Volume free electron lasers
  The equations describing the VFEL lasing in case of an electron beam moving either in a split of a diffraction grating or in a vacuum waveguide containing a diffraction grating (vacuum VFEL) have been obtained. The dispersion equation allowing to find the vacuum VFEL gain in one-mode generation regime have been considered. It is shown that the vacuum VFEL amplification and the generation process develop more intensively then in ordinary FEL using one-dimensional distributed feedback. Such the VFEL, if realised, could be made with much more compact device structure compared with the FEL and therefore, may be interesting for applications in different wavelength ranges: from submillimeter to X-ray. Such the VFEL can be realised on the basis of the existing accelerators. 
Vladimir G. Baryshevsky