Excitation of electromagnetic modes in a dielectric-loaded waveguide via cyclotron resonance interaction

An analytical treatment of the excitation of electromagnetic modes by an axial electron beam in a cylindrical waveguide partially loaded with a dielectric is presented. Equations describing the mode structure of the waves are obtained in cylindrical geometry. Using appropriate boundary conditions a dispersion relation is derived in the weak-beam approximation (ω/sub B/ << ω). In addition to the conventional Cerenkov interaction, the slow-cyclotron resonance interaction (ω approx. = βV0 - ω/sub C/), which involves the coupling of the TM mode of the waveguide with the slow cyclotron beam mode, is also seen to be important. The growth rate of the instability scales as eta0/sup 1/2/ (where eta0 is the beam density), decreases with and increase in V0, and is rather insensitive to the variation in the magnetic field