Leontovich Boundary Condition Research Articles

Mathematical modeling of electromagnetic radiations incident on a symmetric slit with Leontovich conditions in an-isotropic medium

This article presents the rigorous analysis of the an-isotropic medium affecting the diffraction process of EM-signals of high frequency by a symmetric slit of finite width. Leontovich boundary conditions for the present model are taken into consideration to show the existence of impedance. The ionosphere having non-thermal plasma contains the geomagnetic field which turns the medium into an an-isotropic medium. The well-known Helmholtz equation for electromagnetic (EM) waves is formulated through Maxwell’s equations with consideration of dielectric permittivity tensor for an an-isotropic medium due to non-thermal plasma. The Fourier transform is employed for the equations formulated for this model and then a pair of Wiener–Hopf equations (coupled form) is devised. These Wiener–Hopf equations are then tackled and an asymptotic method is used to achieve the target. Results for the isotropic medium can be obtained by assigning the values to permittivity elements controlling the medium. Graphical results are sketched for better visualization of the separated field for the an-isotropic medium and isotropic medium as well.

A fundamental approach: E-polarized electromagnetic wave diffraction by two dimensional arbitrary-shaped objects with impedance boundary condition

Abstract In the present study, a new methodology in computational electromagnetics is developed for two-dimensional arbitrarily-shaped objects with impedance boundary conditions. The proposed approach investigates the E-polarized electromagnetic diffraction by a two-dimensional object with the Leontovich boundary condition. The scattered electric and magnetic fields are expressed as the convolution integral of the corresponding Green’s function and the current induced on the obstacle surface. After obtaining integral equations by applying the boundary condition, the integral equations are solved as in the case of the method of auxiliary sources (MAS) which is a well-known method in computational electrodynamics. The results are compared with first, different methods such as the method of moments (MoM), orthogonal polynomials (OP), and second, different boundary conditions such as Dirichlet, Neumann, and fractional boundary conditions. Some results are also obtained for the different shape scatterers at some values of the surface impedance.

H‐polarized plane wave diffraction by a slotted cylinder with different surface impedances: Solution by the analytical—Numerical approach

The study investigates the H-polarized plane wave diffraction by a slotted cylinder with different surface impedances employing an analytical-numerical approach. The solution is obtained by expressing the current distribution on the obstacle with Gegenbauer polynomials considering the edge conditions. To obtain the field and current distribution on the surface, the Leontovich boundary condition on each side of the slotted cylinder is employed. The results are compared with Dirichlet and Neumann boundary condition cases obtained previously. It is observed that the resonant field amplitudes and the location at the resonances strongly depend on the impedance values.

M-dissipative boundary conditions and boundary tuples for Maxwell operators

For Maxwell operators ▪ in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result to generalized impedance and Leontovich boundary conditions including the cases of singular, degenerate, and randomized impedance coefficients. To this end we construct Riesz bases in the trace spaces associated with the curl-operator and introduce a modified version of boundary triple adapted to the specifics of Maxwell equations, namely, to the mixed-order duality of the related trace spaces. This provides a translation of the problem to operator-theoretic settings of abstract Maxwell operators. In particular, we show that Calkin reduction operators are naturally connected with Leontovich boundary conditions and provide an abstract version of impedance boundary condition applicable to other types of wave equations. Taking Friedrichs and Krein-von Neumann extensions of related boundary operators, it is possible to associate m-dissipative Maxwell operators to arbitrary non-negative measurable impedance coefficients.

Analysis of high frequency EM-waves diffracted by a finite strip with impedance in anisotropic medium

This article presents the rigorous analysis of the EM-plane wave diffraction by a conductible strip of finite length in an anisotropic medium. Leontovich boundary conditions are imposed along the strip to consider the effects of impedance. The presence of geomagnetic field in ionosphere containing cold plasma makes anisotropic medium. Mathematical formulation of this model using Maxwell's equations along with dielectric permittivity of cold plasma gives Helmholtz equation which gets transformed by the application of Fourier transform. Two coupled Wiener–Hopf equations are formulated which are then solved by the standard Wiener–Hopf procedure. The modified stationary phase method is used to find the asymptotic result of separated field in an anisotropic medium. The problem turns out to be for isotropic medium on assigning the particular values to the components of permittivity tensor as under the consideration of large operating frequency as compared to cyclotron frequency while it is of same order with plasma frequency. Graphical analysis is performed to investigate the effects of physical parameter on separated (diffracted by finite plate) field for both isotropic and anisotropic medium.

