Plasma Disruptions In Tokamaks Research Articles

Peridynamic modelling of cryogenic deuterium pellet fragmentation for shattered pellet injection in tokamaks

Abstract Shattered pellet injection (SPI) is a promising method for controlling plasma disruptions in tokamaks. In this study, we present numerical modelling of the fragmentation of cryogenic deuterium pellets within the context of SPI, using the peridynamic (PD) theory. A dedicated in-house code has been developed, leveraging the meshfree method and GPU parallelization. The mechanical properties of cryogenic solid deuterium are obtained from available literature, and calibrated based on the shatter threshold along with the remaining solid mass fraction after shatter. The results from the bond-based peridynamics (BB-PD) successfully reproduce the main experimental results reported in the literature, both qualitatively and quantitatively.

Eddy current actuated fast valve development for disruption mitigation applications

Shattered Pellet Injection (SPI) is a common technique used in Disruption Mitigation Systems to prevent or minimize the effect of plasma disruptions in Tokamaks. To operate an SPI system, a fast-acting valve is needed for accelerating pellets. An eddy current actuated high-pressure fast valve was developed in 2021, dedicated to the SPI system of the ITER DMS Support Laboratory at the Centre for Energy Research. Based on the experiences of SPI operation, a novel fast valve has been developed to improve durability and reliability, while the design has been simplified in terms of manufacturing and assembly aspects. The results of the development and laboratory testing of this novel eddy current actuated fast valve are discussed in this contribution.

Effects of radiation from tungsten impurities on the thermal energy loss during the fast thermal quench stage of major disruption in tokamak plasmas

Recent studies based on the PLT, EAST, WEST, ASDEX-upgrade, JET and other tokamaks have shown that the accumulation of heavy impurities in the core regime is unavoidable, which may lead to the degradation of the plasma confinement and even trigger the major disruptions. The plasma thermal energy loss during the major disruptions mainly occurs during the fast thermal quench (TQ) stage. However, there is no comprehensive physical explanation for the scaling of the timescale of this stage. Tungsten as high <i>Z</i> impurity, which will be used as the wall material in International Thermonuclear Experimental Reactor (ITER), has strong radiation power, and may affect the thermal energy loss during the fast TQ. This work considers both the thermal diffusion induced by the stochastic magnetic fields and the radiation from tungsten impurities as the dominant thermal loss mechanisms in this stage, and construct a one-dimensional model of electron temperature evolution in tokamak plasmas. We numerically calculate and analyze the evolution of the electron temperature in this stage with the typical ITER-like parameters, and here are our main conclusions: 1) The order of magnitude of the fast TQ timescale is mainly determined by the level of thermal diffusion. However, the radiation from tungsten impurities can quantitively influence on the timescale of fast TQ and the electron temperature in the late phase of fast TQ. The higher the tungsten concentration, the shorter the TQ timescale and the lower the electron temperature it will lead to in the late phase. Both the numerical and analytical results show that the timescale is approximately linear with the tungsten impurity concentration. 2) Based on the evolution of the global energy loss and the global power loss during the fast TQ, it can be found that the global thermal energy loss via the radiation from tungsten impurities is much smaller than that via the thermal diffusion induced by the stochastic magnetic fields during the early phase of fast TQ stage. However, in the late phase of fast TQ stage, the global radiation power can be comparable to or even greater than that of the global thermal diffusion power. This is also the reason why the electron temperature in the late phase of fast TQ decreases as the concentration of tungsten impurities increases. Therefore, the contribution of the radiation from tungsten impurities to the thermal loss cannot be ignored in the late phase of fast TQ.

Tokamak plasma disruption precursor onset time study based on semi-supervised anomaly detection

Plasma disruption in tokamak experiments is a challenging issue that causes damage to the device. Reliable prediction methods are needed, but the lack of full understanding of plasma disruption limits the effectiveness of physics-driven methods. Data-driven methods based on supervised learning are commonly used, and they rely on labelled training data. However, manual labelling of disruption precursors is a time-consuming and challenging task, as some precursors are difficult to accurately identify. The mainstream labelling methods assume that the precursor onset occurs at a fixed time before disruption, which leads to mislabeled samples and suboptimal prediction performance. In this paper, we present disruption prediction methods based on anomaly detection to address these issues, demonstrating good prediction performance on J-TEXT and EAST. By evaluating precursor onset times using different anomaly detection algorithms, it is found that labelling methods can be improved since the onset times of different shots are not necessarily the same. The study optimizes precursor labelling using the onset times inferred by the anomaly detection predictor and test the optimized labels on supervised learning disruption predictors. The results on J-TEXT and EAST show that the models trained on the optimized labels outperform those trained on fixed onset time labels.

