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Abstract
Propagation of direct waves around the Earth is considered. A theory of radiowave propagation in an inhomogeneous atmosphere is presented. An approximation formula for the horizon distance in the presence of super-refraction is presented. Radiowave propagation on the surface tropospheric waveguide is discussed.
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... The problem of beyond-the-horizon propagation of SHF radio waves is of great interest for applications (see, for example, [1][2][3]). One method of solving this problem is to describe the wave field as a spherical harmonic series [1 , 2] and calculate the sum of this series accurately [4][5][6][7][8]. ...
... The computational expense is very great in this case. The other method of solving this problem is to describe the wave field as a normal wave series [1,2]. It gives us a smaller computation expense and good agreement with the results of the first method. ...
... It gives us a smaller computation expense and good agreement with the results of the first method. In this case, some difficulties in obtaining complex constants of propagation appear [1,2]. Modification of the invariant imbedding method for the calculation of eigenvalues of acousticgravitational waves is suggested [9]. ...
The present paper studies beyond-the-horizon propagation of SHF in an evaporation duct in the presence of strong anisotropic fluctuations of the refractivity index. An effective technique to obtain numerically complex constants of propagation is suggested. On the basis of this approach, the modelling method of SHF propagation in media with layer fluctuations of refractivity index is formed. Finally, the paper considers some examples of the influence of fluctuations on beyond-the-horizon propagation. A generalization of the adiabatic approximation for opening systems with a complex spectrum of eigenvalues and indefinite eigenfunctions is suggested. On this basis of the rough solution obtained for the atmosphere with nonuniformity in the horizontal direction is revised. The mechanism of exiting the evaporation duct by the high-located SHF source is also discussed.
... The second step is the approximate ray-optics calculation of the radiation exiting the object. This calculation is related to Fock's method for analyzing the reflection of an arbitrary wave from an arbitrary surface [14]; analogous calculations are applied to elaborate different optical systems [15]. In the second step, the incident field is multiplied by the Fresnel transmission coefficient, and then propagation of the radiation is calculated using the rayoptics approach. ...
... where l is a length of the ray path from the surface of the prism to the observation point, and D l is a square of cross section of the ray tube (l 0 corresponds to the start point of the ray on the upper prism surface). The ray tube cross section can be found using methods of differential geometry [14]. We choose cylindrical coordinates ρ 0 , φ 0 as the coordinates of the external prism surface. ...
... The square of the ray-tube cross section is [14] ...
The radiation of a charge moving in the presence of a large (compared with the wavelengths under consideration) dielectric prism of two different configurations is studied: case (I), a charge moving in the channel, and case (II), a charge moving along the prism’s face. The approximate method that combines an exact solution of certain “key problems” (without the external boundaries of the object) and the ray-optics technique for the field outside the prism is used. A general analytical solution of the problems is obtained, a particular case of small angles is considered, and an algorithm for computation of the radiation field is developed. The computed results are visualized in plots of the spectral density of radiation on the plane parallel to the external face of the prism. In case (I), the radiation is found to be more intensive and has a single maximum in the central plane. In case (II), the radiation can have a single maximum in the central plane (for relatively low velocities) or two lateral maxima (for an ultra-relativistic velocity).
... while z 0 (u, ϕ) is given by (2) together with ρ 0 (u). In order to calculate the parameters of the surface it is convenient to use the tensor formalism by V.A. Fock [20,32] and determine the metric tensor of the surface g. Thus, for the elementary square of the surface we obtain dΣ = g(u)dudϕ, where ...
... The last point is the refraction angle θ t which can be calculated using the phase term from (14), (15) and metric tensor of the outer surface (2) (see [20,32] for details): ...
We propose a new type of axisymmetric dielectric target which effectively concentrates Cherenkov radiation (CR) generated in the bulk of the material into a small vicinity of focus point. It can be called the "axicon-based concentrator for CR". A theoretical investigation of radiation field produced by a charge moving through the discussed radiator is performed for the general case where a charge trajectory is shifted with respect to the structure axis. The idea of dielectric target with specific profile of the outer surface was presented and developed in our preceeding papers. However, contrary to the previous configuration of such a target (which was investigated for both centered and shifted charge trajectory), the current version allows efficient concentration of CR energy from relativistic particles, making this device extremely prospective for various applications.
