External Magnetic Measurements Research Articles

Electron ITB formation in EAST high poloidal beta plasmas under dominant electron heating

Plasma confinement and transport in tokamaks play a crucial role in the development of high poloidal beta steady-state operation scenarios. Therefore, it is very important to study the relevant mechanism of internal transport barriers (ITBs), which can help plasmas to obtain better confinement in order to achieve higher fusion gain. This paper mainly introduces the analysis of the characteristics of electron heat transport of discharges with ITB in high βP operation regime in Experimental Advanced Superconducting Tokamak (EAST). Based on the statistical analysis of stable discharges with βP > 1.5, it is found that there is an obvious bifurcation of the normalised electron temperature gradient (ETG) ( R/LTe ) in the range of βP = 2–2.2. Then the discharges of lower βP ( βP < 2, where the value of βP is below the bifurcation threshold) and of higher βP ( βP > 2.2, where the value of βP is above the threshold) were selected for analysis. The diagnostic data provided by Thomson scattering, x-ray crystal spectrometry and charge exchange recombination spectroscopy are used to provide reliable parameter profiles and then combined with the data of external magnetic probe measurements and the polarisation interferometer diagnosis system to fully reconstruct the balance. A relevant plasma current calculation model is used to calculate and analyse the current density profiles and power deposition, and then the transport analysis is carried out. Interestingly, in the higher βP discharges, it is found that the turbulence intensity provided by the CO2 laser collective scattering system gradually decreases and the normalised ETG R/LTe gradually increases. It is also found that the electron heat transport coefficient decreases in the discharge with higher βP and the growth rate of the electron-scale turbulence calculated by transport gyro-Landau fluid (TGLF) is significantly reduced. Meanwhile, similar conclusions are also obtained in the discharges when the βP is further increased.

Fault Detection and Identification for Polymer Electrolyte Membrane Fuel Cell Stack by External Magnetic Field

Many technological locks prevent the deployment of Proton Exchange Membrane Fuel Cell (PEMFC). Particularly for vehicle applications, cost and durability represent two of the most significant challenges to achieve clean, reliable, and cost-effective PEMFC systems. Solving these shortcomings will be a great opportunity for a decisive breakthrough towards mass-diffusion of the current PEMFC technology. The long-term electrical performance losses are associated to either the degradation of the MEA constitutive materials or due to specific operating conditions (flooding, drying, etc.). In perspective, local current density distribution may support stack-level degradation analyzes as well as effective stack control to mitigate the consequences of degradation due to load cycles (electrochemical, thermal, mechanical and humidity effects) or faults.External magnetic field measurement (MFM) shows a high potential in PEMFC non-invasive diagnosis. Thus, 2D and 3D current distributions and their anomalies in the fuel cell can be identified independent of the size of the causing fault.To perform this local characterization, the external magnetic field measurement will enable to model the current density in stationary conditions over the cell surface and for the different cells of the stack. This methodology requires the complementary development of magnetic field techniques and inverse models.In this work, this challenge is tackled by using tailored defective MEAs and specific operating conditions (flooding, drying, ...) to characterize, how local and overall performances of the MEA are affected and to identify the signatures of the various anomalies. Figure 1

Magnetization State and Magnetic Structure of Wiegand Wire Evaluated by External Magnetic Field Measurement

Wiegand wires exhibit unique and fast magnetization reversal features, termed as large Barkhausen jumps, in externally applied alternating magnetic fields. However, the mechanisms and magnetization states yielding these large Barkhausen jumps are yet to be sufficiently elucidated. Thus, in this study, we analyzed the magnetization state and magnetic structure of a Wiegand wire by measuring the magnetic field of the wire. Moreover, we defined a four-layer magnetic structure model of the Wiegand wire and analyzed the magnetization states and processes of these layers in an applied alternating magnetic field. Additionally, we determined the switching field of each layer and specified the magnetization states resulting in the large Barkhausen jump.

