There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow. A long-lived standing wave phase, which we call the Caviton, and a short-lived traveling wave phase (in radial direction) we call the Instanton. For drift wave turbulence driven by ion temperature gradient mode (ITG), these two stages of dynamics were displayed in [Zhang Y Z, Liu Z Y, Xie T, Mahajan S M and Liu J 2017 Physics of Plasmas 24 122304]. In this paper we show that the dynamical attributes of ITG turbulence are readily replicated when the turbulence rotates in the electron direction; our model calculation deals specifically with the toroidal electron drift waves (EDW) in the well-known δ_e model. While the basic calculations are presented in parallel to the ITG counterpart, more emphasis is laid here on the motion of Instanton; several abrupt phenomena observed in tokamaks, such as intermittent excitation of geodesic acoustic mode (GAM) shown in this paper, could be attributed to the sudden and fast radial motion of Instanton. The calculation brings out the defining characteristics of the Instanton: it begins as a linear traveling wave right after the transition. Then, it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz. The modulation to Reynolds stress in zonal flow equation will cause resonant excitation to GAM. The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.
The sputtering of inside wall components of tokamaks can lead to the injection of supersaturated vapour in the plasma edge. The resulting condensation favours the formation of clusters which can give rise to solid particulates by further accretion. Sputtering discharges are proposed to have highlight on the formation of carbonaceous dust observed in the tokamaks with graphite based wall components. The flux of the sputtered carbon atoms is evaluated in the conditions of our laboratory discharges as well as the evolution of their energy distribution. It is shown that a cooling mechanism occurs …
Saskatchewan Torus-Modified (STOR-M) is a small tokamak, well known for various fusion related basic experimental studies such as edge turbulent heating, different instabilities, AC (alternating current) tokamak operation, Ohmic H-mode triggering by the electrode biasing, fueling and momentum injection by Compact Torus (CT) injection, and effects of Resonance Magnetic Perturbations (RMP), among others. Some of those experiments require real time visualization of magnetic surface reconstructions either through EFIT or quick analyses and visualization of experimental data during experiments. Rec…
The turbulence observed in the scrape-off-layer of a tokamak is often characterized by intermittent events of bursty nature, a feature which raises concerns about the prediction of heat loads on the physical boundaries of the device. It appears thus necessary to delve into the statistical properties of turbulent physical fields such as density, electrostatic potential and temperature, focusing on the mathematical expression of tails of the probability distribution functions. The method followed here is to generate statistical information from time-traces of the plasma density stemming from Bra…
Intermittent positive bursts of plasma density detected by Langmuir probes at the edge of the TEXTOR tokamak are investigated. Burst statistical properties and temporal characteristics together with their radial dependence are studied in two different regimes - with electrode biasing and dynamic ergodic divertor (DED). Similar modification of intermittent burst characteristics are observed. Namely, the average burst rate increases and the average burst duration decreases compared to Ohmic conditions. Statistical properties are also modified in the same way in both regimes. The reason is that b…
University of Science and Technology of China（中国科学技术大学）
A model for tokamak discharge through deep learning has been done on a superconducting long-pulse tokamak (EAST). This model can use the control signals (i.e. Neutral Beam Injection (NBI), Ion Cyclotron Resonance Heating (ICRH), etc) to model normal discharge without the need for doing real experiments. By using the data-driven methodology, we exploit the temporal sequence of control signals for a large set of EAST discharges to develop a deep learning model for modeling discharge diagnostic signals, such as electron density $n_{e}$, store energy $W_{mhd}$ and loop voltage $V_{loop}$. Comparin…
