On influence of azimuthal field on the spectra of the magnetoacoustic waves in the plasma cylinder

The dispersion equation for fast magnetosonic waves in the nonuniform plasma cylinder with a longitudinal plasma cylinder with a longitudinal current creating a weak azimuthal magnetic field is analysed on the basis of the perturbation theory. Splitting near cut-off frequancy is shown to be determined with due account of terms quadratic according to the small azimuthal magnetic field