... (the electric field is equal to the magnetic field and orthogonal to it and the ray). Here H ϕ (R 0 , θ ) is the corresponding Fourier-transform at the point of the ray exit and D(l) is the square of the ray tube cross-section [21]. Square root in (7) describes the change in the field magnitude due to the divergence (or convergence) of the ray tube. ...
... Using (6), Cartesian coordinates of the observation point can be obtained as the function of θ and ϕ : x(θ , ϕ ) = r(θ ) cos ϕ , y(θ , ϕ ) = r(θ ) sin ϕ . D(l) can be calculated as follows [21]: ...
Radiation of charged particles moving in the presence of dielectric targets is of significant interest for various applications in the accelerator and beam physics. The size of these targets is typically much larger than the wavelengths under consideration. This fact gives us an obvious small parameter of the problem and allows developing approximate methods for analysis. We develop two methods, which are called the "ray optics method" and the "aperture method". In the present paper, we apply these methods to analysis of Cherenkov radiation from a charge moving through a vacuum channel in a solid dielectric sphere. We present the main analytical results and describe the physical effects. In particular, it is shown that the radiation field possesses an expressed maximum at a certain distance from the sphere at the Cherenkov angle. Additionally, we perform simulations in COMSOL Multiphysics and show a good agreement between numerical and analytical results.
... For a curved surface, the propagation of three types of waves is possible, including leaky, surface, and creeping waves. A concept of creeping waves on a curved surface corresponding to the interface between two media with different dielectric properties has been proposed and analyzed in [6][7][8][9]. For the selected frequency, the type of propagating wave depends on the geometric sizes (radius of the cylinder, thickness of the dielectric coating) and the dielectric permittivity of the dielectric shell of the cylinder. ...
... Unlike (3), expression (10) does not contain the separate components that correspond to the incident and reflected waves, since the equation is the solution to the general differential equation: (11) where w 1 (t) is the Airy-Fock function [7], ...
The results of modeling and an experimental study of electromagnetic (EM) waves in microwave range propagating along the surface of the human body have been presented. The parameters of wave propagation, such as the attenuation and phase velocity, have also been investigated. The calculation of the propagation of EM waves by the numerical method FDTD (finite difference time domain), as well as the use of the analytical model of the propagation of the EM wave along flat and curved surfaces has been fulfilled. An experimental study on a human body has been conducted. It has been shown that creeping waves are slow and exhibit a noticeable dispersion, while the surface waves are dispersionless and propagate at the speed of light in free space. A comparison of the results of numerical simulation, analytical calculation, and experimental investigations at a frequency of 2.55 GHz has been carried out.
... In which It should be emphasized that the M -profile we have chosen has a rather weak inversion: the difference M (0) -M (hi) does not exceed several tenths, such an inversion in some cases may remain unidentified in practice. However, our calculations show that even such an M -profile strongly changes the nature of radio wave propagation, leading to ultra-long-range propagation [2]. The left graph shows two waveguides with the same reverse steepness and different inversion heights. ...
We obtain wavenumber-robust error bounds for the deep neural network (DNN) emulation of the solution to the time-harmonic, sound-soft acoustic scattering problem in the exterior of a smooth, convex obstacle in two physical dimensions. The error bounds are based on a boundary reduction of the scattering problem in the unbounded exterior region to its smooth, curved boundary using the so-called combined field integral equation (CFIE), a well-posed, second-kind boundary integral equation (BIE) for the field's Neumann datum on . In this setting, the continuity and stability constants of this formulation are explicit in terms of the (non-dimensional) wavenumber . Using wavenumber-explicit asymptotics of the problem's Neumann datum, we analyze the DNN approximation rate for this problem. We use fully connected NNs of the feed-forward type with Rectified Linear Unit (ReLU) activation. Through a constructive argument we prove the existence of DNNs with an -error bound in the -norm having a small, fixed width and a depth that increases with the target accuracy . We show that for fixed , the depth of these NNs should increase with respect to the wavenumber whereas the width of the NN remains fixed. Unlike current computational approaches, such as wavenumber-adapted versions of the Galerkin Boundary Element Method (BEM) with shape- and wavenumber-tailored solution spaces, our DNN approximations do not require any prior analytic information about the scatterer's shape.
