined fusion plasmas with reversed magnetic shear is conducted using gyrokinetic particle-in-cell simulations. An electromagnetic instability arising in the low-beta regime is investigated, where beta=8*pi*nT/B^2 denotes the ratio of plasma pressure to magnetic pressure. Within a reversed shear safety factor (q) profile, when a mode rational surface coincides with the position of zero shear, an instability dominated by only one poloidal harmonic emerges, rather than the conventional ion-temperature-gradient (ITG) mode. Simulation results demonstrate that the instability exhibits pronounced electromagnetic polarization even in the low-beta regime, with a real frequency significantly higher than that of ITG modes, and show that it is destabilized by the temperature gradient and not by the density gradient. This instability can be observed even for a monotonic q profile with weak magnetic shear. Based on a systematic comparison with other typical electrostatic and electromagnetic instabilities, this instability is identified as a weak shear Alfvenic-ion-temperature-gradient (WSAITG) mode, which may provide an explanation for the low-frequency Alfven modes (LFAM) observed in experiments. Wave-particle resonance analysis in phase space reveals that, in contrast to the ITG mode, well-passing particles provide an additional resonant population that drives the WSAITG mode.

physics.plasm-ph↗

arXiv2026

A High-order piecewise field-aligned triangular finite element method for electromagnetic gyrokinetic particle simulations of tokamak plasmas with open field lines

A high-order piecewise field-aligned triangular finite element method is developed and implemented for global electromagnetic gyrokinetic particle-in-cell simulations of tokamak plasmas with open field lines. The approach combines locally field-aligned finite element basis functions with unstructured $C^{1}$ triangular meshes in cylindrical coordinates, enabling whole-volume simulations with substantially reduced computational effort, while avoiding the grid distortion associated with globally field-aligned coordinates and the associated singularity at the separatrix of diverted plasmas. The formulation is compatible with both $δf$ and full-$f$ models and employs mixed-variable representations, along with a generalized pullback scheme, to control numerical cancellation in electromagnetic simulations. The method is implemented in the TRIMEG-C1 code and demonstrated using linear and nonlinear electromagnetic simulations of the TCV-X21 configuration. The results indicate that the approach accurately captures the key features of electromagnetic ion-temperature-gradient and kinetic ballooning mode physics, including the separatrix regions in the simulation, thereby providing a robust framework for whole-volume electromagnetic gyrokinetic simulations in realistic tokamak geometries.

physics.plasm-ph↗

arXiv2025

Generalized mixed variable-pullback scheme with non-ideal Ohm's law for electromagnetic gyrokinetic simulations

In this work, the non-ideal Ohm's law is integrated in the mixed variable-pullback scheme for the gyrokinetic particle simulations. This scheme captures the evolution of the symplectic solution of the gyrokinetic model accurately not only in the MHD limit but also in the electrostatic limit. This scheme also provides a pure symplectic ($v_\shortparallel $) scheme for electromagnetic gyrokinetic particle simulations without causing the traditional cancellation problem in the pure Hamiltonian scheme. Various mixed variable schemes have been comprehensively analyzed for the 1D shear Alfvèn wave problem with kinetic electrons, with the connection to the traditional pure Hamiltonian scheme and the symplectic scheme. It is demonstrated that the pure $v_\shortparallel $ form with the non-ideal Ohm's law has comparable performance to the widely used mixed variable-pullback scheme with the ideal Ohm's law. The mixed variable-pullback scheme without Ohm's law is also proposed as a feasible improvement of the traditional pure Hamiltonian scheme with minimum modification and considerable performance improvement in terms of a marker number reduction.

physics.plasm-ph↗

arXiv2025

TRIMEG-GKX: an electromagnetic gyrokinetic particle code with a Piecewise Field-Aligned Finite Element Method for Micro- and Macro-Instability Studies in Tokamak Core Plasmas

