  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.
