Long period solar loop prominence oscillations by the slow magnetosonic wave

The MHD spectrum consists of three different waves: the Alfven wave, and the slow and fast magnetosonic waves. The slow magnetosonic wave and the Alfven wave propagate only along the magnetic field. In inhomogeneous plasma the 'eigenfunctions' consist of solutions oscillating only on a magnetic flux surface. The solutions are not functions but exist only in a distribution sense. Each surface has its own eigenfrequency, which depends on the equilibrium quantities. As these vary smoothly, the eigenfrequencies form continuous sets. Regular solutions may exist outside the continuum and the maximum or minimum of the set can be a cluster point of a Sturmian or anti-Sturmian sequence of eigenmodes. This was discussed by Newcomb in connection with the unstable Suydam modes and by Goedbloed for the stable spectrum. The existence of a discrete spectrum of global Alfven waves in inhomogeneous plasma was first shown by Appert et al. Using a cylindrical plasma column model, de Azevedo et al. explained the short period prominence oscillations as global Alfven waves. The slow magnetosonic waves can also possess a discrete set of regular eigenmodes, similar to the discrete Alfven wave spectrum. By modeling the solar loop prominences as nearly force-free cylindrically symmetric equilibria, we show that the discrete slow wave spectrum can explain the observed long period (75 min) oscillations. Conditions for the existence of a discrete slow wave spectrum are also given.