Abstract
The consistent physic-mathematical model of propagation of an electromagnetic wave in a heterogeneous medium is constructed using the generalized wave equation and the Dirichlet theorem. Twelve conditions at the interfaces of adjacent media are obtained and justified without using a surface charge and surface current in explicit form. The conditions are fulfilled automatically in each section of counting schemes for calculations. A consistent physicomathematical model of interaction of nonstationary electric and thermal fields in a layered medium with allowance or mass transfer is constructed. The model is based on the methods of thermodynamics and on the equations of an electromagnetic field and is formulated without explicit separation of the charge carriers and the charge of an electric double layer. The influence of a slowly moving medium on the electromagnetic wave propagation is considered. The calculation results show the absence of the influence of the medium’s motion on the phase shift of waves, which is consistent with experimental data.
Highlights
Let us consider the interface S between two media having different electrophysical properties
Solution of radiolocation problems requires that the methods of calculation of the diffraction fields of electromagnetic waves excited and scattered by different surface portions of the objects, in particular, by wedge-shaped formations, be known, since the latter are among the main sources of scattered waves
Our numerical investigations have shown that the physical and mathematical model proposed can be used to advantage for simulation of the propagation of a high-frequency electromagnetic wave in a medium consisting of layers having different electrophysical properties
Summary
Let us consider the interface S between two media having different electrophysical properties. As a result of the numerical solution of the system of equations (see Equations (13)-(15)) with the use of conditions S (see Equations (24)-(34)) at the interfaces, we obtained the time dependences of the electric-field strength at different distances from the surface of the layered medium (Figure 3). As a result of our simulation (Figure 5), we obtained changes in the electric-field strength at different depths of the layered medium, which points to the fact that the model proposed can be used to advantage for calculating the propagation of polyharmonic waves in layered media; such a calculation cannot be performed on the basis of the Helmholtz equation. Conclusions We were the first to construct a consistent physicomathematical model of propagation of electromagnetic waves in layered media without recourse to the matrices of the induced-surface-charge impedances This model is based on the Maxwell equations, the electric-charge conservation law, the total-current continuity, and the Dirichlet theorem.
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