Dispersion relation of a bounded, magnetized and warm plasma

The propagation of the electromagnetic waves in a cylindrical waveguide filled with uniform magnetized plasma is studied by the warm plasma theory. Dispersion relations are obtained for several situations, such as, zero and finite temperature, and zero, finite and infinite magnetic field. It is found that the waves cannot be separated into transverse magnetic and transverse electric modes; only hybrid modes are propagated. For the case of finite magnetic field the Faraday's rotation is obtained