Plasma Internal Inductance Research Articles

Retraction Note: Determination of the Plasma Internal Inductance and Evaluation of its Effects on Plasma Horizontal Displacement in IR-T1 Tokamak

Retraction Note: Determination of the Plasma Internal Inductance and Evaluation of its Effects on Plasma Horizontal Displacement in IR-T1 Tokamak

Retraction Note: Effects of Resonant Helical Field on Plasma Internal Inductance in IR-T1 Tokamak

Retraction Note: Effects of Resonant Helical Field on Plasma Internal Inductance in IR-T1 Tokamak

Retraction Note to: Plasma Internal Inductance in the Presence of External Resonant Fields in IR-T1 Tokamak

Retraction Note to: Plasma Internal Inductance in the Presence of External Resonant Fields in IR-T1 Tokamak

Scenario optimization for the tokamak ramp-down phase in RAPTOR: Part B. safe termination of DEMO plasmas

An optimized plasma current ramp-down strategy is critical for safe and fast termination of plasma discharges in a tokamak demonstration fusion reactor (DEMO), both in planned and emergency scenarios, avoiding plasma disruptions and excessive heat loads to the first wall. Plasma stability limits and machine-specific technical requirements constrain the stable envelope through which the plasma must be navigated. Large amounts of auxiliary heating are required throughout the ramp-down phase, to avoid a radiative collapse in the presence of intrinsic tungsten and seeded xenon impurities, as quantitatively estimated in this work. As the plasma current is reduced, the current density becomes increasingly peaked, reflected by a growing value of the internal inductance ℓi3 , resulting in reduced controllability of the vertical position of the plasma. The feasibility of different plasma current ramp-down rates is tested by applying an automated optimization framework embedding the RAPTOR core transport solver. Optimal time traces for plasma current Ip(t) and plasma elongation κ(t) are proposed, to satisfy an Ip -dependent upper limit on the plasma internal inductance, as obtained from vertical stability studies using the CREATE-NL code, as well as a constraint on the time evolution of q 95, to avoid an ideal MHD mode. A negative current density near the plasma edge is observed in our simulations, even for the most conservative Ip ramp-down rate, indicating significant transient dynamics due to a large resistive time.

Exploration of ITER operational space with as-built stiffness of central solenoid modules

The as-built stiffness in the ITER central solenoid (CS) modules (CSM1 thorough to CSM4 are currently manufactured) determines the range of vertical compression forces that can be tolerated by the CS modules during ITER operation. Since the as-built stiffness of the CS modules manufactured (∼32 GPa and ∼34 GPa for CSM1 and CSM2, respectively and similar for the other modules) has been reduced from the design value (53 GPa), the CS axial (vertical) force criteria have been updated assuming a conservative stiffness (25 GPa) with margins for all six CS modules. Initial analysis using the updated CS force criteria has revealed that this reduction affects only the plasma initiation with fully charged CS in the ITER 15 MA Baseline DT scenario, resulting in a slight reduction of poloidal magnetic flux, from 117.5 Wb to 116.2 Wb at initial CS magnetization. Therefore, the 15 MA Baseline scenario has been re-developed with an updated plasma start-up, and then the entire evolution of the CS and poloidal field coil parameters has been validated against all the coil currents, fields and forces criteria. To explore potential risks and opportunities for further optimization of scenarios, the equilibrium operational space (the plasma internal inductance versus the poloidal magnetic flux produced by the coils) at flat-top burn has been analyzed using the CORSICA and DINA codes. The three major ITER reference DT operation scenarios, 15 MA Q = 10 Baseline, 12.5 MA Q > 5 Hybrid and 10 MA Q ∼ 5 Steady-State, satisfy all the coil criteria including the CS force updated reflecting the as-built stiffness. The evolution of the plasma discharge parameters within the equilibrium operational spaces provided a guidance for potential optimization with margins.

Transition of turbulence regime during neutral beam injection on EAST

In recent experiments on EAST with neutral beam injection (NBI) and radio frequency (RF) waves (lower hybrid wave (LHW) and electron cyclotron waves) heating, it was observed that an increase in the line-averaged electron density and a decrease in the plasma internal inductance occurred in the duration of NBI. To explain the experimental observation, the simulations are conducted by using the equilibrium code EFIT and the transport codes ONETWO and TGYRO. It is shown that L-H transition is triggered right after neutral beam is injected, leading to the formation of density pedestal, the plasma density gradient in the outer region (0.4 < ρ < 0.75) is thus changed, which leads to an increase in η i (, where and ), where ρ is the normalized square root of the toroidal magnetic flux. A transition from a trapped electron modes (TEM) to an ion temperature gradient (ITG) modes dominant turbulence regime then happens due to the increase of η i in the region (0.4 < ρ < 0.75), which results in an inward particle pinch. As a result of the rise of plasma density, the parallel refractive index and ray trajectories of the LHW are affected and more power is deposited outside ρ > 0.6, which drives more off-axis current and therefore the internal inductance is reduced.

