  Recently the new method of the Cherenkov fields and loss factors of a
point-like electron bunch passing through longitudinally homogeneous structures
lined with arbitrary slowdown layers was proposed. It was shown that the
Cherenkov loss factor of the short bunch does not depend on the waveguide
system material and is a constant for any given transverse dimensions and
cross-section shapes of the waveguides. It was shown that with the proposed
approach one can use a relatively simple method for the calculation of the
total loss factor using an integral relation based on the cylindrical slowdown
waveguide model. With this paper, we demonstrate that the same integral
relation that we call relativistic Gauss theorem can be applied in case
impedance boundary conditions (IBC) also known as Leontovich boundary
conditions.
