Coordinate-dependent plasma frequency reduction coefficients for planar corrugated periodic structures

A "disk" model for a beam above a planar corrugated structure is considered. Under the assumption of a uniformly-charged transverse cross-section beam, the static Green's function for the uniformly charged interacting disks is derived analytically in the general case without using the properties of a concrete mapping for a specific structure. The coordinate-dependent plasma frequency reduction coefficients and their application for the beam-field interaction in microwave devices are introduced and discussed.