On the self-consistency of boundary value problems of the theory of radiation

The rigorous antenna theory leads to integral equations. In this case, the issue of self-consistency of the radiation problem is usually raised. In most cases, self-consistency is understood as reducing the problem to a singular integral equation with respect to the current function at the antenna aperture, which takes into account the influence of an external field on the distribution of this current. However, the recording of the primary field takes into account the EMF of external forces, which leads to an inhomogeneous integral equation (system of equations), which, generally speaking, violates the meaning of the self-consistency of the problem, since it ultimately leads to the calculation of the radiation field from specified sources. In this case, self-consistency disappears as such. A correction of the concept of "self-consistent task" is proposed. Clarification of terminology, explanation of the meaning of the concept of self-consistency and definition of its place in antenna theory. The method of integral equations. It is shown that a self-consistent task is a closed loop containing feedback like an autogenerator system. As a result of this feedback, a self-consistent radiation problem should lead to homogeneous integral equations, that is, it should be an eigenfunctions and eigenvalues problem. The latter are solutions of the characteristic equation. The concept of "self-consistent task" in the theory of radiation is clarified. It is shown that its strict formulation should generally lead to a system of linear homogeneous integral equations with respect to the tangential components of fields on the radiating surface, that is, to the problem of eigenfunctions and eigenvalues. The latter allows us to obtain a basis for representing the tangential components of the electric and magnetic fields on the radiating surface.