Tokamak Discharges Research Articles

Experiment data-driven modeling of tokamak discharge in EAST

A neural network model of tokamak discharge is developed based on the experimental dataset of a superconducting long-pulse tokamak (EAST) campaign 2016–2018. The purpose is to reproduce the response of diagnostic signals to actuator signals without introducing additional physical models. In the present work, the discharge curves of electron density n e, stored energy W mhd, and loop voltage V loop were reproduced from a series of actuator signals. For n e and W mhd, the average similarity between the modeling results and the experimental data achieve 89% and 97%, respectively. The promising results demonstrate that the data-driven methodology provides an alternative to the physical-driven methodology for tokamak discharge modeling. The method presented in the manuscript has the potential of being used for validating the tokamak’s experimental proposals, which could advance and optimize experimental planning and validation.

Importance of resistivity on edge-localized mode onset in spherical tokamaks

We explore the impact of realistic plasma resistivity on the linear stability of peeling-ballooning (PB) modes in tokamak discharges with low-aspect ratio. For this study we consider discharges that are subject to edge-localized modes (ELMs) in the National Spherical Torus Experiment (NSTX). Employing the state of the art extended-magnetohydrodynamic (MHD) code M3D-C1 it is demonstrated that non-ideal effects can significantly affect PB stability thresholds in NSTX discharges. In particular, robust resistive PB modes are found to exist well before the ideal PB stability threshold is met. These novel results can explain why ideal-MHD theory often does not accurately describe ELM onset in spherical torus configurations, and also present a valuable basis for the development of a predictive model for ELMs in low-aspect ratio tokamaks.

Transport model of plasma heating at the second harmonic of the electron cyclotron frequency

The optical thickness of the plasma is often insufficient to fully absorb the microwaves during heating at the second harmonic of the electron cyclotron frequency. An analysis of the experiments to the T-10 tokamak allows us to find the criteria for the full absorption, and to construct a canonical profile transport model for the full and partial absorptions of microwaves. The conditions to the equivalence of discharges in different tokamaks, and in a pair of tokamaks with the optimized W7-X stellarator are formulated. For equivalent discharges, calculations to the T-15MD tokamak under construction with the obtained model coincide with measurements of electron and ion temperatures in the W7-X over a wide range of plasma densities. The validated model is used to analyze future shots of T-15MD.

Experimental study on fast electron generation during internal crash

Hard x-ray (HXR) burst is found during internal crash in the flat top current stage of experimental advanced superconducting tokamak (EAST) discharges and it is caused by fast electrons. The generated electrons during internal crashes may be an operational safety issue in advanced tokamaks. During an internal crash, locations of fast electron generation from HXR evolution agree with areas of magnetic reconnection from soft x-ray (SXR) tomographic reconstruction. Further statistical analyses show a 27 μs time difference between SXR crashes and HXR bursts, and the agreement between time broadening of HXR bursts and estimated characteristic time of magnetic reconnection in EAST. The magnetic reconnections during internal crash are proved to generate fast electrons, by both spatial and temporal agreements.

Microtearing instabilities and electron thermal transport in low and high collisionality NSTX discharges

Microtearing mode (MTM) real frequency, growth rate, magnetic fluctuation amplitude, and resulting electron thermal transport are studied in systematic NSTX scans of relevant plasma parameters. The dependency of the MTM real frequency and growth rate on plasma parameters, suitable for low and high collision NSTX discharges, is obtained by using the reduced MTM transport model [T. Rafiq et al., Phys. Plasmas 23, 062507 (2016)]. The plasma parameter dependencies are compared and found to be consistent with the results obtained from MTM using the gyrokinetic GYRO code. The scaling trend of collision frequency and plasma beta is found to be consistent with the global energy confinement trend observed in the NSTX experiment. The strength of the magnetic fluctuation is found to be consistent with the gyrokinetic estimate. In earlier studies, it was found that the version of the multi-mode (MM) anomalous transport model, which did not contain the effect of MTMs, provided an appropriate description of the electron temperature profiles in standard tokamak discharges and not in spherical tokamaks. When the MM model, which involves transport associated with MTMs, is incorporated in the TRANSP code and is used in the study of electron thermal transport in NSTX discharges, it is observed that the agreement with the experimental electron temperature profile is substantially improved.