Equilibrium reconstruction of DIII-D plasmas using predictive modeling of the pressure profile

New workflows have been developed for predictive modeling of magnetohydrodynamic (MHD) equilibrium in tokamak plasmas. The goal of this work is to predict the MHD equilibrium in tokamak discharges without having measurements of the kinetic profiles. The workflows include a cold start tool, which constructs all the profiles and power flows needed by transport codes; a Grad–Shafranov equilibrium solver; and various codes for the sources and sinks. For validation purposes, a database of DIII-D tokamak discharges has been constructed that is comprised of scans in the plasma current, toroidal magnetic field, and triangularity. Initial efforts focused on developing a workflow utilizing an empirically derived pressure model tuned to DIII-D discharges with monotonic safety factor profiles. This workflow shows good agreement with experimental kinetic equilibrium calculations, but is limited in that it is a single fluid (equal ion and electron temperatures) model and lacks H-mode pedestal predictions. The best agreement with the H-mode database is obtained using a theory-based workflow utilizing pressure profile predictions from a coupled TGLF turbulent transport and EPED pedestal models together with external magnetics and Motional Stark Effect (MSE) data to construct the equilibrium. Here, we obtain an average root mean square error of 5.1% in the safety factor profile when comparing the predicted and experimental kinetic equilibrium. We also find good agreement with the plasma stored energy, internal inductance, and pressure profiles. Including MSE data in the theory-based workflow results in noticeably improved agreement with the q-profiles in high triangularity discharges in comparison with the results obtained with magnetic data only. The predictive equilibrium workflow is expected to have wide applications in experimental planning, between-shot analysis, and reactor studies.

Neural network based fast prediction of β N limits in HL-2M

Artificial neural networks (NNs) are trained, based on the numerical database, to predict the no-wall and ideal-wall β N limits, due to onset of the n = 1 (n is the toroidal mode number) ideal external kink instability, for the HL-2M tokamak. The database is constructed by toroidal computations utilizing both the equilibrium code CHEASE (Lütjens et al 1992 Comput. Phys. Commun. 69 287) and the stability code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). The stability results show that (1) the plasma elongation generally enhances both β N limits, for either positive or negative triangularity plasmas; (2) the effect is more pronounced for positive triangularity plasmas; (3) the computed no-wall β N limit linearly scales with the plasma internal inductance, with the proportionality coefficient ranging between 1 and 5 for HL-2M; (4) the no-wall limit substantially decreases with increasing pressure peaking factor. Furthermore, both the NN model and the convolutional neural network (CNN) model are trained and tested, producing consistent results. The trained NNs predict both the no-wall and ideal-wall limits with as high as 95% accuracy, compared to those directly computed by the stability code. Additional test cases, produced by the Tokamak Simulation Code (Jardin et al 1993 Nucl. Fusion 33 371), also show reasonable performance of the trained NNs, with the relative error being within 10%. The constructed database provides effective references for the future HL-2M operations. The trained NNs can be used as a real-time monitor for disruption prevention in the HL-2M experiments, or serve as part of the integrated modeling tools for ideal kink stability analysis.

Integrated Control and Actuator Management Strategies for Internal Inductance and Normalized Beta Regulation

An integrated-control architecture for simultaneous regulation of the plasma internal inductance and normalized beta has been designed and tested in simulations using COTSIM (Control-Oriented Transport SIMulator). As present-day tokamaks evolve into nuclear-fusion reactors capable of producing net energy, a significant control-engineering challenge must be solved: regulating a wide variety of plasma variables, often simultaneously, by employing only a reduced number of actuators. As a contribution towards this objective, the present work tackles the problem of controlling the plasma internal inductance, which is a proxy for the broadness of the current-density profile, simultaneously with the plasma normalized beta. Based on zero-dimensional, control-oriented models of the plasma dynamics, individual Lyapunov-theory-based controllers for the internal inductance and normalized beta have been developed. These controllers are integrated by means of an actuator manager that decides, in real time, how the available actuators are utilized in order to fulfill as many control objectives as possible. In addition, the actuator manager is designed to achieve a particular performance metric defined by the control engineer. This metric could be, for example, prioritizing a particular control task over the others and/or minimizing the use of a particular actuator during certain phases of the plasma discharge. Using COTSIM, which includes one-dimensional models of the plasma current-density and electron-temperature dynamics, the performance of the integrated-control framework has been tested in a steady-state scenario for the DIII-D tokamak. These simulation results yield illustrative insights into the plasma current-density and electron-temperature controllability with the current actuation capabilities in DIII-D. Moreover, these simulations show that the way in which the different actuators are employed during the discharge (based on the choice of the aforementioned actuator-manager performance metric) highly determines the value of internal inductance and normalized beta achieved in steady-state conditions, and therefore, the final current-profile shape.

