Dispersion and gain investigation of a Cerenkov grating amplifier

The sheet electron beam propagation over a rectangular deep groove grating is investigated and the interaction between surface harmonic waves, which are evanescent above the grating surface, with a dilute sheet electron beam is analyzed. It is assumed that a strong axial magnetic field is applied to constrain the motion of electrons along the waveguide axis. Under these conditions, a complex dispersion equation is derived and analyzed by using Taylor expansion. This expansion results in an analytical formulation for the gain. Using the derived analytical formulation of the gain, the effects of beam thickness, beam-grating gap, and characteristics of grating on gain is investigated.