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The creation of free electron lasers in the millimeter wavelength region on the base of undulators is connected with a problem of elaboration of undulators of very small period. Also a high-energy accelerators (about 200 MeV) are in this case required. We suggest in this report much simpler scheme of coherent radiation generation on conducting periodical target (grating), placed in millimeter wavelength region resonator. For this purpose the usage of the grating, which consists on thin conducting strips, divided by vacuum gaps, is mostly effective. We can choose the grating parameters to have a Smith-Purcell radiation of necessary wavelength in direction, perpendicular to the beam direction. In this case we can use strips of grating as one of the mirror of resonator. The bunch parameters of microtron of Tomsk Nuclear Physics Institute allows us to use the radiation coherent properties of bunch electrons (Ne2 effect) in a millimeter wavelength region of radiation. The estimations shows, that the radiation power of 100 W from macro pulse in this case may be reached