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Resistive wall implementation for tokamaks has been achieved by both a 'thin wall' approximation in which time-varying fields are matched across a boundary for all modes; and, by meshing the region from the first wall to the outer boundary and setting certain fields to mimic a resistive wall. Both implementations were tested on existing tokamaks.
Magnetohydrodynamics (MHD) provides a useful model to describe the crucial plasma macroscopic equilibrium and stability behaviors in toroidal tokamak devices by considering the plasma as a conducting fluid interacting with a surrounding confining electromagnetic field. MHD is the most basic plasma model, incorporating most large-scale phenomena, including plasma equilibrium and all major instabilities. MHD equations are obtained by taking moments of the Boltzmann equations for different plasma species. They provide a set of comprehensive physics constrains to compute and optimize the equilibrium plasma shape and pressure and current profiles that are critical to its stability and performance. In the ideal case, the equations have special properties that lead to efficient numerical calculation schemes, the most important of which is the ideal MHD energy principle for linear stability against small departures from equilibrium. In a tokamak plasma, equilibrium pressure is mostly destabilizing for MHD modes, whereas equilibrium current is also often a major driving force. Plasma resistivity creates new freedom for a MHD instability to grow, but there are also cases where the plasma resistivity plays a stabilizing role. Equilibrium toroidal flow and/or flow shear can affect MHD instabilities. Principal MHD instabilities include the internal kink mode, sawtooth, fishbone, external kink, resistive wall mode, resistive interchange, tearing and neoclassical tearing modes (NTMs), locked modes, toroidal Alfven eigenmodes (TAEs), and edge localized modes (ELMs). Fast-growing MHD instabilities can lead to an abrupt plasma disruption and termination that can potentially damage the device plasma facing components (PFCs) and in-vessel structures. Furthermore, an important MHD application is to develop robust techniques to mitigate and control MHD instabilities.
One of the biggest challenges to achieve the goal of producing fusion energy in tokamak devices is the necessity of avoiding disruptions of the plasma current due to instabilities. The disruption event characterization and forecasting (DECAF) framework has been developed in this purpose, integrating physics models of many causal events that can lead to a disruption. Two different machine learning approaches are proposed to improve the ideal magnetohydrodynamic (MHD) no-wall limit component of the kinetic stability model included in DECAF. First, a random forest regressor (RFR), was adopted to reproduce the DCON computed change in plasma potential energy without wall effects for a large database of equilibria from the national spherical torus experiment (NSTX). This tree-based method provides an analysis of the importance of each input feature, giving an insight into the underlying physics phenomena. Secondly, a fully-connected neural network has been trained on sets of calculations with the DCON code, to get an improved closed form equation of the no-wall β limit as a function of the relevant plasma parameters indicated by the RFR. The neural network has been guided by physics theory of ideal MHD in its extension outside the domain of the NSTX experimental data. The estimated value has been incorporated into the DECAF kinetic stability model and tested against a set of experimentally stable and unstable discharges. Moreover, the neural network results were used to simulate a real-time stability assessment using only quantities available in real-time. Finally, the portability of the model was investigated, showing encouraging results by testing the NSTX-trained algorithm on the mega ampere spherical tokamak (MAST).
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.
In Izzo et al (2022 Nucl. Fusion 62 096029), state-of-the-art modeling of thermal and current quench (CQ) magnetohydrodynamics (MHD) coupled with a self-consistent evolution of runaway electron (RE) generation and transport showed that a non-axisymmetric (n = 1) in-vessel coil could passively prevent RE beam formation during disruptions in SPARC, a compact high-field tokamak projected to achieve a fusion gain Q > 2 in DT plasmas. However, such suppression requires finite transport of REs within magnetic islands and re-healed flux surfaces; conservatively assuming zero transport in these regions leads to an upper bound of RE current ~1MA compared to ~8.7MA of pre-disruption plasma current. Further investigation finds that core-localized electrons, within r/a < 0.4 and with kinetic energies ~0.2–15 MeV, contribute most to the RE plateau formation. Yet only a relatively small amount of transport, i.e. a diffusion coefficient ~18 m 2 s -1 , is needed in the core to fully mitigate these REs. Properly accounting for (a) the CQ electric field's effect on RE transport in islands and (b) the contribution of significant RE currents to disruption MHD may help achieve this.