Theoretically assisted and empirical scalings in the problem of determination of internal inductance in tokamaks

The problem of inferring the internal inductance from external magnetic measurements in tokamaks is considered. It was practically resolved in JET (Barana O et al 2002 Plasma Phys. Control. Fusion 44 2271), but several questions remain to be addressed before extrapolation of that method on other tokamaks. These naturally arise because of the integral nature of determined by unknown distribution of the magnetic field inside the plasma. Without universal solutions, the quality of approximations should be examined along with potential experimental enforcements of the existing procedures. This is the main goal of the study that is fully analytical. Several relevant quantities are calculated for the large-aspect-ratio plasma with elliptical shifted magnetic surfaces. Usually the plasma elongation is mentioned as a key factor in the task. Here it is explicitly shown that not only , but its radial derivative too plays a role. The latter parameter did not appear in the JET scaling and in the accompanying discussions. It is also shown that the -dependent term representing there the first iteration actually brings a systematic error. Therefore, several improvements to that scaling can be proposed. The study is based on the use of virial relations for the toroidal axisymmetric configurations.

An Innovative PEMFC Magnetic Field Emulator to Validate the Ability of a Magnetic Field Analyzer to Detect 3D Faults

An original non-invasive methodology of the fuel cell diagnosis is proposed to identify different positions of the faults in Proton Exchange Membrane Fuel Cell (PEMFC) stacks from external magnetic field measurements. The approach is based on computing the external magnetic field difference between normal and faulty PEMFC operating conditions. To evaluate the external magnetic field distribution, in this paper, we propose an improved design of the magnetic field analyzer. This analyzer amplifies the magnetic field around the cell to perform an accurate detection of the fault position. Moreover, the main contribution of this work is represented by conceiving and implementing a 3D multi-physical current distribution emulator of a proton exchange membrane fuel cell. The new concept of a proton exchange membrane fuel cell emulator has been specially designed to emulate the magnetic field of a real fuel cell stack. This emulator concept is also beneficial for a new model of the fuel cell, which implies a multi-physical coupling between electrochemical electric conduction and the generated magnetic field. Finally, finally, the numerical model and the emulator have been involved in the realization of numerical simulations and experimental analysis to prove the ability of the system to detect and localize 3D faults.

Efficient fault diagnosis of proton exchange membrane fuel cell using external magnetic field measurement

Fault diagnosis has been considered as a critical solution for improving the reliability of proton exchange membrane fuel cell (PEMFC) system. This study proposes an efficient PEMFC fault diagnosis technique, where PEMFC external magnetic field is measured during its operation, from which PEMFC performance degradation mechanisms and corresponding faults can be identified. In the analysis, a PEMFC numerical model is constructed to explore the relation between external magnetic field and PEMFC state of health. Furthermore, a non-invasive measurement strategy is proposed to collect external magnetic field during the operation. With the measurements, an efficient PEMFC fault diagnosis method is proposed, and its effectiveness in identifying PEMFC water management issues is investigated using PEMFC test data. Results demonstrate that PEMFC flooding and dehydration can be discriminated with good quality, and the faulty level can also be identified accurately.

Reconstruction of the Internal Magnetic Configuration of Two Merging Spherical Tokamak Plasmas by External Probe Measurement and MHD Simulation

A novel model to reconstruct the magnetic configuration inside the TS‐6 spherical tokamak during the merging start‐up is presented, utilizing the external magnetic measurements with a 2D Hall‐MHD numerical simulation. A number of zero size numerical coils outside the measurement domain are responsible to produce the same poloidal flux values as the ones measured by the external probes located on the measurement boundary. This study shows that the reconstruction agrees with the measured one by 6% deviation during the merging. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

New Identification Approach and Methods for Plasma Equilibrium Reconstruction in D-Shaped Tokamaks

The paper deals with the identification of plasma equilibrium reconstruction in D-shaped tokamaks on the base of plasma external magnetic measurements. The methods of such identification are directed to increase their speed of response when plasma discharges are relatively short, like in the spherical Globus-M2 tokamak (Ioffe Inst., St. Petersburg, Russia). The new approach is first to apply to the plasma discharges data the off-line equilibrium reconstruction algorithm based on the Picard iterations, and obtain the gaps between the plasma boundary and the first wall, and the second is to apply new identification methods to the gap values, producing plasma shape models operating in real time. The inputs for on-line robust identification algorithms are the measurements of magnetic fluxes on magnetic loops, plasma current, and currents in the poloidal field coils measured by the Rogowski loops. The novel on-line high-performance identification algorithms are designed on the base of (i) full-order observer synthesized by linear matrix inequality (LMI) methodology, (ii) static matrix obtained by the least square technique, and (iii) deep neural network. The robust observer is constructed on the base of the LPV plant models which have the novelty that the state vector contains the gaps which are estimated by the observer, using input and output signals. The results of the simulation of the identification systems on the base of experimental data of the Globus-M2 tokamak are presented.

