Abstract
An analytical and numerical study is made on the dispersion properties of a cylindrical waveguide filled with plasma. An electron beam and static external magnetic field are considered as the mechanisms for controlling the field attenuation and possible stability of the waveguide. The effects of plasma warmness and inhomogeneity are also considered. Dispersion relations in omega describing different physical situations that govern the mode propagation in the waveguide are obtained. The plasma dielectric tensors and the dispersion relations which describe E and H waves and, hence, the damping rate of these waves are calculated and studied. The necessary conditions for the field stability in the waveguide and amplification coefficients for these waves are also obtained. H-wave modes are always attenuated by collisional effect. The growth of the excited E wave is calculated in the resonance case, and the stability condition for the E wave is obtained. E waves are found to be more stable in warm plasma compared to cold plasma. The results obtained here are of great interest and may be used to analyze how the plasma affects the electromagnetic properties of the cavity of the 1-2 MW 140-170 GHz continuous-wave gyrotron (for W7-X stellarator and ITER), for MW gyrotron development for fusion plasma applications, and for second harmonic generation in a plasma-filled parallel plane waveguide.