Flattening of the tokamak current profile by a fast magnetic reconnection with implications for the solar corona

During tokamak disruptions, the profile of the net parallel current is observed to flatten on a time scale that is so fast that it must be due to a fast magnetic reconnection. After a fast magnetic reconnection has broken magnetic surfaces, a single magnetic field line covers an entire volume and not just a magnetic surface. The current profile, given by K≡μ0j||/B, relaxes to a constant within that volume by Alfvén waves propagating along the chaotic magnetic field lines. The time scale for this relaxation determines the commonly observed disruption phenomena of a current spike and a sudden drop in the plasma internal inductance. An efficient method for studying this relaxation is derived, which allows a better understanding of the information encoded in the current spike and the associated sudden drop in the plasma internal inductance. Implications for coronal heating are also discussed.

Model predictive control of KSTAR equilibrium parameters enabled by TRANSP

Due to the complex behavior of tokamak plasmas and the importance of optimizing performance while avoiding instabilities and machine limits, plasma control algorithms are becoming increasingly dependent on sophisticated model-based control approaches. It is anticipated that the use of integrated modeling codes in the model-based control design process will reduce the amount of experimental time needed to implement new control algorithms by facilitating development of control-oriented models and enabling higher-fidelity closed-loop simulations. In this work, a reduced model is developed from a series of TRANSP simulations and is used to develop a model predictive control (MPC) algorithm for controlling important equilibrium parameters in KSTAR [] discharges. The control algorithm uses the KSTAR neutral beam injection system and the target plasma current and plasma boundary as actuators, and optimizes the plasma stored energy, loop voltage, and internal inductance while avoiding constraints that could lead to disruptions. Higher fidelity testing of the control algorithm is performed using a flexible framework for enabling external processes to actively control plasma parameters in TRANSP simulations. Closed-loop simulations demonstrate the ability of the control algorithm to respond to disturbances in density and confinement, handle actuator failures, and move the discharge to high non-inductive fraction conditions.

Projected global stability of high beta MAST-U spherical tokamak plasmas

Assessment of the limits of stability of tokamak plasmas is key to operation in high fusion performance ranges without disruption of the plasma current. Projected equilibria have been generated for the MAST-U spherical tokamak experiment, an upgrade of the previous MAST device, in order to prepare for operation. These equilibria are scanned in pressure and current profiles, and assessed with the DCON and MARS-F stability codes to find the so-called ‘no-wall’ beta limit, above which resistive wall mode instabilities can be expected in the absence of other stabilising effects. The no-wall limit was generally found to increase as plasma internal inductance increased. The equilibria are also assessed for the ‘with-wall’ limit, theoretically the highest achievable performance point, again with the DCON and MARS-F codes, including different approximate axisymmetric walls, and with the VALEN code which includes a 3D model of the surrounding conducting structure. Similar limits were found, despite the difference between the 2D and 3D codes in the treatment of the wall. Conducting passive stabilisation plates, which were newly installed in MAST-U, are in a region of significant mode perturbation when the plasma βN is sufficiently high and eddy currents are driven in these structures. Due to the increased stabilising effect of the wall in MAST-U vs. MAST, a significant gap exists between the approximate no-wall limits of βN/li = 6.71 and 7.13, found from DCON and MARS-F respectively, and the with-wall limits of βN/li = 8.23 and 8.53 for the equilibrium profiles analysed in this study. This opens a region of high beta operating space in MAST-U for potentially stable operation if non-ideal effects or active control can stabilise the resistive wall mode.