ORNL Progress in Disruption Mitigation Technology in Support of ITER

The mitigation of plasma disruptions in tokamaks has become a very important topic in magnetic fusion research, motived by the potential challenges that may occur in ITER disruptions due to the high magnetic field and high plasma current. Such disruptions can have a deleterious effect on the internal components due to the fast dissipation of the plasma thermal energy and the magnetic stored energy leading to large forces, as well as the possible formation of several megaamperes of energetic runaway electrons during the current quench. Oak Ridge National Laboratory has been developing and deploying technology to inject material into the plasma to rapidly radiate the thermal energy and start a fast plasma current ramp down to dissipate the magnetic stored energy. The choice of materials to inject and the injection technology have evolved over the past decades to arrive at the present systems planned for ITER based on cryogenic pellets of hydrogen-neon mixtures for thermal mitigation and hydrogen pellets for runaway electron mitigation. This scheme injects shattered cryogenic material into the plasma from pellets formed in situ in a pipe gun and fired onto angled metal surfaces at the end of the injection line just before entering the plasma. In this paper, we describe the evolution of schemes and technologies that have been employed for disruption mitigation and runaway electron prevention and dissipation, discuss how they have performed in present-day experiments, and give the outlook for the use of this technology in a burning plasma and how it may continue to evolve in the future.

Initial analytical theory of plasma disruption and experimental evidence

It is a great physical challenge to achieve controlled nuclear fusion in magnetic confinement tokamak and solve energy shortage problem for decades. In tokamak plasma, large-scale plasma instability called disruption will halt power production of reactor and damage key components. Prediction and prevention of plasma disruption is extremely urgent and important. However, there is no analytical theory can elucidate plasma disruption physical mechanism yet. Here we show an analytical theory of tokamak plasma disruption based on nonextensive geodesic acoustic mode theory, which can give the physical mechanism of disruption. The proposed theory has not only been confirmed by experimental data of disruption on T-10 device, but also can explain many related phenomena around plasma disruption, filling the gap in physical mechanism of tokamak plasma disruption.

Disruption avoidance by stabilizing coupled MHD modes using resonant magnetic perturbations on J-TEXT

The coupling of multiple magnetohydrodynamic (MHD) modes can lead to mode locking and major disruption in tokamak plasmas. In the J-TEXT tokamak, the coupling between two small modes, i.e. m/n = 2/1 and 3/1 modes (m and n are poloidal and toroidal mode numbers, respectively), appears when the edge safety factor is reduced to the vicinity of 3. After the mode coupling, the toroidal phase difference between the 2/1 and 3/1 modes equals 0 in the low field side midplane. This phase relation of coupled modes leads to mutual destabilization and even major disruption. A control scheme to avoid disruption caused by coupled modes by resonant magnetic perturbations (RMPs) is presented. It is found that the application of RMP significantly changes the evolution of the coupled modes. The coupling of the 2/1 and 3/1 modes occurs earlier as the RMP amplitude increases. The RMP with moderate amplitude can suppress the growth of 2/1 and 3/1 coupled modes and hence avoid disruption. These results provide a possible strategy for the suppression of neoclassical tearing mode (NTM) seed islands on International Thermonuclear Experimental Reactor (ITER) or future fusion reactors.

Numerical Study on the Effect of Plasma Density on Runaway Electron Suppression in the ADITYA-U Tokamak

Runaway Electrons (REs) generated during plasma disruptions in fusion grade tokamaks have the potential to severely damage the plasma-facing components. Designing optimal plasma discharge scenarios for RE suppression in future experiments requires interpretative modeling of current experiments. Multiple experiments have been carried out on ADITYA-U tokamak to design optimal plasma discharge scenarios for RE avoidance and suppression. In this article, we have numerically studied two representative pairs of ADITYA-U plasma discharges. In the first pair of discharges, plasma density was increased by gas puffs during the flap-top phase which is shown to suppress RE generation. In the second pair of the representative discharges, the effect of a lower ratio of peak electric field during breakdown to the pre-fill pressure is shown on RE generation. We simulate these plasma discharges using the PREDICT code to study the dynamics of Res. The results are consistent with the experimental Hard X-Ray diagnostic observations for both the pair of representative discharges. Additionally, the lowest RE-current is obtained in the discharges with a low ratio of the peak electric field during breakdown to the pre-fill pressure and high plasma density during the flap-top phase due to gas puffs. The suppression of REs is demonstrated by showing the effect of increasing plasma density on the separatrix in momentum space between thermal electrons and REs.

