A Pierce-type mode analysis is presented for a planar electron beam in a ri
ppled planar waveguide. This analysis describes the gain of a traveling-wav
e tube consisting of that geometry. The dispersion relation is given by the
determinant of a matrix based on the coupling of different free-space mode
s through the boundary conditions. For the case of high-frequency, low-powe
r amplifiers, the dispersion relation reduces to a simple cubic expression
for the Compton regime, leading to three roots analogous to the Pierce solu
tion of a standard traveling-wave tube. The analysis shows that this type o
f traveling-wave tube is capable of very high gain at extremely high freque
ncies. (C) 2001 American Institute of Physics.