The effect of line tying on Parker's instability

Abstract

We consider the effect of line tying on the magnetic Rayleigh-Taylor or Parker instability. We find that stabilization occurs if the field lines are sufficiently short that the Alfvén travel time between the boundaries is less than 2π times the instability growth time in an unbounded medium. In a magnetically dominated system, the critical field line length scales linearly with magnetic field strength. This criterion may be relevant to the stabilization of solar prominences.