## Prominence oscillations and stability## Communicating the distant photospheric boundary
The photosphere provides an important boundary condition for
prominence support. The conservation of photospheric 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 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 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 is comparable to or greater than the oscillation period. Also, forced oscillations can only be significant for rather precisely matched values of and the driving period.
## Contents- 1. Introduction
- 2. Magnetic field of a current distribution
- 3. A dynamical Kuperus-Raadu model for prominences
- 4. Solving the equation of motion
- 5. The case of free oscillations
- 6. The case of forced oscillations
- 7. Discussion
- 8. Summary
- Acknowledgements
- Appendix
- Appendix A: magnetic field of an infinite straight wire current in vacuum
- Appendix B: on solving the equation of motion
- B.1. Linearizing the equation of motion
- B.2. On the Laplace transform of the linearized equation of motion
- B.3. Solution of the linearized equation of motion
- Appendix C: on the Cauchy decomposition of meromorphic functions
- Appendix D: the CONTOUR code
- References
© European Southern Observatory (ESO) 1997 Online publication: May 26, 1998 |