Effect of plasma filament toroidality and allipticity on the spectra of MHD-waves

Corrections of magnetohydrodynamic wave eigenfrequencies caused by certain effects are defined by means of the perturbation theory. These effects are as follows: toroidal dependence of the magnetic field and toroidal (Shafranov) shift of the magnetic surfaces as well as ellipticity of poloidal sections of magnetic surfaces. It is shown that these corrections are proportional to the small ellipticity and to the toroidality square