A semi-supervised machine learning detector for physics events in tokamak discharges

Databases of physics events have been used in various fusion research applications, including the development of scaling laws and disruption avoidance algorithms, yet they can be time-consuming and tedious to construct. This paper presents a novel application of the label spreading semi-supervised learning algorithm to accelerate this process by detecting distinct events in a large dataset of discharges, given few manually labeled examples. A high detection accuracy (>85%) for H–L back transitions and initially rotating locked modes is demonstrated on a dataset of hundreds of discharges from DIII-D with manually identified events for which only three discharges are initially labeled by the user. Lower yet reasonable performance (∼75%) is also demonstrated for the core radiative collapse, an event with a much lower prevalence in the dataset. Additionally, analysis of the performance sensitivity indicates that the same set of algorithmic parameters is optimal for each event. This suggests that the method can be applied to detect a variety of other events not included in this paper, given that the event is well described by a set of 0D signals robustly available on many discharges. Procedures for analysis of new events are demonstrated, showing automatic event detection with increasing fidelity as the user strategically adds manually labeled examples. Detections on Alcator C-Mod and EAST are also shown, demonstrating the potential for this to be used on a multi-tokamak dataset.

Tokamak discharge simulation coupling free-boundary equilibrium and plasma model with application to JT-60SA

In order to simulate a full tokamak discharge, a fast integrated tokamak modeling tool for scenario design, METIS, is coupled with a quasi-static free-boundary magnetic equilibrium code, FEEQS. The first code is able to compute at each time the plasma equilibrium, the current density and plasma pressure profiles. The generated outputs are iteratively used by the second code that computes the poloidal field coils currents needed in order to obtain a given plasma shape. This is used to assess the feasibility of scenarios designed by integrated modeling simulations. This approach is much faster with respect to full simulators, equipped with specific feedback controllers, and can be regarded as complementary or preparatory to much more time-consuming scenario control optimisation. The results obtained with the equilibrium code are benchmarked with data already available and computed using the TOSCA code. To illustrate how the coupled codes work, the optimization of one of the reference scenarios of the JT-60SA tokamak is carried out. The use of this new simulation tool for tokamak scenario design is discussed.

MATHEMATICAL MODEL OF THE ADAPTABLE DISCHARGE CONTROL SYSTEM IN A TOKAMAK WITH AN IRON CORE

The previously developed adaptation models of the program regime used the so-called “local” adaptation model, i.e. when the correction of the control currents was carried out at each moment of time regardless of their change at other times. The main element was that the adaptation algorithms used were linear, i.e. are based on the linearization of the Kirchhoff system of equations describing the evolution of the control currents during the discharge. In this paper, an algorithm for “global” adaptation of control currents is proposed. It is based on a mathematical model for controlling the discharge in an iron-core tokamak, taking into account the nonlinear behavior of a ferromagnetic. In this model, the evolution of currents is described by the Kirchhoff equations with nonlinear mutual induction coefficients, and the restrictions on the control currents, voltages, and the equilibrium and stability conditions for the plasma are included in the corresponding discrepancy functional. To find the discharge scenario, the optimal control problem is formulated and solved. The algorithm of “global” adaptation consists in the fact that information about the previous discharges is included in the minimized functional, and then the problem of optimal control is solved and a new program scenario of the discharge and the corresponding control currents and voltages are found. As a result, the model of adaptation of the program regime, first, is nonlinear, i.e. nonlinearized Kirchhoff equations are used to describe the evolution of the control currents, and, secondly, the “global” one, since the correction of all currents is carried out interdependently and consistently during the entire discharge scenario. This approach allows us to redistribute the currents in advance in the critical situation (for example, additional heating) and provide the required program regime. This is especially important in an iron-core tokamak, when the connections between the control currents become highly nonlinear. In this work, using the example of the problem of additional heating for the T-15 tokamak, the work of the “global” adaptation algorithm is demonstrated.

Investigation of radial distribution of atomic hydrogen flux to the plasma facing components in steady state discharges in QUEST tokamak

Abstract To study radial distribution of hydrogen flux in peripheral plasma in long duration tokamak discharges, permeation and Langmuir reciprocate probes are used. The atomic hydrogen flux to the walls at several radial positions is deduced from the permeation flux. Contribution of the ions to the hydrogen flow is deduced from the Langmuir probe ion saturation current. It is found, that the atomic hydrogen has the most contribution to the hydrogen flow behind the plasma facing components (PFCs), while the ion flux there is negligible. The atomic flux behind the PFCs drops to the value of F ~ 4.3 × 10 15 H / m 2 / s , which is ~ 6 % of that just in front of PFCs, F ~ 7.7 × 10 16 H / m 2 / s .