Overview of disruptions with JET-ILW

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

Neural network based prediction of no-wall βN limits due to ideal external kink instabilities

Multi-layer perceptron based neural networks (NNs) are trained to predict the Troyon no-wall beta limits due to the onset of low-n (n = 1–3, n is the toroidal mode number) ideal external kink instabilities in tokamak plasmas. It is found that a well trained NN can predict the n = 1 no-wall beta limit within 10% relative error. The NN performance is somewhat worse for the n = 2 and 3 no-wall beta limits, but still a relative error within 20% is achievable. The trained NNs well reproduce the known dependences of the no-wall beta limits on the plasma pressure (pressure peaking factor) and current (plasma internal inductance) profiles. Other scalings are also easily established with NNs, for parametric dependences such as on the aspect ratio, the elongation and triangularity of the plasma boundary shape. The results show that the semi-analytically generated training database can be used to train NNs for predicting the no-wall limit in realistic experiments. These NN-based Troyon beta limit predictors can be incorporated into integrated modeling platforms, or directly implemented as a real time stability estimator for the purpose of disruption avoidance or mitigation during experiments.

Prediction of high-beta disruptions in JT-60U based on sparse modeling using exhaustive search

Disruption is a critical phenomenon in a tokamak reactor. Although disruption causes serious damage to the reactor, its physical mechanism remains unclear. To realize a tokamak reactor, it is necessary to understand and control the disruption phenomenon. The present research constructs a disruption predictor using experimental high-beta plasma data in the JT-60U tokamak. The predictor was constructed using a support vector machine as a linear discriminant, and we focus on a variable selection problem for the binary classification by sparse modeling, specifically, exhaustively searching the best combinations of variables which maximize the predictor performance. By the sparse modeling, we found that the six input parameters as the best combinations. The selected parameters were the n = 1 mode amplitude |Brn=1| and its time derivative d|Brn=1|/dt, the plasma density (relative to the Greenwald density limit) and its time derivative, and the time derivatives of the plasma internal inductance and plasma elongation. In particular, it was identified that the parameter d|Brn=1|/dt, plays a key role on plasma disruption. We should notice that the combination with other plasma parameters is indispensable and remarkably make it possible to improve the performance of disruption prediction.

Disruption prediction investigations using Machine Learning tools on DIII-D and Alcator C-Mod

Using data-driven methodology, we exploit the time series of relevant plasma parameters for a large set of disrupted and non-disrupted discharges to develop a classification algorithm for detecting disruptive phases in shots that eventually disrupt. Comparing the same methodology on different devices is crucial in order to have information on the portability of the developed algorithm and the possible extrapolation to ITER. Therefore, we use data from two very different tokamaks, DIII-D and Alcator C-Mod. We focus on a subset of disruption predictors, most of which are dimensionless and/or machine-independent parameters, coming from both plasma diagnostics and equilibrium reconstructions, such as the normalized plasma internal inductance ℓi and the n = 1 mode amplitude normalized to the toroidal magnetic field. Using such dimensionless indicators facilitates a more direct comparison between DIII-D and C-Mod. We then choose a shallow Machine Learning technique, called Random Forests, to explore the databases available for the two devices. We show results from the classification task, where we introduce a time dependency through the definition of class labels on the basis of the elapsed time before the disruption (i.e. ‘far from a disruption’ and ‘close to a disruption’). The performances of the different Random Forest classifiers are discussed in terms of several metrics, by showing the number of successfully detected samples, as well as the misclassifications. The overall model accuracies are above 97% when identifying a ‘far from disruption’ and a ‘disruptive’ phase for disrupted discharges. Nevertheless, the Forests are intrinsically different in their capability of predicting a disruptive behavior, with C-Mod predictions comparable to random guesses. Indeed, we show that C-Mod recall index, i.e. the sensitivity to a disruptive behavior, is as low as 0.47, while DIII-D recall is ∼0.72. The portability of the developed algorithm is also tested across the two devices, by using DIII-D data for training the forests and C-Mod for testing and vice versa.

Relationship between locked modes and thermal quenches in DIII-D

Locked modes are known to be one of the major causes of disruptions, but the physical mechanisms by which locking leads to disruptions are not well understood. Here we analyze the evolution of the temperature profile in the presence of multiple coexisting locked modes during partial and full thermal quenches. Partial quenches are often observed to be an initial, distinct stage in the full thermal quench. Near the onset of partial quenches, locked island O-points are observed to align with each other on the midplane, and their widths are sufficient to overlap each other, as indicated by the Chirikov parameter. Energy conservation analysis of one partial thermal quench shows that the energy lost is both radiated in the divertor region, and conducted or convected to the divertor. Nonlinear resistive magnetohydrodynamic simulations support the interpretation of stochastic fields causing a partial axisymmetric collapse, though the simulated temperature profile exhibits less degradation than the experimental profiles. In discharges with minimum values of the safety factor above ∼1.2, locked modes are observed to self-stabilize by inducing, possibly via double tearing modes, a minor disruption that removes their neoclassical drive. These high qmin discharges often exhibit relatively low ratios of the plasma internal inductance to the safety factor at 95% of the poloidal flux, which might imply classical stability, in agreement with the decay of the mode when the neoclassical drive is removed.