Nonlinear 3D magnetohydrodynamic (MHD) modeling of shattered pellet injection (SPI) in JET tokamak plasmas is performed with the JOREK code. The study focuses on the validation of simulation result with respect to experimental observations, addressing in particular figures of merit for the efficiency of the SPI, as a technique to mitigate thermal loads by injecting radiative impurities like neon during the thermal quench (TQ) phase of disruptions. A set of JET pulses with neon/deuterium atomic mixture ratio in the shattered pellet varying from 10% to 100% provides the experimental data to be compared with. Simulations using different models for the ablation of solid fragments and the radiation of neon impurities are considered. Synthetic diagnostics are employed for a direct quantitative comparison with key JET diagnostic systems providing in particular radiation, electron temperature and density, and magnetic measurements. 3D radiation structures from MHD simulations are analyzed to estimate the toroidal asymmetry of radiation, which is difficult to measure in JET due to the presence of only two toroidally displaced multi-channel bolometry systems. JOREK simulations show that, before the TQ, the bulk of the radiation is concentrated in a toroidal region enclosing the radiating fragments that is missed by both multi-channel bolometers, suggesting a possible underestimation of the total radiation by such diagnostic systems in the pre-TQ phase. On the other hand, JOREK predicts that during the TQ the radiation becomes more toroidally symmetric, with positive implications for the heat load to plasma facing components.
The goal of this work is to generate large statistically representative data sets to train machine learning models for disruption prediction provided by data from few existing discharges. Such a comprehensive training database is important to achieve satisfying and reliable prediction results in artificial neural network classifiers. Here, we aim for a robust augmentation of the training database for multivariate time series data using Student t process regression. We apply Student t process regression in a state space formulation via Bayesian filtering to tackle challenges imposed by outliers and noise in the training data set and to reduce the computational complexity. Thus, the method can also be used if the time resolution is high. We use an uncorrelated model for each dimension and impose correlations afterwards via colouring transformations. We demonstrate the efficacy of our approach on plasma diagnostics data of three different disruption classes from the DIII-D tokamak. To evaluate if the distribution of the generated data is similar to the training data, we additionally perform statistical analyses using methods from time series analysis, descriptive statistics and classic machine learning clustering algorithms.
Dispersive shell pellet injection for disruption mitigation on the DIII-D tokamak is modeled with the 3D MHD code NIMROD. The simulations attempt to reproduce as closely as possible a pellet velocity scan that was performed on the DIII-D tokamak [Hollmann, et al., Phys. Rev. Lett. 122, 65001 (2019)]. This scan involved injecting a hollow diamond shell filled with boron dust that is released in the core of the plasma. Trends that are reproduced in the simulation include improved mitigation, reduced plasma current spike amplitude, and increased likelihood of hot-tail runaway electron production with increased pellet speed. The simulations provide additional physics insight into these findings. Limitations of the present model and requirements for a predictive model are discussed.
Abstract We present a model for the particle balance in the post-disruption runaway electron plateau phase of a tokamak discharge. The model is constructed with the help of, and applied to, experimental data from TCV discharges investigating the so-called ‘low- Z benign termination’ runaway electron mitigation scheme. In the benign termination scheme, the free electron density is first reduced in order for a subsequently induced MHD instability to grow rapidly and spread the runaway electrons widely across the wall. We show that the observed non-monotonic dependence of the free electron density with the measured neutral pressure is due to plasma re-ionization induced by runaway electron impact ionization. At higher neutral pressures, more target particles are present in the plasma for runaway electrons to collide with and ionize. Parameter scans are conducted to clarify the role of the runaway electron density and energy on the free electron density, and it is found that only the runaway electron density has a noticeable impact. While the free electron density is shown to be related to the spread of heat fluxes at termination, the exact cause for the upper neutral pressure limit remains undetermined and an object for further study.
The goal of this work is to generate large statistically representative datasets to train machine learning models for disruption prediction provided by data from few existing discharges. Such a comprehensive training database is important to achieve satisfying and reliable prediction results in artificial neural network classifiers. Here, we aim for a robust augmentation of the training database for multivariate time series data using Student-t process regression. We apply Student-t process regression in a state space formulation via Bayesian filtering to tackle challenges imposed by outliers and noise in the training data set and to reduce the computational complexity. Thus, the method can also be used if the time resolution is high. We use an uncorrelated model for each dimension and impose correlations afterwards via coloring transformations. We demonstrate the efficacy of our approach on plasma diagnostics data of three different disruption classes from the DIII-D tokamak. To evaluate if the distribution of the generated data is similar to the training data, we additionally perform statistical analyses using methods from time series analysis, descriptive statistics, and classic machine learning clustering algorithms.
