Vertical Displacement Events Research Articles

Electromagnetic stress analysis of RMP coils during VDEs of the HL-2M tokamak

During tokamak vertical displacement events (VDEs), due to the rapid movement of plasma and rapidly decreasing current, induced currents appear in surrounding conductive components, including Resonant Magnetic Perturbation (RMP) coils. The electromagnetic load caused by the VDEs induced currents constitutes a threat for RMP coils as well as related components. Here the stress condition resulting from the aforementioned electromagnetic load in HL-2M, a large tokamak being assembled at Southwestern Institute of Physics of China, is analyzed using ANSYS. Engineered design of RMP coils in HL-2M is verified, and regions of stress concentration are noticed. To reduce analyzing complexity, a specific method aiming at calculating the transient electromagnetic load on local components around the plasma is proposed. Finite element analysis (FEA), application of Visual Basic Script (VBS) language in ANSYS Maxwell software, and data processing in MATLAB have been used in this analysis.

Dynamic behaviour of DEMO vacuum vessel during plasma vertical displacement events

In tokamaks during plasma vertical displacement events (VDEs) electrical currents occur in the vacuum vessel (VV) and in the in-vessel components (IVCs) that interact with the strong magnetic field generating large electromagnetic (EM) loads. The aim of the present work is the evaluation of the peak displacements and accelerations of the DEMO VV in case of VDEs. Four types of VDEs are investigated that are specified to generate the most severe net loads. The assessment considers also the electromagnetic-mechanical coupling between the VV and the toroidal field (TF) coils whose characteristic stiffness and damping coefficients were determined through a transient EM analysis. In a second step a transient dynamic analysis was performed using a structural finite element (FE) model of the VV to evaluate the displacement and acceleration peaks during the VDEs in relevant locations of the VV.

Overview of disruptions with JET-ILW

The paper presents an analysis of disruptions occurring during JET-ILW plasma operations covering the period from the start of ILW (ITER-like wall) operation up to completion of JET operation in 2016. The total number of disruptions was 1951 including 466 with deliberately induced disruptions. The average rate of unintended disruptions was 16.1 %, which is significantly above the ITER target at 15 MA. The pre-disruptive plasma parameters are: plasma current Ip = (0.82–3.38) MA, toroidal field BT = (0.98–3.4) T, safety factor q95 = (1.52–9.05), plasma internal inductance li = (0.58–1.86), Greenwald density limit fraction FGWL = (0.04–1.61), with 720 X-point plasma pulses from a subset of 1420 unintended disruption shots. Massive gas injection (MGI) has been routinely used in protection mode both to terminate pulses when the plasma is at risk of disruption and to mitigate against disruption effects. The MGI was mainly triggered by the n = 1 locked mode (LM) amplitude exceeding a threshold or by the disruption itself, namely, either dIp/dt (specifically, a fast drop in Ip) or the toroidal loop voltage exceeding threshold values. For mitigation purposes, only the LM was used as a physics precursor and threshold on the LM signal was used to trigger the MGI prior to disruption. Long lasting LM (≥ 100 ms) do exist prior to disruption in 75% of cases. However, 10% of non-disruptive pulses have a LM which eventually vanished without disruption. The plasma current quench (CQ) may result in 3D configurations, termed as asymmetrical disruptions, which are accompanied by sideways forces. Unmitigated vertical displacement events (VDEs) generally have significant plasma current toroidal asymmetries. Unmitigated non-VDE disruptions also have large plasma current asymmetries presumably because there is no plasma vertical position control during the CQ and so they too are subject to large vertical displacements. MGI is a reliable tool to mitigate 3D effects and correspondingly sideways forces during the CQ. The vessel structure loads depend on the force impulse and force time behaviour, including their rotation. The toroidal rotation of 3D configuration may cause resonance with the natural frequencies of the vessel components in large tokamaks such as ITER. The JET-ILW amplitude-frequency interdependence of toroidal rotation of 3D configurations is presented.