Powerful high-orbit gyro-TWT

This paper presents the results of a search for the optimal design of a high-orbit gyro-TWT, which would make it possible to reduce the magnetostatic field when operating at high frequencies close to the millimeter wavelength range, increase the gain and gain bandwidth, and increase the efficiency of the gyro-TWT. To search for the optimal configuration of the high-orbit gyro-TWT, the Gyro-K program was used, in which the equations for the excitation of an irregular waveguide by an electron beam are constructed on the basis of the coordinate transformation method of A.G. Sveshnikov, which is based on replacing the problem of exciting an irregular waveguide with the problem of exciting a regular waveguide with a unit radius. This method allows one to search for the solution of wave equations in the form of expansions in terms of the system of basis functions of a regular cylindrical waveguide. To solve Maxwell's equations, the Galerkin method was used, which is also called the orthogonalization method. The coefficients of the expansion of the field in terms of eigenbasic functions are determined in this method from the condition of the orthogonality of the residuals of the equations for the eigenbasis functions of a regular waveguide. The boundary conditions at the open ends of the waveguide are determined for each mode of the regular waveguide separately, which eliminates the incorrectness of setting the boundary conditions for the full field, as is the case when using the “picˮ technology. As a result, we obtain a system of ordinary differential equations for the expansion coefficients, which now depend only on the longitudinal coordinate. This approach makes it possible to transform the threedimensional problem of excitation of an irregular waveguide into a one-dimensional problem. Ohmic losses in the walls of the waveguide are taken into account on the basis of the Shchukin – Leontovich boundary conditions. For a self-consistent solution of the problem of excitation of an irregular waveguide by an electron beam, the iterative method of sequential lower relaxation was used. An optimized version of a high-orbit gyroTWT has been obtained, which has an electronic efficiency of 28 %, a wave efficiency of 23 %, a gain of 34 dB and a gain band of 11 % at an operating frequency of more than 30 GHz. This was achieved by introducing an additional conducting section of the waveguide into the absorbing part of the waveguide, which led to an improvement in the azimuthal grouping of electrons in the Larmor orbit and, as a consequence, to an increase in the lamp efficiency. A twofold increase in the waveguide length made it possible to increase the lamp gain. Ohmic energy losses in the walls of the waveguide reach 5 % of the power of the electron beam. The implementation of such a powerful gyro-TWT (2 MW) in the millimeter wavelength range will significantly increase the capabilities of radar at long distances and increase the resolution of the radar.

Forward recursion approach of electromagnetic wave propagation characteristics in a slab of inhomogeneous magnetoplasma

Propagation characteristics of electromagnetic radiation incident on an inhomogeneous magnetoplasma slab near a good conducting metallic surface is investigated. The inhomogeneous plasma slab is divided into thin layers (sub-cells) in order to allow for treating each plasma sub-cell as a homogeneous medium. A global matrix is formed upon matching the fields at all interfaces, which allows for the analytical determination of the reflection, absorption and transmission coefficients. For matching the tangential fields at the metallic surface, an impedance (Leontovich) boundary condition has been used. Propagation characteristics are calculated numerically for a set of parameters that may be suitable for many applications including stealth plasma. Numerical results show resonant absorption peaks near the electron cyclotron frequency that increase by increasing the equilibrium plasma density. They also show absorption enhancement by increasing the plasma slab width.

Mathematical Modeling of Impedance Waveguide Systems

A method for constructing eigenmodes of an infinite waveguide of a constant rectangular cross section with low losses in the walls, which are described by the Shchukin—Leontovich boundary conditions, is discussed. The dispersion characteristics of these waveguides are constructed.

On finding the surface admittance of an obstacle via the time domain enclosure method

An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an unknown obstacle. The condition is described by using an unknown positive function on the surface of the obstacle which is called the surface admittance. The wave is generated at the initial time by a volumetric current source supported on a very small ball placed outside the obstacle and only the electric component of the wave is observed on the same ball over a finite time interval. It is shown that from the observed data one can extract information about the value of the surface admittance and the curvatures at the points on the surface nearest to the center of the ball. This shows that a single shot contains a meaningful information about the quantitative state of the surface of the obstacle.

