Three-dimensional modeling of sputtered materials transport in diagnostic ducts of fusion devices

MHD stability limits in the TCV tokamak

Safe and reliable operation is still one of the major challenges in the development of the new generation of ITER-like fusion reactors. The deposited plasma energy during major disruptions, edge-localized modes (ELMs) and vertical displacement events (VDEs) causes significant surface erosion, possible structural failure and frequent plasma contamination. While plasma disruptions and ELM will have no significant thermal effects on the structural materials or coolant channels because of their short deposition time, VDEs having longer-duration time could have a destructive impact on these components. Therefore, modelling the response of structural materials to VDE has to integrate detailed energy deposition processes, surface vaporization, phase change and melting, heat conduction to coolant channels and critical heat flux criteria at the coolant channels. The HEIGHTS 3D upgraded computer package considers all the above processes to specifically study VDE in detail. Results of benchmarking with several known laboratory experiments prove the validity of HEIGHTS implemented models. Beryllium and tungsten are both considered surface coating materials along with copper structure and coolant channels using both smooth tubes with swirl tape insert. The design requirements and implications of plasma facing components are discussed along with recommendations to mitigate and reduce the effects of plasma instabilities on reactor components.

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

Full tokamak discharge simulation and kinetic plasma profile control for ITER

One of the critical technological challenges of future tokamak fusion devices is the ability for plasma-facing components to handle both normal and abnormal plasma/surface interaction events that compromise their lifetime and operation of the machine. Under normal operation plasma/surface interactions that are important include: sputtering, particle implantation and recycling, He pumping and ELM (edge localized modes)-induced erosion. In abnormal or off-normal operation: disruptions and vertical displacement events (VDEs) are important. To extend PFC lifetime under these conditions, liquid-metals have been considered as candidate PFCs (Plasma-Facing Components), including: liquid lithium, tin-lithium, gallium and tin.Liquid lithium has been measured to have nonlinear increase of physical sputtering with rise in temperature. Such increase can be a result of exposure to ELM-level particle fluxes. The significant increase in particle flux to the divertor and nearby PFCs can enhance sputtering erosion by an order of magnitude or more. In addition from the standpoint of hydrogen recycling and helium pumping liquid lithium appears to be a good candidate plasma-facing material (PFM). Advanced designs of first wall and divertor systems propose the application of liquid-metals as an alternate PFC to contend with high-heat flux constraints of large-scale tokamak devices. Additional issues include PFC operation under disruptions and long temporal instabilities such as VDEs. A comprehensive two-fluid model is developed to integrate core and SOL (scrape-off layer) parameters during ELMs with PFC surface evolution using the HEIGHTS package. Special emphasis is made on the application of lithium as a candidate plasma-facing liquid-metal.

In recent years, the nonlinear 3D magnetohydrodynamic codes JOREK, M3D-C1, and NIMROD developed the capability of modeling realistic 3D vertical displacement events (VDEs) including resistive walls. In this paper, a comprehensive 3D VDE benchmark is presented between these state-of-the-art codes. The simulated case is based on an experimental NSTX plasma but with a simplified rectangular wall. There are differences between the physics models and numerical methods, and the VDE evolution leads to sensitivities on the initial conditions that cannot be avoided as can be done in edge localized modes (ELM) and sawtooth simulations (due to the non-cyclical nature of VDEs). Nonetheless, the comparison serves to quantify the level of agreement in the relevant quantities used to characterize disruptions, such as the 3D wall forces and energy decay. The results bring confidence regarding the use of the mentioned codes for disruption studies, and they distinguish aspects that are specific to the models used (e.g., reduced vs full MHD models). The simulations show important 3D features for a NSTX plasma, such as the self-consistent evolution of the halo current and the origin of the wall forces. In contrast to other reduced MHD models based on an ordering in the aspect ratio, the ansatz-based JOREK reduced MHD model allows capturing many aspects of the 3D dynamics even in the spherical tokamak limit considered here.

It has been found that the plasma flow generated by quasistationary plasma accelerators can be used for simulation of high energy plasma interaction with different materials of interest for fusion experiments. It is especially important for the studies of the processes such as ELMs (edge localized modes), plasma disruptions and VDEs (vertical displacement events), during which a significant part of the confined hot plasma is lost from the core to the SOL (scrape off layer) enveloping the core region. Experiments using plasma guns have been used to assess erosion from disruptions and ELMs. Namely, in this experiment modification of different targets, like tungsten, molybdenum, CFC and silicon single crystal surface by the action of hydrogen and nitrogen quasistationary compression plasma flow (CPF) generated by magnetoplasma compressor (MPC) has been studied. MPC plasma flow with standard parameters (1 MJ/m2 in 0.1 ms) can be used for simulation of transient peak thermal loads during Type I ELMs and disruptions. Analysis of the targets erosion, brittle destruction, melting processes, and dust formation has been performed. These surface phenomena are results of specific conditions during CPF interaction with target surface. The investigations are related to the fundamental aspects of high energy plasma flow interaction with different material of interest for fusion. One of the purposes is a study of competition between melting and cleavage of treated solid surface. The other is investigation of plasma interaction with first wall and divertor component materials related to the ITER experiment.