Boundary plasma physics plays an important role in tokamak confinement, but is difficult to simulate in a gyrokinetic code due to the scale-inseparable nonlocal multi-physics in magnetic separatrix and open magnetic field geometry. Neutral particles are also an important part of the boundary plasma physics. In the present paper, noble electrostatic gyrokinetic techniques to simulate the flux-driven, low-beta electrostatic boundary plasma is reported. Gyrokinetic ions and drift-kinetic electrons are utilized without scale-separation between the neoclassical and turbulence dynamics. It is found …
An expression for the extrapolated fusion gain G = Pfusion /5 Pheat (Pfusion being the total fusion power and Pheat the total heating power) of ITER in terms of the confinement improvement factor (H) and the normalised beta (betaN) is derived in this paper. It is shown that an increase in normalised beta can be expected to have a negative or neutral influence on G depending on the chosen confinement scaling law. Figures of merit like H betaN / q95^2 should be used with care, since large values of this quantity do not guarantee high values of G, and might not be attainable with the heating powe…
Improved n=1 Empirical Error Field Penetration Threshold Scaling with Ohmic and L-Mode Conventional Tokamak Plasma Discharges
Columbia University（哥伦比亚大学）；Seoul National University（首尔大学）；Institute of Plasma Physics Chinese Academy of Sciences（中国科学院等离子体物理研究所）；Huazhong University of Science and Technology（华中科技大学）；General Atomics（通用原子公司）；Consorzio RFX (CNR, ENEA, INFN, Universitá di Padova, Acciaierie Venete SpA)（RFX联合体（意大利国家研究委员会、国家新能源与可再生能源署、意大利国家核物理研究所、帕多瓦大学、威尼斯钢铁公司））；University of Padova（帕多瓦大学）；UKAEA, Culham Campus（英国原子能管理局，库姆校区）
An analytic theory of edge localized mode (ELM) suppression in an H-mode tokamak plasma via the application of a static, externally generated, resonant magnetic perturbation (RMP) is presented. This theory is based on the plausible hypothesis that mode penetration at the top of the pedestal is a necessary and sufficient condition for the RMP-induced suppression of ELMs. The theory also makes use of a number of key insights gained in a recent publication (Fitzpatrick R 2019). The first insight is that the response of the plasma to a particular helical component of the RMP, in the immediate vici…
In this work, a purely data-driven discharge prediction model was developed and tested without integrating any data or results from simulations. The model was developed based on the experimental data from the Experimental Advanced Superconducting Tokamak (EAST) campaign 2010-2020 discharges and can predict the actual plasma current $I_{p}$, normalized beta $β_{n}$, toroidal beta $β_{t}$, beta poloidal $β_{p}$, electron density $n_{e}$, store energy $W_{mhd}$, loop voltage $V_{loop}$, elongation at plasma boundary $κ$, internal inductance $l_{i}$, q at magnetic axis $q_{0}$, and q at 95% flux s…
The plasma response to an externally generated, static, n=2, resonant magnetic perturbation (RMP) in the pedestal region of DIII-D discharge #158115 is investigated. In this particular discharge, the resonant amplitudes of the RMP are modulated in a cycloidal manner at a frequency of 1 Hz. Adopting the plausible hypothesis that mode penetration at the top of the pedestal is a necessary and sufficient condition for the RMP-induced suppression of edge localized modes (ELMs), recent cylindrical, nonlinear, reduced-magnetohydrodynamical (MHD) simulations performed by Hu, Nazikian, et al., (2019) c…
For ITER-relevant runaway electron studies, such as suppression, mitigation, termination and/or control of runaway beam, obtaining the runaway electrons after the disruption is important. In this paper we report on the first achieved discharges with post-disruptive runaway electron beam, entitled "runaway plateau", in the COMPASS tokamak. The runaway plateau is produced by massive gas injection of argon. Almost all of the disruptions with runaway electron plateaus occurred during the plasma current ramp-up phase. Comparison between the Ar injection discharges with and without plateau has been …
