  We analyze electromagnetic radiation from a bunch passing through a
corrugated conductive planar structure. The wavelengths of the radiation are
assumed to be much greater than the corrugation period. Under this
approximation, the corrugated structure can be replaced with a smooth surface
on which the so-called equivalent boundary conditions (EBC) are fulfilled.
Here, we also assume that the structure is deeply corrugated, i.e. the
structure depth is of the same order as an inverse wavenumber. Using the EBC we
obtain a general solution and investigate it asymptotically. It is shown that
two types of radiation are generated: volume radiation and surface waves. Both
types of the radiations are analyzed in detail. We demonstrate that the
radiation is highly sensitive to the structure depth, which can be used,
specifically, for generating the powerful surface radiation. The energy losses
of the bunch by both volume and surface radiations are considered as well. In
particular, the dependences of the energy density on the corrugation parameters
are obtained and analyzed.