... The surface Fock functions occur in the asymptotic representation of the surface currents excited on a circular cylinder and are also used in the description of the currents on general convex surfaces (Bowman et al. 1963;Fock 1965;Bird 1985). They are defined as integrals in the complex -plane in terms of the Airy integral w 2 ( ) or its derivative w ′ 2 ( ). ...
... The third step is different for two methods being developed. The ray-optics method uses the ray-optics laws (including those accounting for ray tube transformation [32,33]) for calculation of the wave field outside the object [18,19]. However, this technique has essential limitations. ...
Radiation generated by a charge moving through a vacuum channel in a dielectric cone is analyzed. It is assumed that the charge moves through the cone from the apex side to the base side (the case of "inverted" cone). The cone size is supposed to be much larger than the wavelengths under consideration. We calculate the wave field outside the target using the "aperture method" developed in our previous papers. Contrary to the problems considered earlier, here the wave which incidences directly on the aperture is not the main wave, while the wave once reflected from the lateral surface is much more important. The general formulas for the radiation field are obtained, and the particular cases of the ray optics area and the Fraunhofer area are analyzed. Significant physical effects including the phenomenon of "Cherenkov spotlight" are discussed. In particular it is shown that this phenomenon allows reaching essential enhancement of the radiation intensity in the far-field region at certain selection of the problem parameters. Owing to the "inverted" cone geometry, this effect can be realized for arbitrary charge velocity, including the ultra relativistic case, by proper selection of the cone material and the apex angle. Typical radiation patterns in the far-field area are demonstrated.
... To construct heuristic solutions, one uses mathematically strict solutions of elementary problems, base physical principles of electrodynamics and wave theory such us the field locality principle, the complementarity principle, etc. (see [5,15,25]), the intuition, and the experience. To verify the accuracy of heuristic solutions, they are compared with the strict solution. ...
We propose a new approach to construct heuristic relations describing solutions of diffraction problems. Those relations are based on physical principles and allow one to interpret mathematically strict solutions. Since the heuristic relations possess high performance and accuracy, they can also be used along with any strict approach or experimental results for a significant improvement of efficiency of solutions of practical problems related to applications of the diffraction theory.
Link to English text https://rdcu.be/bCCIa
... while z 0 (θ, ϕ) is given by (1) together with ρ 0 (θ). To calculate parameters of the surface it is convenient to use the tensor formalism by V.A. Fock [40,44] and determine metric tensor of the surface g [40]. Then for element of the surface square we obtain dΣ = √ gdθdϕ, where ...
A theoretical investigation of radiation field produced by a charge moving through the dielectric concentrator for Cherenkov radiation is performed for the general case where a charge trajectory is shifted with respect to the target axis. The idea of dielectric target with specific profile of the outer surface was presented and investigated in our previous papers for the symmetric case. Here we show how non-symmetric field components generated in the bulk of target affect field distribution near the focus where strong concentration of the energy occurs. Possible applications of this target are discussed.
... In [12] it is considered with help of eigenfunction expansion technique. Another method that can be applied to the problem is the method of matching series expansions [13, 14]. For this method the values˜Rvalues˜ values˜R n,m , ˜ T n,m are unknowns of an infinite (truncated somehow) linear algebraic system. ...
The problem of diffraction of a waveguide mode by a thin Neumann screen is
considered. The incident mode is assumed to have frequency close to the
cut-off. The problem is reduced to a propagation problem on a branched surface
and then is considered in the parabolic approximation. Using the embedding
formula approach, the reflection and transmission coefficients are expressed
through the directivities of the edge Green's function of the propagation
problem. The asymptotics of the directivities of the edge Green's functions are
constructed for the case of small gaps between the screen and the walls of the
waveguide. As the result, the reflection and transmission coefficients are
found. The validity of known asymptotics of these coefficients is studied.
... The second step is the approximate calculation of the radiation going out of the object. (This calculation is related to Fock's method for analyzing reflection of waves from an arbitrary surface [9]; analogous calculations are applied to elaborate different optical systems [10].) At the second step, the incident field is multiplied by the Fresnel transmission coefficient, and then propagation of radiation is calculated using the ray optics technique. ...