An insight on beryllium dust sources in the JET ITER-like wall based on numerical simulations

After vertical displacement events (VDEs) in the JET-ILW tokamak, debris is produced in liquid form and ejected from the vessels beryllium upper dump plates (UDPs). Most of the droplets splash near the UDPs outboard tile 8 as documented by an in-vessel photographic survey. Moreover, the systematic collection of ‘dust’ from the main chamber and the divertor region provides evidence of small solid spherical Be particles and flat splats (with fairly circular, ‘pancake-like’, or elongated shapes) related to melting events (with a diameter of few µm prior the deposition). The migration of metallic Be is studied with the numerical code DUSTTRACK, capable of describing the full droplet dynamics in a non-stationary tokamak plasma configuration. The description of the JET plasma during the VDE proposed here allows for a sufficiently consistent reconstruction of the transient conditions of the background plasma, relying on actual physical measurements. Due to the lack of experimental data related to the initial properties of the ejecta, the statistically relevant sample of 4×105 particles was considered in the DUSTTRACK simulations. A reasonable fit of the initial parameters for the ejected droplets, as well as the time-dependent plasma parameters for the VDE resulted in good qualitative agreement with the post-mortem experimental findings from dust collectors and with the Be deposition pattern near UDPs on the low-field side.

Analysis of stress induced by plasma disruption on vacuum vessel through multi-physics modeling

Abstract The analysis of the stresses induced on the vacuum vessel (VV) of a Tokamak and its internal components by the plasma instabilities, such as plasma disruptions, also following a Vertical Displacement Event (VDE), is one of the major concern in the Tokamak mechanical design. So the availability of a fast simulation tool for evaluating the different design options and also able to perform parametric analysis is highly attractive to define the project requirements and to verify the conceptual design. To respond to this wish, a methodology based on the multi-physics modeling capability offered by the Comsol® software platform was developed. It consists in coupled simulations based on the data sharing between two 2D axisymmetric models, everyone coupled with two corresponding 3D models shifted each other of 10 degrees. In the 2D axisymmetric model of every couple, the magnetic and electric fields generated by the plasma VDE and disruption are calculated imposing the plasma time evolution as input. In the corresponding 3D model only the metallic structures are present and on them the Electric and Magnetic fields are extruded, determining so the induced currents diffusion in the passive conductors. Then the resulting Lorentz’s forces are imposed as body loads on the mechanical structures, so a linear stress analysis can be carried out after the constraints assignment. The same procedure is followed with the second couple of 2D/3D models for check purposes, comparing some proper physical quantities, such as the total induced current flowing on the VV. In this paper the methodology is presented by reporting the simulation of a double null plasma VDE, lasting c.a. 100 ms, followed by a full 5.5 MA plasma current quench in about 40 ms, in a medium size Tokamak intended for experimental research purposes.

European DEMO first wall shaping and limiters design and analysis status

Abstract The anticipated heat flux limit of the European DEMO first wall is ∼1−2 MW/m2. During transient and off normal events, the heat load deposited on the wall would be much larger than the steady state heat load and exceed the first wall limit, therefore the breeding blanket first wall needs to be protected. This involves dedicated discrete limiters in certain regions of the machine that would take the brunt of the heat load as well as adequate shaping of the first wall. The current concept envisages limiters at a few (3–4) equatorial ports to cope with the ramp-up of the plasma; upper limiters (in ∼8 upper ports) are considered for upward vertical displacement events. Two design options have been considered for these limiters: a modular design where the limiter plasma facing components are attached to individual plates that are assembled together so that transient electromagnetic loads can be reduced, and in case of damage the plates can be replaced/repaired individually; and a divertor-like design where the plasma facing components are attached to a single Eurofer cassette. Other limiters considered include inner wall limiters in case of plasma contraction and lower limiters may be needed for downward vertical displacement events. The thermal hydraulic finite element analysis results show that the integrity of the cooling pipes can be maintained during the anticipated transient events. The limiters are considered to be sacrificial and designed to be replaceable independently from the breeding blanket system. The design has to allow that installation, removal or replacement of the limiters can be performed remotely. Strategy to tackle outstanding issues and required R&D is also discussed.

Preliminary Design of DSMs for ITER Upper Ports #02 and #08 Integration

Since 2014, Budker Institute of Nuclear Physics (BINP) SB RAS has been working on the design of ITER upper port-plugs (UPPs) #02 and #08. The design of upper diagnostic shielding modules (DSMs) for UP #02 and UP #08 has been performed using CATIA v5.0. DSMs represent a welded structure made of stainless steel SS316L(N)-IG. Cooling water channels to be performed use the unique gundrilling technology. The main conception of structural design of DSMs is in good agreement with ITER recommendations. The engineering calculations of DSM structure were done to demonstrate the sufficient strength of the considered design under thermal (normal operation and baking), electromagnetic (vertical displacement event (VDE) II), and seismic (SL-2) loads. To prove the satisfaction of upper DSMs design to ITER requirements, the load combination dead weight (DW) + normal operation (NO) + SL-1 + VDE II numerical simulations were performed. Further studies of the modular design will be optimized for the use of standardized boron carbide shielding trays.