The J-TEXT capability is enhanced compared to two years ago with several upgrades of its diagnostics and the increase of electron cyclotron resonance heating (ECRH) power to 1 MW. With the application of electron cyclotron wave (ECW), the ECW assisted plasma startup is achieved; the tearing mode is suppressed; the toroidal injection of 300 kW ECW drives around 24 kA current; fast electrons are generated with toroidal injected ECW and the runaway current conversion efficiency increases with ECRH power. The mode coupling between 2/1 and 3/1 modes are extensively studied. The coupled 2/1 and 3/1 modes usually lead to major disruption. Their coupling can be either suppressed or avoided by external resonant magnetic perturbation fields and hence avoids the major disruption. It is also found that the 2/1 threshold of external field is significantly reduced by a pre-excited 3/1 mode, which can be either a locked island or an external kink mode. The disruption control is studied by developing prediction methods capable of cross tokamak application and by new mitigation methods, such as the biased electrode or electromagnetic pellet injector. The high-density operation and related disruptions are studied from various aspects. Approaching the density limit, the collapse of the edge shear layer is observed and such collapse can be prevented by applying edge biasing, leading to an increased density limit. The density limit is also observed to increase, if the plasma is operated in the poloidal divertor configuration or the plasma purity is increased by increasing the pre-filled gas pressure or ECRH power during the start-up phase.
In the last two years, three major technical improvements have been made on J-TEXT in supporting of the expanded operation regions and diagnostic capabilities. (1) The successful commission of the 105 GHz/500 kW/1 s electron cyclotron resonance heating (ECRH) system increasing the core electron temperature from 0.9 keV up to around 1.5 keV. (2) The poloidal divertor configuration with an X-point in the high-field side has been achieved. In particular, the 400 kW electron cyclotron wave has also been successfully injected into the diverted plasma. (3) A 256-channel electron cyclotron emission imaging diagnostic system and two sets of four-channel Doppler backscattering diagnostics have been successfully developed on J-TEXT, allowing detailed measurement of the electron temperature and density fluctuations for turbulence and MHD research. The locked mode (LM), especially the 2/1 LM, is one of the biggest threats to the plasma operation. Both the thresholds of 2/1 and 3/1 LM are observed to vary non-monotonically on electron density. The electrode biasing was applied successfully to unlock the LM from either a rotating or static resonant magnetic perturbation (RMP) field. In the presence of 2/1 LM, three kinds of standing wave (SW) structures have been observed to share a similar connection to the island structure, i.e. the nodes of the SWs locate around the O- or X-points of the 2/1 island. The control and mitigation of disruption is essential to the safe operation of ITER, and it has been systematically studied by applying a RMP field, massive gas injection (MGI) and shattered pellet injection on J-TEXT. When the RMP-induced 2/1 LM is larger than a critical width, the MGI shutdown process can be significantly influenced. If the phase difference between the O-point of LM and the MGI valve is +90° (or –90°), the penetration depth and the assimilation of impurities can be enhanced (or suppressed) during the pre-thermal quench (TQ) phase and result in a faster (or slower) TQ. A secondary MGI can also suppress the runaway electron (RE) generation, if the additional high-Z impurity gas arrives at the plasma edge before TQ. When the secondary MGI has been applied after the formation of the RE current plateau, the RE current can be dissipated, and the dissipation rate increases with the injected impurity quantity but saturates with a maximum of 28 MA s –1 . The non-local transport is experimentally observed in the ion transport channel. The electron thermal diffusivity significantly increases with the ECRH power. Theoretical work shows that significant intrinsic current can be driven by electromagnetic turbulence, and the robust formation mechanism of the E × B staircase is identified from the Hasegawa–Wakatani system.
This article discusses the use of radio frequency (RF) current drive to stabilize large islands, focusing on nonlinear effects that appear when relatively high powers are used to stabilize large islands. We are interested in developing a capability to stabilize large islands via RF driven currents to avoid the need for mitigation to the extent possible. As tokamaks are designed and built with increasing levels of stored energy in the plasma, disruptions become increasingly dangerous. It has been reported that 95% of the disruptions in the Joint European Torus tokamak with the ITER-like wall are preceded by the growth of large locked islands. These large islands are mostly produced by off-normal events other than neoclassical tearing modes. This paper presents theory and modeling for a nonlinear “RF current condensation” effect that can concentrate the RF driven current near the center of a large island, thereby increasing the efficiency of the stabilization. A nonlinear shadowing effect can hinder the stabilization of islands if the aiming of the ray trajectories does not properly consider the nonlinear effects.
The generation of runaway electrons (REs) during disruptions poses a significant challenge for the operation of tokamaks. The production of these high-energy electrons can cause substantial damage, particularly when the plasma current is high, making it a critical concern for ITER. For the high-temperature plasmas anticipated in ITER, the primary generation of REs may be dominated by the hot tail mechanism, which consists of the acceleration of hot electrons from the pre-disruption population which have not yet thermalized with the bulk following the rapid cooling of the plasma. To account for the significant 3D effects on RE production, a hot tail modeling framework has been developed within the non-linear 3D extended MHD code JOREK. This paper presents the structure of this framework, which is based on test electrons evolving in MHD fields. The verification of the method shows good agreement with the reference DREAM code for 0D test cases, as well as for axisymmetric simulations of 15 MA ITER H-mode disruption scenarios. Furthermore, a proof-of-principle application to a DIII-D case demonstrates the framework’s capability to capture for the first time the hot tail generation in 3D MHD simulations in realistic geometry. Preliminary results suggest that the production of REs is significantly reduced by stochastic losses.
