Abstract
The formulation of the Vlasov-Maxwell equations is utilized to investigate the kinetic instabilities caused by the interaction of the electron beam with the electromagnetic wave for the dielectric-loaded cylindrical waveguide in the small signal limit. Using the orthogonality condition of the electromagnetic modes, the dispersion relation is derived for the dielectric-loaded waveguide along which the relativistic electron beam traverses under the constant guiding magnetic field. The growth rates of the Cherenkov and cyclotron Cherenkov instability for azimuthally symmetric transverse-magnetic modes are studied for the various perpendicular momentum distributions, and we find that the cyclotron Cherenkov instability has a growth rate comparable to that of the Cherenkov instability for the finite perpendicular momentum distribution. The results show that the amplification of an electromagnetic wave is possible in the range of millimeter to sub-millimeter from the anomalous Doppler effect.
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