Real-time Equilibrium Reconstruction Research Articles

Real-time equilibrium reconstruction by multi-task learning neural network based on HL-3 tokamak

Abstract A neural network model, EFITNN, has been developed capable of real-time magnetic equilibrium reconstruction based on HL-3 tokamak magnetic measurement signals. The model processes inputs from 68 channels of magnetic measurement data gathered from 1159 HL-3 experimental discharges, including plasmas current, loop voltage, and the poloidal magnetic fields measured by probes. The outputs of the model feature eight key plasmas parameters, alongside high-resolution ( 129 × 129 ) reconstructions of the toroidal current density J P and poloidal magnetic flux distributions Ψ rz . Moreover, the network’s architecture employs a multi-task learning structure, which enables the sharing of weights and mutual correction among different outputs, and leads to increase the model’s accuracy by up to 32%. The performance of EFITNN demonstrates remarkable consistency with the offline EFIT, achieving average R 2 = 0.941, 0.997 and 0.959 for eight plasmas parameters, Ψ rz and J P , respectively. The model’s robust generalization capabilities are particularly evident in its successful predictions of quasi-snowflake (QSF) divertor configurations and its adept handling of data from shot numbers or plasmas current intervals not previously encountered during training. Compared to numerical methods, EFITNN significantly enhances computational efficiency with average computation time ranging from 0.08 ms to 0.45 ms, indicating its potential utility in real-time isoflux control and plasmas profile management.

Implementation of a real-time MSE system.

Motional Stark effect polarimetry is a key diagnostic for plasma fusion research since its usage on PBX-M. The MSE diagnostic measures the radial magnetic pitch angle profile in a plasma from a neutral beam by observation of Stark split D-alpha emission from atoms excited by collision with ions and electrons in the plasma. The pitch angle measurement is used with equilibrium reconstruction codes to determine the q-profile for studies of plasma stability, confinement, and transport. Historically, the algorithm was used in a post-processing fashion. The goal of our work was to apply this method in real time and pass the results to the plasma control system computer for real-time equilibrium reconstruction and control.

Real-time plasma equilibrium reconstruction and shape control for the MAST Upgrade tokamak

Real-time magnetic control has been developed to deliver precise control of multiple plasma shape parameters for advanced divertor configurations, including double-null, Super-X, X-point target and X-divertor for the first time on the MAST Upgrade (MAST-U) spherical tokamak. Successful real-time magnetic equilibrium control of different plasma shape variables has been accomplished in the 2022–2023 MAST-U experimental campaign for the advanced MAST-U divertor configurations. Application of the MAST-U boundary reconstruction algorithm, LEMUR, is described and compared with off-line equilibrium reconstruction and diagnostic measurements. The process of design and verification of the axisymmetric magnetic control schemes using a suite of control analysis tools (known collectively as TokSys) is also described.

Magnetics only real-time equilibrium reconstruction on ASDEX Upgrade

Real-time reconstruction of the magnetic equilibrium provides fundamental control of plasma shape and position in a tokamak. Details of the implementation of the equilibrium reconstruction code developed for the ASDEX Upgrade tokamak (JANET++) are summarized. Cubic Hermite splines are introduced as current density basis functions for solving the Grad–Shafranov equation. The choice of the optimal Tikhonov regularization parameter is discussed. The code is validated by comparing the results of the equilibrium reconstruction with those of further equilibrium reconstructions available on ASDEX Upgrade (CLISTE and IDE). In a high time resolution study of a discharge with edge localized modes (ELM), the poloidal asymmetry of the fits and magnetic probe measurements suggest that the real-time equilibrium reconstruction captures the essential features of the current density redistribution in an ELMing edge plasma. An efficient algorithm to locate multiple X-points and identify the active one in advanced X-divertor and snowflake divertor configurations is presented.

Magnetic pickup coil systems on the HL-3 tokamak

HL-3 is a new medium-sized copper conducting tokamak, which is dedicated to the plasma shaping control for plasma high performance and flexible operation, especially the advanced divertor configurations. According to the physics needs of the project, three types of magnetic pickup coils are designed and developed on HL-3 for magnetic field measurements. The coils emphasize different geometry sizes and array layouts. The coils are installed carefully by using high-precision positioning equipment to ensure the measurement accuracy of the system. After calibration, the magnetic field measurements are supplied for real-time equilibrium reconstruction and plasma control, e.g., with snowflake-shaped divertor configuration reconstruction. Mirnov coils satisfy the requirements for physical analysis, including determining the mode number from raw signals and detecting the magnetohydrodynamic instabilities.

