Electromagnetic Diffusion Research Articles

Evaluating the moisture absorption percentage in the adhesive layers of carbon fiber reinforced plastic joints via electromagnetic induction testing and diffusion analysis

In this study, we propose a method that combines moisture absorption analysis and electromagnetic induction testing (EIT) to detect weak bonds formed in the adhesive layers of carbon fiber reinforced plastic (CFRP) joints due to moisture absorption. Although EIT is effective for assessing CFRP joint adhesive moisture absorption, early detection of weak bonds is challenging. Our method addresses this by combining calculations of moisture absorption percentage via the diffusion equation and EIT-based measurements. First, we conducted diffusion analysis using the finite difference method (FDM). The moisture absorption percentage calculated via the FDM was validated by comparing it with the results of the moisture absorption tests of the CFRP adhesive joints, and good agreement was observed. Second, EIT was applied to the CFRP adhesive joints, and the experimental results indicated that the moisture absorption percentage of the CFRP joint adhesive layer can be qualitatively evaluated using EIT. Finally, the moisture absorption of the CFRP joint adhesive layer was quantitatively evaluated by combining the results of EIT on the CFRP joints with those of the numerical analysis. Therefore, the proposed method enables the previously difficult quantitative evaluation of the initial moisture absorption percentage of CFRP joint adhesive layers and is effective for the early detection of weak bonds created by moisture absorption in CFRP joints.

The transient discharge circuit analysis of single-turn coil

Single-turn coil (STC) is a destructive pulse magnet aiming at a 100–300 T ultra-high magnetic field. A transient discharge circuit model considering the coupling of electromagnetic diffusion and conductor deformation is proposed, and the transient coil impedance characteristics are investigated. The results show that the coil resistance first decreases and then increases due to electromagnetic diffusion and temperature rise, respectively, while the coil inductance always increases because of the conductor’s outward motion. By comparison, the simulation results are consistent with the experimental data, and the correctness of the model is validated.

A numerical simulation method for solving electromagnetic-mechanical coupling field

A new numerical simulation method based on the finite volume method has been proposed to address the challenges associated with the pseudo-oscillation phenomenon that occurs with an increased Péclet number, as well as determining an appropriate time step for electromagnetic-mechanical coupled physical field calculations. This method utilizes the concept of upwind from Computational Fluid Dynamics (CFD) to solve Maxwell's equations, a finite-volume method for discretizing the electromagnetic diffusion equations. Through computing typical electromagnetic field problems such as TEAM problem 9–1 and comparing the results to the literature, it has been confirmed that this method has sufficient computational accuracy to solve electromagnetic field numerical simulation problems containing moving conductors. Additionally, a three-dimensional simulation model of the electromagnetic coil gun has been established to verify the viability of the proposed method for solving magnetic field problems under the electromagnetic launch (EML) system. The study also examined the change in magnetic field strength and current density of the EML device during the launching process. The results lay the foundation for the technical application of this method.

A Robust and Scalable Multigrid Solver for 3-D Low-Frequency Electromagnetic Diffusion Problems

A Robust and Scalable Multigrid Solver for 3-D Low-Frequency Electromagnetic Diffusion Problems

A divergence-free vector finite-element method for efficient 3D magnetotelluric forward modeling

