arXiv subjects

E. Nardon

Publications and source records attributed to E. Nardon.

At least 19 recordsLinked to original sources

arXiv2026

Runaway electron generation in ITER mitigated disruptions with improved physics models

We assess runaway-electron (RE) generation in ITER disruptions mitigated by shattered pellet injection (SPI) using improved physics modelling in the 1D disruption simulation framework Dream. To this end, we extend Dream with four ITER-relevant physics models: (i) a reduced model for RE scrape- off associated with the vertical plasma motion, (ii) a semi-analytical plasmoid- drift model for material deposition, (iii) an adaptive hyper-resistive transport model to suppress unphysical thin-current channels during the current quench (CQ), and (iv) an updated Compton RE generation seed calculated for the new ITER tungsten first-wall design. We simulate full-current 15 MA L-mode (H26, non-nuclear) and H-mode (DTHmode24, nuclear) scenarios, and an intermediate- current 7.5 MA H-mode non-nuclear case, from realistic ITER inputs. Complete avoidance of a multi-MA RE beam is found to require a long pre-thermal quench (TQ) duration to thermalize the hot-tail electrons, high deuterium assimilation with limited neon, and a representative seed current comparable to a single RE in ITER. As previously found with lower fidelity setups [Vallhagen et al, Nucl. Fusion 64 (2024)], these conditions are met by staggered or low-Ne injections in H26, but are typically violated in DT H-mode when nuclear seeds are present. In addition to analyzing the effect of the new models, we investigate the role of the current spike associated with the TQ and importance of radial transport of runaways in the CQ. After incorporating these additional physical effects into a comprehensive disruption model and analyzing their impact, we present a representative ITER DT H-mode SPI scenario which provides a theoretically viable route to tolerable RE currents in ITER fusion power operation.

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

Numerical model for pellet rocket acceleration in PELOTON

A direct numerical simulation model for the rocket acceleration of pellets in thermonuclear fusion devices has been developed for PELOTON, a 3D Lagrangian particle pellet code [R. Samulyak et al, Nuclear Fusion 61 (4), 046007 (2021)], and validated using shattered pellet injection (SPI) experiments in JET. The pellet rocket acceleration is driven by grad-B drift of the ablation cloud that creates asymmetry and non-uniform heating of the cloud. The model accounts for non-uniform charging of the ablation cloud by hot plasma electrons as well as local plasma gradients. The increased pressure on the high-field-side compared to the low-field-side leads to pellet (fragment) rocket acceleration. Pure deuterium and deuterium-neon mixture models have been implemented. The background plasma states have been obtained by using a new plasma cooling model for PELOTON. The cooling model distributes the ablated material within the corresponding flux volumes and accounts for ionization and other energy losses, Ohmic heating by toroidal currents, and the energy exchange between ions and electrons. Plasma profiles predicted by PELOTON cooling model have been compared with JOREK and INDEX simulations. PELOTON simulations of rocket acceleration and the corresponding trajectories of deuterium fragments are consistent with experimentally measured trajectories in JET. We show that composite deuterium-neon pellets containing 0.5% of neon experienced smaller deviation of their trajectories compared to the pure deuterium case. We simulate various spatial configurations of pellet fragments and demonstrate the cloud overlap impact on rocket acceleration. Additionally, we demonstrate the effect of plasma state gradients on the rocket acceleration. Future work will focus on the rocket acceleration of SPI in projected ITER plasmas and the development of the corresponding scaling law for the rocket acceleration.

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

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↗

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

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 Alfv\'en wave (SAW) packets from both ends of the plasmoid (``SAW braking'') and the development of external resistive currents along magnetic field lines (``P\'egouri\'e 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 P\'egouri\'e 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

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↗

arXiv2021

Collisional-radiative non-equilibrium impurity treatment for JOREK simulations

A collisional-radiative non-equilibrium impurity treatment for JOREK 3D nonlinear magneto-hydrodynamic (MHD) simulations has been developed. The impurities are represented by super-particles flowing along the fluid velocity field lines, while ionizing and recombining independently according to ADAS data and local fluid density and temperature. The non-equilibrium impurity contributions are then projected back to the fluid field for self-consistent time evolution. A 2D test case is used to compare the new non-equilibrium impurity model against previous Coronal Equilibrium (CE) impurity treatment, as well as to compare the non-equilibrium impurity behavior between the single and the two temperature model. Further, we conduct benchmark with previously published coronal non-equilibrium results by other 3D nonlinear MHD codes such as M3D-C1 and NIMROD. The new non-equilibrium treatment is shown to successfully capture the early phase cooling by weakly ionized impurities which the CE model missed. The benchmarks with M3D-C1 and NIMROD show general agreement in both the integrated quantities and the 2D profile evolution, despite the difference in the atomic model used. The above comparison and benchmark cases demonstrate the capability of the non-equilibrium impurity model for JOREK, paving the way for more sophisticated 3D non-linear Massive Material Injection (MMI) simulations which have important applications in disruption mitigation studies.