Validation of the Fenix ASDEX Upgrade flight simulator

• Validation of the Fenix ASDEX Upgrade flight simulator. • Comparison of experimental and simulated data. • Fenix simulates the entire tokamak discharge. • Fenix simulates control system, actuators, diagnostics and tokamak plasma. Fenix [1] , [2] is the ASDEX Upgrade (AUG) flight simulator based on the 1-D transport code ASTRA coupled with the 2-D equilibrium solver [ 3 ] SPIDER and Simulink (simulation platform integrated with MATLAB). Fenix is designed to simulate the entire discharge from the ramp up of the poloidal field (PF) coils, through the plasma phase, finishing with the ramp down of the PF coils. Currently, controllers for position, shape, fuelling and heating are implemented according to the AUG control system setup. Also, a model of the poloidal field coils and the models of their corresponding power supplies are provided, as well as basic models of heating actuators such as electron cyclotron resonant heating (ECRH), neutral beam injection (NBI) and fuelling using either pellets or gas. As a next step, the Fenix simulations have to be validated against an already existing database of the discharges. This article compares the behaviour of Fenix simulations against various AUG AUGAUGAUG discharge measurements. It shows that it succeeds in its goal as a comprehensive tokamak discharge simulator.

Application of Doppler Backscattering for Alfvén Mode Study on the Globus-M Spherical Tokamak

The Alfven oscillations were studied using the multifrequency Doppler backscattering (DBS) method on the Globus-M spherical tokamak during the neutral deuterium injection. The principles of Alfven mode registration by the DBS method are discussed. Microwave schemes of multifrequency probing are described. It is shown that the observed plasma rotation velocity oscillations are due to the oscillations of the drift velocity in crossed radial electric field of the Alfven wave and the magnetic field. The absolute values of the magnetic field perturbations of the toroidal Alfven eigenmode (TAE) in the internal regions of the tokamak discharge are determined. The obtained data are compared with the results of the magnetic field oscillations measurements obtained by a magnetic probe located outside the plasma region. The use of multifrequency probing in the DBS method made it possible to determine the radial distributions of the amplitude of magnetic field oscillations. These data were obtained for oscillations at the TAE fundamental frequency and at harmonic frequencies, which were found to correspond to different toroidal mode numbers. In general, the data obtained can be compared with the results of numerical modeling of the Alfven spectrum in the Globus-M tokamak. The prospects for the further use of the DBS method for studying Alfven oscillations in toroidal installations are discussed.

Design of HL-2A plasma position predictive model based on deep learning

In tokamak discharge experiments, the plasma position prediction model’s research is to understand the law of plasma motion and verify the correctness of the plasma position controller design. Although Maxwell equations can completely describe plasma movement, obtaining an accurate physical model for predicting plasma behavior is still challenging. This paper describes a deep neural network model that can accurately predict the HL-2A plasma position. That is a hybrid neural network model based on a long short-term memory network. We introduce the topology, training parameter setting, and prediction result analysis of this model in detail. The test results show that a trained deep neural network model has high prediction accuracy for plasma vertical and horizontal displacements.

Temporal Profiling of Electron Temperatures Using the Hα–Hβ Line Emission and Triple Langmuir Probe Array in the Pre-Ionization Discharge of the MT-I Spherical Tokamak

Photodiodes masked with narrow-band filters have been used to obtain the temporal profiles of Hα and Hβ line emissions in the pre-ionization phase of hydrogen discharge in the MT-I Spherical Tokamak. The line ratio method relating the emission intensities of the above mentioned lines, having different excitation thresholds, provides the temporal profile of electron temperature. A triple Langmuir probe array having three individual sets of triple probes, arranged linearly, has also been used to measure the temporal profile of electron temperature at three different radial positions simultaneously. Additionally, a spectrometer HR4000+ is used to get the line-integrated emission intensity of H-Balmer lines. The objective of this experiment is to demonstrate the successful development of the optical and electric probe as a diagnostic tool for tokamak discharge.

Ion energy distribution in a radio frequency sheath of plasma with Kappa electron velocity distribution

AbstractA hybrid model consisting of a one‐dimensional radio frequency sheath model and an equivalent circuit model is used to investigate the effect of the non‐Maxwellian plasma with enhanced electron tails on ion energy distribution (IED) at the plasma–wall interface. With the assumption that electrons obey the Kappa distribution in which the parameter κ characterizes the deviation from Maxwellian distribution, the bimodal shape of the IED can always be found with the decrease of κ under the condition of current experimental advanced superconducting tokamak (EAST) discharges during the ion cyclotron range of frequency wave heating. However, the height of the low‐energy peak of the IED decreases, while the high‐energy peak does not change significantly. In addition, the IED shifts towards the higher‐energy regime, and the width of the IED expands with the decrease of κ. It is also shown that frequency and amplitude of the disturbance current, bulk plasma density, and ion temperature are the crucial parameters for determining the shape of IED even in the presence of super‐thermal electrons.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

Development of a broad band AC power amplifier for real time turbulence feedback control experiment in the Saskatchewan Torus-modified (STOR-M) tokamak.