Comparison of unfolding methods for the inference of runaway electron energy distribution from γ-ray spectroscopic measurements

Unfolding techniques are employed to reconstruct the 1D energy distribution of runaway electrons from Bremsstrahlung hard X-ray spectrum emitted during plasma disruptions in tokamaks. Here we compare four inversion methods: truncated singular value decomposition, which is a linear algebra technique, maximum likelihood expectation maximization, which is an iterative method, and Tikhonov regularization applied to χ 2 and Poisson statistics, which are two minimization approaches. The reconstruction fidelity and the capability of estimating cumulative statistics, such as the mean and maximum energy, have been assessed on both synthetic and experimental spectra. The effect of measurements limitations, such as the low energy cut and few number of counts, on the final reconstruction has also been studied. We find that the iterative method performs best as it better describes the statistics of the experimental data and is more robust to noise in the recorded spectrum.

Demonstration of Safe Termination of Megaampere Relativistic Electron Beams in Tokamaks.

For the first time it is experimentally demonstrated on the JET tokamak that a combination of a low impurity concentration bulk plasma and large magnetohydrodynamic instabilities is able to suppress relativistic electron beams without measurable heat loads onto the plasma facing components. Magnetohydrodynamic simulations of the instability and modeling of the postinstability plasma confirm the prompt loss of runaways and the absence of regeneration during the final current collapse. These surprising findings motivate a new approach to dissipate runaway electrons generated during tokamak plasma disruptions.

Analysis of the Shattered Pellet Injection Fragment Plumes Generated by Machine Specific Shatter Tube Designs

Shattered pellet injector systems have been installed on DIII-D, JET, and KSTAR and used to experimentally determine the effectiveness of the shattered pellet injection (SPI) process in mitigating the deleterious effects of a tokamak plasma disruption. Pellets are fired, and before entering the plasma, strike a bent tube known as a shatter tube causing the pellet to shatter. The process of pellet fragmentation is a chaotic process that can be described in terms of fragment size distribution through a statistical model that incorporates the effects of the pellet material and impact characteristics. In addition to the fragment size distribution, the shatter plume has other characteristics of interest, such as a fragment velocity distribution and temporal mass evolution. The fragment velocity distribution is important because it is needed to accurately model the spread and location of the ablation and the deposition of impurities in the plasma over time. The temporal mass evolution is necessary to determine the time-resolved delivery of mass to the plasma. Due to installation constraints, the shatter tube currently installed on JET has a unique geometry with a modest S-bend followed by a 20-deg bend at the end of the tube. The DIII-D and KSTAR shatter tube design is a simple tube bent through an angle of 20 deg followed by a straight section. The resulting shatter sprays from the JET shatter tube and a 20-deg miter bend shatter tube were experimentally characterized for various pellet materials and speeds. Laboratory testing of these shatter tubes allows for the use of fast cameras to capture the fragment spray traveling through a large vacuum chamber. These high-speed videos of the shatter plumes allow the fragment size distribution, temporal mass evolution, and velocity distribution of the fragments within the plume to be determined. This paper presents a comparison of the unique geometry of the JET shatter tube to the miter bend geometries used for shattering and some insight into the variables that may be adjusted to produce the optimal shatter spray. The impact of entrained propellant gas on the resulting shatter spray was examined during testing.

