arXiv subjects

the JOREK team

Publications and source records attributed to the JOREK team.

13 recordsLinked to original sources

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

3D modelling of thermal loads during unmitigated vertical displacement events in ITER and JET

Predicting three-dimensional thermal loads during tokamak disruptions is essential for ITER yet remains weakly developed. We present a physics-based workflow that couples MHD simulations of vertical displacement events with field line tracing on a realistic 3D first wall model and a transient wall thermal response. The approach is validated against JET discharges with beryllium main chamber armour, reproducing key global dynamics, non-axisymmetric current features, and the occurrence (or absence) of melting, thereby building confidence in the methodology. We then apply the same workflow to ITER-relevant conditions with tungsten (W) armour, consistent with the new 2024 ITER re-baseline, to assess disruption heat loads and their 3D localization. The resulting analysis demonstrates the resilience of the ITER W first wall against these events and provides predictions for the energy deposition and current flow profiles. Beyond these studies, the workflow enables scenario-by-scenario estimates of disruption-induced thermal loading, allowing to assess the disruption-budget consumption for these events in future devices.

physics.plasm-ph↗

arXiv2025

A comparison of low-n Mercier unstable Wendelstein stellarators and quasi-interchange modes in tokamaks

Mercier's criterion is typically enforced as a hard operational limit in stellarator design. At the same time, past experimental and numerical studies have shown that this limit may often be surpassed, though the exact mechanism behind this nonlinear stability is not well understood. This work aims to contribute to our current understanding by comparing the nonlinear evolution of Mercier unstable Wendelstein stellarators to that of nonlinearly stable quasi-interchange modes in tokamaks. A high mirror, very low $ι$, W7-X-like configuration is first simulated. A second case is then considered using experimental reconstructions of intermediate $β$ W7-AS discharges, where saturated low-n modes were observed experimentally, with sustained MHD signatures over tens of milliseconds. The possible reasons for the discrepancies between experiment and simulation, and the observation of partial reconnection in contrast to flux pumping are discussed, in view of reproducing and designing for operation of stellarators beyond the Mercier stability limit.

physics.plasm-ph↗

arXiv2025

Quantitative Magnetohydrodynamic Modelling of Flux Pumping in ASDEX Upgrade

The sawtooth-free hybrid scenario has been achieved recently in ASDEX Upgrade (AUG) with applied non-inductive current sources and auxiliary heating [A. Burckhart et al 2023 Nucl. Fusion 63 126056]. Control experiments in AUG suggest that the self-regulating magnetic flux pumping mechanism, characterized by anomalous current redistribution, is responsible for clamping the central safety factor (q_0) close to unity, thereby preventing the sawtooth onset. This work presents a numerical and theoretical investigation of flux pumping in the AUG hybrid scenario based on the two-temperature, visco-resistive, full magnetohydrodynamic (MHD) model with the JOREK code. To quantitatively model the flux pumping, we choose realistic parameters, plasma configurations, and source terms based on AUG experiments. During the initial saturation stage of the unstable 1/1 quasi-interchange mode (on millisecond timescales), q_0 exhibits fast under-damped oscillation and reaches a value closer to unity, which is attributed to the self-regulation of core plasma and the fast dynamo effect on the order of V/m. On the longer resistive diffusion timescale of seconds, the slow negative dynamo effect on the order of mV/m induced by the 1/1 MHD instability plays an effective role in flux pumping, which provides quantitative agreement with experimental observations for the first time. The final saturated 1/1 MHD instability exhibits features of the quasi-interchange mode and tearing mode, and the associated convective plasma flow velocity is a few m/s. The toroidal negative electric field from the slow dynamo dominantly offsets the positive current drive and continuously redistributes the current density and pressure. As a result, q_0 is maintained close to unity due to the low-shear profiles of current density and pressure in the plasma core, and the system enters a sawtooth-free and quasi-stationary helical state.

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

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

Probing non-linear MHD stability of the EDA H-mode in ASDEX Upgrade

Regimes of operation in tokamaks that are devoid of large ELMs have to be better understood to extrapolate their applicability to reactor-relevant devices. This paper describes non-linear extended MHD simulations that use an experimental equilibrium from an EDA H-mode in ASDEX Upgrade. Linear ideal MHD analysis indicates that the operational point lies slightly inside of the stable region. The non-linear simulations with the visco-resistive extended MHD code, JOREK, sustain non-axisymmetric perturbations that are linearly most unstable with toroidal mode numbers of n = \{6 \dots 9\}, but non-linearly higher and lower n become driven and the low-n become dominant. The poloidal mode velocity during the linear phase is found to correspond to the expected velocity for resistive ballooning modes. The perturbations that exist in the simulations have somewhat smaller poloidal wavenumbers (k_θ \sim 0.1 to 0.5 cm^{-1} ) than the experimental expectations for the quasi-coherent mode in EDA, and cause non-negligible transport in both the heat and particle channels. In the transition from linear to non-linear phase, the mode frequency chirps down from approximately 35 kHz to 13 kHz, which corresponds approximately to the lower end of frequencies that are typically observed in EDA H-modes in ASDEX Upgrade.