First demonstration of real-time kinetic equilibrium reconstruction on TCV by coupling LIUQE and RAPTOR

Kinetic equilibrium reconstruction (KER) in tokamaks is the solution of the free-boundary MHD equilibrium that best fits the external magnetic measurements and the internal plasma profiles as imposed from modeling and/or available internal measurements. In this paper, for the first time, the KER has been performed in real-time by coupling the free-boundary equilibrium code LIUQE to the 1.5D transport code RAPTOR, during a TCV discharge. The transport code is used as a dynamic state observer evolving the current diffusion equation, the electron heat and particle diffusion equations and correcting the prediction with the measurements available in real-time, making use of the extended Kalman filter (EKF) method. The simple coupling strategy, based on a matching of the free functions ( and ) on the right-hand-side of the Grad Shafranov equation, is shown to be effective in providing consistency of pressure and current density profiles between the two codes. We also show that, despite this highly non-linear system, this technique does not require significant additional computational time with respect to the running times of the two independent codes and does not require a tight coupling of the two codes allowing therefore their independent development. The KER is compared to standard real-time equilibrium reconstruction, performed routinely in TCV, where only the external magnetic measurements are taken into account. The following cases are considered: flat central ne, current density broadening due to applied electron cyclotron current drive and neoclassical tearing mode causing a temperature drop. The KER reproduces the expected changes of the internal profiles, tracking their dynamic evolution in their physical timescales.

A framework for the assessment and control of ITER main chamber heat loads

A control-oriented approach, based on real-time equilibrium reconstruction, has been developed to monitor power fluxes to ITER plasma-facing components (PFC). The model describes the deposited heat flux as a poloidal flux function with two main input parameters: the power exhausted across the plasma boundary and the scrape-off layer heat flux width. A module containing weighting factors accounts for the real PFC 3D geometry. These factors are obtained using a new sophisticated GUI interface, SMITER, hosting a magnetic field line tracing code permitting the import and appropriate meshing of full PFC CAD descriptions. This new methodology has been used to examine two critically important first wall (FW) power loading issues for ITER: the start-up phase at low current and power, but requiring direct contact with the inboard wall, and the case of an upward plasma shift in a diverted configuration under high power, high current H-mode burning plasma conditions, which imposes very high power loads on the upper chamber FW panels.

Mineral insulated cable assessment for inductive magnetic diagnostic sensors of a hot-wall tokamak

The COMPASS-U tokamak, designed to be a 5 T magnetic field device with a full-metal first wall and operating at plasma-facing component temperatures up to 500°C, will start its operation in 2022 at IPP Prague. This device will address ITER and DEMO relevant plasma exhaust physics, including operation with liquid metal divertor. Inductive magnetic diagnostics based on conductive loops of different geometry and orientation are crucial for magnetic confinement fusion devices. Due to the high temperatures of the vacuum vessel upon which they will be operated, a suitable cable insulation needs to be chosen carefully. Mineral-insulated cables (MIC) have proven to be compatible with high baking temperatures. However, the steel sheath of MIC attenuates the response of the sensor at higher frequencies which could affect real-time plasma control feedback and magnetic equilibrium reconstruction. In this work, characterization and testing of multiple MgO MIC of different diameters was conducted. A variety of electrical property measurements, such as frequency attenuation, resistance and capacitance, for each cable is presented, both at low and high temperatures up to 300°C. Cutoff frequencies from 65 kHz to 335 kHz were identified and attributed to the shielding in a flux loop configuration. Using an external RLC circuit, the frequency response of MIC coils is compared to an electrical model for shielded coils, yielding an useful calibrated model for future probe prototypes with different geometries in the frequency range of interest.

ISTTOK poloidal field coils positioning assessment

The construction of any machine have inherent structural assembling errors. With aging and stresses these tend to increase and can particularly deform the original structures leading to significant deviations from original designs. To assess ISTTOK poloidal coils fixtures after almost 30 years of operation at IST, Lisbon a series of tests were conducted. Due to its inherent robustness and reliability, the magnetic diagnostic is the prime candidate for real-time plasma position control applications. ISTTOK is equipped with a set of digital integrators for magnetic reconstruction in line with W7-X and in the future with ITER. Incoherence in the data analysis of the poloidal Mirnov coils array suggested a misalignment of the poloidal field (PF) coils. This contribution explores this possibility, relying on the analysis of the magnetic diagnostic data in order to determine the magnetic position of the PF coil circuits. A significant deviation on the positions of said coils was found and a back-propagated correction based on vacuum measurements is proposed for future magnetic data analysis both for real-time control applications and equilibrium reconstruction codes.