Cherenkov radiation is widely used for detection of charged particles and can be also applied for particle bunch diagnostics. As a rule, dielectric objects applied for these goals have complex forms. Therefore development of methods of calculation of bunch radiation in presence of complex dielectric objects is now of a great interest. The approximate method developed by us allows to take into account influence of the object boundaries closed to the charge trajectory as well as "external" boundaries of the object. The case of the charge crossing a dielectric plate was considered as a test problem. The exact solution of this problem is in a good agreement with our approximate solution. Next, the cases of more complex objects were analyzed. One of them is a dielectric cone with a vacuum channel. Particularly, it was shown that radiation can be convergent under certain conditions, that is the field outside the cone can be more intensive than on the cone boundary. Radiation of the bunch in the case of dielectric prism was considered as well.
... For n 2 = 1 Fock [3] and Weinstein [7] have obtained asymtotic solution of reduced wave equation for many important problems. In [4] R.L.Holford has discussed the elemantery solution of reduced wave equation in two dimension for which the refraction index is the form n = (A + Bx + +Cy + Dx 2 + Exy + ...
We present the exact solution of reduced wave equation with a variable coefficient Δu(x)+k 2 n(x)u(x)=0 for n(x)=n(r), r=|x| by the solution of a classic Riccati differential equation. By constructing an “iteration” technique for a differential equation of the form z '' =λz we present not only partial solution of a classical Riccati differential equation but olso the exact solution of the reduced wave equation with a variable coefficient. In addition we present a simple criterion for the existence of polynomial solution of a differential equation of the form z '' =λz. Where λ is a function in C ∞ .
Application method of parabolic equations is presented in this paper for calculating diffraction of sea waves behind converging breakwaters, which entrance is not parallel to front of approaching waves. For this, the method of linear superposition of results obtained separately for each breakwater was used. Based on a comparison of results obtained by this method with results of physical (obtained in a wave basin) and numerical (obtained using DHI MIKE 21 BW) model experiments with different settings (40 models in total), a conclusion about using allowability of the obtained equations was made. Results of the study make it possible to recommend the obtained equations for practical use in studies of seaports wave regimes, where diffraction phenomena are strong. Complexity of a function used in the parabolic method causes appearance of “petals” of diffraction coefficient isolines in protected water area. Approximate equations are presented for smoothing the oscillations of the complex amplitude function along lines parallel and perpendicular to axis of breakwaters. It is shown that associated error in obtaining diffraction coefficient varies on average within 2–5 %, and maximum error obtained was 12.5 %.
Calculation of the electromagnetic field exited by a charged particle flying close to dielectric object is one of the important problems of charged particle radiation theory. In some cases, geometric optics area is preferable for calculations. In the article, two methods of solution of such problem with dielectric prism possessing large size (in comparison with the wavelength under consideration) are considered. One of them is based on geometric optics method, another one is based on asymptotics of aperture integrals. It is shown that, in geometric optics area, the first method has a series of advantages. For example, ray tube cross-section expression obtained within geometric optics method allows one to find caustics or to show their abscence, which is demonstrated in the article for three objects of various shapes.
Thematic justification . When planning HF radio communication using surface waves, it is necessary to determine the signal-to-noise ratio at the inputs of each radio link receiver. Given a sufficiently high ratio, a conclusion can be drawn concerning the effective functionality of the analyzed radio link in a radio communication system. The planning process will be significantly simplified if the radius of the electromagnetic availability zone (REAZ) can be defined for surface waves at each radio station. Thus, the task of developing a methodology for engineering calculation of REAZ is relevant and practically important.
Goal. To develop an estimating technique for engineering calculations of a REAZ based on a surface wave source with a given isotropically emitted signal spectrum density.
Results. A technique for calculation of the radius of the electromagnetic accessibility zone was developed. A general approach for determining the limiting length of radio links of surface waves is proposed, based on the introduced "technical factor of a radio link" concept.
Practical implications. Nomograms for determining the radius of an electromagnetic accessibility zone were constructed. The dependence of the maximum temperature of external noise on frequency in the HF range can be approximated using an analytical expression. The developed frequency dependence of the temperature coefficient of the input of an ShT4N81 antenna is presented in a graphical form. The feasibility of using the proposed technique for solving practical problems is demonstrated on the example of calculating the radius of the electromagnetic accessibility zone of a TTR-2101M radio station for a monopulse direction finder with a ring antenna array consisting of eight elements of the ShT4N81 type.