Characterization of the plasma current quench during disruptions in ADITYA tokamak

The rate of plasma current-quench during tokamak plasma disruptions determines the electromagnetic forces on the in-vessel components/vacuum vessel. Also halo currents and rapid changes of poloidal field due to the plasma vertical displacement contribute to loads on vessel and in-vessel components and hence needs to be studied thoroughly to safeguard these tokamak peripherals. The plasma current quench occurrence during the spontaneous major disruption has been investigated for a set of ADITYA tokamak disrupted discharges and average plasma current quench and instantaneous current quench rates have been estimated. The fastest area-normalized plasma current (IP) quench time is observed to be ∼5 ms m−2. The estimated post disruption plasma electron temperatures (PDET) are observed to be ∼15–35 eV and proportional to area-normalized plasma current quench time. Further analysis of several disruptive discharges of ADITYA tokamak reveal that the current quench time is inversely proportional to the pre-disruptive values of edge safety factor, qa, and the current quench properties are strongly correlated with the prevailing pre-disruptive plasma magnetohydrodynamic (MHD) activities. For larger values of pre-disruptive qa, the larger island widths of m= 2 and m = 3 MHD modes leads to a significant overlap of these islands. Such an overlap along with the deeper locations of the islands inside the plasma column, as compared to discharges having smaller values of pre-disruptive qa, seems to facilitate the faster current quench.

Kinetic modelling of runaway electron generation in argon-induced disruptions in ASDEX Upgrade

Massive material injection has been proposed as a way to mitigate the formation of a beam of relativistic runaway electrons that may result from a disruption in tokamak plasmas. In this paper we analyse runaway generation observed in eleven ASDEX Upgrade discharges where disruption was triggered using massive gas injection. We present numerical simulations in scenarios characteristic of on-axis plasma conditions, constrained by experimental observations, using a description of the runaway dynamics with a self-consistent electric field and temperature evolution in two-dimensional momentum space and zero-dimensional real space. We describe the evolution of the electron distribution function during the disruption, and show that the runaway seed generation is dominated by hot-tail in all of the simulated discharges. We reproduce the observed dependence of the current dissipation rate on the amount of injected argon during the runaway plateau phase. Our simulations also indicate that above a threshold amount of injected argon, the current density after the current quench depends strongly on the argon densities. This trend is not observed in the experiments, which suggests that effects not captured by zero-dimensional kinetic modelling – such as runaway seed transport – are also important.

Simulation of the electromagnetic wall response during Vertical Displacement Events (VDE) in ITER tokamak

The key basis for tokamak plasma disruption modeling is to understand how currents flow to the plasma facing surfaces during plasma disruption events. In ITER tokamak, the occurrence of a limited number of major disruptions will definitively damage the chamber with no possibility to restore the device. In the current exchange plasma-wall-plasma, according to the Helmholtz decomposition theorem, our surface current density in the conducting shell - the unknown of our problem - being a vector field twice continuously differentiable in 3D, has been splited into two components: an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field. Developing a weak formulation form and minimizing the correspondent energy functionals in a Finite Element approach, we have obtained the space and time distribution of the surface currents. We verified successfully our numerical simulation with an analytical solution with pure homogeneous Neumann B.C. and satisfying the necessary existence condition. By considering the iron core presence in JET tokamak, we have split the magnetization currents - the unknowns in some integral equations - into two components, the first producing a magnetic field in the iron region only and the second producing a magnetic field in the vacuum, obtaining thus a better evaluation of the influence of the iron core on the plasma equilibrium. To reduce the influence of the singularities appearing during the surface currents determination in multiply connected domains (L-shaped domains) we have used a conformal transformation method.

Interpretation of machine-learning-based disruption models for plasma control

While machine learning techniques have been applied within the context of fusion for predicting plasma disruptions in tokamaks, they are typically interpreted with a simple ‘yes/no’ prediction or perhaps a probability forecast. These techniques take input signals, which could be real-time signals from machine diagnostics, to make a prediction of whether a transient event will occur. A major criticism of these methods is that, due to the nature of machine learning, there is no clear correlation between the input signals and the output prediction result. Here is proposed a simple method that could be applied to any existing prediction model to determine how sensitive the state of a plasma is at any given time with respect to the input signals. This is accomplished by computing the gradient of the decision function, which effectively identifies the quickest path away from a disruption as a function of the input signals and therefore could be used in a plasma control setting to avoid them. A numerical example is provided for illustration based on a support vector machine model, and the application to real data is left as an open opportunity.

