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Self-consistency of boundary value problems of the theory of radiation

Keywords:

A. S. Raevskii – Dr.Sci. (Eng.), Professor, Head of Department of Physics and Technique of Optical Communications of Niznii Novgorod State Technical University named after R.E. Alekseev. E-mail: raevsky@nntu.nnov.ru
S. B. Raevskii – Dr.Sci. (Eng.), Professor of Niznii Novgorod State Technical University named after R.E. Alekseev, Department of Physics and Technique of Optical Communications


Strict antenna theory leads to the integral equations. Thus, as a rule, the question is raised of self-consistency problem of radiation. Under the self-consistency refers mostly to reduce the problem to a singular integral equation for the stream function at the aperture of the antenna, which takes into account the influence of the external field on the distribution of power. However, in the record of the primary field is taken into account electromotive force external forces, which leads to an inhomogeneous integral equation (system of equations) that, in general, violates the sense of self-consistency problem, since ultimately leads to the calculation of the radiation field at a given source. The self-consistency in this case, as such, will disappear. In a strict representation consistent problem - a vicious cycle that contains the feedback system like the oscillator. As a result of the presence of this feedback self-consistent problem of the radiation should lead to homogeneous integral equations, that is, should be the task on its own functions and eigenvalues. The latter are the solutions of the characteristic equation. Only on solutions of this equation are obtained non-trivial solution of the boundary problem of radiation. The self-consistency problem can be treated as its "self-sufficiency" - independence from primary sources. This means that in itself does not allow consistent problem to calculate antenna characteristics, but is only the basis of organization procedures. It allows you to find a basis for the representation of the function of the current distribution on the antenna aperture. Based on this basis produced a rigorous calculation of the antenna with the specified characteristics of radiation. We can say that self-consistent problem is a fundamental fragment of a rigorous theory of antennas, but the algorithm for calculating them. Given statements are an attempt to clarify the terminology, explain the meaning of the concept of self-consistency and to determine its place in the theory of antennas. By decision of the self-consistent problem of the radiation field produced by the decomposition of its finding as solutions of inhomogeneous integral equation (system of equations), which results in the calculation specific antenna. Problems which are reduced to non-uniform integral equations containing (in or another one form) the source function, should not be classified as a self-consistent.
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