In this paper, a mathematical model of a communication channel with an unmanned aerial vehicle and taking into account the specifics of the locations of a ground communication point when determining the effects of refraction, diffraction and interference of electromagnetic waves is proposed. A meaningful statement of the problem based on the mathematical relationship between the energy parameters of the first transmission equation and the quality indicators (BER) of the second transmission equation has been formed. The main features of calculating the parameters of the first equation are to determine the rules for calculating the level of attenuation due to the influence of the earths surface. The calculation of attenuations for cases of removal of an unmanned aerial vehicle from a ground communication point within the areas of line of sight, partial shade and shadow has been clarified. The second transmission equation is based on the mathematical model of the Rice communication channel. With respect to the energy parameters and the selected communication quality indicator for the formed mathematical model, examples of graphical dependencies are given in the study of typical computational problems. With respect to the energy parameters and the selected communication quality indicator for the formed mathematical model, examples of graphical dependencies in the study of typical computational problems are given.
This chapter investigates mutual coupling in finite antenna arrays that are conformal to curved surfaces. It describes a Green's function representation of two quadric surfaces, the cylinder and sphere. The chapter provides a brief review of the literature on the application of asymptotic techniques to the analysis of mutual coupling in apertures in convex surfaces. The problem of diffraction by a smooth convex surface on which, or near to, a source is located has been of considerable interest since the early days of radio. The Green's function or its asymptotic forms can be used to determine the mutual admittance of apertures in the surface. The chapter also describes an analysis of mutual coupling between apertures using canonical solutions for the cylinder and sphere. The Euler–Lagrange equations can be used to find the geodesic on any curved surface. The chapter provides computed and experimental results for a variety of antenna structures.
Numerical solution of the wave parabolic equation on a rectangular grid is analyzed when the discrete split-step Fourier transform (FT) method is used to calculate the field values in an inhomogeneous medium on the next step in the range. The goal is to find out the limiting possibilities of the FT method itself, so studies have been carried out for radio wave propagation in free space only. Two related problems have been solved. First, the minimum value of the root-mean-square error (RMSE) of the calculated field has been estimated. Second, the same has been done for the transmission coefficients of the Fourier series harmonics and of the coefficients of the artificial absorbing layer (AL), which are dependent on the parameters of the computational scheme. It is shown that the dependence of the RMSE value on the distance to the source always has a maximum. The forms of the optimal ALs differ from those used conventionally primarily by the presence of a significant imaginary component.
The form of a quasi-optical equation for a beam of monochromatic radiation propagating through a layer of a weakly absorbing linear medium is analyzed. It is concluded that the standard form of this equation should be modified using an “effective diffusion coefficient.”
Studies devoted to the application of numerical solutions of the parabolic equation to the prediction of propagation conditions of radio waves traveling above the ground surface are briefly reviewed. Emphasis is placed on the analysis of the physical irregularities of propagation of radio waves in difficult conditions (above the sea surface, including formation of evaporation ducts and in forests, including the influence of forest and terrain profiles on the radiation field of phased array antennas).
In this paper, we consider the construction of a system of smart wireless sensors for monitoring the parameters of the evaporation duct. A brief description of the theoretical foundations of the evaporation duct in the troposphere is given. Described the process of system development, the structure of the sensors used, and the algorithm for processing and accumulating data.
Recently we have reported on axisymmetric dielectric concentrator for Cherenkov radiation that focuses almost the whole radiation in the vicinity of the given point (focus) located on the trajectory of the charge. Here we continue investigation of this concentrating target and analyze in more detail the field in the focal spot depending on parameters of the target. We also discuss how the concentrating properties of this device depend on variations in velocity of a moving charge.
If in an asymptotic method the sense of the word “symmetry” is some form of “commensurabihty”, then the construction of an asymptotics often becomes a search for sharp, clearly marked noncommensurabilities (large-small, long-short, slow-fast, and so on)1
The plane problem of high-frequency acoustic wave diffraction by a segment with impedance boundary conditions is considered. The angle of incidence of waves is assumed to be small (oblique). The paper generalizes the method previously developed by the authors for an ideal segment (with Dirichlet or Neumann boundary conditions). An expression for the directional pattern of the scattered field is derived. The optical theorem is proved for the case of the parabolic equation. The surface wave amplitude is calculated, and the results are numerically verified by the integral equation method.