Influence of high power density plasma irradiation on the boron carbide coating on tungsten

The paper considers an influence of T-10 tokamak plasma disruption on boron carbide (B4C) coating on tungsten. The power density of coating irradiation reached 100 MW/m2. The relief and composition of the boron carbide coating sample areas heated up to different temperature due to influence of disruption is determined. Conclusion is made that B4C does not change integrity, when heated to temperatures of up to 2000 K. Local melting was observed in areas heated up to 2500 K. In the range of 2500–3600 K most of the coating was melted and collected into droplets. Composition rate is reduced to B:C = 1:1. In all temperature ranges the coating remained continuous and provided protection of tungsten from direct plasma irradiation.

Electromagnetic thin-wall model for simulations of plasma wall-touching kink and vertical modes

The understanding of plasma disruptions in tokamaks and predictions of their effects require realistic simulations of electric current excitation in three-dimensional vessel structures by the plasma touching the walls. As discovered at JET in 1996 (Litunovski JET Internal Report contract no. JQ5/11961, 1995; Noll et al., Proceedings of the 19th Symposium on Fusion Technology, Lisbon (ed. C. Varandas & F. Serra), vol. 1, 1996, p. 751. Elsevier) the wall-touching kink modes are frequently excited during vertical displacement events and cause large sideways forces on the vacuum vessel which are difficult to withstand in large tokamaks. In disruptions, the sharing of electric current between the plasma and the wall plays an important role in plasma dynamics and determines the amplitude and localization of the sideways force (Riccardo et al., Nucl. Fusion, vol. 40, 2000, p. 1805; Riccardo & Walker, Plasma Phys. Control. Fusion, vol. 42, 2000, p. 29; Zakharov, Phys. Plasmas, vol. 15, 2008, 062507; Riccardo et al., Nucl. Fusion, vol. 49, 2009, 055012; Bachmann et al., Fusion Engng Des., vol. 86, 2011, pp. 1915–1919). This paper describes a flat triangle representation of the electric circuits of a thin conducting wall of arbitrary three-dimensional geometry. Implemented into the shell simulation code (SHL) and the source sink current code (SSC), this model is suitable for modelling the electric currents excited in the wall inductively and through current sharing with the plasma.

General approach to the problem of disruption forces in tokamaks

An approach for calculating the force on the vessel wall during plasma disruptions in tokamaks is proposed. It is mainly based on the Maxwell equations and, therefore, is general. Another essential element is the integral force balance on the plasma that strongly constrains the possible solutions. The derived expressions are valid at any disruption scenario and finally give the net forces in terms of the magnetic perturbations behind the wall. The result can be used with magnetic measurements alone. It shows that the geometrical inhomogeneity of the wall and its resistivity are the key factors determining the direction and amplitude of the force.

Mechanism of runaway electron beam formation during plasma disruptions in tokamaks

A new physical mechanism of formation of runaway electron beams during plasma disruptions in tokamaks is proposed. The plasma disruption is caused by a strong stochastic magnetic field formed due to nonlinearly excited low-mode number magnetohydrodynamic (MHD) modes. It is conjectured that the runaway electron beam is formed in the central plasma region confined inside the intact magnetic surface located between q = 1 and the closest low–order rational magnetic surfaces [q = 5/4 or q = 4/3,…]. It results in that runaway electron beam current has a helical nature with a predominant m/n = 1/1 component. The thermal quench and current quench times are estimated using the collisional models for electron diffusion and ambipolar particle transport in a stochastic magnetic field, respectively. Possible mechanisms for the decay of the runaway electron current owing to an outward drift electron orbits and resonance interaction of high–energy electrons with the m/n = 1/1 MHD mode are discussed.

Adaptive Grids in Simulations of Toroidal Plasma Starting from Magneto-Hydrodynamic Equilibrium

This paper introduces the notion of Tokamak Magneto-Hydrodynamics (TMHD), which explicitly reflects the anisotropy of a high temperature tokamak plasma. The set of TMHD equations is formulated for simulation of macroscopic plasma dynamics and disruptions in tokamaks. Free from the Courant restriction on the time step, this set of equations is adequate to plasma dynamics with realistic parameters of high performance plasmas and does not require any extension of the MHD plasma model. At the same time, TMHD requires the use of magnetic field aligned numerical grids. Examples of their use in 2-dimensional cases of tokamak equilibria and dynamics of the wall touching kink mode are presented. For the 3-dimensional case of an ergodic magnetic field, this paper introduces the reference magnetic coordinates as a practical algorithm for generating adaptive grids for TMHD.