Convergence improvement for iterative solutions of the electric fields integral equation at very low frequencies

2003 ◽  
Author(s):  
Jun-Sheng Zhao ◽  
Weng Cho Chew
Keyword(s):  
Integral Equation ◽  
Electric Fields ◽  
Low Frequencies ◽  
Iterative Solutions

Electromagnetic response of a discretely grounded circuit—An integral equation solution

Geophysics ◽  
1994 ◽  
Vol 59 (11) ◽  
pp. 1680-1694 ◽  
Author(s):  
Wei Qian ◽  
David E. Boerner
Keyword(s):  
Integral Equation ◽  
Electric Fields ◽  
Skin Depth ◽  
Electromagnetic Response ◽  
Square Root ◽  
Electromagnetic Excitation ◽  
Low Frequencies ◽  
Magnetic Dipoles ◽  
Equation Solution ◽  
Effective Impedance

We derive an integral equation to describe the electromagnetic response of a discretely grounded circuit. This investigation is relevant to the study of man‐made structures such as metallic fences, grounded powerlines, and pipelines, all of which may fall into the class of discretely grounded conductors. The solution developed here is an extension to existing circuit theory and takes into account the self and mutual interaction of the circuit elements. It is possible to ignore these interactions at low frequencies where the grounding impedances dominate the effective impedance of the circuit. However, at frequencies where the electromagnetic skin depth is comparable to the length between adjacent grounding points, the effective impedance of the circuit is proportional to frequency, and the inductance of the circuit dominates its electromagnetic response. Within the quasi‐static limit (i.e., where displacement currents can be neglected) electromagnetic excitation by either horizontal electric or vertical magnetic dipoles produces a constant primary electric field at high frequencies (far‐field). Thus, the electric current in the discretely grounded circuit will always be inversely proportional to frequency for these types of sources. Horizontal magnetic dipole or vertical electric dipole sources generate primary electric fields that are proportional to the inverse square root of frequency in the high frequency limit of the quasi‐static domain, and thus the current in a circuit excited by such sources will decrease as the inverse of square root of frequency. The integral equation solution derived here can be used to investigate the influence from cultural conductors on actual electromagnetic surveys and also provides further insights into the current channeling response of surficial conductors.

Generation of Short-scale Electrostatic Fields in the Solar Atmosphere and the Role of Helium Ions

2021 ◽  
Vol 922 (1) ◽  
pp. 48
Author(s):  
H. Saleem ◽  
Shaukat Ali Shan ◽  
A. Rehman
Keyword(s):  
Shear Flow ◽  
Transition Region ◽  
Electric Fields ◽  
Hydrogen Plasma ◽  
Theoretical Models ◽  
Inhomogeneous Field ◽  
Helium Ions ◽  
Low Frequencies ◽  
Short Scale

Abstract Theoretical models are presented to show that expansion of plasma in the radial direction from a denser solar surface to a rarefied upper atmosphere with short-scale inhomogeneous field-aligned flows and currents in the form of thin threads itself is an important source of electrostatic instabilities. Multifluid theory shows that the shear flow–driven purely growing electric fields appear in the transition region. On the other hand, plasma kinetic theory predicts that the short-scale current sheets (or filaments) produce current-driven electrostatic ion acoustic (CDEIA) waves in the hydrogen plasma of the transition region that damp out in the system through wave–particle interactions and increase the temperature. Similar processes take place in the solar corona and act positively for increasing the temperature further and maintaining it. The shear flow–driven instabilities and CDEIA waves have short perpendicular wavelengths of the order of 1 m and low frequencies of the order of 1 or several Hz when the ions’ shear flow scale length is considered to be of the order of 1 km. It is pointed out that the purely growing fluid instabilities turn into oscillatory instabilities and the growth rates of kinetic CDEIA wave instabilities are reduced when the dynamics of 10% helium ions is taken into account along with 90% hydrogen ions. Therefore, the role of helium ions should not be ignored in the study of wave dynamics in solar plasma.