Analysis of a Rectangular Waveguide with Allowance for Losses in the Walls

We propose a model of an infinite waveguide of constant rectangular cross section with losses in the walls which are described by the Schukin–Leontovich boundary conditions. The waveguide is analyzed using the non-complete Galerkin method. We use the standard basis for waveguide with ideally conducting walls supplemented with functions providing precise fulfillment of the boundary conditions. The eigen modes of the waveguide in the THz range are calculated and dispersion characteristics are obtained.

On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method

An inverse obstacle scattering problem for the wave governed by the Maxwell system in the time domain, in particular, over a finite time interval is considered. It is assumed that the electric field $\mbox{\boldmath $E$}$ and magnetic field $\mbox{\boldmath $H$}$ which are solutions of the Maxwell system are generated only by a current density at the initial time located not far a way from an unknown obstacle. The obstacle is embedded in a medium like air which has constant electric permittivity $\epsilon$ and magnetic permeability $\mu$. It is assumed that the fields on the surface of the obstacle satisfy the impedance-or the Leontovich boundary condition $\mbox{\boldmath $\nu$}\times\mbox{\boldmath $H$} -\lambda\,\mbox{\boldmath $\nu$}\times(\mbox{\boldmath $E$}\times\mbox{\boldmath $\nu$})=\mbox{\boldmath $0$}$ with $\lambda$ an unknown positive function and $\mbox{\boldmath $\nu$}$ the unit outward normal. The observation data are given by the electric field observed at the same place as the support of the current density over a finite time interval. It is shown that an indicator function computed from the electric fields corresponding two current densities enables us to know: the distance of the center of the common spherical support of the current densities to the obstacle; whether the value of the impedance $\lambda$ is greater or less than the special value $\sqrt{\epsilon/\mu}$.

Multiscale Modeling of a Short Relativistic Electron Bunch Interacting With Long Resistive Structures at Cryogenic Temperatures

This paper presents multiscale modeling of electromagnetic interaction between a short relativistic electron bunch and long resistive structures at cryogenic temperatures. The considered physical problems include multiple spatial scales such as structure, bunch size, and skin depth. In order to simulate such multiscale problems, a directionally implicit finite-difference time-domain (FDTD) scheme based on Maxwell's equations in the presence of a relativistic bunch current is developed by using a magnetically mixed Newmark-leapfrog formulation. With the so-called magic time step, the resultant FDTD scheme has no accumulation of numerical dispersion errors for all frequencies in the direction of the motion. In order to model the anomalous skin effect (ASE) of metals in time domain, the developed scheme is combined with a rational function approximation of the first-order Leontovich surface impedance boundary condition. The scheme is verified in comparison with analytical approaches. ASE resistive wall effects are assessed for beam pipes and a step collimator.

Electromagnetic surface waves on a conducting cylinder

We study propagation of electromagnetic surface waves on a metal-air interface in the case when the wave frequency is below the plasma frequency. We derive a reduced wave equation for a metal cylinder with a given radius of curvature. Using the Leontovich boundary condition we find solutions to this equation which we classify as outgoing and incoming surface waves. We derive the dispersion relations of the surface waves of both types and argue that the earlier studies overlooked the waves of the second type although they are the only type which can propagate on a planar metal-air boundary.

A Mathematical Model for SAR Imaging beyond the First Born Approximation

The assumption of weak scattering is standard for the mathematical analysis of synthetic aperture radar (SAR), as it helps linearize the inverse problem via the first Born approximation and thus makes it amenable to solution. Yet it is not consistent with another common assumption, that the interrogating waves do not penetrate into the target material and get scattered off its surface only, which essentially means that the scattering is strong. In the paper, we revisit the foundations of the SAR ambiguity theory in order to address this and other existing inconsistencies, such as the absence of the Bragg scale in scattering. We introduce a new model for radar targets that allows us to compute the scattered field from first principles. This renders the assumption of weak scattering unnecessary yet keeps the overall inverse scattering problem linear. Finally, we show how one can incorporate the Leontovich boundary condition into SAR ambiguity theory.

