Analytical Loss Factors in Approximation of the Leontovich Boundary Conditions

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.