The Landau-Pomeranchuk-Migdal effect and transition radiation in structured targets

The radiation from high-energy electrons is investigated for the case when a target consists of several separated plates. The spectrum of radiation is considered in the region in which the bremsstrahlung is under influence of the multiple scattering of a projectile (the LPM effect), the polarization of a medium and the hard part of the boundary radiation contribute. In this region the general expression for the radiation spectrum is obtained for the $N$-plate target. A qualitative description of the arising interference pattern is given.