ABSTRACT

Excitation equations for waveguides and cavities excited by extraneous sources are used for solving problems in electrodynamics, microwave and terahertz electronics. In some monographs authors suggest an algorithm for solving the excitation problem, which describes a waveguide (or a cavity) in the area of extraneous currents as a regular one, and hence it is considered in terms of orthogonality of eigen modes of the regular waveguide in this area. In fact, extraneous currents are specified for excitation elements (pins, loops, slots and apertures in the walls of a waveguide or cavity), which means that the mentioned electrodynamic systems are irregular, with diffraction and wave scattering in the area of extraneous sources. Therefore, the well-known excitation equations are inapplicable for solving problems of irregular electrodynamic systems excited by extraneous sources. Vacuum electron microwave devices are free from this limitation: extraneous currents are formed by flows of free electrons, and excitation elements i.e. slots, loops and apertures are absent. However, there is another obstacle: in contrast to passive electrodynamics in vacuum microwave sources, the areas of excitation are not fixed in space, which results in a cross-phasing of electrons. In this paper we formulated equations in general form for waveguides and cavities excited by electron flows in case of 3D electron phasing. These equations can considerably expand the circle of problems to be solved in electrodynamics and vacuum microwave electronics (namely in electronic engineering of advanced gyrotrons).