Pierce gain analysis for a sheet beam in a rippled waveguide traveling-wave tube

A Pierce-type mode analysis is presented for a planar electron beam in a rippled planar waveguide. This analysis describes the gain of a traveling-wave tube consisting of that geometry. The dispersion relation is given by the determinant of a matrix based on the coupling of different free-space modes through the boundary conditions. For the case of high-frequency, low-power amplifiers, the dispersion relation reduces to a simple cubic expression for the Compton regime, leading to three roots analogous to the Pierce solution of a standard traveling-wave tube. The analysis shows that this type of traveling-wave tube is capable of very high gain at extremely high frequencies.