We have seen in Chap. 2, how a formal series representation, which is more general than the Luneberg-Kline series, can be used to describe the propagation of the diffracted rays. We have also seen that the formal series provides a description of the field only in regions where it is a ray field, and in the present chapter we will concern ourselves with the calculation of the field in the boundary layers.
Today the problem of the radar visibility zone modelling under hydrometeorological conditions is essential. Using such modelling we can predict radar maximum capabilities for detection of various objects within the required environment in specific hydrometeorological conditions. Obtained information allows not only to provide the high efficiency of radar operation but to improve its work, save material and energy resources. With the active development of GIS and environmental monitoring systems (including space system) accounting more fully for hydrometeorological conditions such as atmospheric precipitates, heaving of the sea and other becomes realizable. However it is required to improving the mathematical methods of the operational creation of the radar visibility zone with hydrometeorological conditions.
The effects of polarization suppression of diffraction spatial intensity variations are studied for a plane electromagnetic wave with elliptical polarization near the edge of a perfectly conducting rectangular wedge.
A concept of a quasi-wave method (QWM) of the order p = n − s is introduced with n and s being the total number of coordinates and the number of slow coordinates, respectively. The exact method (EM) at p = n, the parabolic equation method for 2 ≤ p < n, the QWM at p = 1, and geometric optics (GO) at p = 0 are particular cases of the QWM. It is shown for n = 3 that, under weaker assumptions, the QWM makes it possible to avoid difficulties intrinsic to the EM and GO as well as severe restrictions imposed on calculation models for GO and the theory of plane waves.
Using the Green function method and dynamic elasticity theory, we obtain a solution to the problem of sound diffraction by elastic shells of noncanonical shapes formed by spheroidal, cylindrical, and spherical bodies. The angular scattering characteristics of such compound bodies with different wave sizes are calculated.
The structure of the target strength in oceanic waveguides is analyzed. The role of the target strength is discussed as one of the key parameters for designing and estimating the efficiency of promising underwater observation systems.
Electromagnetic ground wave propagation has been a topic of practical interest for broadcasting and underground prospection in the medium and lower radio frequencies for more than a century. A brief review of ground wave propagation and its development since the work of Zenneck and Sommerfeld a century ago is presented. Recently interest has been revived in using ground waves for wireless communication with remote under-populated areas using the high frequency (HF) range which extends from 3-30 MHz. We present numerical results for the fields excited by a vertical electric dipole (VED) on the earth' surface in this range of frequencies and study the effect of ground conductivity on the received fields. In addition, we explore the possibility of using horizontal electric dipoles (HED) as transmitting and receiving dipoles. In this case, it is necessary to elevate both dipoles above the earth's surface by a distance comparable to a wavelength in order to enhance the received signal level. This is practically feasible in the HF regime where the wavelengths are sufficiently short We conclude that elevated HED's can perform as well as the VED, or even better, when the operating frequency lies in the upper end of the HF range.
A high-order parabolic equation (PE) method is applied to calculate the Bistatic RCS of two-dimensional (2-D) Electrically-large Objects. According to the shapes of objexts, Crank-Nicolson and Pade (1,0) schemes are introduced to solve the high-order PE. The numerical results demonstrate that the method not only extends the accurate angle range but also decreases the rotation times and computational time in comparison with the traditional low-order parabolic equation method.
TE and TM polarized electromagnetic wave diffraction on a perfectly conductive wedge with arbitrary apex angle is numerically studied. Amathematical model for calculating the diffraction field amplitude and intensity is developed. The solution is constructed in the entire range of physical angles without restriction to the observation point remoteness. The diffraction and field interference effects near the wedge walls are studied.
In this paper the mutual coupling between two apertures flush-mounted on a convex, perfectly conducting surface with variable curvature is analyzed by considering the surface ray propagating from the source to the receiver along the geodesic path. The problem-matched, surface magnetic Green's function is presented here from two asymptotic formulations and one of them has been incorporated as a EM simulation software, uCAST. Numerical results for the isolation (S12) between two axial slots on a circular cone from uCAST, FEKO and measured data are presented. The initial comparison of the three shows very good agreement.
