arXiv subjects

M. Hoelzl

Publications and source records attributed to M. Hoelzl.

At least 19 recordsLinked to original sources

arXiv2026

JOREK simulations of the X-point radiator formation and its movement in ASDEX Upgrade

Future large-scale magnetic confinement fusion reactors require operational regimes that can avoid extreme heat fluxes onto the plasma-facing components. One promising regime is the X-point radiator (XPR), which relies on a highly radiative, cold and dense plasma volume forming above the X-point, and which can be accessed via impurity seeding. Experimentally, the height of the XPR can be controlled by adjusting the seeding rate and heating power. This contribution presents axisymmetric (2D) simulations of the XPR regime in ASDEX Upgrade using the nonlinear MHD code JOREK extended with a kinetic particle framework for the main species neutrals and nitrogen impurities. With the time-dependent simulations, the progression from attached divertors to a complete detachment with the XPR formation is shown, highlighting the effects of the neutrals and impurities separately. Amidst this progression, the formation and the loss of the high-field-side high-density are observed. After the XPR is well-formed at the height of 6.8 cm, the fuelling and seeding rates are adjusted so that the XPR remains stationary. From the stationary case, the seeding rate is then changed to see how the XPR location reacts. By increasing and decreasing the seeding rate, the XPR responds by moving upwards and downwards, respectively. These simulations show JOREK's capability of simulating time-varying XPR, which will provide a baseline for the transition to 3D simulations, so the MHD activities and their interaction with the XPR can be studied.

physics.plasm-ph↗

arXiv2026

Evolution of SPI-induced disruptions in ASDEX Upgrade

Disruptions are a major concern for future fusion reactors based on the tokamak principle. To ensure machine protection, the thermal loads and vessel forces that arise during disruptions have to be mitigated reliably. For the ITER disruption mitigation system (DMS), the shattered pellet injection (SPI) technology has been selected. It can provide a prompt delivery of the injection material into the plasma core, with the mitigation efficiency depending on fragment size and velocity. A highly flexible SPI system was built and installed at the tokamak ASDEX Upgrade (AUG) to aid the finalization process of the ITER DMS and provide crucial input for modeling. The SPI-induced disruptions in the 2022 AUG experiments follow a typical chain of events, which are discussed in this paper: The first light, main fragment arrival, plasma movement event, MARFE, thermal quench/plasma current spike, current quench, and vertical displacement event phase. Depending on the injection parameters, these phases may vary significantly or some might not be present at all. In this paper, we will focus on the characterization of these disruption phases and figures of merit for the mitigation efficiency, depending on the SPI configuration. With increasing amount of assimilated neon in the plasma - primarily influenced by the neon content in the pellet but also the shattering parameters - the disruptions exhibit different behaviors. This disruption evolution seems to be a continuous process, with the most prominent feature being the changing disruption time scales and plasma current time trace shape during the CQ from convex (poorly or unmitigated) $\rightarrow$ concave (well mitigated/radiation dominated). Depending on the injection, pre-TQ durations between 15 - 0.5 ms and early CQ durations ($\Delta \textrm{t}_\textrm{CQ}^{100 \rightarrow 80}$) between 13.3 - 8.2 ms had been achieved at AUG.

physics.plasm-ph↗

arXiv2026

Flux pumping and bifurcated relaxations of helical core in 3D magnetohydrodynamic modelling of ASDEX Upgrade plasmas