Through a systematically developed theory, we demonstrate that the motion of instanton identified in [Y. Z. Zhang, Z. Y. Liu, T. Xie, S. M. Mahajan, and J. Liu, Physics of Plasmas 24, 122304 (2017)] is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode (GAM) that are observed in tokamaks. While many numerical simulations have observed the phenomena, it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation. The preceding work is based on the micro-turbulence associated with toroidal ion temperature grad…
An international experiment, ITER is proposed as the next essential and critical step on the path to demonstrating the scientific and technological feasibility of fusion energy. ITER would give unique opportunities to explore, in reactor relevant conditions, the physics of α-particle heating, plasma turbulence and turbulent transport, stability limits to the plasma pressure and exhaust of power and particles. Improved understanding of the physical processes occurring in tokamak plasmas give enhanced confidence in ITER achieving its goals. In particular, progress has been made in research …
Huazhong University of Science and Technology（华中科技大学）；Institute of Plasma Physics, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院等离子体物理研究所）；Shenzhen University（深圳大学）
Predicting disruptions across different tokamaks is a great obstacle to overcome. Future tokamaks can hardly tolerate disruptions at high performance discharge. Few disruption discharges at high performance can hardly compose an abundant training set, which makes it difficult for current data-driven methods to obtain an acceptable result. A machine learning method capable of transferring a disruption prediction model trained on one tokamak to another is required to solve the problem. The key is a disruption prediction model containing a feature extractor that is able to extract common disrupti…
The purpose of this paper is to further investigate the major disruptions occurring in low-q(a) discharges in Iran Tokamak 1, and to compare the theoretical and experimental results for the rate of island growth. The study of precursor phase of disruption can be predicted and avoided using suitable control systems. In this paper are described the stability analysis and the observed growth rates indicate that the rotating modes are tearing modes.
A first-principles scaling law, based on turbulent transport considerations, and a multi-machine database of density limit discharges from the ASDEX Upgrade, JET and TCV tokamaks, show that the increase of the boundary turbulent transport with the plasma collisionality sets the maximum density achievable in tokamaks. This scaling law shows a strong dependence on the heating power, therefore predicting for ITER a significantly larger safety margin than the Greenwald empirical scaling (Greenwald et al, Nucl. Fusion, 28(12), 1988) in case of unintentional H-L transition.
Theory-based scaling laws of the near and far scrape-off layer (SOL) widths are analytically derived for L-mode diverted tokamak discharges by using a two-fluid model. The near SOL pressure and density decay lengths are obtained by leveraging a balance among the power source, perpendicular turbulent transport across the separatrix, and parallel losses at the vessel wall, while the far SOL pressure and density decay lengths are derived by using a model of intermittent transport mediated by filaments. The analytical estimates of the pressure decay length in the near SOL is then compared to the r…
Fusion power production in tokamaks uses discharge configurations that risk producing strong Type I Edge Localized Modes. The largest of these modes will likely increase impurities in the plasma and potentially damage plasma facing components such as the protective heat and waste divertor. Machine learning-based prediction and control may provide for online mitigation of these damaging modes before they grow too large to suppress. To that end, large labeled datasets are required for supervised training of machine learning models. We present an algorithm that achieves 97.7% precision when autom…
Global electromagnetic gyrokinetic simulations show the existence of near threshold conditions for both a high-$n$ kinetic ballooning mode (KBM) and an intermediate-$n$ kinetic version of peeling-ballooning mode (KPBM) in the edge pedestal of two DIII-D H-mode discharges. When the magnetic shear is reduced in a narrow region of steep pressure gradient, the KPBM is significantly stabilized, while the KBM is weakly destabilized and hence becomes the most-unstable mode. Collisions decrease the KBM's critical $β$ and increase the growth rate.