Magnetically Guided Liquid Metal Divertor (MAGLIMD) with Resilience to Disruptions and ELMs

An innovative concept for power and particle removal from the divertor is proposed. This scheme takes full advantage of both liquid metal convection and conduction to remove heat from the divertor, which is the most difficult issue for fusion reactor design. We propose that a liquid metal (LM) should replace the solid divertor plates on the bottom of the vacuum vessel. The LM is continuously supplied from openings located at the inner separatrix strike point on the floor of the LM container on the bottom of the vacuum vessel, and exhausted from openings located at the outer separatrix strike point on the floor of the LM container. The LM flow is guided along the field line to reduce MHD drag. In the event of a disruption, the current induced in the LM during the current quench is in the same direction of the plasma current. The induced LM current would either attract the plasma toward the LM divertor (leading to a benign Vertical Displacement Event), or force the LM toward the core plasma, providing automatic disruption mitigation, not requiring a learning process. The use of liquid tin instead of liquid lithium would provide greater stability against Rayleigh-Taylor and Kelvin-Helmholtz instabilities in quiescent plasmas.

Analysis method for magneto-mechanical coupled vibration of the in-vessel structures considering halo current effect and application to HL-2M tokamak

Abstract The tokamak in-vessel structures serve in strong magnetic fields. During plasma disruptions such as the vertical displacement events, the induced eddy current and the injected halo current in in-vessel structures cause the vibration of the plasma-facing components. The vibration is coupled to the magnetic field in the form of the motional eddy current. Such magneto-mechanical coupling effect may have a considerable influence on the dynamic mechanical behavior of the in-vessel structures. This paper presents a numerical approach to analyze this magneto-mechanical coupled problem based on the hybrid method of the finite element and boundary element formulation. The plasma current and the halo current are taken into account in a form of a series of movable current filaments and a pair of current source and sink. The proposed approach is applied to the numerical analysis of a simplified model of the vacuum vessel of HL-2 M tokamak under an l -mode plasma disruption. Simulation results show that the vibration is strongly damped and the maximum vertical displacement is reduced by around 30 % when considering the magneto-mechanical coupling.

Eddy Current Analysis of TF Coil Case for EAST

Plasma major disruptions and plasma vertical displacement events represent two extreme examples of fast transient electromagnetic processes, which will induce large current and electromagnetic loads that exceed those of loads during magnet normal operation and seismic loads. Eddy current and electromagnetic loads of the conducting structures need to be analyzed to verify the mechanical reliability of the tokamak during these transients. An integrated module, which consists of the mechanical design of the three-dimensional computer-aided design (CAD) solid modeling, generation of the finite element modeling, and external parameters input into the module, was integrated to perform the calculation of the electromagnetic loads and power losses. The developed integrated module can be used to calculate the Eddy current, electromagnetic forces, and power losses of the toroidal field (TF) coil-case for EAST tokamak during plasma disruptions and vertical displacement events. The simplified geometric model with 22.5° sector for EAST tokamak was used in view of the toroidal symmetry. The plasma current and position as functions of time are given by the numerical method. In this article, the module integration and evaluation of the electromagnetic loads and power losses on the conducting structures of the EAST tokamak by the finite element methods are described.

A Real-Time Disruption Prediction Tool for VDE on EAST

Vertical displacement event (VDE) is one of the most important events related to disruptions. A real-time disruption prediction tool for VDE is presented in this article. Vertical growth rate is an essential parameter to describe vertical instability, which can be obtained based on the rigid plasma response model. A real-time vertical growth rate calculation system is built, which utilizes graphics process unit (GPU) parallel computation and reflective memory (RFM) boards communication with plasma control system (PCS). Based on real-time vertical growth rate calculation system, an alarm algorithm for detecting vertical instability is integrated into experimental advanced superconducting tokamak (EAST) PCS. It is designed to provide the capabilities of a switching control method and to trigger a warning signal in PCS when uncontrollable vertical instability is detected. Such a disruption prediction tool has been preliminarily applied in the 2019 EAST spring experiment.

Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1, NIMROD, and JOREK

A benchmark exercise for the modeling of vertical displacement events (VDEs) is presented and applied to the 3D nonlinear magnetohydrodynamic codes M3D-C1, JOREK, and NIMROD. The simulations are based on a vertically unstable NSTX equilibrium enclosed by an axisymmetric resistive wall with a rectangular cross section. A linear dependence of the linear VDE growth rates on the resistivity of the wall is recovered for sufficiently large wall conductivity and small temperatures in the open field line region. The benchmark results show good agreement between the VDE growth rates obtained from linear NIMROD and M3D-C1 simulations and from the linear phase of axisymmetric nonlinear JOREK, NIMROD, and M3D-C1 simulations. Axisymmetric nonlinear simulations of a full VDE performed with the three codes are compared, and an excellent agreement is found regarding the plasma location and plasma currents, as well as eddy and halo currents in the wall.

Reduction of asymmetric wall force in JET and ITER disruptions including runaway electrons

It was shown that asymmetric vertical displacement event disruptions in JET and ITER do not produce a large asymmetric force on conducting structures surrounding the plasma, provided that the current quench (CQ) time is less than the resistive wall penetration time. This is verified with JET data. In ITER, the CQ is expected to be comparable to the resistive wall penetration time, which gives a small wall force. It is shown that runaway electrons (REs) in JET do not produce a large wall force, and this is verified with JET data. This occurs if the RE current is about half of the initial plasma current. In ITER, the RE current might be comparable to the initial current, and REs might lengthen the CQ time sufficiently to produce a large wall force.

First wall energy deposition during vertical displacement events on ITER

The beryllium (Be) first wall energy deposition and melt damage profiles resulting from the current quench phase of an unmitigated, 5 MA/1.8 T upward vertical displacement event for ITER are investigated. Time dependent 2D magnetic flux profiles are calculated with the DINA code and used as input for the SMITER 3D field line tracing software. 3D maps of the wetted area and perpendicular heat flux show that the majority of the energy deposition occurs on the upper first wall panels #8 and #9. SMITER simulations predict on the surfaces of upper FWPs #8 and #9 at the end of the ∼450 ms current quench. The surface heat flux maps generated by SMITER are used as input in the MEMOS-U code, which models Be melt formation and dynamics. Simulations reveal peak surface temperatures of ∼2200 K, inward surface damage of ∼0.5 mm in depth, and average melt velocities of ∼2 m s−1. Although VDEs are in principle the easiest disruptive instability to avoid, the analysis demonstrates that any non-mitigated events or intentional VDEs taking place during low Ip, early operational phases of ITER for the purposes of estimating disruption forces, must be kept to a low number.

Simulation of disruptions triggered by Vertical Displacement Events (VDE) in tokamak and leading edge effect in plasma energy deposition to material surfaces

The paper describes two major non-linear properties of the vertical instability of a tokamak plasma, which has a vertical elongation: (a) inductive excitation of surface (edge) currents stabilizing the instability and converting it into fast equilibrium evolution, and (b) creation of a wetting zone without the normal component of the magnetic field when the plasma has contact with material surfaces. Two major disruption effects for both mitigated and non-mitigated disruptions, important for JET and ITER, were considered: (a) excitation of vertical disruption during the current quench (i.e., abnormal plasma current ramp down) and (b) related to the wetting zone, potential leading edge effect in plasma energy deposition to the in-vessel tiles during disruptions. Our considerations together with a 2-D version of the VDE (Vertical Disruption Event) code are based on a new mathematical model, called Tokamak MHD (TMHD), as a replacement for the conventional model, a model that cannot solve numerical problems related to extreme plasma anisotropy and negligible mass. The code includes a 3-D model of surface currents on a thin conductive wall and has a well-specified algorithm for extension to vertical disruptions that excite asymmetric kink modes.

Vertical forces during vertical displacement events in an ITER plasma and the role of halo currents

Vertical displacement events (VDEs) can occur in elongated tokamaks causing large currents to flow in the vessel and other adjacent metallic structures. To better understand the potential magnitude of the associated forces and the role of the so called ‘halo currents’ on them, we have used the M3D-C1 code to simulate potential VDEs in ITER. We used actual values for the vessel resistivity and pre-quench temperatures and, unlike most of the previous studies, the halo region is naturally formed by triggering the thermal quench with an increase in the plasma thermal conductivity. We used the 2D non-linear version of the code and vary the post-thermal quench thermal conductivity profile as well as the boundary temperature in order to generate a wide range of possible cases that could occur in the experiment. We also show that, for a similar condition, increasing the halo current does not increase the total force on the wall since it is offset by a decrease in the toroidal contribution.

