Five-Wave Equation for Small-Signal Analysis of Traveling-Wave Tubes Considering the Effects of Axial Periodicity of the Interaction Structure

The conventional Pierce theory is used to analyze traveling-wave tube (TWT) amplifiers. This theory is a convenient method to design helix TWTs. However, in some cases such as coupled-cavity TWTs and folded-waveguide TWTs, this approach yields nonphysical results. In fact, backward-wave excitation may not be ignored for high-power wideband coupled cavities as well as for devices operating near the band edges. The Pierce-type equation is modified to include both backward and forward RF waves simultaneously. A fifth-order algebraic equation is derived that yields TWT small-signal gain in approximately the entire frequency band, including near cutoff frequencies. This approach is based on the coupling between two fast and slow space-charge waves and three RF space-harmonic waves, using independent space-harmonic approximation. The obtained equation may be used to analyze the coupled-cavity folded waveguide and ladder TWT structures.