Reconstruction Of Current Density Research Articles

Volumetric Reconstruction of Ionospheric Electric Currents From Tri‐Static Incoherent Scatter Radar Measurements

AbstractWe present a new technique for the upcoming tri‐static incoherent scatter radar system EISCAT 3D (E3D) to perform a volumetric reconstruction of the 3D ionospheric electric current density vector field, focusing on the feasibility of the E3D system. The input to our volumetric reconstruction technique are estimates of the 3D current density perpendicular to the main magnetic field, j⊥, and its covariance, to be obtained from E3D observations based on two main assumptions: (a) Ions fully magnetized above the E region, set to 200 km here. (b) Electrons fully magnetized above the base of our domain, set to 90 km. In this way, j⊥ estimates are obtained without assumptions about the neutral wind field, allowing it to be subsequently determined. The volumetric reconstruction of the full 3D current density is implemented as vertically coupled horizontal layers represented by Spherical Elementary Current Systems with a built‐in current continuity constraint. We demonstrate that our technique is able to retrieve the three dimensional nature of the currents in our idealized setup, taken from a simulation of an active auroral ionosphere using the Geospace Environment Model of Ion‐Neutral Interactions (GEMINI). The vertical current is typically less constrained than the horizontal, but we outline strategies for improvement by utilizing additional data sources in the inversion. The ability to reconstruct the neutral wind field perpendicular to the magnetic field in the E region is demonstrated to mostly be within ±50 m/s in a limited region above the radar system in our setup.

A Forward Scattering Model in Two-Dimensional Half-Space for Scatterers’ Size Estimation Using Linear Inversion

Analytic expressions of scattered electric fields for different categories of cylindrical targets buried in the half-space have been developed. In all the cases, investigation domains have been considered two-dimensional and are infinitely long in the remaining dimension. The investigation domains have been excited by the fields generated by a z-directed line source of constant amplitude, operating in the microwave frequencies. The usefulness and validity of these scattering models have been examined by inversion of the scattered electric field generated by the same. The inversion is based on the fact that the scattered field is mapped by a linear operator containing the induced current density and Green’s function of the investigation domain. On application of the incident field, the presence of a discontinuity in half-space induces the current density. By using the information retrieved from the reconstruction of current density by inversion and analytical expressions of the scattered electric field, information about the diameter and the type of the scatterer have been obtained. In addition, the performance of the linear sampling method for shape reconstruction of the scatterer in half-space is also explored.

Application of Whitney elements for the reconstruction of electric arc current density in low-voltage circuit breakers

Purpose This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker. Design/methodology/approach Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W2 in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W1 in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W1. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values. Findings With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W2 and using edge elements in space W1. When solving the inverse problem in space W1, the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred. Originality/value The proposed approaches are able to reconstruct the three-dimensional electric arc current density from its magnetic field in a non-intrusive manner. The formulations enable us to incorporate a priori knowledge of the unknown current density into the solution of the inverse problem, including the zero divergence condition and the boundary conditions. A common mode approach is proposed, which can significantly improve the current density reconstruction.

Determination of current and rotational transform profiles in a current-carrying stellarator using soft x-ray emissivity measurements

Collimated soft X-ray (SXR) emissivity measurements from multi-channel cameras on the Compact Toroidal Hybrid (CTH) tokamak/torsatron device are incorporated in the 3D equilibrium reconstruction code V3FIT to reconstruct the shape of flux surfaces and infer the current distribution within the plasma. Equilibrium reconstructions of sawtoothing plasmas that use data from both SXR and external magnetic diagnostics show the central safety factor to be near unity under the assumption that SXR iso-emissivity contours lie on magnetic flux surfaces. The reconstruction results are consistent with those using the external magnetic data and a constraint on the location of q = 1 surfaces determined from the sawtooth inversion surface extracted from SXR brightness profiles. The agreement justifies the use of approximating SXR emission as a flux function in CTH, at least within the core of the plasma, subject to the spatial resolution of the SXR diagnostics. This improved reconstruction of the central current density indicates that the current profile peakedness decreases with increasing external transform and that the internal inductance is not a relevant measure of how peaked the current profile is in hybrid discharges.

Multishot echo-planar MREIT for fast imaging of conductivity, current density, and electric field distributions.