Predictive multi-channel integrated modeling of a reversed magnetic shear H-mode discharge with internal transport barrier in EAST

A reversed magnetic shear high plasma performance H-mode discharge with internal transport barrier (ITB) has been realized and modeled on experimental advanced superconducting tokamak (EAST) in deuterium (D) plasmas with an ITER-like tungsten (W) upper divertor. In this shot (#71326), the dimensionless parameter G () can reach to 0.25 (H 89 ⩽ 2, β N ⩽ 2, q 95 ∼ 4, I p ⩽ 450 kA, B T ⩽ 1.6 T). The ITB has been observed in the channels of particle (electron density n e), electron and ion temperature (T e and T i) and toroidal rotation velocity (V t). However, in the formation process of V t and n e ITBs, the heavy impurities accumulate in the core plasmas, which may be one of the most important reasons for the limitation of the improvement of plasma performance. A time slice (t = 4.65 s) of the high plasma performance phase with n e, T i and V t ITBs has been analyzed. It is found that the position of minimum safety factor (q min) is at about normalized radius ρ = 0.4 where may be the location of ion ITB foot, during equilibrium reconstruction from EFIT using external magnetic and internal polarimeter-INTferometer (POINT) measurement constraints. Based on this equilibrium, the source is self-consistently calculated by ONETWO and NUBEAM. Then the n e, T e, T i and V t have been modeled predictively and simultaneously by TGYRO utilizing the reconstructed equilibrium, the self-consistent source and the experimental radiated power for the first time in EAST. This modeling well reproduces the experimental n e and T i profiles in the reversed magnetic shear plasmas. In addition, it is shown that reversed magnetic shear rather than shear of radial electric field (E r) mainly produced by V t plays a key role to the formation of n e and T i ITBs. The reasons for central accumulation of W impurity are also clarified by computing both neoclassical and turbulent transport components of W. It turns out that the neoclassical transport dominates over turbulent transport for W and neoclassical pinch of W causes its central accumulation.

Plasma current profile reconstruction for EAST based on Bayesian inference

Determining the distribution of plasma current in the equilibrium state is one of the most important steps to realize effective and safe operation of tokamak. In this study, a novel reconstruction code based on Bayesian inference is developed to infer the plasma current distribution for experiment analysis of EAST. Without iteratively solving Grad-Shafranov (G-S) equation to find an optimal fit for the external magnetic diagnostic measurements, the distribution of toroidal current density and poloidal flux can be rapidly derived in a probabilistic manner. The reconstructed results are consistent with the results based on equilibrium fitting (EFIT) code, and the execution time is less than 1 ms for each time slice, which indicates its potential for application in future real-time plasma feedback control.

MHD simulation of supersonic FRC merging corrected by non-invasive magnetic measurements

In this study, a newly developed correction method with external magnetic measurements for the magnetohydrodynamics (MHD) simulation of the collisional merging formation of a field-reversed configuration (FRC) realized the estimation of the internal structure of the FRCs without invasive internal measurements. In the collisional merging formation of FRCs, an FRC is formed via merging of two initial FRC-like plasmoids at supersonic/Alfvénic velocity. An invasive diagnostic may also interfere with the collisional merging formation process. A two-dimensional resistive MHD simulation was conducted to evaluate the global behavior and internal structure of FRCs in the collisional merging formation process without invasive measurements. This code simulated the initial formation and collisional merging processes of FRCs including discharge circuits. However, the translation velocity and the pressure of initial FRCs did not simultaneously agree with the experimental values because the magnetic pressure gradient in each formation region could not be reproduced without the artificial adjustment of the initial condition. The experimentally measured current distribution was given as the initial condition of the circuit calculation in the developed correction method. The initial FRCs were successfully translated at the translation velocity and plasma pressure in the corrected simulation, both of which were equivalent to the experiments. The properties of the merged FRCs in the experiments such as volume, total temperature, and average electron density were reproduced in the corrected simulation. The detailed radial profile of the internal magnetic field of the FRC was also measured and found to agree very well with the simulation results.