The features of the TRIMEG-GKX code are described with emphasis on the exploration using novel/different schemes compared to other gyrokinetic codes, particularly the use of object-oriented programming, filter/buffer-free treatment, and a high-order piecewise field-aligned finite element method. The TRIMEG-GKX code solves the electromagnetic gyrokinetic equation using the particle-in-cell scheme, taking into account multi-species effects and shear Alfvén physics. The mixed-variable/pullback scheme has been implemented to enable electromagnetic studies. This code is parallelized using particle decomposition and domain cloning among computing nodes, replacing traditional domain decomposition techniques. The applications to study the micro- and macro-instabilities are demonstrated, including the energetic-particle-driven Alfvén eigenmode, ion temperature gradient mode, and kinetic ballooning mode. Good performance is achieved in both ad hoc and experimentally reconstructed equilibria, such as those of the ASDEX Upgrade (AUG), Tokamak à configuration variable (TCV), and the Joint European Torus (JET). Future studies of edge physics using the high-order $C^1$ finite element method for triangular meshes in the TRIMEG-C1 code will be built upon the same numerical methods.

physics.plasm-ph↗

arXiv2025

Self-consistent full MHD coupling of JOREK and STARWALL for advanced plasma free boundary simulation

An adequate modelling of the electromagnetic interaction of the plasma with the surrounding conductors is paramount for the correct reproduction of 3D plasma dynamics. Simulations of the latter provide in turn useful predictions regarding the plasma evolution, the related MHD modes leading to disruptions and the electromagnetic forces acting on the vacuum vessel's components when said disruptions occur. The latest modelling efforts with the 3D FEM non-linear JOREK code have been directed towards the eddy current coupling of a reduced magnetohydrodynamic (MHD) plasma model with thin and volumetric wall codes (STARWALL and CARIDDI). In this contribution, we present an eddy current coupling between the full MHD model of JOREK and the STARWALL code; this new coupling scheme describes the full three-dimensional interactions of the plasma with the vacuum region and external conductors, modeled by natural boundary conditions linking the magnetic vector potential $\mathbf{A}$ to the magnetic field $\mathbf{B}$. The consistency of the new coupling scheme is validated via benchmarks for axisymmetric Vertical Displacement Events and multi-harmonics simulations of MHD modes.

physics.plasm-ph↗

arXiv2024

Reduced kinetic modelling of shattered pellet injection in ASDEX Upgrade

Plasma-terminating disruptions represent a critical outstanding issue for reactor-relevant tokamaks. ITER will use shattered pellet injection (SPI) as its disruption mitigation system to reduce heat loads, vessel forces, and to suppress the formation of runaway electrons. In this paper we demonstrate that reduced kinetic modelling of SPI is capable of capturing the major experimental trends in ASDEX Upgrade SPI experiments, such as dependence of the radiated energy fraction on neon content, or the current quench dynamics. Simulations are also consistent with the experimental observation of no runaway electron generation with neon and mixed deuterium-neon pellet composition. We also show that statistical variations in the fragmentation process only have a notable impact on disruption dynamics at intermediate neon doping, as was observed in experiments.

physics.plasm-ph↗

arXiv2024

Piecewise Field-Aligned Finite Element Method for Multi-Mode Nonlinear Particle Simulations in tokamak plasmas

This paper presents a novel approach for simulating plasma instabilities in tokamak plasmas using the piecewise field-aligned finite element method in combination with the particle-in-cell method. Our method traditionally aligns the computational grid but defines the basis functions in piecewise field-aligned coordinates to avoid grid deformation while naturally representing the field-aligned mode structures. This scheme is formulated and implemented numerically. It also applied to the unstructured triangular meshes in principle. We have conducted linear benchmark tests, which agree well with previous results and traditional schemes. Furthermore, multiple-$n$ simulations are also carried out as a proof of principle, demonstrating the efficiency of this scheme in nonlinear turbulence simulations within the framework of the finite element method.

physics.plasm-ph↗

arXiv2024

Gyrokinetic Electromagnetic Particle Simulations in Triangular Meshes with C1 Finite Elements

The triangular mesh-based gyrokinetic scheme enables comprehensive axis-to-edge studies across the entire plasma volume. Our approach employs triangular finite elements with first-derivative continuity (C1), building on previous work to facilitate gyrokinetic simulations. Additionally, we have adopted the mixed variable/pullback scheme for gyrokinetic electromagnetic particle simulations. The filter-free treatment in the poloidal cross-section with triangular meshes introduces unique features and challenges compared to previous treatments using structured meshes. Our implementation has been validated through benchmarks using ITPA-TAE (Toroidicity-induced Alfvén Eigenmode) parameters, showing its capability in moderate to small electron skin depth regimes. Additional examinations using experimental parameters confirm its applicability to realistic plasma conditions.