Exploratory Machine Learning Studies for Disruption Prediction Using Large Databases on DIII-D

Using data-driven methodology, we exploit the time series of relevant plasma parameters for a large set of disrupted and non-disrupted discharges from the DIII-D tokamak with the objective of developing a disruption classification algorithm. We focus on a subset of disruption predictors, most of which are dimensionless and/or machine-independent parameters such as the plasma internal inductance and the Greenwald density fraction , coming from both plasma diagnostics and equilibrium reconstructions. The utilization of dimensionless indicators will facilitate a more direct comparison between different tokamak devices.In order to eventually develop a robust disruption warning algorithm, we leverage Machine Learning techniques, and in particular, we choose the Random Forests algorithm to explore the DIII-D database. We show the results coming from both binary (disrupted/non-disrupted) and multiclass classification problems. In the latter, the time dependency is introduced through the definition of class labels on the basis of the elapsed time before the disruption (i.e., ‘far from a disruption’, ‘within 350 ms of disruption’, etc.). Depending on the formulation of the problem, overall disruption prediction accuracy up to 90% is demonstrated, approaching 97% when identifying a stable and a disruptive phase for disrupted discharges. The performances of the different Random Forest classifiers are discussed in terms of accuracy, by showing the percentages of successfully detected samples, together with the false positive and false negative rates.

Multi-machine analysis of termination scenarios with comparison to simulations of controlled shutdown of ITER discharges

To improve our understanding of the dynamics and control of ITER terminations, a study has been carried out on data from existing tokamaks. The aim of this joint analysis is to compare the assumptions for ITER terminations with the present experience basis. The study examined the parameter ranges in which present day devices operated during their terminations, as well as the dynamics of these parameters. The analysis of a database, built using a selected set of experimental termination cases, showed that, the H-mode density decays slower than the plasma current ramp-down. The consequential increase in fGW limits the duration of the H-mode phase or result in disruptions. The lower temperatures after the drop out of H-mode will allow the plasma internal inductance to increase. But vertical stability control remains manageable in ITER at high internal inductance when accompanied by a strong elongation reduction. This will result in ITER terminations remaining longer at low q (q95 ~ 3) than most present-day devices during the current ramp-down. A fast power ramp-down leads to a larger change in βp at the H–L transition, but the experimental data showed that these are manageable for the ITER radial position control. The analysis of JET data shows that radiation and impurity levels significantly alter the H–L transition dynamics. Self-consistent calculations of the impurity content and resulting radiation should be taken into account when modelling ITER termination scenarios. The results from this analysis can be used to better prescribe the inputs for the detailed modelling and preparation of ITER termination scenarios.

Simulation of profile evolution from ramp-up to ramp-down and optimization of tokamak plasma termination with the RAPTOR code

The present work demonstrates the capabilities of the transport code RAPTOR as a fast and reliable simulator of plasma profiles for the entire plasma discharge, i.e. from ramp-up to ramp-down. This code focuses, at this stage, on the simulation of electron temperature and poloidal flux profiles using prescribed equilibrium and some kinetic profiles. In this work we extend the RAPTOR transport model to include a time-varying plasma equilibrium geometry and verify the changes via comparison with ATSRA code simulations. In addition a new ad hoc transport model based on constant gradients and suitable for simulations of L–H and H–L mode transitions has been incorporated into the RAPTOR code and validated with rapid simulations of the time evolution of the safety factor and the electron temperature over the entire AUG and TCV discharges. An optimization procedure for the plasma termination phase has also been developed during this work. We define the goal of the optimization as ramping down the plasma current as fast as possible while avoiding any disruptions caused by reaching physical or technical limits. Our numerical study of this problem shows that a fast decrease of plasma elongation during current ramp-down can help in reducing plasma internal inductance. An early transition from H- to L-mode allows us to reduce the drop in poloidal beta, which is also important for plasma MHD stability and control. This work shows how these complex nonlinear interactions can be optimized automatically using relevant cost functions and constraints. Preliminary experimental results for TCV are demonstrated.