FINITE ELEMENT BASED EIGENANALYSIS FOR THE STUDY OF ELECTRICALLY LARGE LOSSY CAVITIES AND REVERBERATION CHAMBERS

An eigenanalysis-based technique is presented for the study and design of large complicated closed cavities and particularly Reverberation Chambers, including conductor and dielectric material losses. Two different numerical approaches are exploited. First, a straightforward approach is adopted where the finite walls conductivity is incorporated into the Finite Element Method (FEM) formulation through the Leontovich Impedance boundary conditions. The resulting eigenproblem is linearized through an eigenvalue transformation and solved using the Arnoldi algorithm. To address the excessive computational requirements of this approach and to achieve a fine mesh ensuring convergence, a novel approach is adopted. Within this, a linear eigenvalue problem is formulated and solved assuming all metallic structures as perfect electric conductors (PEC). In turn, the resulting eigenfunctions are post- processed within the Leontovich boundary condition for the calculation of the metals finite conductivity losses. Mode stirrer design guidelines are setup based on the eigenfunction characteristics. Both numerical eigenanalysis techniques are validated against an analytical solution for the empty cavity and a reverberation chamber simulated by a commercial FEM simulator. A series of classical mode stirrers are studied to verify the design guidelines, and an improved mode stirrer is developed.

On the Limitations of the Time-Domain Impedance Boundary Condition

Limitations of the time-domain Leontovich impedance boundary condition are discussed for a canonical problem consisting of a planar interface with a conducting half-space. The exact analytical solution obtained using an extension of the Cagniard-DeHoop technique is presented and compared with the approximate one found via the impedance boundary concept. Ranges of applicability of the latter are introduced and numerically tested on illustrative examples. A proper understanding of these limitations may prove to be crucial in the emerging field of time-domain integral equation formulations in planar stratified media.

A two-dimensional model of propagation of long and medium waves above inhomogeneous paths

A 2D model of a radio path for the field of a vertical electric dipole over the Earth surface is considered. The field components on the interface of the media satisfy the Leontovich boundary conditions. A quadrature formula taking into account irregularities of the path within the first several Fresnel zones is proposed for calculating the attenuation function of the surface wave field.

H10 WAVE DIFFRACTION ON A JOINT OF REGULAR AND NON-REGULAR WAVEGUIDES WITH DIELECTRIC PLATE OF FINITE LENGHT

On the basis of the projection method the rigorous solution of the basic wave Н10 diffraction problem on a joint of a regular and non-regular waveguides with a dielectric plate placed parallel to narrow impedance walls is presented. The problem is solved by the method of partial areas. For each of three dedicated areas subject to boundary conditions on the waveguide walls solution of Helmholz equation is put down in the form of cross-section eigenfunction. For a non-regular area including impedance walls and a dielectric plate the solution of Helmholz equation leads to a dispersion equation from which the propagation constants in the area under investigation is determined. Meanwhile, the influence of the impedance walls is considered by means of the Leontovich boundary conditions.

Eigenanalysis of Electromagnetic Structures Based on the Finite Element Method

This article presents a review of our research effort on the eigenanalysis of open radiating waveguides and closed resonating structures. A two dimensional (2-D) hybrid Finite Element method in conjunction with a cylindrical harmonics expansion is established to formulate the open waveguide generalized eigenvalue problem. The key element of this approach refers to the adoption of a vector Dirichlet-to-Neumann map to rigorously enforce the continuity of the two field expansions along a truncation surface. The resulting algorithm was able to evaluate both surface and leaky eigenmodes. The eigenanalysis of three dimensional (3-D) structures involves vast research challenges, especially when they are electrically large and open-radiating. The effort herein is focused on the electrically large case including the losses due to the finite conductivity of metallic walls and objects as well as the loading material losses. The former is introduced through impedance or Leontovich boundary condition, resulting to a non-linear-polynomial generalized eigenvalue problem. A straightforward linearization solution is adopted along with a more efficient alternative technique which mimics analytical approaches. For this one the linear eigenproblem formulated assuming metals as perfect electric conductors is initially solved and their finite conductivity is accounted through impedance boundary conditions enforced locally on the resulting eigenvectors. Finally, some numerical results are presented to verify the performance of these methodologies along with a discussion on their possibilities for extension to open 3D structures as well as to characteristic modes eigenanalysis.

An integral equation model for radiowave propagation over inhomogeneous smoothly irregular terrain

AbstractThis work introduces an integral equation formulation to model the radiowave propagation over inhomogeneous smoothly irregular terrain. The ground energy loss is estimated via the Leontovich boundary condition and the fast far‐field algorithm accelerating technique is applied in order to improve the computational performance when solving the integral equation. The proposed formulation was implemented in a prediction software named SPRad, which was numerically tested with two measurement campaigns performed in Denmark and Brazil. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:26–31, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26473