Flux pumping was achieved in recent hybrid scenario experiments in the ASDEX Upgrade (AUG) tokamak, which is characterized by a sawtooth-free helical quiescent state and the anomalous radial redistribution of toroidal current density and poloidal magnetic flux. In this article, the self-regulation mechanism of the AUG core plasma during flux pumping is investigated at realistic parameters using the JOREK code based on the two-temperature, nonlinear, full magnetohydrodynamic (MHD) model. A key milestone in AUG flux pumping modelling is achieved by quantitatively reproducing the clamped current density and safety factor profiles in the plasma core, demonstrating the effectiveness of the dynamo effect in sustaining the flux pumping state. The dynamo term, that is of particular interest, is primarily generated by the pressure-gradient driven m/n = 1/1 quasi-interchange-like MHD instability. The work systematically extrapolates the parameter regimes of flux pumping from the above AUG base case by scanning dissipation coefficients and plasma beta. The simulation results reveal bifurcated plasma behaviours at different Hartmann numbers, including distinct states such as flux pumping (helical core with a flat current density), sawteeth (periodic kink-cycling), single crash (without subsequent cycle), and quasi-stationary magnetic island (peaked current density). Transitions from marginal flux pumping state to sawteeth are observed in long-term simulations. The relationships between system dissipation, plasma beta, and different plasma states are carefully analyzed. For practical purposes, the potential operational window for flux pumping, as determined by plasma density and temperature, is estimated. The modelling efforts advance the understanding of flux pumping and facilitate the development of a fast surrogate model for efficient evaluation of flux pumping.

physics.plasm-ph↗

arXiv2026

Quantitative 3D non-linear simulations of shattered pellet injection in ASDEX Upgrade using JOREK

Shattered pellet injection (SPI) as primary mitigation method for major disruptions in ITER has a large parameter space available for optimization including the total amount of injected material, the size of the individual pellet fragments, the material composition, and the timing of multiple injections. This flexibility needs to be exploited to simultaneously minimize thermal heat loads, electromagnetic vessel forces, and formation of relativistic electrons and their impacts on plasma facing components. In this article, we apply 3D non-linear magnetohydrodynamic modelling to SPI experiments in the ASDEX Upgrade tokamak, going beyond our previous work [Tang et al Nucl. Fusion 65 116003 (2025)] by resolving some discrepancies between simulations and experiment and thus opening the path to quantitative model validation and experiment interpretation. The key element that enables the transition from merely qualitative comparisons to quantitatively reliable predictions of the thermal quench duration and the radiation fraction is the incorporation of a simplified treatment of parallel heat-flux limiting. The work increases the confidence of matching the key processes of disruption mitigation with this high fidelity modelling in view of predictive studies for ITER.

physics.plasm-ph↗

arXiv2025

Runaway electron avalanche and macroscopic beam formation: simulations of the DTT full power scenario

The transition of the Divertor Tokamak Test (DTT) facility from its initial commissioning phase (Day-0, plasma current $I_{p}=2$ MA) to the full power scenario ($I_{p}=5.5$ MA) introduces a critical shift in the dynamics of runaway electrons (REs) generation. While previous predictive studies of the low-current scenario indicated a robust safety margin against RE beam formation, this work reveals that the exponential scaling of the RE avalanche gain with plasma current severely narrows the safe operational window in the full power scenario. Using the non-linear magnetohydrodynamic code JOREK, we perform comprehensive 2D simulations of the current quench (CQ) phase of several disruption scenarios, systematically scanning initial RE seed currents and injected impurity levels. The results demonstrate that in the full power scenario, the avalanche multiplication factor is sufficiently high ($G_\text{av} \approx 1.3 \cdot 10^5$) to convert a mere 5.5 A seed current into macroscopic RE beams of $\approx 0.7$ MA when large amounts of impurities are present. For even higher RE seeds, the RE current can peak at $ \approx 3.2$ MA, constituting up to $\approx$ 80% of the total plasma current during the CQ. These findings suggest that, unlike the Day-0 phase, the disruption mitigation strategy for the full power scenario involves a careful balance between thermal load mitigation and RE avoidance, necessitating a well-chosen quantity of injected impurities. This work provides the baseline needed for future estimations of RE loads on the plasma-facing components of DTT, which will be essential for designing and positioning mitigation components like sacrificial limiters.

physics.plasm-ph↗

arXiv2025

Comparison of MHD and gyrokinetic simulations of linear instabilities at the q = 1 surface

