Abstract
The problem of excitation of a cylindrical metal waveguide by a source located in the cross section is considered. We assume that the source is surface currents on a flat, infinitely thin metal plate with a smooth boundary. The plate is connected to the generator of non-harmonic oscillations. The boundary of the cross section of a waveguide filled with a homogeneous dielectric is a closed piecewise-smooth contour. The initial physical problem is formulated as a mixed boundary problem for the system of the Maxwell equations. Components of the desired solution for the problem is presented in the form of a series in two sets of two-dimensional eigenfunctions of the Laplace operator. The first set of the eigenfunctions corresponds to the operator with Dirichlet boundary conditions, the second set to the operator with Neumann boundary conditions. We show that the expansion coefficients of the longitudinal components (components directed along the waveguide axis) of the electric and magnetic intensity vectors must be solutions to the jump problem for a system of telegraph equations. The problem of finding the unknown coefficients of the expansion of the longitudinal component of the vector of electric intensity is reduced to solving a system of the Volterra integral equations of the first kind with respect to the derivatives of the desired coefficients. The unknown coefficients of the expansion of the longitudinal component of the vector of magnetic intensity are found by solving a system of the Volterra integral equations of the second kind.
Highlights
Metal waveguides are widely used in electronics and engineering
We show that the longitudinal components of the field must be solutions of the system of telegraph equations
After calculating the trace of the function on the waveguide cross section, solving the jump problem is reduced to the recovery of two functions and by the following formulas from [16]: The jump problem for Ez,m (z, t) takes the following form: In this problem, we have a homogeneous second condition, and the limit value of the function on the cross section of the waveguide we find as a solution for the Volterra integral equation of the first kind by formula (19): (25)
Summary
Metal waveguides are widely used in electronics and engineering. The study of such waveguide structures includes both the description of the set of eigenwaves and the search for the conditions of their excitation (Barybin, 2007). Adjacent transducer waves are used or, more often, probes inside the waveguide (Yirmiyahu, Niv, Biener, Kleiner, & Hasman, 2007; Kong, 2002; Pan & Li, 2013; Eslami & Ahmadi, 2019; Jabbari et al, 2019; Nakhaee & Nasrabadi, 2019). In this case, the probes can have both a simple dipole shape and a loop shape. The non-harmonic electromagnetic field excited in the waveguide is sought as a solution to the jump problem for the Maxwell equations. The jump problem for such the system of equations is reduced to the system of the Volterra integral equations
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