The problem of determining the dispersion relations,nElectromagnetic field, and power flow in a cylindrical plasma-filled guide with a finite axial magnetic field is discussed. The quasi-static analysis used and the conditions for its validity are presented. The hybrid structure (coupled TE and TM modes with two eigenvalues) of the fields that is present in the exact analysis is brought out from an extension of the quasi-static analysis. It is shown that under certain conditions the dispersion relation and electromagnetic field derived from the quasi-static analysis agree with the exact solution even though the phase velocities for the wave modes are greater than the velocity of light.
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