Abstract Reliable vertical position control will be an essential element of any future tokamak-based fusion power plant in order to reduce disruptions and maximize performance. We investigate methods to improve vertical controllability boundary determination in plasma operational space and demonstrate a data-driven approach based on direct pseudoinversion of operational space data that is rigorously quantitative, applicable in real-time plasma control systems, and physically intuitive to interpret. Applied to historical shot data from entire run campaigns on the MAST-U, KSTAR, and NSTX tokamaks, this approach, implemented in DECAF, improves vertical displacement event identification accuracy to 98.9%–100%. Further, we explore the application of a physics-based vertical stability metric as an early warning forecaster for vertical displacement events. The development of a linear surrogate model for the plasma current density profile, with a coefficient of determination of 0.992 on the training dataset, enables potential employment of this forecaster in real-time. The application of this approach on historical data from the MAST-U MU02 campaign yields a forecaster with 62.6% accuracy, indicating promise for this method when further refined and potentially coupled with other stability metrics.
Novel disruption prevention solutions spanning a range of control regimes are being developed and tested on DIII-D to enable ITER success. First, a new real-time control algorithm has been developed and tested for regulating nearness to stability limits and maintaining safety-margins. Its first application has been for reliable prevention of vertical displacement events (VDEs) by adjusting plasma elongation (κ) and the inner-gap between the plasma and inner-wall in response to real- time open-loop VDE growth rate (γ) estimators. VDEs were robustly prevented up to average open-loop growth rates of 800 rad/s with initial tunings, with only applying shape modification when near safety limits. Second, the disruption risk during fast, emergency shutdown after large tearing and locked modes can be significantly improved by transitioning to a limited topology during shutdown. More than 50% of emergency limited shutdowns after locked modes reach a final normalized current I_N < 0.3 before terminating, scaling to the 3 MA ITER requirement. Furthermore, this is in contrast to diverted shutdowns, the majority of which disrupt at I_N > 0.8. Despite improvements, these results highlight the critical importance of early prevention. Third, a novel emergency shut down method has been developed which excites instabilities to form a warm, helical core post-thermal quench. The current quench extends to ~100ms and avoids VDEs and runaway electron generation. Novel real-time machine learning disruption prediction has been integrated with the DIII-D proximity controller, and a real- time compatible multi-mode MHD spectroscopy technique has been developed. Results presented here were enabled by a focused effort, the Disruption Free Protocol, in DIII-D’s 2019-20 campaign to complement disruption prevention experiments with a large piggy-back program. In addition to testing novel techniques, it is estimated to have helped avoid 32 potential disruptions in piggyback operations with rapid, early shutdowns after large rotating n=1 or locked modes.
In the pursuit of the goal of commercial fusion as an abundant and safe source of energy, the stellarator is a leading concept with compelling attractiveness and demonstrated performance. A new mid-size stellarator is needed to retire risks and innovate towards a high performance, economically attractive, stellarator Fusion Pilot Plant. In this presentation we, as a community of US researchers from Universities, National Laboratories, and Private Industry, involved in studying the stellarator concept, lay out the programmatic and technical motivation for a new and modern mid-size stellarator research facility. A new mid-scale stellarator is needed to realize the potential predicted by a solid body of theory and simulation along with advances in computational tools for optimization and non-linear turbulence modeling. Notably, it is possible to combine the advantages of the stellarator (steady state, no current drive, no disruptions) with the good confinement regularly achieved in tokamaks. The top priorities for experimental work, and the motivation for a mid-scale stellarator experiment are: turbulence control, non-resonant divertor, MHD stability at large beta, confinement of fast particles, and coil simplification. A new mid-size quasi-symmetric stellarator, built as a user facility, would complement existing research at Wendelstein 7-X and LHD and strongly augment private industry. It would provide a program of innovative research, concept validation, theoretical advancement, and workforce development. Growing support and interest for stellarators by the fusion community and private industry affirms this rationale.
This document is the final technical report for the UC Davis project DE-SC00023500, detailing the development and implementation of a Fast Recurrent Neural Network (FRNN) software. The software was designed to enable predictive, real-time control of plasma instabilities within the DIII-D Plasma Control System (PCS).