Prominence oscillations and stability

The photosphere provides an important boundary condition for prominence support. The conservation of pho-tospheric flux (sometimes called line tying) sets a serious constraint on the evolution of coronal magnetic fields. This boundary condition can only be communicated to the prominence by Alfvén and magneto-acoustic waves. As a result, the boundary condition as experienced by the prominence at height h lags behind a time h/v A (v A : Alfvénspeed) as compared to the instantaneous situation at the location of the photosphere. In this paper I study vertical oscillations and stability of prominences, taking retardation effects into account. An equation of motion for a Kuperus-Raadu prominence is derived, describing the prominence as a line current and the photosphere as a perfectly conducting plate. Solving this equation of motion implies solving the full time-dependent Maxwell equations, thus guaranteeing a realistic field evolution under the assumption of photospheric line tying. In terms of the currents that flow, such a description is equivalent to the corresponding MHD picture. The results indicate that the travel time h/v A is an important parameter of the system as it influences the decay or growth times of prominence oscillations greatly. A new kind of instability is found, whereby the prominence experiences oscillations growing in time, even in the nonlinear regime. This instability occurs when the travel time h/v A is comparable to or greater than the oscillation period. Also, forced oscillations can only be significant for rather precisely matched values of h/v A and the driving period.