Spontaneous and induced parametric and Smith–Purcell radiation from electrons moving in a photonic crystal built from the metallic threads

Spontaneous and induced parametric and Smith–Purcell radiation from electrons moving in periodic structures are considered. The electrodynamical properties of a crystal-like artificial periodic structure (a photonic crystal) formed by a periodic structure built from the metallic threads (“grid” volume resonator) is considered. The equation, which describes lasing of volume-free electron laser with a “grid” resonator (photonic crystal), are obtained.