Scattering of a shear horizontal wave by a circular cavity in a piezoelectric bi-material strip based on guided wave theory

2020 ◽  
Vol 25 (4) ◽  
pp. 968-985 ◽  
Author(s):  
Hui Qi ◽  
Meng Xiang ◽  
Jing Guo
Keyword(s):  
Integral Equation ◽  
Electric Fields ◽  
Concentration Factor ◽  
Scattering Problem ◽  
Reference Value ◽  
Wave Theory ◽  
Guided Wave ◽  
Circular Cavity ◽  
Two Phase ◽  
Shear Horizontal

The scattering problem of a shear horizontal guided wave in a piezoelectric bi-material strip is analysed by means of the "mirror method," the Green’s function method and guided wave theory. A harmonic out-of-plane line-source force is applied at the junction of two-phase materials. Then, the bi-material strip is divided into two parts, and a pair of in-plane electric fields and a pair of counter-planar forces are applied to the vertical boundary. According to the boundary conditions, the Fredholm integral equation of the first kind is established by using the conjunction method. By effectively truncating the integral equation, the integral equation is simplified to an algebraic equation. The electric field intensity concentration factor and dynamic stress concentration factor around the circular cavity are obtained. The research content of this article is of great reference value in non-destructive testing, providing a reference for the judgement of the reliability of a piezoelectric bi-material strip.

A hybrid solver based on the integral equation method and vector finite-element method for 3D controlled-source electromagnetic method modeling

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. E319-E333 ◽  
Author(s):  
Rong Liu ◽  
Rongwen Guo ◽  
Jianxin Liu ◽  
Changying Ma ◽  
Zhenwei Guo
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Integral Equation ◽  
Finite Element ◽  
Differential Equations ◽  
Electric Fields ◽  
Hybrid Method ◽  
Linear Equations ◽  
Integral Equation Method ◽  
Controlled Source

The integral equation method (IEM) and differential equation methods have been widely applied to provide numerical solutions of the electromagnetic (EM) fields caused by inhomogeneity for the controlled-source EM method. IEM has a bounded computational domain and has been well-known for its efficiency, whereas differential equation methods are commonly used for complex geologic models. To use the advantages of the two types of approaches, a hybrid method is developed based on the combination of IEM and the edge-based finite-element method (vector FEM). In the hybrid scheme, Maxwell’s differential equations of the secondary electric fields in the frequency domain are derived for a volume with boundary placed slightly away from the inhomogeneity. The vector FEM is applied to solve Maxwell’s differential equations, and a system of linear equations for the secondary electric fields can be derived by the minimum theorem. The secondary electric fields on the boundary are represented by IEM in terms of the secondary electric fields inside the inhomogeneity. The linear equations from substituting the boundary values into the vector FEM linear equations then can be solved to obtain the secondary electric fields inside the inhomogeneity. The secondary electric fields at receivers are calculated by IEM based on the secondary electric field solutions inside the inhomogeneity. The hybrid algorithm is verified by comparison of simulated results with earlier works on canonical 3D disc models with a high accuracy. Numerical comparisons with two conventional IEMs demonstrate that the hybrid method is more accurate and efficient for high-conductivity contrast media.

Removal of static shift in two dimensions by regularized inversion

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2102-2106 ◽  
Author(s):  
Catherine deGroot‐Hedlin
Keyword(s):  
Electric Fields ◽  
Apparent Resistivity ◽  
Skin Depth ◽  
Two Dimensions ◽  
Small Scale ◽  
Low Frequencies ◽  
Near Surface ◽  
Regularized Inversion ◽  
Conductivity Anomalies ◽  
Local Distortions

A common problem in magnetotelluric (MT) sounding is the presence of static shifts in the data, i.e., a vertical shifting of the log‐apparent‐resistivity versus period curves relative to regional values (Jones, 1988; Jiracek, 1990; Berdichevsky et al., 1989). These static shifts are due to the presence of small‐scale, shallow conductivity anomalies near the measurement site. Electric charge builds up on near‐surface anomalies that are small in comparison to the skin depth of the electromagnetic (EM) fields. The charge buildup produces a perturbation of the measured electric fields from their regional values that persists to arbitrarily low frequencies. Incorrect removal of these local distortions leads to incorrect interpretation of the deeper targets of investigation.