Experimental implementation of a real-time power flux estimator for the ITER first wall on the TCV tokamak

A control-oriented approach to the monitoring of wall power flux densities on ITER has been successfully developed. It is based on real-time equilibrium reconstruction in 2-D which is then used to describe the deposited heat flux as a poloidal flux function with user specified parameters for the power exhausted into the scrape-off layer (SOL) and the SOL heat flux width. To account for the real 3-D geometry of the plasma-facing components (PFC), appropriate weighting factors are derived from magnetic field line tracing in 3-D. Integration of the 3-D effect is performed with a new GUI-based software environment, SMITER, incorporating a field line tracer and permitting import and meshing of PFC CAD models. The paper discusses the experimental demonstration of the model-based wall heat flux algorithm on the TCV tokamak, reporting on the benchmarking of the new code package, SMITER against infra-red camera heat flux measurements and the derivation of the component shaping weighting factors. A comparison of the real-time estimation of the peak power flux and its spatial location against the off-line infra-red measurement for limiter plasma configurations is presented.

First implementation of plasma shape GAP control method in EAST

Preliminary implementation of plasma GAP shape control in EAST is presented. Compared with ISOFLUX method, GAP control could work together with not only real-time equilibrium reconstruction but also real-time boundary reconstruction. Based on the plasma response matrix, the GAP controller is designed and the PID parameter has been optimized for EAST plasma shape control. P-EFIT provides real-time gap calculation and GAP controller is integrated into EAST PCS. Successful plasma shape with GAP control scheme is achieved in EAST 2018 summer campaign. Experimental results prove that GAP control algorithm and controller could achieve similar control ability as ISOFLUX and provide an option for shape control with optical-based boundary reconstruction in EAST and future device CFETR.

Improvement of GPU parallel real-time equilibrium reconstruction for plasma control

Improvements of GPU parallel real-time equilibrium reconstruction code P-EFIT are presented. P-EFIT is based on the EFIT framework, but built with the CUDA™ architecture to take advantage of massively parallel Graphical Processing Unit(GPU) cores to significantly accelerate the computation. Newly designed architecture and applied technique make P-EFIT integrate into plasma control system(PCS) as a sub-algorithm. Efficient parallel strategy and algorithms allow P-EFIT to achieve good computational performance. P-EFIT can complete one equilibrium iteration and transfer real-time diagnostics, control signals and equilibrium data in 375us with 129 × 129 spatial grid. P-EFIT has high spatial resolution, customized modules and internal current profile reconstruction for real-time plasma control in EAST.

Implementation and applications of a new real-time framework for plasma control system in HL-2A

Plasma Control Systems (PCS) that contain various functions and algorithms are applied in different tokamak devices. A real-time framework which allows various control functions and algorithms to be developed and deployed is very important to a PCS. A modular-based Multi-thread Real-time Framework (MRTF) is developed by HL-2A for this purpose. A multi-thread scheduling solution is provided by the framework to run the modules in PCS, and also to synchronize the modules and make them shared with each other. CPU affinity has been made for every thread in MRTF. In order to integrate control modules, an abstraction interface for PCS functions is defined by the framework. Several tests have been made to assess the performance of the real-time framework. A plasma real-time equilibrium reconstruction module is developed and integrated in MRTF. The module can calculate the flux distribution of plasma profile by the grid of 129*129 within 700 us on HL-2A experiment. The framework has been implemented in HL-2A experiment and achieved expectations. More control functions and strategies of PCS will be integrated by the framework in the future.