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.

Simulation of damage to tokamaks plasma facing components during intense abnormal power deposition

Can tokamaks PFC survive a single event of any plasma instabilities?

Resonant magnetic perturbations are used to stabilize plasma edge instabilities, so-called edge localized modes (ELMs), in high-performance (H-mode) plasmas explored for fusion energy. These ELMs cause repetitive outburst of confined energy and particles and cause cyclic loading of plasma facing components (PFCs). This endangers the integrity of the PFCs and hence limits the lifetime and hence commercial viability of fusion. It was shown that these ELMs can be stabilized by application of small amplitude resonant magnetic perturbation (RMP) fields. This removes the ELMs as edge instabilities but also induces three-dimensional (3D) effects to the plasma boundary, which was formerly toroidally axisymmetric. The impact of this 3D perturbation on the plasma boundary solution needs to be understood to extrapolate the effects to ITER and towards a fusion reactor, if ELM control by RMP fields would be utilized.

Off normal operating conditions resulting from plasma instabilities such as disruptions, edge-localized modes (ELM), and vertical displacement events (VDE) in tokamaks are to be expected with the potential of high energy deposition on plasma facing components (PFC). This high-energy dump in short duration, will result in extremely high temperatures of the PFC leading to melting and evaporation of the surfaces. Erosion resulting from these processes is life-limiting for the PFC as well as potential plasma contamination and degradation of performance. A comprehensive understanding based on the interplay of all physical processes during plasma instabilities on the divertor plate is necessary in order to improve reliability and characterize the performance of this key component. A novel particle-in-cell (PIC) technique has been developed and integrated into the existing HEIGHTS package in order to verify and have another perspective in assessing these problems.The HEIGHTS multi-dimensional integrated models take into account different stages of the plasma material interaction and its evolution along time. The extent of the damage will essentially depend on the intensity and duration of energy deposited on PFC. Both bulk and surface damages can take place depending on these parameters. For this reason different deposition times have been considered ranging from several microseconds to tens of milliseconds in order to provide comprehensive evolution of material erosion and transport. Comparison of the newly implemented PIC methods with current HEIGHTS existing models are discussed.

Summary form only given. Plasma instabilities such as disruptions, edge-localized modes (ELM), and vertical displacement events (VDE) in tokamaks are the biggest concern for the design and performance of plasma facing component (PFC). These life threatening events are characterized by high-energy dump in short durations, resulting in extremely high temperatures of the PFC that can cause melting, evaporation of the surfaces and eventual contamination of the plasma. Erosion resulting from these processes can be significant and potentially prevent successful operations of the reactor and shorten PFC lifetime.Comprehensive models and simulation efforts are developed and integrated into the well-known and well benchmarked HEIGHTS package using a novel particle-in-cell (PIC) technique in order to characterize the performances of the divertor and reactor walls. The package has several self consistent models that integrate different stages of plasma material interaction during plasma instabilities. Plasma energy deposition, divertor/wall material erosion, and vapor plasma evolution are calculated for the predicted disruption parameters in ITER-like geometry. Photon radiation, its transport and deposition around the divertor area are also calculated. The multi-dimensional models take into account different stages of plasma material interaction and its evolution along time. The extent of the damage depends on the intensity of plasma energy deposited and the time of the deposition since both bulk and surface damages can take place depending on these parameters. For this reason different deposition times for the instability events have been considered ranging from fractions of milliseconds a hundred milliseconds in order to provide comprehensive evolution of material erosion and transport. Simulation results of the integrated modeling show clearly that a single plasma disruption event can cause a significant local damage of the divertor plate, therefore severely limiting the component lifetime. Comparison with other numerical methods and recent experiments are also analyzed and discussed.

In this paper, the thermal–mechanical responses of the first wall (FW) composed of pure tungsten (W) and China Low Activation Martensitic steel in China Fusion Engineering Test Reactor are predicted under the normal state and the transient events, i.e., major disruption (MD), vertical displacement events (VDEs) and edge localized modes (ELMs), using finite element method (FEM). The temperature distribution in the armor material and structural material is predicted and analyzed, and the temperature induced thermal stress is obtained through a fully coupled thermal-stress analysis module. The comparative simulation results reveal that the short duration time of MD and ELMs have less thermal/mechanical effects on the FW than that of the long deposition time of VDEs.

Vertical displacement events: A serious concern in future ITER operation