Accurate modeling of core instabilities in tokamak plasmas is essential to understand the underlying physical mechanisms and their impact on plasma confinement. The ideal stability of the internal kink mode and the m = 1 collisionless tearing mode are analyzed numerically both with gyrokinetic and MHD codes. We compare the different models implemented in the codes and show that the gyrokinetic equations without collisions inherently contain the ideal MHD limit. The simulation results show that the stability of the internal kink mode strongly depends on the choice of several setup parameters like the inclusion of parallel magnetic field fluctuations, the tokamak aspect ratio, the drift- or gyrokinetic treatment of the ions and the electron mass. Furthermore, we demonstrate the stabilization of the instabilities by diamagnetic effects. Our results indicate that gyrokinetic and MHD models can be reconciled in the description of the internal kink mode by careful consideration of the simulation setup and model assumptions, but instabilities like the collisionless tearing mode require a more advanced treatment beyond MHD.

physics.plasm-ph↗

arXiv2025

Thermal resilience of the ITER tungsten first wall to runaway electron impact

The fast volumetric deposition of multi-MeV high current runaway electron (RE) beams constitutes the most critical issue for the ITER tungsten (W) first wall (FW) longevity. Such relativistic electron beams could generate extreme volumetric power densities inside the FW armour which lead to significant vaporization, deep melting and even material explosions, as well as to elevated temperatures at the bond interface with the cooling substrate that could cause rupture and water leaks. Here the thermal response of the ITER FW is modeled with a three-stage, one-way coupled workflow focusing on assessments of the extent of the wall damage and the increase of the bond interface temperature for varying W thickness. Increased W thickness is found to be essential for wall protection against intense RE dissipation events in terms of both W tile damage and cooling system integrity.

physics.plasm-ph↗

arXiv2025

Non-linear MHD modelling of shattered pellet injection in ASDEX Upgrade

Shattered pellet injection (SPI) is selected for the disruption mitigation system in ITER, due to deeper penetration, expected assimilation efficiency and prompt material delivery. This article describes non-linear magnetohydrodynamic (MHD) simulations of SPI in the ASDEX Upgrade tokamak to test the mitigation efficiency of different injection parameters for neon-doped deuterium pellets using the JOREK code. The simulations are executed as fluid simulations, while additional marker particles are used to evolve the charge state distribution and radiation property of impurities based on OpenADAS atomic data, i.e., a collisional-radiative model is used. Neon fraction scans between 0 - 10% are performed. Numerical results show that the thermal quench (TQ) occurs in two stages. In the first stage, approximately half of the thermal energy is abruptly lost, primarily through convective and conductive transport in the stochastic fields. This stage is relatively independent of the neon fraction. In the second stage, where the majority of the remaining thermal energy is lost, radiation plays a dominant role. In case of pure deuterium injection, this second stage may not occur at all. A larger fraction ($\sim $20%) of the total material in the pellet is assimilated in the plasma for low neon fraction pellets ($\leq 0.12\%$) due to the full thermal collapse of the plasma occurring later than in high neon fraction scenarios. Nevertheless, the total number of assimilated neon atoms increases with increasing neon fraction. The effects of fragment size and penetration speed are then numerically studied, showing that slower and smaller fragments promote edge cooling and the formation of a cold front. Faster fragments result in shorter TQ duration and higher assimilation as they reach the hotter plasma regions quicker.