Reinforcement learning for vertical position control on the EXL-50U spherical tokamak
Beijing ENN Fusion Energy Science and Technology Co., Ltd.（北京恩诺聚变能源科技有限公司）；Beijing Key Laboratory of High Magnetic Field Spherical Torus Fusion Energy（北京市高磁场球形托卡马克聚变能重点实验室）；Hebei Key Laboratory of Compact Fusion（河北省紧凑型聚变重点实验室）；School of Nuclear Science and Engineering, East China University of Technology（华东理工大学核科学与技术学院）；Institute of Robotics and Automatic Information System, Nankai University（南开大学机器人与自动化信息系统研究所）；Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics, Dalian University of Technology（大连理工大学物理学院教育部 beam 材料改性重点实验室）；Dalian University of Technology（大连理工大学）
The Tore Supra tokamak is the largest superconducting magnetic fusion facility, has been devoted to long-duration high-performance discharge research. With a steady-state magnetic field and water cooled plasma facing components, discharges up to 6 minutes 24 seconds duration with injected / extracted energy up to 1 GJ have been performed. The Tore Supra real time measurements and control (RTMC) system has been upgraded to address schemes dedicated to long pulse operation with simultaneous control of an increasing number of plasma parameters. This includes plasma equilibrium control with possib…
A model system of equations has been derived to describe a toroidally rotating tokamak plasma, unstable to Resistive Wall Modes (RWMs) and metastable to Neoclassical Tearing Modes (NTMs), using a linear RWM model and a nonlinear NTM model. If no wall is present, the NTM growth shows the typical threshold/saturation island widths, whereas a linearly unstable kink mode grows exponentially in this model plasma system. When a resistive wall is present, the growth of the linearly unstable RWM is accelerated by an unstable island: a form of coupled RWM-NTM mode. Crucially, this coupled system has no…
Steering tokamak plasmas is commonly viewed as a way to avoid disruptions and runaway electrons. Plasma steering sounds as safe as driving to work but will be shown to more closely resemble driving at high speed through a dense fog on an icy road. The long time required to terminate an ITER discharge compared to time over which dangers can be foreseen is analogous to driving in a dense fog. The difficulty of regaining plasma control if it is lost resembles driving on an icy road. Disruptions and runaways are associated with three issues -- a solution to one tends to complicate the solution to …
Several new results in the physics of edge poloidal flows, turbulent stresses and momentum transport are reported. These are based on experiments on the HL-2A tokamak. Significant deviation from neoclassical prediction for mean poloidal flow in Ohmic and L mode discharges is deduced from direct measurements of the turbulent Reynolds stress. The deviation increases with heating power. The turbulent poloidal viscosity is synthesized from fluctuation data, and is found to be comparable to the turbulent particle diffusivity. The intrinsic poloidal torque is deduced from synthesis, for the first ti…
A new model of fast ion source induced by Neutral Beam Injection (NBI) in tokamaks has been implemented in the hybrid kinetic-magnetohydrodynamic code XTOR-K. This source, combined with the collisions also recently implemented, allows for the modeling of realistic slowing-down populations and their interplay with macroscopic modes. This paper describes the Neutral Beam injection and ionization model designed to reproduce experimental configurations and its validation for a typical discharge of the ASDEX Upgrade tokamak. The application to the interaction of NBI-induced fast particles with a ki…
A new version of GBS (Ricci et al. Plasma Phys. Control. Fusion 54, 124047, 2012; Halpern et al. J. Comput. Phys. 315, 388-408, 2016; Paruta et al. Phys. Plasmas 25, 112301, 2018) is described. GBS is a three-dimensional, flux-driven, global, two-fluid turbulence code developed for the self-consistent simulation of plasma turbulence and kinetic neutral dynamics in the tokamak boundary. In the new version presented here, the simulation domain is extended to encompass the whole plasma volume, avoiding an artificial boundary with the core, hence retaining the core-edge-SOL interplay. A new toroid…
The impact of electromagnetic stabilization and flow shear stabilization on ITG turbulence is investigated. Analysis of a low-$β$ JET L-mode discharge illustrates the relation between ITG stabilization, and proximity to the electromagnetic instability threshold. This threshold is reduced by suprathermal pressure gradients, highlighting the effectiveness of fast ions in ITG stabilization. Extensive linear and nonlinear gyrokinetic simulations are then carried out for the high-$β$ JET hybrid discharge 75225, at two separate locations at inner and outer radii. It is found that at the inner radius…
