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In the framework of the earlier derived dispersion equation, we study inducedSmith Purcell (SP) radiation of relativistic electron beam in the absence of aresonator. We offer a new method for calculation of coefficients for partialamplitudes in the case of rectangular grating. Using this method we calculatethe growth rate of the SPFEL with a rectangular grating. The growth ratedependences on harmonic number, beam current, observation angle andrelativistic factor are presented.

Growth Rates in Smith-Purcell FEL