For large-scale magnetotelluric (MT) forward modeling using vector finite-element methods, iterative solvers are commonly applied. However, as frequency decreases close to zero, the iterative solution process struggles to converge. This is mainly caused by the fact that the weak conductivity term in the curl-curl equation governing the electromagnetic (EM) diffusion in the earth fades during the iterative solution for EM fields. This can lead to violation of the divergence-free condition for current and false jumps in the calculated fields. We develop a regularization technique for vector finite-element MT forward modeling, in which a scaled grad-div operator for electrical fields is included in the curl-curl equation to enforce the divergence-free condition explicitly. Because of its use of basis functions, the direct edge element discretization of the scaled term can lead to zero coefficients. To address this, an equivalent substitute of the scaled grad-div operator based on potential representation of electrical fields is used, discretized with node elements. For one specific element, this is finally reduced to a scaled gradient of the surface integral of current across all the surfaces of the element, resulting in better connectivity of the linear system of equations. The correctness of our algorithm is verified with two synthetic models and an inversion model from real data. The numerical performance is compared to the traditional iterative divergence correction technique (and without the application of the divergence correction for one case) for each of the three models. The results indicate that our algorithm is generally more efficient and stable compared to the traditional technique for all models at all periods considered, with significant improvement at long periods.

RCS reduction of composite transparent flexible coding metasurface combined phase cancellation and absorption.

A wideband low-scattering metasurface with optical transparency and flexibility is proposed by using the combination of phase cancellation and absorption mechanisms. Electromagnetic (EM) diffusion is achieved through the random phase distribution design of the two coding elements. The enhanced energy absorption can be obtained in a wide spectrum by using indium tin oxide (ITO) with suitable sheet resistance in the supercells. The experimental results show that the radar cross section (RCS) reductions of less than -10 dB under the planar and conformal cases are in 6.65-19.40 GHz and 6.11-17.37 GHz, corresponding relative bandwidth are 97.89% and 95.91%, respectively. Both theoretical analysis and simulated results are good accordance with the experiment. Furthermore, the analyses of the surface current, EM field distribution and power loss density are given to explain the hybrid RCS reduction mechanism. The proposed composite transparent flexible coding metasurface (CTFCM) maintains good angular stability within 0°-60° oblique incidence and has polarization insensitivity. The CTFCM has excellent flexibility and high optical transparency, which provides a way to reduce RCS in a wider band and has important application potential for stealth aircraft cockpit and transparent radome.

A New 3D Marine Controlled-Source Electromagnetic Modeling Algorithm Based on Two New Types of Quadratic Edge Elements

This study proposes a new algorithm for a higher-order vector finite element method based on two new types of second-order edge elements to solve the electromagnetic field diffusion problem in a 3D anisotropic medium. To avoid source singularity in the quasistatic variant of Maxwell’s function, a secondary field formulation was adopted. The modeling domain was discretized using two types of quadratic edge hexahedral elements, which were obtained using the edge unification method to reduce variables on each side of two conventional quadratic edge elements. Compared with the traditional quadratic element, the number of unknowns that needed to be solved was significantly reduced. The sparse linear equation of the finite element system was solved using an open-source direct solver called MUMPS. The numerical results demonstrated that the proposed algorithm has the same level of accuracy as the conventional vector finite element method and has a significant advantage over it in terms of computational cost.

2-D Modeling and Analysis of Time-Domain Electromagnetic Anomalous Diffusion With Space-Fractional Derivative

Recently, the electromagnetic (EM) anomalous diffusion phenomenon has been observed in time-domain EM (TDEM) surveys. Furthermore, the data interpretation accuracy has been reduced by adopting the traditional EM theory and methods. A number of models, such as random medium and roughness electrical conductivity theory, have been adopted to model the EM anomalous diffusion. However, problems such as modeling difficulty and massive discretization exist regarding characterizing the long-range correlation of EM anomalous diffusion. The space-fractional derivative has been proven to preferably describe the long-range correlation characteristic. Only a handful of studies on TDEM anomalous diffusion with space-fractional derivative have been conducted due to the difficulties in computational engineering problems. Therefore, we performed a series of studies about 2-D TDEM anomalous diffusion with space-fractional derivative. The 2-D TDEM space-fractional diffusion equation was constructed based on the space-fractional Ohm’s law model. Furthermore, the discretization and iteration forms of the control equation were derived based on the finite element method (FEM) by introducing the Riemann–Liouville (R–L)-type Riesz fractional derivatives. The 2-D mountain-shaped function and partial integration method (PIM) were combined to convert the fractional derivative into the primitive function form. Hence, the 2-D modeling of the space-fractional EM diffusion was realized. The effectiveness of our method was verified by the function construction method and wavenumber-domain analytical solution. The spatial and temporal characteristics of the space-fractional EM diffusion were analyzed by different geological models. Furthermore, we discuss the differences with the classical EM diffusion. Our method can effectively model the space-fractional EM diffusion in TDEM surveys and provide theoretical bases for improving the TDEM interpretation accuracy with complex geological conditions.

