Magnetic Equilibrium Reconstruction Research Articles

Retraction Note to: Magnetic System and Equilibrium Reconstruction for ITER using the GSE Solution and TEQ Code

Retraction Note to: Magnetic System and Equilibrium Reconstruction for ITER using the GSE Solution and TEQ Code

A machine-learning-based tool for last closed-flux surface reconstruction on tokamaks

Tokamaks allow to confine fusion plasma with magnetic fields. The prediction/reconstruction of the last closed-flux surface (LCFS) is one of the primary challenges in the control of the magnetic configuration. The evolution in time of the LCFS is determined by the interaction between the actuator coils and the internal tokamak plasma. This task requires real-time capable tools to deal with high-dimensional data and high resolution at same time, where the interaction between a wide range of input actuator coils with internal plasma state responses adds an additional layer of complexity. In this work, we present the application of a novel state-of-the-art machine learning model to LCFS reconstruction in an experimental advanced superconducting tokamak (EAST) that learns automatically from the experimental data of EAST. This architecture allows not only offline simulation and testing of a particular control strategy but can also be embedded in a real-time control system for online magnetic equilibrium reconstruction and prediction. In real-time modeling tests, our approach achieves very high accuracies, with an average similarity of over 99% in the LCFS reconstruction of the entire discharge process.

Implementation of a Kalman filter-based eddy current estimator for the P-EFIT magnetic equilibrium reconstruction code

This article discusses the integration of a Kalman filter in the P-EFIT equilibrium reconstruction code, with the aim of estimating the currents induced in the passive structures of a tokamak. The filter is based on a vacuum electromagnetic model of the reactor, and takes advantage of an estimate of the effect of the plasma on the magnetics, provided by the equilibrium reconstruction algorithm. On the other hand, the observer is integrated into the equilibrium reconstruction, which exploits the eddy currents estimates provided by the Kalman filter to refine the obtained solution. To analyze the interplay of the reconstruction code and the proposed observer, the ITER tokamak is considered as a case-study, and the algorithm is tested on a variety of plasma conditions, selected in such a way to maximize the relevance of an accurate knowledge of the passive currents. The code performance is evaluated in terms of convergence metrics, eddy currents estimation accuracy and reconstruction of plasma-related quantities such as plasma–wall gaps, plasma current and plasma profile parameters.

Advances in the DTT poloidal interferometer/polarimeter design

A multi-channels poloidal interferometer/polarimeter is under development for the Divertor Tokamak Test (DTT) facility, a new tokamak device whose construction is starting in Italy. The aim of the diagnostics is the simultaneous measurement of the line integrated electron density, Faraday rotation and Cotton Mouton effect. The measurement of two polarimetric signals together with the interferometric one would allow for a robust electron density estimate, for the internal magnetic field measurement as well as for the magnetic equilibrium reconstruction. In this work, we present the advances in the diagnostics design whose characteristics are constrained by scientific requirements as well as the DTT structural aspects. In this regards, we have analyzed the possibility of accommodating up to 16 lines of sight in the available space and the contribution of different chords positions in the magnetic equilibrium reconstruction. In particular, we have used the VMEC and V3FIT codes to evaluate the expected interferometric/polarimetric signals and their contribution in the reconstruction of the q profile. These results have been used to optimize the chords positions. Eventually, we present a realistic CAD-driven design of the diagnostic, with details of the most critical components (e.g. the corner cube retroreflectors in the high field side), which would allow for the selected chords configurations implementation.

GPU-optimized fast plasma equilibrium reconstruction in fine grids for real-time control and data analysis

P-EFIT, a GPU parallel equilibrium reconstruction code, is based on the EFIT framework, but built with the CUDA™ (Compute Unified Device Architecture) to take advantage of massively parallel Graphical Processing Unit (GPU) cores to significantly accelerate the computation. With the parallelized Grad-Shafranov solver and middle-scale matrix calculation modules, P-EFIT can accurately reproduce the EFIT reconstruction algorithms at a fraction of the EFIT computational time. Integrated into EAST plasma control system, P-EFIT not only provides control signal results but also enhances EAST plasma control capacity with unique designed function modules. Using the synthetic magnetic diagnostic signals from ITER plasma equilibria obtained by the CREATE-L and CREATE-NL codes in standalone and streaming mode, P-EFIT has good enough accuracy and time latency performance in most of the considered cases. P-EFIT achieves full kinetic equilibrium reconstruction algorithms and repeats the EFIT results with the DIII-D internal plasma current and kinetic profile measurements in one-percent cost time of EFIT. All these works suggest that P-EFIT can provide quality magnetic equilibrium reconstruction in real-time, offer full kinetic equilibrium reconstruction with high spatial resolution and high speed, support more detailed, better plasma control and data analysis for tokamak devices.

