Wednesday

Solar magneto-seismology (SMS) is a popular subject that involves the study of MHD waves and oscillations present in the entire magnetized solar atmosphere. Magnetically confined features such as flux tubes are an important aspect that have been studied in great detail. Inhomogeneities in the structuring of the magnetic field enables the flux tubes to act as wave-guides for a variety of the MHD wave modes. A flux tube with a cylindrical core surrounded by a magnetic shell is a good initial model capturing radial inhomogeneities observed in solar atmospheric waveguides. We investigate standing ideal MHD waves in the magnetic annulus geometry. We consider an annular cylinder of fixed length with appropriate line-tying boundary conditions to derive a dispersion relation for the sausage and kink MHD modes. We find analytical solutions to the dispersion relation by considering the weakly homogeneous flux tube and thin annulus approximations (TAA). Further, we also consider the wide and thin flux tube cases and apply our results to solar magnetic loops from lower atmospheric oscillations (sub-photospheric tubes and chromospheric fibrils) to coronal loops. We find, in general, two purely surface and two body mode solutions in the considered structuring that we use then to determine the period ratio of the fundamental and first excited harmonic, for SMS purposes. We analyze the role of annular structuring on the period ratios of standing waves and discuss its importance in the context of solar magneto-seismology.