physics.plasm-ph↗

arXiv2025

Runaway electron-induced plasma facing component damage in tokamaks

This Roadmap article addresses the critical and multifaceted challenge of plasma-facing component (PFC) damage caused by runaway electrons (REs) in tokamaks, a phenomenon that poses a significant threat to the viability and longevity of future fusion reactors such as ITER and DEMO. The dramatically increased RE production expected in future high-current tokamaks makes it difficult to avoid or mitigate REs when a plasma discharge terminates abnormally. Preventing damage from the intense localised heat loads REs can cause requires a holistic approach that considers plasma, REs and PFC damage. Despite decades of progress in understanding the physics of REs and the thermomechanical response of PFCs, their complex interplay remains poorly understood. This document aims to initiate a coordinated, interdisciplinary approach to bridge this gap by reviewing experimental evidence, advancing diagnostic capabilities, and improving modelling tools across different scales, dimensionalities and fidelities. Key topics include RE beam formation and transport, damage mechanisms in brittle and metallic PFCs, and observations in major facilities such as JET, DIII-D, WEST and EAST. The Roadmap emphasises the urgency of predictive, high-fidelity modelling validated against well-diagnosed controlled experiments, particularly in the light of recent changes in ITER's wall material strategy and the growing importance of private sector initiatives. Each section of the article is written to provide a concise overview of one area of this multidisciplinary subject, with an assessment of the status, a look at current and future challenges, and a brief summary. The ultimate goal of this initiative is to guide future mitigation strategies and design resilient components that can withstand the loads imposed by REs, thus ensuring the safe and sustainable operation of the next generation of fusion power plants.

physics.plasm-ph↗

arXiv2024

3D MHD modelling of plasmoid drift following massive material injection in a tokamak

Mechanisms of plasmoid drift following massive material injection are studied via 3D non-linear MHD modelling with the JOREK code, using a transient neutral source deposited at the low field side midplane of a JET H-mode plasma to clarify basic processes and compare with existing theories. The simulations confirm the important role of the propagation of shear Alfvén wave (SAW) packets from both ends of the plasmoid (``SAW braking'') and the development of external resistive currents along magnetic field lines (``Pégourié braking'') in limiting charge separation and thus the $\mathbf{E}\times \mathbf{B}$ plasmoid drift, where $\mathbf{E}$ and $\mathbf{B}$ are the electric and magnetic fields, respectively. The drift velocity is found to be limited by the SAW braking on the few microseconds timescale for cases with relatively small source amplitude while the Pégourié braking acting on a longer timescale is shown to set in earlier with larger toroidal extent of the source, both in good agreement with existing theories. The simulations also identify the key role of the size of the $\mathbf{E}\times \mathbf{B}$ flow region on plasmoid drift and show that the saturated velocity caused by dominant SAW braking agrees well with theory when considering an effective pressure within the $\mathbf{E}\times \mathbf{B}$ flow region. The existence of SAWs in the simulations is demonstrated and the 3D picture of plasmoid drift is discussed.

physics.plasm-ph↗

arXiv2024

Runaway electron beam formation, vertical motion, termination and wall loads in EU-DEMO

Runaway electron loads onto material structures are a major concern for future large tokamaks due to the efficient avalanching at high plasma currents. Here, we perform predictive studies using the JOREK code for a plausible plasma configuration in the European DEMO fusion power plant with focus on a pessimistic scenario in which a multi mega-ampere runaway electron beam is formed. The work first comprises axisymmetric predictions of runaway electron beam formation in a mitigated scenario and of the simultaneous vertical motion of the beam due to loss of position control. The subsequent runaway electron beam termination triggered by a burst of MHD activity during the course of the vertical motion is then simulated in 3D with the runaway electron fluid self-consistently coupled to the MHD modes. Finally, the resulting deposition pattern of the runaway electrons onto wall structures is calculated with a relativistic test particle approach. This way, the suitability of a possible sacrificial limiter concept for the protection of first wall components is assessed.

physics.plasm-ph↗

arXiv2024

Axisymmetric predictions for mitigated and vertically unstable disruptions in ITER with runaway electrons

We present two-dimensional global simulations of mitigated and vertically unstable disruptions in ITER in the presence of runaway electrons. An elongated plasma in free-boundary equilibrium is subjected to an artificial thermal quench and current-profile flattening, followed by one or more massive material injections and RE avalanche. Scenarios of major disruptions as well as upward and downward vertical displacement events are considered. Results provide important insights into the effects of runaway electron formation, post thermal quench current-profile, injection quantities and timings, and impurity flushout on the overall evolution of disruption and the plasma vertical motion thereof. Interplay between the various effects offers scope for potentially beneficial runaway electron mitigation scenarios.