Is Kp the Best Single Magnetic Activity Parameterization for Electromagnetic Radial Diffusion in the Outer Radiation Belt?

AbstractSpecifying radial diffusion magnitude is one of the main requirements for most physics‐based radiation belt models. Yet, radial diffusion quantification remains uncertain. The most commonly used parameterization for the logarithm of radial diffusion magnitude is a linear function of a magnetic index, , with a coarse time resolution of 3 hours. This work presents alternate linear parameterizations of similar quality for the logarithm of radial diffusion magnitude, considering other magnetic indices and solar wind parameters. Using a publicly available time series for the logarithm of electromagnetic radial diffusion magnitude, we investigate linear relationships with magnetic indices such as Kp, Hp60, Hp30, AE, SymH, and Dst and solar wind parameters such as solar wind dynamic pressure, solar wind speed, and the north‐south component of the interplanetary magnetic field. We find that Kp, Hp60, Hp30, and solar dynamical pressure yield the strongest linear correlation with the logarithm of radial diffusion magnitude. We also provide simple, energy‐dependent, linear models of the logarithm of radial diffusion magnitude that best fit the time series, as well as quantifications of the root‐mean square errors. This work contributes to improving the time resolution for radial diffusion parameterization and operational radiation belt models. In particular, it suggests that the new 30‐min and 60‐min geomagnetic indices Hpo (Hp30 and Hp60, respectively) could also be used in place of Kp in the most commonly used Kp‐driven parameterizations for radiation belt radial diffusion, to improve the time resolution of the models.

Wideband low-RCS circularly polarized antenna with metasurface combining wave diffusion and polarization conversion

A novel and simple low-profile high-gain wideband circularly polarized (CP) slot antenna with low radar cross section (RCS) is presented. The proposed antenna is composed of a traditional linearly polarized (LP) slot antenna and an integrated metasurface-based superstrate. The superstrate consists of a center array with metasurface (MS) unit cells and four surrounding arrays with 4×4 MS unit cells. On the one hand, a wideband and high-gain CP radiation in the frequency band of 5.27-6.18 GHz (a relative bandwidth of 15.9%) is achieved by the polarization conversion property of the MS and four surrounding arrays. On the other hand, a broadband RCS reduction in the frequency band of 4.5-20 GHz (a relative bandwidth of 126.5%) is obtained by the combination of two electromagnetic wave diffusion principles. Inspired by C-band, X-band and Ku-band radar applications, a low-cost stealthy prototype with broadband low RCS and CP radiation is realized.

Optically transparent and microwave diffusion coding metasurface by utilizing ultrathin silver films.

The past few years have witnessed the great success of artificial metamaterials with effective medium parameters to control electromagnetic waves. Herein, we present a scheme to achieve broadband microwave low specular reflection with uniform backward scattering by using a coding metasurface, which is composed of a rational layout of subwavelength coding elements, via an optimization method. We propose coding elements with high transparency based on ultrathin doped silver, which are capable of generating large phase differences (∼180°) over a wide frequency range by designing geometric structures. The electromagnetic diffusion of the coding metasurface originates from the destructive interference of the reflected waves in various directions. Numerical simulations and experimental results demonstrate that low reflection is achieved from 12 to 18 GHz with a high angular insensitivity of up to ±40° for both transverse electric and transverse magnetic polarizations. Furthermore, the excellent visible transparency of the encoding metasurface is promising for various microwave and optical applications such as electronic surveillance, electromagnetic interference shielding, and radar cross-section reduction.

