Excitation of electromagnetic waves by relativistic electron beam in a plasma filled rippled wall waveguide

An analytical and numerical study is presented herewith to get an insight into the excitation of forward and backward waves caused by an intense relativistic electron beam in a rippled wall plasma filled waveguide with weak modulation. The numerical results of growth rate are derived in the case of weak modulation at k_z=π/z₀ (the π point). Numerical results also show that no excitation of waves takes place if relativistic factor of the beam γ<(1+μ²_0s/R²₀k²₀)^1/2. For γ≳(1−μ²_0s/R²₀k²₀)^−1/2, the beam excites both forward and backward waves, and only forward waves if (1+μ²_0s/R²₀k²₀)^1/2<γ< (1−μ²_0s/R²₀k²₀)^−1/2. The dependence of the frequency of the generated forward waves on beam energy is also studied numerically and the results are compared with those of the experiment [IEEE Trans. Plasma Sci. PS‐18, 490 (1990)]. The effect of corrugation depth of rippled wall plasma filled backward wave oscillator (BWO) on minimum frequency generated is also studied.