Systematic errors in tokamak magnetic equilibrium reconstruction: a study of EFIT++ at tokamak COMPASS

Uncertainties and errors in magnetic equilibrium reconstructions are a wide-spread problem in interpreting experimental data measured in the tokamak edge. This study demonstrates errors in EFIT++ reconstructions performed on the COMPASS tokamak by comparing the outer midplane separatrix position to the Velocity Shear Layer (VSL) position. The VSL is detected as the plasma potential peak measured by a reciprocating ball-pen probe. A subsequent statistical analysis of nearly 400 discharges shows a strong systematic trend in the reconstructed separatrix position relative to the VSL, where the primary factors are plasma triangularity and the magnetic axis radial position. This dependency is significantly reduced after the measuring coils positions as recorded in EFIT input are optimised to provide a closer match between the “synthetic” coil signal calculated by the Biot-Savart law in a vacuum discharge and the actual coil signal. In conclusion, we suggest that applying this optimisation may lead to more accurate and reliable reconstructions of the COMPASS equilibrium, which would have a positive impact on the accuracy of measurement analysis performed in the edge plasma.

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.

First heat flux estimation in the lower divertor of WEST with embedded thermal measurements

The present paper deals with the surface heat flux estimation with thermocouples (TC) and fiber Bragg grating (FBG) embedded in the plasma facing components (PFC) of the WEST tokamak. A 2D heat transfer model combined with the conjugate gradient method and the adjoint state is used to estimate the plasma heat flux deposited on the PFC. The plasma heat flux is characterized by the time evolution of its amplitude and spatial shape on the target (heat flux decay length λqt, power spreading in the private flux region St and the strike point location x0). As a first step, five ohmic pulses have been investigated with different magnetic configuration and divertor X-point height varying from 44 to 68 mm from the surface. Despite an outboard shift, the relative displacements of the outer strike point as well as the heat flux decay length derived from the TC/FBG systems are consistent with the magnetic equilibrium reconstruction.

Tests of a full-scale ITER toroidal interferometer and polarimeter (TIP) prototype on the DIII-D tokamak (invited).

A full-scale ITER toroidal interferometer and polarimeter (TIP) prototype, including an active feedback alignment system, has been installed and tested on the DIII-D tokamak. In the TIP prototype, a two-color interferometry measurement of line-integrated density is carried out at 10.59 μm and 5.22 μm using a CO2 and quantum cascade laser, respectively, while a separate polarimetry measurement of the plasma-induced Faraday effect is made at 10.59 μm. The TIP prototype is equipped with a piezo tip/tilt stage active feedback alignment system that minimizes noise in the measurement and keeps the diagnostic aligned throughout DIII-D discharges. The measured phase resolution for the polarimeter and interferometer is 0.05° (100 Hz bandwidth) and 1.9° (1 kHz bandwidth), respectively. The corresponding line-integrated density resolution for the vibration-compensated interferometer is δnL = 1.5 × 1018 m-2, and the magnetic field-weighted line-integrated density from the polarimeter is δnBL = 1.5 × 1019 Tm-2. Both interferometer and polarimeter measurements during DIII-D discharges compare well with the expectations based on calculations using Thomson scattering measured density profiles and magnetic equilibrium reconstructions. Additionally, larger bandwidth interferometer measurements show that the diagnostic is a sensitive monitor of core density fluctuations with demonstrated measurements of Alfvén eigenmodes and tearing modes.

A novel plasma position and shape controller for advanced configuration development on the TCV tokamak

A novel plasma position and shape controller has been developed for the highly flexible shaping poloidal-field coil set of the TCV tokamak, to aid in the precise control of advanced configurations such as negative-triangularity plasmas, snowflake and super-X divertors, and doublets. This work follows and relies on the deployment of a new, sub-ms, real-time magnetic equilibrium-reconstruction algorithm. The controller formulation ensures flexibility through an ordering of controlled variables from the most easily to the least easily controlled, while respecting the hardware limits on the poloidal-field coil currents. A rigid, linearised plasma response model for the TCV tokamak is used for the verification and determination of the control parameters. The controller has been applied successfully to a variety of TCV plasma discharges.

Influence of non-local thermodynamic equilibrium and Zeeman effects on magnetic equilibrium reconstruction using spectral motional Stark effect diagnostic.