physics.plasm-ph↗

arXiv2021

Latest results on quiescent and post-disruption runaway electron mitigation experiments at Frascati Tokamak Upgrade

Results from the last FTU campaigns on the deuterium large (wrt FTU volume) pellet REs suppression capability, mainly due to the induced burst MHD activity expelling REs seed are presented for discharges with 0.5 MA and 5.3T. Clear indications of avalanche multiplication of REs following single pellet injection on 0.36 MA flat-top discharges is shown together with quantitative indications of dissipative effects in terms of critical electrical field increase due to fan-like instabilities. Analysis of large fan-like instabilities on post-disruption RE beams, that seem to be correlated with low electrical field and background density drops, reveal their strong RE energy suppression capability suggesting a new strategy for RE energy suppression controlling large fan instabilities. We demonstrate how such density drops can be induced using modulated ECRH power on post-disruption beams.

physics.plasm-ph↗

arXiv2020

Radiation asymmetry and MHD destabilization during the thermal quench after impurity Shattered Pellet Injection

The radiation response and the MHD destabilization during the thermal quench after a mixed species Shattered Pellet Injection (SPI) with impurity species neon and argon are investigated via 3D non-linear MHD simulation using the JOREK code. Both the $n=0$ global current profile contraction and the local helical cooling at each rational surface caused by the pellet fragments are found to be responsible for MHD destabilization after the injection. Significant current driven mode growth is observed as the fragments cross low order rational surfaces, resulting in rapidly inward propagating stochastic magnetic field, ultimately causing the core temperature collapse. The Thermal Quench (TQ) is triggered as the fragments arrive on the $q=1$ or $q=2$ surface depending on the exact $q$ profile and thus mode structure. When injecting from a single toroidal location, strong radiation asymmetry is found before and during the TQ as a result of the unrelaxed impurity density profile along the field line and asymmetric outward heat flux. Such asymmetry gradually relaxes over the course of the TQ, and is entirely eliminated by the end of it. Simulation results indicate that the aforementioned asymmetric radiation behavior could be significantly mitigated by injection from toroidally opposite locations, provided that the time delay between the two injectors is shorter than $1ms$. It is also found that the MHD response are sensitive to the relative timing and injection configuration in these multiple injection cases.

physics.plasm-ph↗

arXiv2020

Fast plasma dilution in ITER with pure Deuterium Shattered Pellet Injection

JOREK 3D non-linear MagnetoHydroDynamic (MHD) simulations of pure Deuterium Shattered Pellet Injection in ITER are presented. It is shown that such a scheme could allow diluting the plasma by more than a factor 10 without immediately triggering large MHD activity, provided the background impurity density is low enough. This appears as a promising strategy to reduce the risk of hot tail Runaway Electron (RE) generation and to avoid RE beams altogether in ITER, motivating further studies in this direction.

physics.plasm-ph↗

arXiv2020

Post-Thermal Quench Shattered Pellet Injection for small Runaway Electron seed depletion in ITER

The possibility of using Shattered Pellet Injection(s) after the Thermal Quench phase of an ITER disruption in order to deplete Runaway Electron (RE) seeds before they can substantially avalanche is studied. Analytical and numerical estimates of the required injection rate for shards to penetrate into the forming RE beam and stop REs are given. How much material could be assimilated before the Current Quench (CQ) becomes too short is also estimated. It appears that, if Hydrogen pellets were used, the required number of pellets to be injected during the CQ would be prohibitive, at least considering the present design of the ITER Disruption Mitigation System (DMS). For Neon or Argon, the required number of pellets, although large, might be within reach of the ITER DMS, but the assimilated fraction would have to be very small. Other materials may be better suited but would require a modification of the ITER DMS.

physics.plasm-ph↗

arXiv2020

Understanding the reduction of the edge safety factor during hot VDEs and fast edge cooling events

In the present work a simple analytical approach is presented in order to clarify the physics behind the edge current density behaviour of a hot plasma entering in contact with a resistive conductor. When a plasma enters in contact with a highly resistive wall, large current densities appear at the edge of the plasma. The model shows that this edge current originates from the plasma response, which attempts to conserve the poloidal magnetic flux ($Ψ$) when the outer current is being lost. The loss of outer current is caused by the high resistance of the outer current path compared to the plasma core resistance. The resistance of the outer path may be given by plasma contact with a very resistive structure or by a sudden decrease of the outer plasma temperature (e.g. due to a partial thermal quench or due to a cold front penetration caused by massive gas injection). For general plasma geometries and current density profiles the model shows that given a small change of minor radius ($δa$) the plasma current is conserved to first order ($δI_p = 0 + \mathcal{O}(δa^2)$). This conservation comes from the fact that total inductance remains constant ($δL = 0$) due to an exact compensation of the change of external inductance with the change of internal inductance ($δL_\text{ext}+δL_\text{int} = 0$). As the total current is conserved and the plasma volume is reduced, the edge safety factor drops according to $q_a \propto a^2/I_p$. Finally the consistency of the resulting analytical predictions is checked with the help of free-boundary MHD simulations.

