Non-axisymmetric oscillations of thin prominence fibrils

We study non-axisymmetric oscillations of thin prominence fibrils. A fibril is modeled by a straight thin magnetic tube with the ends frozen in dense plasmas. The density inside and outside the tube varies only along the tube and it is discontinuous at the tube boundary. Making a viable assumption that the tube radius is much smaller than its length, we show that the squares of the frequencies of non-axisymmetric tube oscillations are given by the eigenvalues of the Sturm-Liouville problem for a second-order ordinary differential equation on a finite interval with the zero boundary conditions. For an equilibrium density that is constant outside the tube and piecewise constant inside we derived a simple dispersion equation determining the frequencies of non-axisymmetric oscillations. We carry out a parametric study of this equation both analytically and numerically, restricting our analysis to the first even mode and the first odd mode. In particular, we obtained a criterion that allows to find out if each of these modes is a normal or leaky mode.