The quasi-magnetostatic (briefly, magnetostatic) microwave propagation in a long, circular cross section waveguide having a metallic wall that is filled with an anisotropic uniaxial magnetic medium (here, a metamaterial consisting of split-ring resonators) is studied. Such waves do not exist in the case of a hollow metallic waveguide or a metallic waveguide filled with an isotropic medium. Physically, the present magnetostatic waves owe their existence to the anisotropic property of the system, where in the absence of this property, these magnetostatic waves disappear. A theoretical analysis is carried out and characteristics of these magnetostatic microwaves in circular metallic waveguides filled with uniaxial negative permeability media are determined. The presented results include the dispersion relation of magnetostatic waves and their corresponding cutoff frequencies, group velocities, transverse modal field distributions, power flows, and stored energies.
