In this paper, the dispersion relation of the relativistic travelling-wave tube (RTWT) and relativistic backward-wave oscillator (RBWO) filled with plasma is obtained in the presence of an annular electron beam and solved by an exact numerical solution. The interaction of the beam with the waveguide modes is clearly identified and beam line splitting into the slow and fast waves is observed. In addition, the growth rates of each structure are investigated. The results show that the effect of plasma on the temporal growth rate of the TM01 mode in the RBWO is negligible and the higher modes are not affected. Conversely, the spatial growth rate in the RTWT increases significantly with the plasma density.
Mode crossing effects at electron beam–plasma interaction and related phenomena