Plasma boundary shape control and real-time equilibrium reconstruction on NSTX-U

The upgrade to the National Spherical Torus eXperiment (NSTX-U) included two main improvements: a larger center-stack, enabling higher toroidal field and longer pulse duration, and the addition of three new tangentially aimed neutral beam sources, which increase available heating and current drive, and allow for flexibility in shaping power, torque, current, and particle deposition profiles. To best use these new capabilities and meet the high-performance operational goals of NSTX-U, major upgrades to the NSTX-U control system (NCS) hardware and software have been made. Several control algorithms, including those used for real-time equilibrium reconstruction and shape control, have been upgraded to improve and extend plasma control capabilities. As part of the commissioning phase of first plasma operations, the shape control system was tuned to control the boundary in both inner-wall limited and diverted discharges. It has been used to accurately track the requested evolution of the boundary (including the size of the inner gap between the plasma and central solenoid, which is a challenge for the ST configuration), X-point locations, and strike point locations, enabling repeatable discharge evolutions for scenario development and diagnostic commissioning.

Acceleration optimization of real-time equilibrium reconstruction for HL-2A tokamak discharge control

Real-time equilibrium reconstruction is crucially important for plasma shape control in the process of tokamak plasma discharge. However, as the reconstruction algorithm is computationally intensive, it is very difficult to improve its accuracy and reduce the computation time, and some optimizations need to be done. This article describes the three most important aspects of this optimization: (1) compiler optimization; (2) some optimization for middle-scale matrix multiplication on the graphic processing unit and an algorithm which can solve the block tri-diagonal linear system efficiently in parallel; (3) a new algorithm to locate the X&O point on the central processing unit. A static test proves the correctness and a dynamic test proves the feasibility of using the new code for real-time reconstruction with 129 × 129 grids; it can complete one iteration around 575 μs for each equilibrium reconstruction. The plasma displacements from real-time equilibrium reconstruction are compared with the experimental measurements, and the calculated results are consistent with the measured ones, which can be used as a reference for the real-time control of HL-2A discharge.

Fast parallel Grad–Shafranov solver for real-time equilibrium reconstruction in EAST tokamak using graphic processing unit**Project supported by the National Magnetic Confinement Fusion Research Program of China (Grant No. 2014GB103000), the National Natural Science Foundation of China (Grant No. 11575245), and the National Natural Science Foundation of China for Youth (Grant No. 11205191).

To achieve real-time control of tokamak plasmas, the equilibrium reconstruction has to be completed sufficiently quickly. For the case of an EAST tokamak experiment, real-time equilibrium reconstruction is generally required to provide results within 1ms. A graphic processing unit (GPU) parallel Grad–Shafranov (G-S) solver is developed in P-EFIT code, which is built with the CUDA architecture to take advantage of massively parallel GPU cores and significantly accelerate the computation. Optimization and implementation of numerical algorithms for a block tri-diagonal linear system are presented. The solver can complete a calculation within with 65 × 65 grid size and with 129 × 129 grid size, and this solver supports that P-EFIT can fulfill the time feasibility for real-time plasma control with both grid sizes.

Enhancement of EAST plasma control capabilities

In order to improve the plasma control performance and enhance the capability for advanced plasma control, new algorithms such as PEFIT/ISOFLUX plasma shape feedback control, quasi-snowflake plasma shape development and vertical control under new vertical control power supply, have been implemented and experimentally tested and verified in EAST 2014 campaign. P-EFIT is a rewritten version of EFIT aiming at fast real-time equilibrium reconstruction by using GPU for parallelized computation. Successful control using PEFIT/ISOFLUX was established in dedicated experiment. Snowfldivertor plasma shape has the advantage of spreading heat over the divertor target and a quasi-snowflake (QSF) configuration was achieved in discharges with Ip=0.25 MA and Bt=1.8T, κ∼1.9, by plasma position feedback control. The shape feedback control to achieve QSF shape has been preliminary implemented by using PEFIT and the initial experimental test has been done. For more robust vertical instability control, the inner coil (IC) and its power supply have been upgraded. A new control algorithm with the combination of Bang-bang and PID controllers has been developed. It is shown that new vertical control power supply together with the new control algorithms results in higher vertical controllability.