External Magnetic Field Measurements in UME Kibble Balance

The new definition of kilogram in terms of the fixed value of Planck constant ensures the long-term stability of SI mass unit and enables traceability from more than one source. Kibble balance experiments offer an effective primary realization method for the new definition of kilogram. Kibble Balance apparatus operating at National Metrology Institute of Turkey is designed with a stationary coil and an oscillating magnet. In contradistinction to traditional moving coil Kibble balance experiments, external magnetic field brings an asymmetry between the Ampere’s law of force and the Faraday’s law of induction in moving magnet experiments. In this paper, we develop a method based on the external magnetic flux density difference measurements in vertical direction to take into account the effect of the external magnetic field on the realization of kilogram. The proposed model in this approach fits well with the data such that the kilogram realization requirement is met within the accuracy of the measuring instrument.

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 Stacked Autoencoder Neural Network Algorithm for Breast Cancer Diagnosis With Magnetic Detection Electrical Impedance Tomography

Magnetic detection electrical impedance tomography (MDEIT) is a novel imaging technique that aims to reconstruct the conductivity distribution with electrical current injection and the external magnetic flux density measurement by magnetic sensors. Aiming at improving the resolution and accuracy of MDEIT and providing an efficient imaging method for breast cancer diagnosis, a new algorithm based on stacked auto-encoder (SAE) neural network is proposed. Both numerical simulation and phantom experiments are done to verify its feasibility. In the numerical simulation, an amount of sample data with different conductivity distribution are calculated. Then a neural network model is established and trained by training these samples. Finally, the conductivity distribution of an imaging target with the anomaly location can be reconstructed by the network model. The reconstruction result of the SAE algorithm is compared with the reconstruction results of the traditional sensitivity matrix (SM) algorithm and the back propagation (BP) neural network algorithm. Under the noise of 30dB, the relative errors of BP algorithm, SM algorithm and SAE algorithm are 137.19%, 24.90% and 15.28% respectively. Result shows by the SAE algorithm, the location of anomalies is reconstructed more accurately, the conductivity value is more closely to the real one and the anti-noise performance is more robust. At last, a breast phantom experiment by self-made platforms is completed to verify the application feasibility of the new algorithm. The relative reconstruction error of conductivity by proposed SAE algorithm can be reduced to 14.56%. The results show that by SAE algorithm, MDEIT can be a promising approach in clinical diagnosis of breast cancer, and it also provide more potential application prospect for the extensive application of MDEIT.

Fault Identification on a Fuel Cell by 3-D Current Density Reconstruction From External Magnetic Field Measurements

An original approach of fuel cell diagnosis is presented. It is based on the solving of an inverse linear problem linking the magnetic field signature outside of the fuel cell to the current density distribution inside. The searched solution is a linear combination of conservative current distribution obtained by a set of electrokinetic problems solved by a finite face element method. As the problem is ill-posed, the solution is stabilized using a truncated singular value decomposition. The approach is validated to reconstruct a 3-D current density distribution in a stack simulator and in a fuel cell stack operating in the laboratory conditions.

Fault detection for polymer electrolyte membrane fuel cell stack by external magnetic field

An original non-invasive approach of fuel cell diagnosis is proposed in order to locate different kinds of faults in PEMFC stacks from magnetic field measurements. The method is based on the solving of an inverse linear problem linking the magnetic field signature outside of the fuel cell to the current density distribution inside. The searched solution is a linear combination of conservative current distribution obtained by a set of electrokinetic problems solved by a finite face element method. As the problem is ill-posed, the solution is stabilized using a truncated singular value decomposition. In this work, 30 sensors are used to perform the magnetic tomography of a PEMFC stack consisting of 100 cells with a large active area of 220 cm2. External magnetic measurement makes possible to identify 2D or 3D changes of current density distribution induced either by a cell flooding or membrane drying as well as by material degradation in a PEMFC stack.

