A new method of formulation of problems in macroscopic electrodynamics is proposed. Maxwell equations are written in the abstract-operator form. A solution to the formal problem of eigenvalues and eigenfunctions of the introduced Maxwell operator allows us to use the well-developed mathematical technique of linear operator theory for various electrodynamical problems. In particular, calculation of the momentum-energy tensor, wave generation, perturbation theory, and variational approach can be applied for electrodynamical systems ͑cavities, waveguides, free space͒ filled with media of arbitrary dispersion. In the first part of the paper we deal with a formal foundation of the method and calculation of the momentum-energy tensor.
This part of the work deals with perturbation theory. The standard technique permits us to solve problems of volume disturbances in free space, waveguides, and cavities, of disturbances of boundary conditions caused by finite conductivity of walls, and of disturbances of the boundary shape. Expressions for frequency and wave number shifts caused by the perturbation are obtained by the unified method. Several examples are presented: wave amplification in the waveguide filled with a resonant medium like an electron beam in a longitudinal magnetic field, the frequency shift ͑and increment/decrement͒ of a cavity loaded by an electron beam, and the field disturbance in the waveguide caused by finite conductivity of the walls.
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