Mode nomenclature of circular gyromagnetic and anisotropic waveguides with magnetic and open walls

The problem of propagation along a longitudinally magnetised gyromagnetic circular waveguide with a magnetic wall has not been fully treated in the literature. This waveguide, unlike the electric wall problem, for which only the phase constants are split, exhibits both split phase constants and cutoff numbers. It is also of note that, in keeping with the solution of the electric wall problem, a single continuous cutoff curve, belonging to one of the two factors of the characteristic equation, need not necessarily describe the same mode throughout its entire length. Such discontinuities are displayed whenever the order and polarity of the Bessel functions at the intersection of any two cutoff curves coincide. Some calculations on the open anisotropic waveguide are also included for completeness.