Electromagnetic-mechanical coupling method and stress evaluation of the Chinese Fusion Engineering Test Reactor helium cooled solid breeder under a vertical displacement event scenario

The helium cooled solid breeder (HCSB) blanket is one of the candidate blanket schemes proposed for the Chinese Fusion Engineering Test Reactor (CFETR). Plasma vertical displacement events (VDE) are considered to be important for evaluating the structural integrity of the blanket. The change of the magnetic field caused by the movement of the plasma and the rapid loss of current induces extra electromagnetic loads, which will cause significant structural damage to the blanket. This study aims to investigate the electromagnetic-mechanical coupling method and the coupling effects on the HCSB under plasma VDE. Based on the design of the HCSB for the CFETR, a finite element model is established by using the MAXWELL software, in which 69 current filaments are used to describe the plasma. The distribution of the induced current and magnetic field inside the HCSB under the plasma VDE, as well as the electromagnetic force are obtained by the ANSYS finite element software. Meanwhile, the distributions of stress inside each component of the blanket are obtained under electromagnetic-structure load and an evaluation of the stress is carried out. The results show that the existing design meets the requirements when plasma VDE occurs.

The thermal stability of dispersion-strengthened tungsten as plasma-facing materials: a short review

One key challenge for the development of fusion energy is plasma-facing materials. Tungsten-based materials are promising candidates for plasma-facing components (PFCs) in the magnetic confinement nuclear fusion reactors because of their high melt temperature, high-thermal conductivity, high-thermal load resistance, low tritium retention, and low sputtering yield. In fusion reactors, PFCs are exposed to high-thermal flux, because there are some transient events such as plasma disruptions, edge-localized modes, and vertical displacement events (VDEs). Especially, in VDEs, a heat flux of 10–100 MW m−2 with duration of milliseconds-to-several seconds can induce recrystallization and then change the microstructure of tungsten-based plasma-facing materials, leading to instability of microstructures. Then, a significant degradation of material properties is caused such as a reduction of mechanical strength and fracture toughness, a rise in the ductile-to-brittle-transition temperature well, and decrease of irradiation/high-thermal load resistance. Therefore, many efforts were devoted to improve the thermal stability of tungsten-based materials as high as possible, such as oxide dispersion strengthening, carbide dispersion strengthening, and K bubbles dispersion strengthening. Here, the thermal stabilities of various dispersion-strengthened tungsten materials are reviewed by evaluating their recrystallization temperature and the corresponding hardness evolutions. In addition, the possible development trends are proposed.

Simulations of plasma disruptions in ITER due to ingress of Be

ITER plasma will be surrounded by the first wall, which is mostly blankets made of beryllium (Be) and divertor plates made of tungsten (W). When the plasma is subjected to vertical displacement events (VDEs), it could come in contact with these first wall materials—be it in the upper dome during upward-moving VDEs or radial plasma movements and W divertor in the downward-moving VDEs. We investigate in this paper specifically the first case of plasma moving upwards, hitting the top dome and ejecting a small piece of Be. The piece of Be falls freely through the plasma, ablating as it moves down causing the plasma temperature to crash, although in a rather slow process of few hundred milliseconds, finally creating plasma disruption and generating a runway current. This whole scenario is simulated using the tokamak simulation code. We have also carried out preliminary simulation studies of possible mitigation of the runaways generated following the Be ingress through injection of deuterium pellets.

Simulating the nonlinear interaction of relativistic electrons and tokamak plasma instabilities: Implementation and validation of a fluid model

For the simulation of disruptions in tokamak fusion plasmas, a fluid model describing the evolution of relativistic runaway electrons and their interaction with the background plasma is presented. The overall aim of the model is to self-consistently describe the nonlinear coupled evolution of runaway electrons (REs) and plasma instabilities during disruptions. In this model, the runaway electrons are considered as a separate fluid species in which the initial seed is generated through the Dreicer source, which eventually grows by the avalanche mechanism (further relevant source mechanisms can easily be added). Advection of the runaway electrons is considered primarily along field lines, but also taking into account the E×B drift. The model is implemented in the nonlinear magnetohydrodynamic (MHD) code jorek based on Bezier finite elements, with current coupling to the thermal plasma. Benchmarking of the code with the one-dimensional runaway electron code go is done using an artificial thermal quench on a circular plasma. As a first demonstration, the code is applied to the problem of an axisymmetric cold vertical displacement event in an ITER plasma, revealing significantly different dynamics between cases computed with and without runaway electrons. Though it is not yet feasible to achieve fully realistic runaway electron velocities close to the speed of light in complete simulations of slowly evolving plasma instabilities, the code is demonstrated to be suitable to study various kinds of MHD-RE interactions in MHD-active and disruption relevant plasmas.