Constitutive modeling of pH-sensitive hydrogel: Multi-physics coupling of electromagnetics with mechanics and thermodynamics

The field theory of pH-sensitive hydrogel deformation is presented coupling electro-magnetic (EM) field (external or internal) and diffusion (Poisson–Nernst–Planck and Maxwell equations) of mobile ionic species through irreversible thermodynamics. The evolution of fixed-charge in the hydrogel is modeled by Langmuir monolayer adsorption theory. The important contribution of present work is a derivation of Cauchy stress tensor constitutive relation with EM field and species diffusion through Maxwell’s stress and spherical tensors. The EM field work done is computed in the frame-invariant settings employing Poynting vector concept, which is another novel contribution of the present work. The hydrogel deformation is finally computed by mechanical equilibrium equation coupled with the diffusion equations through traction boundary conditions. The applicability of the presented framework is successfully demonstrated by several pH-sensitive hydrogel simulations (one- and two-dimensional). The constitutive relations derived here are also verified with the other published results.

A method of rapidly designing graphene-based terahertz diffusion surface

Electromagnetic diffusion surface can reduce the radar cross section, thus profiting stealth of targets. Terahertz diffusion surface has a wide prospect in the field of next-generation radar and communication, promising to act as a kind of intelligent smart skin. In this paper, utilizing the excellent tunable properties of graphene in the terahertz band, a hybrid structure of graphene and metal which has inverse phase response of reflecting waves is proposed. The reflection phase switches in the mechanism of resonant modes and can be controlled efficiently by the bias voltage. Meanwhile, unlike metal materials, graphene has a non-negligible loss characteristic, which leads the response amplitudes corresponding to the two different switching states to be inconsistent with each other. According to the interference and superposition principle of electromagnetic field, it is not conducive to eliminating the coherent far-field, leading to an unsatisfactory diffusion result. In this paper, we present a “molecular” structure by secondary combination of the above-mentioned reverse phase element states, and take it as the basic element of the diffusion surface. Finally, we use particle swarm optimization to optimize the arrangement of “molecular” structures. The final diffusion surface consists of a combinatorial design of “molecules” rather than randomly distributed reflection units. In addition, molecules designed artificially have similar amplitude responses but different phase responses, which improves the convergence speed and reduces the computation quantity during algorithm evolution. The method of designing molecular structure, described in this paper, is simple, rapid and widely applicable, which effectively improves the amplitude-to-phase modulation ability of graphene metasurface against electromagnetic waves. When diffuse reflection optimization is applied to most of graphene metasurfaces, the method described in this paper can achieve the results that are the same as or even better than the results after a large number of iterations of traditional particle swarm optimization in the most computation-efficient manner. The results show that the dynamic diffusion surface designed by this method has the advantages of fast convergence speed and small far-field peak.

Time-Domain Electromagnetic Fractional Anomalous Diffusion Over a Rough Medium

The theory of magnetic-source electromagnetic anomalous diffusion is developed in this article. As the geological medium is spatially rough, the late-time tail phenomenon can be explained as a multiscale electromagnetic anomalous diffusion, which is a union of fractional subdiffusion and regular diffusion. The roughness parameter β and weighting parameter W are introduced into the generalized electrical conductivity to indicate the roughness level and ratio. The characteristics and superiority of the improved generalized electrical conductivity are analyzed in the time domain. A 3-D modeling method is proposed based on the fractional finite-difference time-domain method. The introduced Caputo fractional derivative in the time domain is calculated by the Alikhanov superconvergent approximation method, so that the stability of the solution is improved. Several half-space models are designed to verify the 3-D modeling efficiency. It turns out that the improved generalized electrical conductivity can model the electromagnetic late-time tail efficiently, which is characterized by responses that coincide with the classical attenuation law at earlier times and the departure at later times. Moreover, this approach is also applied to anomalous models with 3-D bodies; the results indicate that the proposed method can recognize 3-D anomalous bodies efficiently. The improved method can model the complex electromagnetic propagation in the rough geologic medium more accurately, providing a theoretical basis for multiscale and refined detection.