The Motional Stark Effect (MSE) diagnostic is a well established technique to infer the local internal magnetic field in fusion plasmas. In this paper, the existing forward model which describes the MSE data is extended by the Zeeman effect, fine-structure, and relativistic corrections in the interpretation of the MSE spectra for different experimental conditions at the tokamak ASDEX Upgrade. The contribution of the non-Local Thermodynamic Equilibrium (non-LTE) populations among the magnetic sub-levels and the Zeeman effect on the derived plasma parameters is different. The obtained pitch angle is changed by 3°…4° and by 0.5°…1° including the non-LTE and the Zeeman effects into the standard statistical MSE model. The total correction is about 4°. Moreover, the variation of the magnetic field strength is significantly changed by 2.2% due to the Zeeman effect only. While the data on the derived pitch angle still could not be tested against the other diagnostics, the results from an equilibrium reconstruction solver confirm the obtained values for magnetic field strength.

Extensions to the charge exchange recombination spectroscopy diagnostic suite at ASDEX Upgrade.

A new core charge exchange recombination spectroscopy diagnostic has been installed in the ASDEX Upgrade tokamak that is capable of measuring the impurity ion temperature, toroidal rotation, and density on both the low field side (LFS) and high field side (HFS) of the plasma. The new system features 48 lines-of-sight (LOS) with a radial resolution that varies from ±2 cm on the LFS down to ±0.75 cm on the HFS and has sufficient signal to run routinely at 10 ms and for special circumstances down to 2.5 ms integration time. The LFS-HFS ion temperature profiles provide an additional constraint on the magnetic equilibrium reconstruction, and the toroidal rotation frequency profiles are of sufficiently high quality that information on the poloidal velocity can be extracted from the LFS-HFS asymmetry. The diagnostic LOS are coupled to two flexible-wavelength spectrometers such that complete LFS-HFS profiles from two separate impurities can be imaged simultaneously, albeit with reduced radial coverage. More frequently, the systems measure the same impurity providing very detailed information on the chosen species. Care has been taken to calibrate the systems as accurately as possible and to include in the data analysis any effects that could lead to spurious temperatures or rotations.

An efficient technique for magnetic equilibrium reconstruction with q profile constraints and its application on the EAST tokamak

An efficient technique for building plasma equilibria with preset or constrained q profiles by solving the nonlinear Grad–Shafranov equation iteratively is proposed. The technique uses a set of dynamic virtual poloidal field probes in the plasma core region. Numerical examples are shown for monotonic q profiles and negative central magnetic shear equilibria which are obtained with this technique. As a proof of principle, the technique is applied on the EAST tokamak, to constrain the plasma equilibrium reconstruction with the experimental q = 1 surface information from the ECE diagnostic in addition to the external magnetic measurements.

Eqtools: Modular, extensible, open-source, cross-machine Python tools for working with magnetic equilibria

As plasma physics research for fusion energy transitions to an increasing emphasis on cross-machine collaboration and numerical simulation, it becomes increasingly important that portable tools be developed to enable data from diverse sources to be analyzed in a consistent manner. This paper presents eqtools, a modular, extensible, open-source toolkit implemented in the Python programming language for handling magnetic equilibria and associated data from tokamaks. eqtools provides a single interface for working with magnetic equilibrium data, both for handling derived quantities and mapping between coordinate systems, extensible to function with data from different experiments, data formats, and magnetic reconstruction codes, replacing the diverse, non-portable solutions currently in use. Moreover, while the open-source Python programming language offers a number of advantages as a scripting language for research purposes, the lack of basic tokamak-specific functionality has impeded the adoption of the language for regular use. Implementing equilibrium-mapping tools in Python removes a substantial barrier to new development in and porting legacy code into Python. In this paper, we introduce the design of the eqtools package and detail the workflow for usage and expansion to additional devices. The implementation of a novel three-dimensional spline solution (in two spatial dimensions and in time) is also detailed. Finally, verification and benchmarking for accuracy and speed against existing tools are detailed. Wider deployment of these tools will enable efficient sharing of data and software between institutions and machines as well as self-consistent analysis of the shared data. Program summaryProgram title: eqtoolsCatalogue identifier: AFBK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 27204No. of bytes in distributed program, including test data, etc.: 1217844Distribution format: tar.gzProgramming language: Python, C.Computer: PCs.Operating system: Linux, Macintosh OS X, Microsoft Windows.RAM: Several megabytes, depends on resolution of dataClassification: 19.4.External routines: F2PY [1], matplotlib [2], MDSplus [3], NumPy [4], SciPy [5]Nature of problem:Access to results from magnetic equilibrium reconstruction code, conversion between various coordinate systems tied to the magnetic equilibrium.Solution method:Data are stored in an object-oriented data structure with human-readable getter methods. Coordinates are converted using bivariate or trivariate splines.Running time:Coordinate transformations on a 66x66 point spatial grid take between 1 and 5 ms per time slice, depending on the transformation used and how many intermediate results have been stored.

Real-time diamagnetic flux measurements on ASDEX Upgrade.

