Nina Schwarz

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 (FL), main fragment arrival (MFA), plasma movement event (PME), MARFE, thermal quench (TQ)/plasma current spike (IP-spike), current quench (CQ), and vertical displacement event (VDE) 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) → concave (well mitigated/radiation dominated). Depending on the injection, pre-TQ durations between 15 and 0.5 ms and early CQ durations ( Δ t CQ 100 → 80 ) between 13.3 and 8.2 ms had been achieved at AUG.

Transient phenomena and their control are of high relevance in magnetic confinement fusion plasmas to guarantee a stable and safe plasma operation. Interpretative simulations can maximize the insights gained from experiments on present machines and predictive simulations can help in the preparation of design, mitigation techniques and operational scenarios for future devices. In this article, we provide an overview of recent advances and novel scientific results obtained with the 3D non-linear hybrid fluid-kinetic code JOREK, covering physics of plasma transients from the core to the scrape-off layer (SOL) both for tokamak and stellarator devices. Substantial progress was made in the physics understanding, model validation with experiments and experiment interpretation, thus, giving confidence for predictions to devices like DTT, ITER and DEMO. The topics addressed comprise a wide range: the edge physics of new operation scenarios and edge localized mode suppression; major disruptions with a focus on runaway electrons and vertical displacement events as well as disruption mitigation by shattered pellet injection; the physics mechanisms and operational limits of the flux pumping regime for sawtooth control; MHD limits of stellarators and work towards incorporating advanced edge/SOL/exhaust dynamics; continuing improvements of the code for more efficient hybrid simulations on conventional and accelerated high performance computing architectures.

The transition of the Divertor Tokamak Test (DTT) facility from its initial commissioning phase (Day-0 scenario, plasma current Ip=2 MA) to the full power scenario, characterized by its highest nominal plasma current (Ip=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 (Gav≈1.3×105) to convert an initial 5.5 A seed current into macroscopic RE beams of ≈0.7 MA when large amounts of impurities are present. For even higher RE seeds, the RE current can peak at ≈3.2 MA, constituting up to ≈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.

The possibility of describing the magnetic field due to currents within a finite control volume via an equivalent surface current distribution on the boundary of such volume is given by the well-known Virtual Casing Principle. This has been illustrated and implemented in the past for the case of solenoidal currents in the volume of interest, i.e. when the currents to represent have a null normal component to the boundary of the control volume. Here, we illustrate how to apply and implement the Virtual Casing Principle for the more general case where the currents to represent can cross the boundary.

Transient magneto-hydrodynamic (MHD) events like edge localized modes (ELMs) or disruptions are a concern for magnetic confinement fusion power plants. Research with the MHD code JOREK towards understanding control of such instabilities is reviewed here in a concise way to provide a complete overview, while we refer to the original publications for details. Experimental validation for unmitigated vertical displacement events progressed. The mechanism of vertical force mitigation by impurity injection was identified. Two-way eddy current coupling to CARIDDI was completed. Shattered pellet injection was simulated in JET, KSTAR, ASDEX Upgrade (AUG) and ITER. Benign runaway electron beam termination in JET and ITER was studied. Coupling of kinetic REs to the MHD is ongoing and a virtual RE synchrotron radiation diagnostic was developed. Regarding pedestal physics, regimes devoid of large ELMs in AUG were simulated and predictive JT60-SA simulations are ongoing. For ELM suppression by resonant magnetic perturbations (RMPs), AUG, ITER and EAST simulations were performed. A free boundary RMP model was validated against experiments. Evidence for penetrated magnetic islands at the pedestal top based on AUG experiments and simulations was found. Simulations of the naturally ELM-free quiescent H-mode in AUG and HL-3 show external kink mode formation prevents pedestal build-up towards an ELM within windows of the edge safety factor. With kinetic neutral particles, high field side high density formation in ITER was simulated and with kinetic impurities, tungsten transport in AUG RMP plasmas was studied. To capture turbulent transport, electro-static full-f particle in cell models for ion temperature gradient and trapped electron modes were established and benchmarked. Application to RMP plasmas shows enhanced turbulence in comparison to unperturbed states. Energetic particle interactions with MHD were studied. Flux pumping that prevents the safety factor on axis from dropping below unity was simulated. First non-linear stellarator applications include current relaxation in l = 2 stellarators, while verification for advanced stellarators progresses.

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.

In this paper, we revisit the physics of mitigated and unmitigated vertical displacement events (VDEs) and present a summary of present modelling efforts and code capabilities. While 3D MHD simulations of VDEs for AUG and JET are now approaching realistic plasma parameters (e.g. resistivity) and getting closer to experimental observations (e.g. CQ times and vessel forces), the time scales of ITER VDEs (∼500 ms) are still out of computational reach. Therefore, re-scaling of plasma parameters, model simplifications or demanding matrix pre-conditioning techniques are required. We describe such techniques and compare AUG, JET and ITER unmitigated VDE simulations in terms of the dynamics of the CQ and total vacuum vessel forces. In JET simulations, the safety factor (q ₉₅) falls to unity during the current quench, which destabilizes a 1/1 kink mode. On the other hand, in AUG and ITER simulations, MHD activity is more effective preventing the drop of q ₉₅, leading to comparatively smaller forces in these devices. We will also discuss the applicability of axisymmetric plasma simulations and their success on simulating mitigated disruptions. Finally we review the remaining modelling challenges and future plans for unmitigated disruptions. For example, MHD codes need to improve their scrape-off-layer modelling, such as including the limitation of the halo current to the ion saturation current. Although crucial, this remains numerically challenging even for axisymmetric simulations.

The self-consistent electromagnetic integration of tokamak plasma magnetohydrodynamic (MHD) models with external conductors is considered in this manuscript. We integrate the extended MHD code JOREK and the eddy current code CARIDDI, via a scheme based on the virtual casing principle enabling two-way coupled fully implicit simulations. The robustness of this new integrated tool is validated against JOREK-STARWALL and CarMa0NL simulations for vertical displacement events in a simplified ASDEX Upgrade-like geometry and for n = 1 tearing modes in a circular high-aspect-ratio tokamak. The impact of 3D wall structures on the plasma evolution is highlighted introducing ports at different locations of a simplified axisymmetric wall and characterizing its effect on the plasma evolution. In addition to realistically capturing the 3D interactions between plasma and wall structures, the coupled codes will allow in the future 1:1 comparisons to experiments using virtual magnetic diagnostics that capture screening effects accurately.

Disruptions lead to a rapid loss of thermal and magnetic energy and can cause large heat loads, mechanical forces, and the excitation of a beam of relativistic runaway electrons. The operation of tokamaks at high energy and plasma current requires the use of a mitigation system to limit such detrimental effects. Mitigation techniques rely mainly on the injection of a large amount of impurities to radiate the majority of the thermal and magnetic energies. Heat loads and electro-magnetic (EM) forces as well as their toroidal asymmetries can be greatly reduced by such measures. In this paper, a theory is lined out to explain the reduction of the global vertical force based on large toroidal halo currents that keep the current centroid stationary in the midplane. As a consequence, the vertical current moment, which is linked to the EM-force, is reduced. The theory is backed up by experimental observations in shattered pellet injection mitigated vertical displacement event experiments in ASDEX Upgrade (AUG) and JET as well as by 2D simulations with the extended MHD code JOREK. Scans in the boundary heat flux are carried out to estimate the correct scrape-off layer temperature and the influence of the fraction of conducted energy. Finally, predictive simulations for ITER confirm the reduction of the vertical force by the injection of impurities.