Analysis of the instability in relativistic traveling wave tube

The relativistic traveling wave tube is an important high power microwave source. The corrugated cylindrical waveguide is usually used as slow wave structure of this device. Starting from wave equation and using boundary conditions, dispersion relation is derived for the corrugated waveguide, in which an intense relativistic electron beam propagates along the axis. Two cases which are shorter period and longer period are discussed in this paper respectively. The small signal gain of the relativistic traveling wave tube is analyzed and some conclusions are drawn. The analysis method presented in this paper can be extended to other types of slow wave structures of relativistic traveling wave tube.