physics.plasm-ph↗

arXiv2022

Modelling of saturated external MHD instabilities in tokamaks: a comparison of 3D free boundary equilibria and nonlinear stability calculations

3D free boundary equilibrium computations have recently been used to model external kinks and edge harmonic oscillations (EHOs), comparing with linear MHD stability codes, and nonlinear analytic theory [Kleiner et al, PPCF 61 084005 (2019)]. In this study, results of the VMEC equilibrium code are compared further with nonlinear reduced MHD simulations, using the JOREK code. The purpose of this investigation is to understand the extent to which the modelling approaches agree, and identify the important physical effects which can modify the dynamics. For the simulated external kink, which is dominated by a single toroidal harmonic, good agreement is found when a large Lundquist number is used in the JOREK simulation, such that resistive effects are sub-dominant. Modelling EHOs where multiple toroidal harmonics are linearly unstable, the saturated perturbation observed can differ in the dominant toroidal harmonic. On the ideal timescale, a n=2 EHO is observed in JOREK, while the saturated perturbation predicted by VMEC is a n=1 mode. Extending simulations into timescales where resistive effects can play a role, similar n=1 perturbations can be found. The coupling of different linearly unstable toroidal harmonics in the JOREK simulation broadens the magnetic energy spectrum and ergodises the plasma edge region, resulting in a more localised pressure perturbation. These effects are not observed in VMEC, because closed magnetic flux surfaces are enforced. Despite the sensitivity of JOREK results on the assumed resistivity, saturated states can be found using both approaches that are in reasonable agreement, even for this more advanced case.

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

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↗

arXiv2021

Comparing spontaneous and pellet-triggered ELMs via non-linear extended MHD simulations

Injecting frozen deuterium pellets into an ELMy H-mode plasma is a well established scheme for triggering edge localized modes (ELMs) before they naturally occur. Based on an ASDEX Upgrade H-mode plasma, this article presents a comparison of extended MHD simulations of spontaneous type-I ELMs and pellet-triggered ELMs allowing to study their non-linear dynamics in detail. In particular, pellet-triggered ELMs are simulated by injecting deuterium pellets into different time points during the pedestal build-up described in [A. Cathey et al. Nuclear Fusion 60, 124007 (2020)]. Realistic ExB and diamagnetic background plasma flows as well as the time dependent bootstrap current evolution are included during the build-up to capture the balance between stabilising and destabilising terms for the edge instabilities accurately. Dependencies on the pellet size and injection times are studied. The spatio-temporal structures of the modes and the resulting divertor heat fluxes are compared in detail between spontaneous and triggered ELMs. We observe that the premature excitation of ELMs by means of pellet injection is caused by a helical perturbation described by a toroidal mode number of n = 1. In accordance with experimental observations, the pellet-triggered ELMs show reduced thermal energy losses and narrower divertor wetted area with respect to spontaneous ELMs. The peak divertor energy fluency is seen to decrease when ELMs are triggered by pellets injected earlier during the pedestal build-up.

physics.plasm-ph↗

arXiv2020

Non-linear extended MHD simulations of type-I edge localised mode cycles in ASDEX Upgrade and their underlying triggering mechanism

A triggering mechanism responsible for the explosive onset of edge localised modes (ELMs) in fusion plasmas is identified by performing, for the first time, non-linear magnetohydrodynamic simulations of repetitive type-I ELMs. Briefly prior to the ELM crash, destabilising and stabilising terms are affected at different timescales by an increasingly ergodic magnetic field caused by non-linear interactions between the axisymmetric background plasma and growing non-axisymmetric perturbations. The separation of timescales prompts the explosive, i.e. faster than exponential, growth of an ELM crash which lasts ${\sim}$ 500 $μ$s. The duration and size of the simulated ELM crashes compare qualitatively well with type-I ELMs in ASDEX Upgrade. As expected for type-I ELMs, a direct proportionality between the heating power in the simulations and the ELM repetition frequency is obtained. The simulations presented here are a major step forward towards predictive modelling of ELMs and of the assessment of mitigation techniques in ITER and other future tokamaks.

physics.plasm-ph↗