Magnetic resonance electrical impedance tomography (MREIT) sequences typically use conventional spin or gradient echo-based acquisition methods for reconstruction of conductivity and current density maps. Use of MREIT in functional and electroporation studies requires higher temporal resolution and faster sequences. Here, single and multishot echo planar imaging (EPI) based MREIT sequences were evaluated to see whether high-quality MREIT phase data could be obtained for rapid reconstruction of current density, conductivity, and electric fields. A gel phantom with an insulating inclusion was used as a test object. Ghost artifact, geometric distortion, and MREIT correction algorithms were applied to the data. The EPI-MREIT-derived phase-projected current density and conductivity images were compared with simulations and spin-echo images as a function of EPI shot number. Good agreement among measures in simulated, spin echo, and EPI data was achieved. Current density errors were stable and below 9% as the shot number decreased from 64 to 2, but increased for single-shot images. Conductivity reconstruction relative contrast ratios were stable as the shot number decreased. The derived electric fields also agreed with the simulated data. The EPI methods can be combined successfully with MREIT reconstruction algorithms to achieve fast imaging of current density, conductivity, and electric field. Magn Reson Med 79:71-82, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

The Forward and Inverse Problem Based on Magneto-Acoustic Tomography with Current Injection

The Magneto-acoustic Tomography with Current Injection (MAT-CI) is a new biological electrical impedance imaging technique that combines Electrical Impedance Tomography (EIT) with Ultrasonic Imaging (UI), which possesses the non-invasive and high-contrast of the EIT and the high-resolution of the UI. The MAT-CI is expected to acquire high quality image and embraces a wide application. Its principle is to put the conductive sample in the Static Magnetic Field(SMF) and inject a time-varying current, during which the SMF and the current interact and generate the Lorentz Force that inspire ultrasonic signal received by the ultrasonic transducers positioned around the sample. And then according to related reconstruction algorithm and ultrasonic signal, electrical conductivity image is obtained. In this paper, a forward problem mathematical model of the MAT-CI has been set up to deduce the theoretical equation of the electromagnetic field and solve the sound source distribution by Green’s function. Secondly, a sound field restoration by Wiener filtering and reconstruction of current density by time-rotating method have deduced the Laplace’s equation that caters to the current density to further acquire the electrical conductivity distribution image of the sample through iteration method. In the end, double-loop coils experiments have been conducted to verify its feasibility.

Collection of simulated data for validation of methods of analysis of extracellular potentials

Collection of simulated data for validation of methods of analysis of extracellular potentials

Imaging ac losses in superconducting films via scanning Hall probe microscopy

Various local probes have been applied to understanding current flow through superconducting films, which are often surprisingly inhomogeneous. Here we show that magnetic imaging allows quantitative reconstruction of both current density, J, and electric field, E, resolved in time and space, in a film carrying subcritical ac current. Current reconstruction entails inversion of the Biot-Savart law, while electric fields are reconstructed using Faraday's law. We describe the corresponding numerical procedures, largely adapting existing work to the case of a strip carrying ac current, but including new methods of obtaining the complete electric field from the inductive portion determined by Faraday's law. We also delineate the physical requirements behind the mathematical transformations. We then apply the procedures to images of a strip of YBa2Cu3O7 (YBCO) carrying an ac current at 400 Hz. Our scanning Hall probe microscope produces a time-series of magnetic images of the strip with 1 micron spatial resolution and 25 microsecond time resolution. Combining the reconstructed J and E, we obtain a complete characterization including local critical current density, E-J curves, and power losses. This analysis has a range of applications from fundamental studies of vortex dynamics to practical coated conductor development.

Effects of fMRI–EEG mismatches in cortical current density estimation integrating fMRI and EEG: A simulation study