physics.plasm-ph↗

arXiv2024

Plasmoid drift and first wall heat deposition during ITER H-mode dual-SPIs in JOREK simulations

The heat flux mitigation during the Thermal Quench (TQ) by the Shattered Pellet Injection (SPI) is one of the major elements of disruption mitigation strategy for ITER. It's efficiency greatly depends on the SPI and the target plasma, and is ultimately checked by the heat deposition on to the PFCs. To investigate this, JOREK simulations of neon-mixed dual-SPIs into ITER baseline H-mode and a "degraded H-mode" with and without good injector synchronization are performed with focus on the first wall heat flux and its energy impact. It is found that low neon fraction SPIs into the baseline H-mode plasmas exhibit strong major radial plasmoid drift as the fragments arrive at the pedestal, accompanied by edge stochasticity. Significant density expulsion and outgoing heat flux occurs as a result, reducing the mitigation efficiency. Such drift motion could be mitigated by injecting higher neon fraction pellets', or by considering the pre-disruption confinement degradation, thus improving the radiation fraction. The radiation heat flux is found to peak in the vicinity of the fragment injection location in the early injection phase, while it relaxes later on due to parallel impurity transport. The overall radiation asymmetry could be significantly mitigated by good synchronization. Time integration of the local heat flux is carried out to provide its energy impact for wall heat damage assessment. For the baseline H-mode case with full pellet injection, melting of the stainless steel of the diagnostic port could occur near the injection port, which is acceptable, without any melting of the first wall tungsten tiles. For the degraded H-mode cases with quarter-pellet SPIs, which have 1/4 total volume of a full pellet, the maximum energy impact approaches the tolerable limit of the stainless steel with un-synchronized SPIs, and stays well below such limit for the perfectly synchronized ones.

physics.plasm-ph↗

arXiv2024

Neural-Parareal: Dynamically Training Neural Operators as Coarse Solvers for Time-Parallelisation of Fusion MHD Simulations

The fusion research facility ITER is currently being assembled to demonstrate that fusion can be used for industrial energy production, while several other programmes across the world are also moving forward, such as EU-DEMO, CFETR, SPARC and STEP. The high engineering complexity of a tokamak makes it an extremely challenging device to optimise, and test-based optimisation would be too slow and too costly. Instead, digital design and optimisation must be favored, which requires strongly-coupled suites of High-Performance Computing calculations. In this context, having surrogate models to provide quick estimates with uncertainty quantification is essential to explore and optimise new design options. Furthermore, these surrogates can in turn be used to accelerate simulations in the first place. This is the case of Parareal, a time-parallelisation method that can speed-up large HPC simulations, where the coarse-solver can be replaced by a surrogate. A novel framework, Neural-Parareal, is developed to integrate the training of neural operators dynamically as more data becomes available. For a given input-parameter domain, as more simulations are being run with Parareal, the large amount of data generated by the algorithm is used to train new surrogate models to be used as coarse-solvers for future Parareal simulations, leading to progressively more accurate coarse-solvers, and thus higher speed-up. It is found that such neural network surrogates can be much more effective than traditional coarse-solver in providing a speed-up with Parareal. This study is a demonstration of the convergence of HPC and AI which simply has to become common practice in the world of digital engineering design.

physics.plasm-ph↗

arXiv2022

Development and application of a hybrid MHD-kinetic model in JOREK

Energetic particle (EP) driven instabilities will be of strongly increased relevance in future burning plasmas as the EP pressure will be very large compared to the thermal plasma. Understanding the interaction of EPs and bulk plasma is crucial for developing next-generation fusion devices. In this work, the JOREK MHD code is extended to allow for the simulation of EP instabilities at high EP pressures using realistic plasma and EP parameter in a full-f formulation with anisotropic pressure coupling to the bluid background. The code is first benchmarked linearly for the ITPA-TAE as well as the experiment based AUG-NLED cases, obtaining good agreement to other codes. Then, it is applied to a high energetic particle pressure discharge in the ASDEX Upgrade tokamak using a realistic non-Maxwellian distribution of EPs, reproducing aspects of the experimentally observed instabilities. Non-linear applications are possible based on the implentation, but will require dedicated verification and validation left for future work.

