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The dispersion characteristics of electrostatic and electromagnetic modes of an electron tube, with ion channel guiding, in a cylindrical waveguide are presented. The analysis takes into account a relativistic hollow electron beam guided by an ion channel. Dispersion relations are derived and solved numerically to study the waveguide, betatron, and space charge modes. The effect of the annular electron beam thickness on frequencies of the electrostatic and electromagnetic waves is investigated. This paper reveals the strong dependence of the electromagnetic and electrostatic waves' frequencies on the electron beam thickness. The results of this paper are compared with previous works where an electron tube is guided with an axial magnetic field.