Rigorous analytical theory of wave propagation along a cylindrical wav
eguide filled with plasmas in a dielectric tube immersed in finite mag
netic field is presented. The field components' expressions, eigenvalu
es, dispersion equations and complex wave power transmission equations
have been obtained rigorously and discussed in detail. It is shown an
alytically that there is no disruption of the wave propagation in the
ECR (omega = omega(oe)) case, although the electrical permittivities a
pproach to infinite in the case, and it has been found that a real res
onance takes place in this case while omega = (omega(oe)(2) + omega(pe
)(2))(1/2), in which the wave propagation of any mode is broken. The e
ffective collisions are taken into consideration in the theory. Based
on the above theory, the analytical theory of corrugated plasma wavegu
ide immersed in finite axial magnetic field is also presented. The Flo
quet's expansion of field components, the dispersion equations, and th
e coupling coefficients of the corrugated plasma waveguide have been d
erived rigorously and discussed in detail.