Real-time diamagnetic flux measurements are now available on ASDEX Upgrade. In contrast to the majority of diamagnetic flux measurements on other tokamaks, no analog summation of signals is necessary for measuring the change in toroidal flux or for removing contributions arising from unwanted coupling to the plasma and poloidal field coil currents. To achieve the highest possible sensitivity, the diamagnetic measurement and compensation coil integrators are triggered shortly before plasma initiation when the toroidal field coil current is close to its maximum. In this way, the integration time can be chosen to measure only the small changes in flux due to the presence of plasma. Two identical plasma discharges with positive and negative magnetic field have shown that the alignment error with respect to the plasma current is negligible. The measured diamagnetic flux is compared to that predicted by TRANSP simulations. The poloidal beta inferred from the diamagnetic flux measurement is compared to the values calculated from magnetic equilibrium reconstruction codes. The diamagnetic flux measurement and TRANSP simulation can be used together to estimate the coupled power in discharges with dominant ion cyclotron resonance heating.

Diagnostic development for current density profile control at KSTAR

The current density profile diagnostics are critical for the control of the steady-state burning plasma operations. A multi-channel motional Stark effect (MSE) diagnostic system has been implemented for the measurements of the internal magnetic field structures that constrain the magnetic equilibrium reconstruction to accurately produce the tokamak safety factor and current density profiles for the Korea Superconducting Tokamak Advanced Research (KSTAR). This work presents the design and fabrication of the front optics and the filter modules and the calibration activities for the MSE diagnostic at KSTAR.

RETRACTED ARTICLE: Magnetic System and Equilibrium Reconstruction for ITER using the GSE Solution and TEQ Code

The superconducting magnet system of ITER consists of four main sub-systems: toroidal field coils, central solenoid coils; poloidal field coils; and correction coils. Like many other ITER systems, the magnet components are supplied in-kind by six domestic agencies. The technical specifications, manufacturing processes and procedures required to fabricate these components are particularly challenging. The management structure and organization to realize this procurement within the tight ITER construction schedule is very complex. On the other hand, all plasma processes including linear and early nonlinear stages of MHD instabilities, transport and plasma flows, waves, micro-instabilities and turbulence, represent different kinds of deviations from MHD equilibrium and thus require accurate calculations of equilibrium configurations. The simplest useful mathematical model to describe equilibrium in fusion plasmas is achieved by combining MHD equations with Maxwell’s equations. The final result is the Grad–Shafranov (GS) equation. Analytical solutions to the GS equation are an aid to theoretical investigations into plasma equilibrium, stability and transport in axisymmetric plasmas. In this paper a special analytical solution for GS equation and also simulation of equilibrium by TEQ code for ITER were presented.

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.

Motional Stark effect diagnostics for KSTAR

The motional Stark effect (MSE) diagnostic is used to measure the radial magnetic pitch-angle profile in neutral-beam-heated plasmas. The diagnostic relies upon the measurement of the polarization direction of Stark-split D-alpha emission from injected fast neutral atoms in a magnetic field. Measurements of the magnetic pitch angle are used with magnetic equilibrium reconstruction codes such as EFIT to calculate the safety factor in shaped plasmas. The MSE diagnostic is important for determining the shape of the q profile to optimize confinement and stability, and it has become a key element in high-performance tokamaks. For the purpose of achieving the high-performance operating region in the Korea Superconducting Tokamak Advanced Research KSTAR device, two types of methods are being studied. In KSTAR, a multichord PEM (photo-elastic modulator)-based MSE system is being developed, and an imaging MSE polarimetry system using the coherence imaging technique has been showing promising initial results during the last two KSTAR experimental campaigns in 2012 and 2013, respectively. In this paper, we describe the progress of the KSTAR MSE diagnostics.

Instrumentation for a multichord motional Stark effect diagnostic in KSTAR.

The motional Stark effect (MSE) diagnostic is used to measure the radial magnetic pitch angle profile in neutral beam heated plasmas. This information is used to calculate the safety factor, q, with magnetic equilibrium reconstruction codes such as EFIT. The MSE diagnostic is important during active shaping of the q profile to optimize confinement and stability, and it has become a key diagnostic in high performance tokamaks. A multichord photo-elastic modulator (PEM) based MSE system is being developed for a real-time plasma current profile control in Korea Superconducting Tokamak Advanced Research (KSTAR). The PEM-based approach is a standard method that measures the polarization direction of a single Stark line with narrow tunable bandpass filters. A tangential view of the heating beam provides good spatial resolution of 1-3 cm, which provides an opportunity to install 25 spatial channels spanning the major radius from 1.74 m to 2.84 m. Application of real-time control is a long-term technical goal after commissioning the diagnostic in KSTAR, which is expected in 2015. In this paper, we describe the design of this newly-constructed multichord MSE diagnostic in KSTAR.