Results from the last FTU campaigns on the deuterium large (wrt FTU volume) pellet REs suppression capability, mainly due to the induced burst MHD activity expelling REs seed are presented for discharges with 0.5 MA and 5.3T. Clear indications of avalanche multiplication of REs following single pellet injection on 0.36 MA flat-top discharges is shown together with quantitative indications of dissipative effects in terms of critical electrical field increase due to fan-like instabilities. Analysis of large fan-like instabilities on post-disruption RE beams, that seem to be correlated with low e…
Geodesic acoustic modes (GAMs) are studied by means of the gyrokinetic global particle-in-cell code ORB5. Linear electromagnetic simulations in the low electron beta limit have been performed, in order to separate acoustic and Alfvénic time scales and obtain more accurate measurements. The dependence of the frequency and damping rate on several parameters such as the safety factor, the GAM radial wavenumber and the plasma elongation is studied. All simulations have been performed with kinetic electrons with realistic electron/ion mass ratio. Interpolating formulae for the GAM frequency and dam…
A new gas puff imaging (GPI) diagnostic has been developed on the HL-2A tokamak to study two-dimensional plasma edge turbulence in poloidal vs. radial plane. During a discharge, neutral helium or deuterium gas is puffed at the edge of the plasma through a rectangular multi-capillary nozzle to generate a gas cloud on the observing plane. Then a specially designed telescope and a high-speed camera are used to observe and photograph the emission from the neutral gas cloud. The brightness and contrast in the 2-D poloidal vs. radial frames reveal the structures and movements of the turbulence. The …
The results of the analysis of the deviation of the force equilibrium for ions from the neoclassical theory prediction, calculated using the direct measurements of the radial electric field, in the view of its possible local and nonlocal correlation with the profiles of electron, Te, and ion, Ti, temperatures in the T-10 tokamak are presented. Local correlations are analyzed by means of the Pearson's correlation. Nonlocal correlations are treated with an inverse problem under the assumption of an integral equation relationship between the deviation and Te and Ti profiles. The discharges with z…
The tearing mode, a large-scale MHD instability in tokamak, typically disrupts the equilibrium magnetic surfaces, leads to the formation of magnetic islands, and reduces core electron temperature and density, thus resulting in significant energy losses and may even cause discharge termination. This process is unacceptable for ITER. Therefore, the accurate identification of a magnetic island in real time is crucial for the effective control of the tearing mode in ITER in the future. In this study, based on the characteristics induced by tearing modes, an attention-aware convolutional neural net…
Understanding of the transport in a Tokamak plasma is an important issue. Various mechanisms have been reported in the literature to relate the core phenomenon to edge phenomenon. Sawtooth and Mirnov oscillations caused by MHD instabilities are generally observed in Tokamak discharges. Observation of these effects in the visible radiation from outer edge may offer a possible means to understand the transport.Oscillations in the visible radiation from outer region of the plasma have been observed during recent Aditya discharges. Percentage modulation of these oscillations vary with the Lines of…
Evolution of electron temperature, electron density and its fluctuation with high spatial and temporal resolutions are presented for the cold pulse propagation induced by super-sonic molecular beam injection (SMBI) in ohmic plasmas in the EAST tokamak. The non-local heat transport occurs for discharges with plasma current $I_p$=450 kA ($q_{95}\sim5.55$), and electron density $n_{e0}$ below a critical value of $(1.35\pm0.25)\times10^{19}~\mathrm{m^{-3}}$. In contrary to the response of core electron temperature and electron density (roughly 10 ms after SMBI), the electron density fluctuation in…
A gyrokinetic simulation of the influence of electron cyclotron current drive and ion kinetic effect on the m/n=2/1 tearing mode (TM) instabilities is presented in HL-2A and DIII-D tokamak configurations. The TM evolution is calculated with a finite mass electron model and the rf current source is obtained by ray-tracing and the Fokker-Planck method. The TMs are found to be perfectly stabilized by a continuous 1MW 68GHz X2-mode in HL-2A tokamak, while instabilities in the DIII-D discharge (with lower value of CR=I_{rf}/I_{0}, where Irf is the wave driven current and I0 is the equilibrium plasm…
