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Solntsev V. A. Theory of waveguides excitation. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2009, vol. 17, iss. 3, pp. 55-89. DOI: 10.18500/0869-6632-2009-17-3-55-89

# Theory of waveguides excitation

The theory of waveguide excitation is presented, based on expansions of the electromagnetic field by proper waves of waveguide. Necessary properties of smooth and periodic waveguides, including the conditions of orthogonality of plane and the volume of the waveguide are given. Main properties of pseudo-periodic waveguides are described. This is a new class of waveguide systems. Different forms of the waveguides-excitation theory are considered. The waveguide form of the theory uses the expansion of the excited electromagnetic field by series of proper waves at a frequency of excitation, and with unexpansable part of the field, which may be caused by the longitudinal current (L. Weinstein), or by quasi-static field (V. Solntsev), etc. Essential improvement of series convergent at quasi-static field separation is proved. Another, waveguide-resonator form of the waveguide-excitation theory uses the expansion of a field by series of proper waves with fixed wave-numbers and different frequencies. In this case the quasi-static electric field is separated also. The equivalence of waveguide form and resonator form of excitation theory is proved. The analyze of total excited electromagnetic field is carried out. A finitedifference equation of excitation of modes is given with no singularities and applicable inside, outside, and on the boundary of waveguides bandwidth. The possibility is notes of dynamic correction influence on electrons interaction laws in the charge space.

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