Abstract: The full three-dimensional self consistent equations which illustrate the nonlinear beam-wave interaction in the sheet beam traveling-wave tubes (SBTWT) are given. The equations include excited equation, motion equations, energy conversion equation and phase evolving equation. Divide the beam into a set of discrete rays, or ―beam-lets‖, combine the fields’ distribution in the staggered double-grating slow wave structure and the self consistent equations, nonlinear analysis of the staggered double-grating SBTWT is done.