A gated oscillating power amplifier has been developed for high frequency biasing and real time turbulent feedback experiments in the Saskatchewan Torus-modified tokamak. This oscillator is capable of providing a peak to peak oscillating output voltage of around ±60 V with a current around 30 A within the frequency band 1 kHz-50 kHz without any distortions. The overall output power is amplified by a two-stage metal oxide semiconductor field-effect transistor power op-amp as well as nine identical push-pull amplifiers in the final stages. The power amplifier input signal, collected from the plasma floating potential during the tokamak discharge, is optically isolated from the tokamak vessel ground. The filtered floating potential fluctuations with a band width of 5 kHz-40 kHz were amplified and fed to an electrode inserted into the plasma edge to study the response of the plasma turbulence. We observe that magnetic fluctuations are suppressed due to real time feedback of the floating potential.

Mitigation of disruption on IR-T1 tokamak by means of low-energy neutral beam injection to control runaway electron generation

In a tokamak, the poloidal magnetic field provided by the toroidal plasma current forms an essential part of the magnetic field confining the plasma. However, instabilities of magnetohydrodynamic equilibrium can lead to an uncontrolled sudden loss of plasma current and energy, which is called a disruption. Disruptions are of significant concern to future devices due to the large amount of energy released during the rapid quenching of the plasma. One important consequence of disruption is the generation of significant current carried in multi-MeV runaway electrons that are eventually lost into plasma components. They can damage the tokamak walls and its structure if they are not controlled. Disruption control by neutral beam injection has been performed on IR-T1 to study the effect on runaway electron generated by plasma disruptions. Noble gases are used for injection, pure Hydrogen, Helium and Argon. The use of these non-reactive gases for disruption control ensures they fast removed from the vessel after the termination of a tokamak discharge. A piezo-valve is used for injection which has the precision of 1 ms. The effect of runaway electron generation control during disruption is studied using a comparison between reference disruptive discharge and a discharge into which different impurity species are injected. The data collected can then be used to optimize the performance of these energetic electrons control generated in disruption.

Modeling of the HL-2A plasma vertical displacement control system based on deep learning and its controller design

The modeling and control of the plasma equilibrium response is still one of the more important research areas in tokamak discharge experiments. Although theoretically, first principles can predict the plasma instability, how to build a physical model for accurate prediction is still a challenging problem. Therefore, a deep learning method is proposed to model the plasma vertical displacement system in the HL-2A tokamak experiment, whose method expands the modeling strategy for tokamak plasma control systems. Through the training of a large number of high-dimensional experimental data, the obtained deep neural network model in this paper has a higher precision prediction ability. Additionally, to illustrate the significance of the predictive model in controller design, a data-driven adaptive control algorithm is proposed to replace the traditional proportional-integral-derivative control algorithm for controlling the vertical displacement of plasma. The simulation results showed that the proposed algorithm had less adjustable parameters, strong self-adaptability, and effective control for the HL-2A plasma vertical displacement.

Phase-space dynamics of Alfvén mode chirping

In tokamak discharges, toroidal Alfvén eigenmodes often experience complex semi-periodic frequency modulation known as chirping. These events modify the local high energy particle distribution and are expected to occur in many future fusion devices, which include energetic beams or fusion products. This paper presents a study of simulations of mode chirping made in order to better understand its phase-space properties in a realistic tokamak configuration. We find a mechanism that permits rapid repeated chirping with strong amplitude variation in each chirp. Each chirp is associated with an amplitude crash to low magnitude and local manipulation of the density gradients through a shift of mode phase through π. The chirping produces high density clumps, which propagate down the fast ion density gradient and low density holes that propagate up the density gradient away from the resonance. This flow of particles across the resonance provides an energy source and local gradients for repeated chirping.

Design and fabrication of an optimized Rogowski coil for plasma current sensing and the operation confidence of Alvand tokamak

To understand the fundamental parameters of Alvand tokamak, A Rogowski coil with an active integrator was designed and constructed. Considering the characteristics of the Alvand tokamak, the structural and electrical parameters affecting the sensor function, were designed. Calibration was performed directly in the presence of plasma. The sensor has a high resistance against interference of external magnetic fields. Plasma current was measured in various experiments. Based on the plasma current profile and loop voltage signal, the time evolution of plasma discharge was investigated and plasma behavior was analyzed. Alvand tokamak discharge was divided into several regions that represents different physical phenomena in the plasma. During the plasma discharge time, plasma had significant changes and its characteristic was not uniform. To understand the plasma behavior in each of the phases, the Rogowski sensor should have sufficient time resolution. The Rogowski sensor with a frequency up to 15 kHz was appropriate for this purpose.