Three-dimensional magnetotelluric numerical simulation of realistic geologic models

We have developed a workflow for constructing realistic mesh-based magnetotelluric (MT) models from 3D geologic models. The routine is developed for unstructured meshes that adapt to the complex shapes of geologic bodies including 3D surfaces and volumes in realistic modeling scenarios. The methodology is applied to the complexly altered Lalor volcanogenic massive sulfide deposit in Manitoba, Canada. The host rock envelope of the Lalor deposit is compartmentalized into lithostratigraphic units leading to a watertight model. This model then is meshed into unstructured tetrahedral meshes suitable for synthetic geophysical modeling of the MT method. Subsequently, two 3D resistivity models are generated from wireline logs: (1) a host rock background model in which each tetrahedral cell is attributed with the average resistivity of each lithostratigraphic unit and (2) a heterogeneous background-ore model in which the resistivity values of the cells are resampled from a 3D curvilinear grid model, generated by computing sequential Gaussian simulations from the resistivity data for each unit of a 3D lithofacies model produced by categorical kriging. To calculate the synthetic response of this model for MT, a numerical-modeling code is developed based on solving the vector-scalar potential formulation of the electromagnetic diffusion equation using the finite-element method on unstructured meshes. After validating the numerical method for the Commemi test model, the MT response of the Lalor model is investigated. A reasonable agreement is observed between the survey field data and the data synthesized from our constructed heterogeneous model. Using an investigation of the inductive and galvanic parts, we conclude with the ideal frequency range for detecting the ore deposit. We also conclude with and visualize the importance of regional-scale alteration zones around the ore deposits and model inhomogeneities in boosting the detectability of the ore formations through feeding electrical currents as a result of galvanic field dominance at depth.

Electromagnetic Radial Diffusion in the Earth's Radiation Belts as Determined by the Solar Wind Immediate Time History and a Toy Model for the Electromagnetic Fields

AbstractDiffusion‐driven radiation belt models require multiple physics‐based inputs to specify the radiation environment through which spacecraft travel, including diffusion coefficients. Even though event‐specific coefficients are necessary for model accuracy, their routine integration in operational models has not yet been achieved. In fact, one of the key inputs, the radial diffusion coefficient, is still commonly determined by a Kp‐driven parameterization. This work presents a method to determine continuous time series of time‐varying radial diffusion coefficients. A theoretical model is developed in which electromagnetic radial diffusion is controlled by the magnetopause immediate time history. Specifically, radial diffusion is described as a function of the average, variance, and autocorrelation time of the geocentric standoff distance to the subsolar point on the magnetopause. Because the magnitudes of these three magnetopause parameters vary with time and magnetic activity, so does radial diffusion. To a lesser extent, radial diffusion is also controlled by the drift frequency of the radiation belt population. Moreover, radial diffusion is quantified using a standard model in which the magnetopause is controlled by the solar wind. Although the resulting diffusion coefficients span several orders of magnitude per Kp index, the median magnitudes are remarkably similar to the ones provided by the standard Kp‐driven statistical parameterization.

A hybridizable discontinuous Galerkin method for electromagnetics with a view on subsurface applications

Two Hybridizable Discontinuous Galerkin (HDG) schemes for the solution of Maxwell’s equations in the time domain are presented. The first method is based on an electromagnetic diffusion equation, while the second is based on Faraday’s and Maxwell–Ampère’s laws. Both formulations include the diffusive term depending on the conductivity of the medium. The three-dimensional formulation of the electromagnetic diffusion equation in the framework of HDG methods, the introduction of the conduction current term and the choice of the electric field as hybrid variable in a mixed formulation are the key points of the current study. Numerical results are provided for validation purposes and convergence studies of spatial and temporal discretizations are carried out. The test cases include both simulation in dielectric and conductive media.