Real-Time Detection for Magnetic Island of Neoclassical Tearing Mode in EAST Plasma Control System**supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2014GB103000, 2012GB103000, and 2012GB103002), National Natural Science Foundation of China (No. 11205200)

Accurate detection of a magnetic island in real time is one of the important issues for the tearing mode (TM) and neoclassical tearing mode (NTM) control. This paper presents a real-time detection system for the magnetic island of NTM control in the EAST Plasma Control System (PCS). Diagnosis is based on magnetic periodic perturbation and electron temperature fluctuation caused by the magnetic island. Therefore, a Mirnov measurement has been selected to calculate the island's parameters, such as island width, frequency of island rotation, and toroidal number. The electron cyclotron emission (ECE) system can detect the island position, which is calculated by two fast detection algorithms called correlation analysis and Hilbert transform. For future NTM control, real-time equilibrium reconstruction (rt-EFIT) is needed to locate the rational q-surface where the island is detected. This fast detection system is able to detect an island within 3 ms. It can be integrated into PCS to provide effective parameters of the island for NTM control by using EC resonance heating (ECRH) in the next experiment of EAST.

Improvements for real-time magnetic equilibrium reconstruction on ASDEX Upgrade

Real-time magnetic equilibria are needed for NTM stabilization and disruption avoidance experiments on ASDEX Upgrade. Five improvements to real-time magnetic equilibrium reconstruction on ASDEX Upgrade have been investigated. The aim is to include as many features of the offline magnetic equilibrium reconstruction code in the real-time equilibrium reconstruction code. Firstly, spline current density basis functions with regularization are used in the offline equilibrium reconstruction code, CLISTE [1]. It is now possible to have the same number of spline basis functions in the real-time code. Secondly, in the presence of edge localized modes, (ELM's), it is found to be necessary to include the low pass filter effect of the vacuum vessel on the fast position control coil currents to correctly compensate the magnetic probes for current oscillations in these coils. Thirdly, the introduction of ferromagnetic tiles in ASDEX Upgrade means that a real-time algorithm for including the perturbations of the magnetic equilibrium generated by these tiles is required. A methodology based on tile surface currents is described. Fourthly, during current ramps it was seen that the difference between fitted and measured magnetic measurements in the equilibrium reconstruction were larger than in the constant current phase. External loop voltage measurements and magnetic probe pairs inside and outside the vessel wall were used to measure the vacuum vessel wall resistivity. This is the first step towards including vacuum vessel currents during the plasma current ramp in the real-time equilibrium reconstruction. Fifthly, the introduction of a constraint of the safety factor on the magnetic axis is found to be a helpful method to improve the prediction of the location of rational surfaces for NTM stabilization and disruption avoidance experiments. Soft X-ray tomography is used to assess the quality of the real-time magnetic equilibrium reconstruction using this internal constraint.

The science program of the TCV tokamak: exploring fusion reactor and power plant concepts

TCV is acquiring a new 1 MW neutral beam and 2 MW additional third-harmonic electron cyclotron resonance heating (ECRH) to expand its operational range. Its existing shaping and ECRH launching versatility was amply exploited in an eclectic 2013 campaign. A new sub-ms real-time equilibrium reconstruction code was used in ECRH control of NTMs and in a prototype shape controller. The detection of visible light from the plasma boundary was also successfully used in a position-control algorithm. A new bang-bang controller improved stability against vertical displacements. The RAPTOR real-time transport simulator was employed to control the current density profile using electron cyclotron current drive. Shot-by-shot internal inductance optimization was demonstrated by iterative learning control of the current reference trace. Systematic studies of suprathermal electrons and ions in the presence of ECRH were performed. The L–H threshold power was measured to be ∼50–75% higher in both H and He than D, to increase with the length of the outer separatrix, and to be independent of the current ramp rate. Core turbulence was found to decrease from positive to negative edge triangularity deep into the core. The geodesic acoustic mode was studied with multiple diagnostics, and its axisymmetry was confirmed by a full toroidal mapping of its magnetic component. A new theory predicting a toroidal rotation component at the plasma edge, driven by inhomogeneous transport and geodesic curvature, was tested successfully. A new high-confinement mode (IN-mode) was found with an edge barrier in density but not in temperature. The edge gradients were found to govern the scaling of confinement with current, power, density and triangularity. The dynamical interplay of confinement and magnetohydrodynamic modes leading to the density limit in TCV was documented. The heat flux profile decay lengths and heat load profile on the wall were documented in limited plasmas. In the snowflake (SF) divertor configuration the heat flux profiles were documented on all four strike points. SF simulations with the EMC3-EIRENE code, including the physics of the secondary separatrix, underestimate the flux to the secondary strike points, possibly resulting from steady-state E × B drifts. With neon injection, radiation in a SF was 15% higher than in a conventional divertor. The novel triple-null and X-divertor configurations were also achieved in TCV.