physics.plasm-ph↗

arXiv2021

Complete 3D MHD simulations of the current quench phase of ITER mitigated disruptions

Complete 3D simulations of the current quench phase of ITER disruptions are key to predict asymmetric forces acting into the ITER wall. We present for the first time such simulations for ITER mitigated disruptions at realistic Lundquist numbers. For these strongly mitigated disruptions, we find that the edge safety factor remains above 2 and the maximal integral horizontal forces remain below 1 MN. The maximal integral vertical force is found to be 13 MN and arises in a time scale given by the resistive wall time as expected from theoretical considerations. In this respect, the vertical force arises after the plasma current has completely decayed, showing the importance of continuing the simulations also in the absence of plasma current. We conclude that the horizontal wall force rotation is not a concern for these strongly mitigated disruptions in ITER, since when the wall forces form, there are no remaining sources of rotation.

physics.plasm-ph↗

arXiv2021

A quasi-continuous exhaust scenario for a fusion reactor: the renaissance of small edge localized modes

Tokamak operational regimes with small edge localized modes (ELMs) could be a solution to the problem of large transient heat loads in future fusion reactors because they provide quasi-continuous exhaust while keeping a good plasma confinement. A ballooning mode mechanism near the last closed flux surface (LCFS) governed by an interplay of the pressure gradient and the magnetic shear there has been proposed for small ELMs in high density ASDEX Upgrade and TCV discharges. In this manuscript we explore different factors relevant for plasma edge stability in a wide range of edge safety factors by changing the connection length between the good and the bad curvature side. Simultaneously this influences the stabilizing effect of the local magnetic shear close to the LCFS as well as the $E \times B$ flow shear. Ideal ballooning stability calculations with the HELENA code reveal that small ELM plasmas are indeed unstable against ballooning modes very close to the LCFS but can exhibit second ballooning stability in the steep gradient region which correlates with enhanced confinement. We also present first non-linear simulations of small ELM regimes with the JOREK code including the $E \times B$ shear which indeed develop ballooning like fluctuations in the high triangularity limit. In the region where the small ELMs originate the dimensionless parameters are very similar in our investigated discharges and in a reactor, making this regime the ideal exhaust scenario for a future reactor.

physics.plasm-ph↗

arXiv2021

MHD simulations of small ELMs at low triangularity in ASDEX Upgrade

The development of small- and no-ELM regimes for ITER is a high priority topic due to the risks associated to type-I ELMs. By considering non-linear extended MHD simulations of the ASDEX Upgrade tokamak with the JOREK code, we probe a regime that avoids type-I ELMs completely provided that the separatrix density is high enough. The dynamics of the pedestal in this regime are observed to be qualitatively similar to the so-called quasi-continuous exhaust (QCE) regime in several ways. Repetitive type-I ELMs are substituted by roughly constant levels of outwards transport caused by peeling-ballooning modes (with dominant ballooning characteristics) which are localised in the last 5\% of the confined region (in normalised poloidal flux). The simulated low triangularity plasma transitions to a type-I ELMy H-mode if the separatrix density is sufficiently reduced or if the input heating power is sufficiently increased. The stabilising factors that play a role in the suppression of the small ELMs are also investigated by analysing the simulations, and the importance of including diamagnetic effects in the simulations is highlighted. By considering a scan in the pedestal resistivity and by measuring the poloidal velocity of the modes (and comparing to theoretical estimates for ideal and resistive modes), we identify the underlying instabilities as resistive peeling-ballooning modes. Decreasing the resistivity below experimentally-relevant conditions (i.e., going towards ideal MHD), the peeling-ballooning modes that constrain the pedestal below the type-I ELM stability boundary display sharply decreasing growth rates.

physics.plasm-ph↗