The ground-wave calculation software GRWAVE is based on Rotheram's method, and it has been recommended by the International Telecommunication Union Radio communication Sector(ITU-R). But it has two problems which are the complex programming and the lack of the phase value. Aiming at the issues, a new method is presented, which combines Fock's method of residue series for the smooth and electrically homogeneous earth and Rotheram's equivalent radius method to consider the influence of the exponential atmosphere. Firstly, the mode equation is transformed into differential equation, then the differential equation is solved by 4th order Runge-Kutta algorithm. Secondly, the ground-wave field is calculated in flat region and spherical region respectively, and Rotheram's equivalent radius is used to consider the influence of the exponential atmosphere. Lastly, the field strength of the vertical electric dipole antenna of 1kW has been calculated. It is found that the error is within 0.2dB when it is compared with that of the ITU-R. The curves of the ground-wave field strength drawn by this method is in excellent agreement with that of the ITU-R. This paper simplifies the calculation of the ground-wave field strength in the exponential atmosphere while it can give the phase value. So it has some theory guidance significance and practical engineering value for the application of the ground-wave communication system.
A new method for predicting the far-field scattered pressure due to a plane wave incident upon an infinitely long cylinder of noncircular cross section is presented. The method, referred to herein as the Fourier matching method (FMM), involves conformally mapping the exterior and interior of a closed surface to a semi-infinite strip. This method is new in that the boundary conditions are satisfied using constraints described in the new angular variable. The resultant formulation is numerically efficient (much more so than the T-matrix method under certain conditions, for example) and works well for both small and large deviations from a circular cross section, as well as penetrable and impenetrable materials. Furthermore, the basis functions generated in the calculation can also improve the efficiency of other methods such as the T-matrix method. Example calculations are presented for elliptic, square, and three-leaf clover cross sections for several types of boundary conditions. In all cases, the results compare extremely well with exact or high-frequency asymptotic results.
Optimization of high frequency antenna systems is impossible without efficient numerical method for direct calculation of antenna characteristics and radiated fields. Over the past 40–50 years, research in the field of high-frequency (HF) wave scattering from various objects with complex geometry and material filling, was focused on development of the methods accounting diffraction effects on the edges accurately, using high-frequency asymptotic techniques, such as Keller's Geometrical Theory of Edge Diffraction (GTD), Physical Theory of Diffraction (PTD), method of Physical Optics (PO) and the Method of Equivalent Currents (MEC). It can be shown, that these methods usually generate the most simple calculation formulas, but give inaccurate results outside backscattering direction. This paper proposes a hybrid method based on MoM, PO and modified MEC, which takes into account contribution of electric and magnetic edge currents, calculated using method of Induced Electromotive Force (EMF), into the scattered field. It is shown that, in contrast to the methods outlined above, the values of proposed edge currents are independent on the direction of radiation.
This tutorial review presents the formulation of some diffraction problems involving half-plane structures as Riemann-Hilbert problems. The formulations of the problems of diffraction by an infinite set of Rawlins’s type half-planes, a bifurcated and a trifurcated waveguide and by a special infinite strip grating are considered in detail.
Several recent numerical schemes for high frequency scattering simulations are based on the extraction of known phase functions from an oscillatory solution. The remaining function is typically no longer oscillatory, and as such it can be approximated numerically with a number of degrees of freedom that does not depend on the frequency of the original problem. Knowledge of the phase of a solution typically comes from asymptotic analysis, for example, from geometrical optics. We consider integral equation formulations of time-harmonic scattering by a smooth and convex obstacle and focus on the so-called shadow boundaries. They are the points where the incoming waves are tangential to the boundary of the scatterer. We devise a numerical method that incorporates advanced results from asymptotic analysis which describe the frequency-dependent transitional behavior of the solution uniformly across these points. We describe and resolve an apparent conflict between two theories that describe the asymptotic behavior of this problem. They are the well-known geometric theory of diffraction and the rigorous asymptotic analysis by R. B. Melrose and M. E. Taylor [Adv. Math. 55, 242–315 (1985; Zbl 0591.58034)], based on microlocal analysis.
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