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The expression for the gain of an free electron laser (FEL), in which a high current electron beam interacts with laser beat waves (LBW), is obtained. In case of a Gaussian distribution the gain has a maximum near the relativistic plasma frequency of the beam. For frequencies much higher than the plasma frequency, the gain decreases exponentially. In the case of a uniform distribution the gain decreases according to a power-like law, which produces higher values for the same frequencies. It is proposed to use asymmetrically distributed electron beams interacting with LBW to produce intense radiation in the submillimeter region.

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Coherent emission at zero angle by a relativistic electron beam interacting with two laser lines in the helical undulator is studied. The laser waves generate axially directed periodical ponderomotive force, which bunches the electron beam. Thereby, electrons produce powerful quasi monochromatic and narrow directed high brilliance photon beam in the sub millimeter region. Analytic calculation of the gain in coherent radiation from modulation beam is presented.