Optimization of the Method of Auxiliary Sources by the Genetic Algorithm for electromagnetic scattering problem

In this paper, we propose to apply a technique of optimization of the convergence of the auxiliary sources method (MAS) for the problems of electromagnetic diffusion by a perfectly conducting and infinite obstacle. This technique is based on the use of the genetic algorithm (GA). Previous studies have shown that the convergence of the MAS solution depends on many parameters such as the number of auxiliary sources and the auxiliary distance between the real surface of the cylinder and the fictitious surface, and so on. The solution is obtained for a good choice of these parameters. In this article, the genetic algorithm is chosen to facilitate the choice of MAS parameters.

Identification and analysis of static and dynamic magnetization behavior sensitive to surface laser treatments within the electromagnetic field diffusion inside GO SiFe electrical steels

Surface laser treatment of soft magnetic materials, such as GO SiFe electrical steels, is mainly used to reduce iron losses by modifying the static and the dynamic magnetic properties. Laser treatment effect on mesoscopic electromagnetic properties of soft magnetic materials is presented. An experimental procedure using the Single Sheet Tester is performed on a magnetized sheet with specific exciting induction level and frequency. Transient average magnetic flux density through the sample cross-section and its corresponding applied magnetic field are measured. Data are identified in the time-domain with numerical results obtained by solving the diffusion equation using a 1-D discretization approach. The identification strategy requires a material law that includes both non-linear static and dynamic properties and describes the magnetic behavior due to domains and walls dynamics. Next, parametric and physical studies are performed on materials submitted to different laser treatments in order to determine and interpret their effects on the identified magnetic properties and the time response in the sheet’s depth. The results show that the static and the dynamic properties can be simultaneously improved. This analysis help to understand the impact of laser treatments on the static and the dynamic behaviour in order to improve the material magnetic performances within magnetic circuits inside electrical machines and transformers.

Numerical Modelling of Borehole-Surface CSEM Response of Onshore Gas Hydrate Deposit with Higher Order Finite Difference Method

The recent increase in energy demand has propelled research on the discovery of unconventional energy sources as conventional oil and gas reservoirs are been depleted. Hence, in this study, we investigate the feasibility of using the Borehole Controlled Source Electromagnetic (BSCSEM) method for gas hydrate exploration in Qilian Mountain, China. To achieve this, we developed an accurate and efficient forward modeling code for the simulation of electromagnetic diffusion problems based on the total field formulation using the Frequency Domain Finite Difference (FDFD) approach. We used large grid sizes to reduce the computational cost of simulating the borehole to surface responses and also examined the effect of applying the Perfectly Matched Layer (PML) on the BSCSEM computational area. Subsequently, we investigate the effects of the higher and lower-order approximations and used spatial operators of the lower order and first-order accuracy in substantial parts of the computational domain including but not limited to layer boundaries during the solution process. We also investigate responses from different source orientations and source length, with a focus on the electric dipoles for 2D and 3D models of buried resistive targets. Finally, we performed 2D modeling to detect onshore gas hydrate deposit for known scenarios using a suitable BSCSEM configuration for 200 m borehole dipole with an average current of 10 A. Our results generally indicate that the BSCSEM responses from the vertical transmitters were highly effective in characterizing the resistive layers as well as the measurement of the vertical component of the electric field. By changing the depth of the vertical dipole sources, we found out that BSCSEM showed the ability to gain information about the subsurface medium from different angles. Hence, we conclude that in a complex environment, the combined use of the horizontal and the vertical transmitters to acquire three component (3C) field data and the joint analysis of their electric responses helps to delineate the subsurface structure more clearly.