physics.plasm-ph↗

arXiv2019

First predictive simulations for deuterium shattered pellet injection in ASDEX Upgrade

First simulations of deuterium shattered pellet injection (SPI) into an ASDEX Upgrade H-Mode plasma with the JOREK MHD code are presented. Resistivity is increased by one order of magnitude in most simulations to reduce computational costs and allow for extensive parameter scans. The effect of various physical parameters onto MHD activity and thermal quench (TQ) dynamics is studied and the influence of MHD onto ablation is shown. TQs are obtained quickly after injection in most simulations with a typical duration of 100 microseconds, which slows down at lower resistivity. Although the n=1 magnetic perturbation dominates in the simulations, toroidal harmonics up to n=10 contribute to stochastization and stochastic transport in the plasma core. The post-TQ density profile remains hollow for a few hundred microseconds. However, when flux surfaces re-form around the magnetic axis, the density has become monotonic again suggesting a beneficial behaviour for runaway electron avoidance/mitigation. With $10^{21}$ atoms injected, the TQ is typically incomplete and triggered when the shards reach the q=2 rational surface. At a larger number of injected atoms, the TQ can set in even before the shards reach this surface. For low field side injection considered here, repeated formation of outward convection cells is observed in the ablation region reducing material assimilation. Responsible is a sudden rise of pressure in the high density cloud when the stochastic region expands further releasing heat from the hot core. After the TQ, strong sheared poloidal rotation is created by Maxwell stress, which contributes to re-formation of flux surfaces.

physics.plasm-ph↗

arXiv2014

Non-linear Simulations of MHD Instabilities in Tokamaks Including Eddy Current Effects and Perspectives for the Extension to Halo Currents

The dynamics of large scale plasma instabilities can strongly be influenced by the mutual interaction with currents flowing in conducting vessel structures. Especially eddy currents caused by time-varying magnetic perturbations and halo currents flowing directly from the plasma into the walls are important. The relevance of a resistive wall model is directly evident for Resistive Wall Modes (RWMs) or Vertical Displacement Events (VDEs). However, also the linear and non-linear properties of most other large-scale instabilities may be influenced significantly by the interaction with currents in conducting structures near the plasma. The understanding of halo currents arising during disruptions and VDEs, which are a serious concern for ITER as they may lead to strong asymmetric forces on vessel structures, could also benefit strongly from these non-linear modeling capabilities. Modeling the plasma dynamics and its interaction with wall currents requires solving the magneto-hydrodynamic (MHD) equations in realistic toroidal X-point geometry consistently coupled with a model for the vacuum region and the resistive conducting structures. With this in mind, the non-linear finite element MHD code JOREK has been coupled with the resistive wall code STARWALL, which allows to include the effects of eddy currents in 3D conducting structures in non-linear MHD simulations. This article summarizes the capabilities of the coupled JOREK-STARWALL system and presents benchmark results as well as first applications to non-linear simulations of RWMs, VDEs, disruptions triggered by massive gas injection, and Quiescent H-Mode. As an outlook, the perspectives for extending the model to halo currents are described.

physics.plasm-ph↗

arXiv2013

Characteristics of X-point Lobe Structures in Single-Null Discharges on MAST

Lobe structures due to the application of resonant magnetic perturbations (RMPs) have been observed using wide-angle imaging of light from He1+ ions in the vicinity of the lower X-point in MAST. The data presented are from lower single-null discharges where RMPs of toroidal mode number, n, of 4 and 6 were applied. It has been found that, above a threshold value, the lobe structures extend radially, linearly with the coil current, both in L-mode and H-mode. It is observed that after the application of the RMP, as the toroidal rotation in the confined plasma decreases, the lobes extend radially, suggesting the plasma is less effectively screening the RMP field. Comparing the imaging data with results from vacuum modelling shows that this technique can accurately predict the number and poloidal location of the lobes, but over-estimates their radial extent. More accurate estimates of the extent of the lobes can be made by accounting for plasma screening of the RMP field. Qualitative agreement between simulation and experiment is found if it is assumed that the RMP penetrates 2% in normalised radius from the last closed flux surface.

physics.plasm-ph↗