This paper is the continuation and development of the discussion started in our previous work with the same title. For the first time, eigen waves of the plane boundary separating vacuum and an artificial plasma-like medium are considered in reasonably substantiated way and in a sufficiently extensive and profound volume. The possibility of extending the results obtained for a plane boundary to the case of a weakly profiled periodically uneven boundary is shown. This paper demonstrates the potential and urge to use the analytical results in the studies of the resonant transformation of the field of a plane, density modulated electron beam flying over a periodically uneven boundary of a natural or artificial medium in the field of bulk outgoing waves.
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