Generation of radiation in free electron lasers with diffraction gratings (photonic crystal) with the variable spacial period

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The equations providing to describe generation process in FEL with varied parameters of diffraction grating (photonic crystal) are obtained. It is shown that applying diffraction gratings (photonic crystal) with the variable period one can significantly increase radiation output. It is mentioned that diffraction gratings (photonic crystal) can be used for creation of the dynamical wiggler with variable period in the system. This makes possible to develop double-cascaded FEL with variable parameters changing, which efficiency can be significantly higher that of conventional system.