ObjectiveMultimodal functional neuroimaging by combining functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) has been studied to achieve high-resolution reconstruction of the spatiotemporal cortical current density (CCD) distribution. However, mismatches between these two imaging modalities may occur due to their different underlying mechanisms. The aim of the present study is to investigate the effects of different types of fMRI–EEG mismatches, including fMRI invisible sources, fMRI extra regions and fMRI displacement, on the fMRI-constrained cortical imaging in a computer simulation based on realistic-geometry boundary-element-method (BEM) model. MethodsTwo methods have been adopted to integrate the synthetic fMRI and EEG data for CCD imaging. In addition to the well-known 90% fMRI-constrained Wiener filter approach (Liu AK, Belliveau JW, Dale AM. PNAS 1998;95:8945–8950.), we propose a novel two-step algorithm (referred to as ‘Twomey algorithm’) for fMRI–EEG integration. In the first step, a ‘hard’ spatial prior derived from fMRI is imposed to solve the EEG inverse problem with a reduced source space; in the second step, the fMRI constraint is removed and the source estimate from the first step is re-entered as the initial guess of the desired solution into an EEG least squares fitting procedure with Twomey regularization. Twomey regularization is a modified Tikhonov technique that attempts to simultaneously minimize the distance between the desired solution and the initial estimate, and the residual errors of fitness to EEG data. The performance of the proposed Twomey algorithm has been evaluated both qualitatively and quantitatively along with the lead-field normalized minimum norm (WMN) and the 90% fMRI-weighted Wiener filter approach, under repeated and randomized source configurations. Point spread function (PSF) and localization error (LE) are used to measure the performance of different imaging approaches with or without a variety of fMRI–EEG mismatches. ResultsThe results of the simulation show that the Twomey algorithm can successfully reduce the PSF of fMRI invisible sources compared to the Wiener estimation, without losing the merit of having much lower PSF of fMRI visible sources relative to the WMN solution. In addition, the existence of fMRI extra sources does not significantly affect the accuracy of the fMRI–EEG integrated CCD estimation for both the Wiener filter method and the proposed Twomey algorithm, while the Twomey algorithm may further reduce the chance of occurring spurious sources in the extra fMRI regions. The fMRI displacement away from the electrical source causes enlarged localization error in the imaging results of both the Twomey and Wiener approaches, while Twomey gives smaller LE than Wiener with the fMRI displacement ranging from 1–2cm. With less than 2cm fMRI displacement, the LEs for the Twomey and Wiener approaches are still smaller than in the WMN solution. ConclusionsThe present study suggests that the presence of fMRI invisible sources is the most problematic factor responsible for the error of fMRI–EEG integrated imaging based on the Wiener filter approach, whereas this approach is relatively robust against the fMRI extra regions and small displacement between fMRI activation and electrical current sources. While maintaining the above advantages possessed by the Wiener filter approach, the Twomey algorithm can further effectively alleviate the underestimation of fMRI invisible sources, suppress fMRI spurious sources and improve the robustness against fMRI displacement. Therefore, the Twomey algorithm is expected to improve the reliability of multimodal cortical source imaging against fMRI–EEG mismatches. SignificanceThe proposed method promises to provide a useful alternative for multimodal neuroimaging integrating fMRI and EEG.

Distribution of cathode current density and breaking capacity of medium voltage vacuum interrupters with axial magnetic field

A high-speed photographic technique incorporating computer-aided reconstruction of the cathode current density was applied to butt solid contacts with an external axial magnetic field (AMF) at relatively low current density j<2 kA/cm/sup 2/. In the present work, we have further developed this technique. This advanced technique is applicable for the analysis of the current density distribution on the complicated electrodes of commercial vacuum interrupters (VIs) carrying currents up to I=50 kA at current density up to j/spl sim/4 kA/cm/sup 2/. The experiments have been carried out for three types of electrode designs generating AMFs with different configurations. The results obtained by this new technique proved a previously derived conclusion that current density tends to distribute evenly across that part of the contact surface where the AMF induction fits the inequality B/sub z//sup (1)/<B/sub z/<B/sub z//sup (2)/, where B/sub z//sup (1)/, B/sub z//sup (2)/ are characteristic induction fields defined in our previous work. Results of the analysis of erosion tracks on the electrodes are also in agreement with this conclusion. Slots on the electrode surface lead to substantial nonuniformity of current density distribution even if the AMF is properly configured. Comparison of the breaking capacity and distribution of current density for different electrode designs proves that interruption failure occurs at peak current density /spl sim/3.5 kA/cm/sup 2/. This value exceeds by at least 50% previous estimates of maximum current density interruptible by a commercial VI. We have also found that changing the configuration of the AMF may substantially improve breaking capacity. In our experiments, a slight modification of the AMF distribution provides a 12% increase of the breaking capacity.

Towards magnetic detection electrical impedance tomography: data acquisition and image reconstruction of current density in phantoms and in vivo

The objective of magnetic detection electrical impedance tomography (MD-EIT) is to reconstruct in vivo images of conductivity from magnetic field measurements taken around the body. MD-EIT is performed by applying an alternating current, at one of a range of frequencies, to a conducting object through a pair of electrodes fixed to the surface of the object. Magnetic field measurements recorded by search coils at a number of positions around the object are used to determine the current distribution that is generating the magnetic field. From this distribution, a conductivity map of a cross-section of the object can be reconstructed. This paper describes the development of an MD-EIT data acquisition system and discusses the related image reconstruction issues. The ill-conditioned nature of the inverse problem is examined and a number of image reconstruction methods are compared. The technical feasibility of MD-EIT data collection and image reconstruction is demonstrated with example images of current density from both phantom and human data.

