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An analysis of the high-frequency eigenmodes of a coaxial waveguide
containing a magnetized annular plasma column is presented. A transcendental equation is derived from the boundary conditions in the form of an eighth-order determinant equated to zero. Simultaneous solution of this determinantal equation and a polynomial equation derived from the wave equation yields the dispersion relation for the eigenmodes. By reduction of the order of the determinant the appropriate transcendental equation is easily obtained for some special cases, e.g., partially filled coaxial waveguide. The electrostatic treatment of a coaxial cylindrical waveguide is also presented. The corresponding transcendental equation is reduced to some special cases, e.g., conventional waveguide containing an annular plasma column under electrostatic approximation. Numerical
solutions are obtained for some azimuthally symmetric $EH$ (perturbed $TM$) and $HE$ (perturbed $TE$) waveguide modes, cyclotron modes, and space-charge modes. A strong dependence of the frequencies of these
electromagnetic/electrostatic waves on the radii of the coaxial
waveguide and the plasma column is revealed.
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