Dispersion properties of a magnetoactive plasma-filled waveguide in the vicinity of the upper hybrid frequency. Part I

The dispersion properties of a magnetoactive plasma-filled waveguide in the vicinity of the upper hybrid frequency ω 1 = (ω p 2 + ω B 2 ) 1/2 (ω 1 ≤ ω < ω 1 + δ) are studied. In this frequency range, the eigenfrequency spectrum and the structure of the waveguide eigenfields are difficult to analyze, because one of the transverse wavenumbers tends to infinity as the upper hybrid frequency is approached. It is shown that this problem can be solved by transforming the dispersion relation into a form independent of this transverse wavenumber. It is also found that the upper hybrid frequency itself can also be a solution to the dispersion relation. The influence of the properties of the magnetoactive plasma-filled waveguide on such solutions is studied. The structure of the fields for modes with frequencies equal to the upper hybrid frequency and an infinitely large absolute value of one of the transverse wavenumbers is analyzed.