A direct optimization approach for source reconstruction and NF-FF transformation using amplitude-only data

In this paper, we present a direct optimization procedure that utilizes phaseless electric field data over arbitrary shaped surfaces for the reconstruction of an equivalent magnetic current density that represents the radiating structure of an antenna under test. Once the equivalent magnetic current density is determined, the electric field at any point can be calculated. Numerical results (both simulated and experimental) are presented to illustrate the applicability of this approach for nonplanar near-field to far-field (NF-FF) transformation as well as to antenna diagnostics. The results are presented using both theoretical and experimental phaseless data over one and two planes.

Inverse‐scattering method for dielectric objects based on the reconstruction of the nonmeasurable equivalent current density

Usual inverse‐scattering methods for the reconstruction of dielectric objects are limited by the information that can be collected at the measurement locations. In this paper, an inverse‐scattering method is proposed that allows one to reconstruct the unmeasured components of the equivalent current density and then to improve the dielectric reconstruction. The mathematical formulation is provided, and the theory is supported by the results of numerical simulations.

Separation of sources of neuromagnetic examinations

Phantom experiments and computer simulations in combination with the Wiener-Helstrom filter reconstruction technique demonstrate the ability of the improvement of source separation in distributed current arrangements. A spatial region of interest (ROI), in which the current distribution is expected, is defined and discretized into three-dimensional voxel elements. Inside the ROI the number and spatial extension of the current sources are determined by reconstructing the impressed current density distribution separately from volume conductor effects. The volume currents can be determined depending on the actual head shape and the location of the ROI using finite difference methods before the reconstruction of the impressed current density. As a result the reconstruction procedure is very fast. Without a priori information about the number of active generators and the spatial extension inside the ROI, the method improves the separation of simultaneously active sources and distributed sources in comparison with the reconstruction of the total current density.

Numerical solution to three-dimensional inverse scattering for dielectric reconstruction purposes

The possibility of reconstructing the distribution of the dielectric characteristics of unknown inhomogeneous dielectric objects contained inside a fixed investigation volume V, where the scatterers can be placed at arbitrary positions is considered. It is assumed that the localisation of the scatterers and the determination of their surface shapes can be accomplished through the reconstruction of the equivalent current density, following a previously proposed approach. The method is based on an inverse-scattering formulation, and makes use of the moment method, together with a pseudoinversion algorithm, to face the problems associated with ill-conditioning. The approach does not require any plane-wave illumination or first-order approximations. It can potentially be used even in the case of strong scatterers. The advantages of using suitable thresholds for the reconstruction of the equivalent current density is considered. The capabilities and limitations of the approach have been assessed by means of numerical computer simulations, for which even data strongly affected by Gaussian noise have been used.

Computer simulation of electron beams. II. Low-cost beam-current reconstruction

Reconstruction of current density in electron beams is complicated by distortion of phase space which can require very fine discretization of the beam into trajectories. An efficient discretization of phase space is exploited, using conservation of charge and current in hypertriangle patches, to reconstruct the current density by fitting Gaussians through the distorted hypertriangles. Advantages and limitations are discussed.

Developments in Non-Destructive Beam Diagnostics

With the large average beam currents being achieved in accelerators and storage rings, there is an increasing need for non-destructive beam diagnostic devices. For continuous beams, position monitors of the capacitive pick-up type are replaced by resonant devices that respond to the transverse displacement of the beam centroid. Bunch length monitors of the SLAC type using resonant cavities operating in the TM0l0 mode can be used for continuous beams. The more detailed information derivable from beam profile scanners requires development of improved non-destructive devices. Profile monitors which scan the visible light produced by high current beams may be more reliable than ones using the residual ionization if the light intensity from gas molecules following nonionizing collisions with beam particles gives a measure of the beam current density independent of the local electron density. The intense Balmer series lines from neutral hydrogen beams have been used successfully to measure beam profiles. At CRNL and at LASL, beam light profile monitors are being developed for high average current accelerators. Three or more projections will be recorded to allow tomographic reconstruction of the two-dimensional beam current density. Light detection is either by intensified Reticons or ISIT vidicons. The use of three or more beam light monitors on a beam transport line will also permit estimates of the transverse emittance to be made through the reconstruction technique.