Diffraction of the Field of a Grounded Cable on an Elongated Dielectric Spheroid in a Conducting Layer

Abstract

Based on a rigorous solution to the problem, analytical expressions are obtained for calculating the diffraction of the electromagnetic field of a grounded cable on an elongated dielectric spheroid in a conductive layer. The field of a grounded AC cable in a conductive layer is determined by solving the Helmholtz equation for the vector potential by using the method of integral Fourier–Bessel transformations, taking into account the boundary conditions at the bottom and surface of the conductive layer. The process of finding the secondary field of an elongated dielectric spheroid on an alternating current in a conducting layer is divided into two stages. First, we find an exact solution to the problem of an elongated dielectric spheroid at a constant current in a homogeneous field, in free space, decomposing this solution into a Taylor series and retaining the first term, which is a dipole approximation. In the second stage, the resulting field as the sum of the fields of the horizontal and vertical dipoles is analytically continued into the frequency domain. The field of the horizontal and vertical dipoles in the conducting layer is obtained by using the method of integral Fourier–Bessel transformations, taking into account the boundary conditions at the bottom and surface of the conducting layer. The resulting solution is presented in a closed form in elementary functions and has an accuracy level acceptable for the practice. Graphs showing the flow characteristics of an elongated dielectric spheroid modeling a swimmer in a light diving suit are given. The influence of the water–air boundary on the increase in the secondary field of the dielectric spheroid, which leads to an increase in the reliability of object detection, is revealed. The practical implementation of the described device protected by a patent and the experimental data of testing the device layout on the Gulf of Finland are given. A good agreement between the theoretical and experimental flow characteristics of a dielectric object both in shape, amplitude, and phase, is revealed.