Based on a sheet electron beam propagating through the tunnel of a staggered double-grating arrays waveguide (SDGAW) slow-wave structure (SWS), a three dimensional linear theory for describing beam-wave interaction is presented, in which the higher order terms inside the groove were retained.

With the optimized parameters, a 1THz SDGAW Cerenkov traveling wave amplifier (CTWA) may obtain a moderate net gain larger than 10dB/cm in 0.92THz to 1.145THz considering the serious Ohmic losses in THz frequency range.