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The dispersion relation of guided electromagnetic waves propagating in an elliptical metallic waveguide with a dielectric rod driven by relativistic elliptical electron beam (REEB) is investigated. The electric field profiles and the growth rates of the waves are numerically calculated by using Mathieu functions. The effects of relative permittivity constant of dielectric rod, accelerating voltage, and current density of REEB on the growth rate are presented.

The dispersion relation of electromagnetic waves propagating in an elliptical plasma waveguide with a cold collisionless unmagnetized plasma column and a dielectric rod is studied analytically. The frequency spectrum of the hybrid waves and the growth rate for excitation of the waves by a thin annular relativistic elliptical electron beam (TAREEB) is obtained. The effects of relative permittivity constant of dielectric rod, geometrical dimensions, plasma frequency, accelerating voltage, and current density of TAREEB on the growth rate and frequency spectra of the waveguide will be investigated.

The propagation of electromagnetic waves in an elliptical plasma waveguide including strongly magnetized plasma column and a dielectric rod is investigated. The dispersion relation of guided hybrid electromagnetic waves is obtained. Excitation of the waves by a thin annular relativistic elliptical electron beam will be studied. The time growth rate of electromagnetic waves is obtained. The effects of relative permittivity constant of dielectric rod, radius of dielectric rod, accelerating voltage, and current density of the annular elliptical beam on the growth rate and the frequency spectra are numerically presented.

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