Theory of parametric free-electron lasers

A theory of parametric free-electron lasers is developed for the general case of a particle beam which is density-modulated not only in the coordinate space but also in the momentum space, so that this beam becomes "unfrozen" in the region of its interaction with an undulator. An allowance is made for the angular and energy scatter of the particle beam. Studies are made of the capabilities of such lasers in the far vacuum ultraviolet range of wavelengths.