The Negative Triangularity Tokamak Path for Fusion Pilot Plants: Experimental Progress and Future Prospects
General Atomics（通用原子能公司）；Institute for Fusion Studies, University of Texas – Austin（德克萨斯大学奥斯汀分校聚变研究所）；Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；University of California, San Diego（加州大学圣地亚哥分校）；Columbia University（哥伦比亚大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Plasma Science and Fusion Center, MIT（麻省理工学院等离子体科学与聚变中心）
Disruptions in tokamak plasmas may lead to the generation of runaway electrons that have the potential to damage plasma-facing components. Improved understanding of the runaway generation process requires interpretative modelling of experiments. In this work we simulate eight discharges in the ASDEX Upgrade and JET tokamaks, where argon gas was injected to trigger the disruption. We use a fluid modelling framework with the capability to model the generation of runaway electrons through the hot-tail, Dreicer and avalanche mechanisms, as well as runaway electron losses. Using experimentally base…
During a tokamak discharge, the plasma can vary between different confinement regimes: Low (L), High (H) and, in some cases, a temporary (intermediate state), called Dithering (D). In addition, while the plasma is in H mode, Edge Localized Modes (ELMs) can occur. The automatic detection of changes between these states, and of ELMs, is important for tokamak operation. Motivated by this, and by recent developments in Deep Learning (DL), we developed and compared two methods for automatic detection of the occurrence of L-D-H transitions and ELMs, applied on data from the TCV tokamak. These method…
The dynamic interplay between the core and the edge plasma has important consequences in the confinement and heating of fusion plasma. The transport of the Scrape-Off-Layer (SOL) plasma imposes boundary conditions on the core plasma, and neutral transport through the SOL influences the core plasma sourcing. In order to better study these effects in a self-consistent, time-dependent fashion with reasonable turn-around time, a reduced model is needed. In this paper we introduce the SOL Box Model, a reduced SOL model that calculates the plasma temperature and density in the SOL given the core-to-…
Edge shear flow and its effect on regulating turbulent transport have long been suspected to play an important role in plasmas operating near the Greenwald density limit $ n_G $. In this study, equilibrium profiles as well as the turbulent particle flux and Reynolds stress across the separatrix in the HL-2A tokamak are examined as $ n_G $ is approached in ohmic L-mode discharges. As the normalized line-averaged density $ \bar{n}_e/n_G $ is raised, the shearing rate of the mean poloidal flow $ ω_{\rm sh} $ drops, and the turbulent drive for the low-frequency zonal flow (the Reynolds power $ \ma…
The aim of the present work is to investigate tokamak equilibria with reversed magnetic shear and sheared flow, which may play a role in the formation of internal transport barriers (ITBs), within the framework of two-fluid model. The study is based on exact self-consistent solutions in cylindrical geometry by means of which the impact of the magnetic shear, s, and the "toroidal" (axial) and "poloidal" (azimuthal) ion velocity components on the radial electric field, its shear and the shear of the ExB velocity is examined. For a wide parametric regime of experimental concern it turns out that …
We present experimental results of magnetic feedback control on the m=2, n=1 tearing mode in RFX-mod operated as a circular ohmically heated tokamak. The feedback suppression of the non-resonant m=2, n=1 Resistive Wall Mode (RWM) in q(a)<2 plasmas is a well-established result of RFX-mod. The control of the tearing counterpart, which develops in q(a)>2 equilibrium, is instead a more difficult issue. In fact, the disruption induced by a growing amplitude m=2, n=1 tearing mode can be prevented by feedback only when the resonant surface q=2 is close to the plasma edge, namely 2<q(a)<2.5, and the e…
Gyrokinetic simulations of ion temperature gradient mode and trapped electron mode driven impurity transport in a realistic tokamak geometry are presented and compared with results using simplified geometries. The gyrokinetic results, obtained with the GENE code in both linear and non-linear modes are compared with data and analysis for a dedicated impurity injection discharge at JET. The impact of several factors on heat and particle transport is discussed, lending special focus to tokamak geometry and rotational shear. To this end, results using s-alpha and concentric circular equilibria are…