physics.plasm-ph↗

arXiv2024

Implementation of matrix compression in the coupling of JOREK to realistic 3D conducting wall structures

JOREK is an advanced non-linear simulation code for studying MHD instabilities in magnetically confined fusion plasmas and their control and/or mitigation. A free-boundary and resistive wall extension was introduced via coupling to the STARWALL and CARIDDI codes, both able to provide dense response matrices describing the electromagnetic interactions between plasma and conducting structures. For detailed CAD representations of the conducting structures and high resolutions for the plasma region, memory and computing time limitations restrict the possibility of simulating the ITER tokamak. In the present work, the Singular Value Decomposition provided by routines from the ScaLAPACK library has been successfully applied to compress some of the dense response matrices and thus optimize memory usage. This is demonstrated for simulations of Tearing Mode and Vertical Displacement Event instabilities. An outlook to future applications on large production cases and further extensions of the method are discussed.

physics.plasm-ph↗

arXiv2024

Understanding Large-Scale Plasma Simulation Challenges for Fusion Energy on Supercomputers

Understanding plasma instabilities is essential for achieving sustainable fusion energy, with large-scale plasma simulations playing a crucial role in both the design and development of next-generation fusion energy devices and the modelling of industrial plasmas. To achieve sustainable fusion energy, it is essential to accurately model and predict plasma behavior under extreme conditions, requiring sophisticated simulation codes capable of capturing the complex interaction between plasma dynamics, magnetic fields, and material surfaces. In this work, we conduct a comprehensive HPC analysis of two prominent plasma simulation codes, BIT1 and JOREK, to advance understanding of plasma behavior in fusion energy applications. Our focus is on evaluating JOREK's computational efficiency and scalability for simulating non-linear MHD phenomena in tokamak fusion devices. The motivation behind this work stems from the urgent need to advance our understanding of plasma instabilities in magnetically confined fusion devices. Enhancing JOREK's performance on supercomputers improves fusion plasma code predictability, enabling more accurate modelling and faster optimization of fusion designs, thereby contributing to sustainable fusion energy. In prior studies, we analysed BIT1, a massively parallel Particle-in-Cell (PIC) code for studying plasma-material interactions in fusion devices. Our investigations into BIT1's computational requirements and scalability on advanced supercomputing architectures yielded valuable insights. Through detailed profiling and performance analysis, we have identified the primary bottlenecks and implemented optimization strategies, significantly enhancing parallel performance. This previous work serves as a foundation for our present endeavours.

physics.plasm-ph↗

arXiv2024

RMP screening in JOREK-CARIDDI

Edge localized modes (ELMs) are instabilities at the tokamak edge that can have short outbursts of highly energetic particles and heat, which can severely damage the walls of a plasma reactor. Resonant magnetic perturbations (RMPs) are used to mitigate or eliminate ELMs from the plasma. One effect that can reduce the intensity of the RMP is screening, which is caused by eddy currents in conducting structures or a plasma that are induced by a time-varying magnetic field. The eddy current code CARIDDI was recently coupled with the magnetohydrodynamics (MHD) code JOREK, and is able to capture the behavior of volumetric conducting structures that surround a plasma. The objective of this study is to characterize screening behavior in the JOREK-CARIDDI coupling. The analysis is divided in three parts. First, CARIDDI results are benchmarked against results from STARWALL, another JOREK extension that captures interactions of (two-dimensional) conducting structures. It is found that CARIDDI and STARWALL show good agreement, with slight variations. The second part covers the screening of time-varying RMP fields by conducting structures, oscillating at frequencies from 3 Hz to 10 kHz. The overall trends in screening behavior align qualitatively with findings from a previous analysis. However, an additional contribution to the screening at frequencies above 1 kHz was not observed, because the simulation in this report does not include screening by the RMP coil casing. Finally, a few tests were performed using a plasma configuration, to study the effect of plasma screening, including realistic plasma background flows. The results demonstrated the induction of eddy currents at rational surfaces within the plasma. These results contribute to an improved understanding of the screening of RMP fields, which is relevant for several applications to the operation of fusion reactors.

