LAUSR

This paper considers how the finite dimensions of a photonic crystal placed inside a resonator or waveguide affect the law of electron beam instability. The dispersion equations describing e-beam instability in the finite photonic crystal placed inside the resonator or waveguide (a bounded photonic crystal) are obtained. Two cases are considered: the conventionally considered case, when diffraction is suppressed, and the case of direct and diffracted waves having almost equal amplitudes. The instability law is shown to be responsible for increase of increment of instability and decrease of length, at which instability develops, for the case when amplitude of diffracted wave is comparable with that of direct one, that happens in the vicinity of $\pi$-point of dispersion curve. Application of photonic crystals for development of THz sources at electron beam current densities available at modern accelerators is discussed.