Equilibrium Reconstruction and Equilibrium Properties in QUEST Tokamak

Plasma shape reconstruction is an important part of tokamak data analysis. An off-line plasma shape reconstruction, based on the EFIT code in Linux system, can be carried out in Q-shu Univ. Experiment in Steady-State Spherical Tokamak (QUEST). In this paper, the algorithm about equilibrium reconstruction is described in detail. Magnetic reconstruction in QUEST, which is calculated by the EFIT code according to the external magnetic measurements, is introduced and the results are presented in detail. It is known that the eddy current effect is large in QUEST experiment, the eddy current effect is first considered into equilibrium reconstruction. Fourier expansion is applied to reconstruct the vessel current distribution in EFIT code. To test the accuracy of the result, a comparison with the result of Cauchy condition surface method has made, which suggests the reliability of the result. A visualization interface is made, which is convenient for physicists and operators to analyze the behavior of plasma. At the same time, the operation space of elongated discharges is discussed based on the QUEST database. The real time EFIT will be applied to the plasma control system of QUEST in the future.

Study of plasma equilibrium reconstruction on HL-2A

An equilibrium reconstruction code is a basic tool for determining the plasma position, boundary, shape and current density profile in a tokamak discharge. The equilibrium reconstruction code CPF has been written to make these calculations. It uses a polynomial to describe the spatial distribution of current density. The coefficients of the polynomial are determined by the best least squares fit to the internal and external magnetic measurement data. A finite difference method is used to solve the Grad-Shafranov equation. The equilibrium magnetic surfaces satisfying the convergence criterion is obtained by Picard iteration. The CPF equilibrium reconstruction is also checked by comparing to results obtained by the equilibrium code SWEQU. The CPF code is stable and has been used for several years.

Magnetic polarization measurements of the multi-modal plasma response to 3D fields in the EAST tokamak

A multi-modal plasma response to applied non-axisymmetric fields has been found in EAST tokamak plasmas. Here, multi-modal means the radial and poloidal structure of an individually driven toroidal harmonic is not fixed. The signature of such a multi-modal response is the magnetic polarization (ratio of radial and poloidal components) of the plasma response field measured on the low field side device mid-plane. A difference in the 3D coil phasing (the relative phase of two coil arrays) dependencies between the two responses is observed in response to n = 2 fields in the same plasma for which the n = 1 responses are well synchronized. Neither the maximum radial nor the maximum poloidal field response to n = 2 fields agrees with the best applied phasing for mitigating edge localized modes, suggesting that the edge plasma response is not a dominant component of either polarization. GPEC modeling reproduces the discrepant phasing dependences of the experimental measurements, and confirms the edge resonances are maximized by the coil phasing that mitigates ELMs in the experiments. The model confirms the measured plasma response is not dominated by resonant current drive from the external field. Instead, non-resonant contributions play a large role in the diagnostic signal for both toroidal harmonics n = 1 and n = 2. The analysis in this paper demonstrates the ability of 3D modeling to connect external magnetic sensor measurements to the internal plasma physics and accurately predict optimal applied 3D field configurations in multi-modal plasmas.

Improvement of q profile by the polarimeter/interferometer system on EAST tokamak

A novel equilibrium fitting method, which combining the polarimeter/interferometer (POINT) measurements with the external magnetic measurements, has been developed to improve the accuracy of safety factor (q) profile on the EAST tokamak. The POINT system, measuring the accurate line-integrated electron density and Faraday rotation angle, provides the magnetic field information inside the plasma. By adding these data to the equilibrium constraints, the fitting results with new method show clear difference with the initial equilibrium and the difference becomes larger gradually from boundary to core of the plasma. This method, overcoming the difference of the EFIT results from the external magnetic measurements, shows a great improvement on q profile, especially in the core plasma. Results with and without these corrections are presented, comparisons of the corrected results and experimental results are also shown and these are found consistent with each other. The feasibility and reliability of the correction process are also discussed in this paper.