physics.plasm-ph↗

arXiv2024

Nonlinear MHD modeling of soft $β$ limits in W7-AS

An important question for the outlook of stellarator reactors is their robustness against pressure driven modes, and the underlying mechanism behind experimentally observed soft $β$ limits. Towards building a robust answer to these questions, simulation studies are presented using a recently derived reduced nonlinear MHD model. First, the initial model implementation is extended to capture fluid compression by including the influence of parallel flows. Linear benchmarks of a (2, 1) tearing mode in W7-AS geometry, and interchange modes in a finite $β$, net-zero current carrying stellarator with low magnetic shear are then used to demonstrate the modeling capabilities. Finally, a validation study is conducted on experimental reconstructions of finite $β$ W7-AS discharges. In agreement with past experimental analysis, it is shown that (i) the MHD activity is resistive, (ii) a soft $β$ limit is observed, when the plasma resistivity approaches the estimated experimental value, and (iii) low $n$ MHD activity is observed at intermediate $β$ values, particularly a nonlinearly dominant (2, 1) mode. The MHD activity is mild, explaining the soft $β$ limit, because the plasma volume remains separated into distinct sub-volumes in which field lines are ergodically confined. For the assumed transport parameters, the enhanced perpendicular transport along stochastic magnetic field lines can be overcome with the experimental heating power. The limitations in the current modeling are described, alongside an outlook for characterising soft $β$ limits in more detail in future work.

physics.plasm-ph↗

arXiv2023

Towards Robust Solvers for Nuclear Fusion Simulations Using JOREK: A Numerical Analysis Perspective

One of the most well-established codes for modeling non-linear Magnetohydrodynamics (MHD) for tokamak reactors is JOREK, which solves these equations with a Bézier surface based finite element method. This code produces a highly sparse but also very large linear system. The main solver behind the code uses the Generalized Minimum Residual Method (GMRES) with a physics-based preconditioner, but even with the preconditioner there are issues with memory and computation costs and the solver does not always converge well. This work contains the first thorough study of the mathematical properties of the underlying linear system. It enables us to diagnose and pinpoint the cause of hampered convergence. In particular, analyzing the spectral properties of the matrix and the preconditioned system with numerical linear algebra techniques, will open the door to research and investigate more performant solver strategies, such as projection methods.

physics.plasm-ph↗

arXiv2023

MHD simulations of formation, sustainment and loss of Quiescent H-mode in the all-tungsten ASDEX Upgrade

Periodic edge localized modes (ELMs) are the non-linear consequences of pressure-gradient-driven ballooning modes and current-driven peeling modes becoming unstable in the pedestal region of high confinement fusion plasmas. In future tokamaks like ITER, large ELMs are foreseen to severely affect the lifetime of wall components as they transiently deposit large amounts of heat onto a narrow region at the divertor targets. Several strategies exist for avoidance, suppression, or mitigation of these instabilities, such as the naturally ELM-free quiescent H-mode (QH-mode). In the present article, an ASDEX Upgrade equilibrium that features a QH-mode is investigated through non-linear extended MHD simulations covering the dynamics over tens of milliseconds. The equilibrium is close to the ideal peeling limit and non-linearly develops saturated modes at the edge of the plasma. A dominant toroidal mode number of $n=1$ is found, for which the characteristic features of the edge harmonic oscillation are recovered. The saturated modes contribute to heat and particle transport preventing pedestal build-up to the ELM triggering threshold. The non-linear dynamics of the mode, in particular its interaction with the evolution of the edge safety factor is studied, which suggest a possible new saturation mechanism for the QH-mode. The simulations show good qualitative and quantitative agreement to experiments in AUG. In particular, the processes leading to the termination of QH-mode above a density threshold is studied, which results in the transition into an ELM regime. In the vicinity of this threshold, limit cycle oscillations are observed.

physics.plasm-ph↗