Low-frequency response of a buried object in a lossy ground

1990 ◽  
Vol 68 (1) ◽  
pp. 111-120 ◽  
Author(s):  
A. Helaly ◽  
L. Shafai ◽  
A. Sebak
Keyword(s):  
Magnetic Field ◽  
Integral Equation ◽  
Scattered Field ◽  
Numerical Results ◽  
Low Frequencies ◽  
Impedance Boundary ◽  
Buried Object ◽  
Magnetic Field Integral Equation ◽  
The Magnetic Field ◽  
Field Integral

An approximate method is developed for treating problems of electromagnetic scattering, at low frequencies, from a buried object in a lossy ground and excited by a source located in the air region above. The field incident on the object's surface is calculated using the dyadic Green's functions for a half-space. Neglecting the coupling between the air–Earth interface and the object as a first-order approximation at low frequencies, we formulate the scattering problem in terms of the magnetic-field integral equation in conjunction with the impedance boundary conditions. The method of moments is then used to reduce the magnetic-field integral equation to a matrix one in order to determine the induced surface currents. The total scattered field is separated into two terms. One is the direct scattered field, which acts as if no buried inhomogeneity were present. The other term is the anomalous field, which represents the presence of the inhomogeneity. Solutions have been generated, and the numerical results are examined for a few limiting cases to confirm their accuracy. The formulation is then applied for investigating scattering by buried steel spheres. The numerical results show that the method can be used for detecting buried objects.

scholarly journals Broad-band electric field measurements above thunderstorms by the IME-HF instrument prepared for the TARANIS mission

2020 ◽  
Author(s):  
Ondřej Santolík ◽  
Ivana Kolmašová ◽  
Radek Lán ◽  
Luděk Uhlíř ◽  
Jean-Louis Rauch ◽  
...  
Keyword(s):  
Electric Fields ◽  
Gamma Ray ◽  
Broad Band ◽  
Field Measurements ◽  
Detection Algorithm ◽  
X Rays ◽  
Scientific Instruments ◽  
Frequency Range ◽  
Low Frequencies ◽  
Blue Jets

<p>A broad-band analyzer of the IME-HF instrument (“Instrument de Mesure du champ Electrique Haute Frequence”) is prepared for the TARANIS (Tool for Analysis of RAdiation from lightNIng and Sprites) micro-satellite of the French space agency CNES. The spacecraft is based on the MYRIADE series platform. It will be launched on a Sun synchronous polar orbit at 700 km altitude. TARANIS will carry a complex payload of six scientific instruments to study radiation from lightning and optical phenomena (Transient Luminous Events) observed at altitudes between 20 and 100 km (blue jets, red sprites, halos, elves). The scientific instruments onboard TARANIS will detect electromagnetic radiation from very low frequencies up to 37 MHz, optical radiation, X rays (with an aim to study the Terrestrial "Gamma-ray" Flashes), and energetic electrons.</p><p>The IME-HF instrument will record waveform measurements of fluctuating electric fields in the frequency range from a few kHz up to 37 MHz, with the following scientific aims: (i) Identification of possible wave signatures associated with transient luminous phenomena during storms; (ii)    Characterization of lightning flashes from their HF electromagnetic signatures; (iii) Identification of possible HF electromagnetic or/and electrostatic signatures of precipitated and accelerated particles; (iv) Determination of characteristic frequencies of the medium using natural waves properties; (v) Global mapping of the natural and artificial waves in the HF frequency range, with an emphasis on the transient events. The instrument will be also able to trigger and record interesting intervals of data using a flexible event detection algorithm.</p>

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