Belarusian State University , Belarus

We consider generation of radiation by relativistic electron beams in photonic (electromagnetic) crystals in conditions of Volume Free Electron Lasers (VFEL). Such crystals include natural crystals and artificial three-dimensional periodical structures. In VFEL while relativistic electron beam passing through such photonic crystals in conditions of dynamical diffraction quasi-Cherenkov parametric radiation appears and obeys to special law [Baryshevsky V. G., Feranchuk I. D. Phys. Lett. A. 102 (1984), 141]. This law is valid for all wavelength ranges and substantially differs from its analogues in other electronic devices such as traveling wave tubes, backward-wave tubes, free electron lasers and other. Different sides of chaotic dynamics of such generation are investigated. The complicated root to chaos in VFEL is demonstrated starting with the generation threshold.