Nonlinear development of the kink instability in coronal flux tubes

Solar prominences and flares are believed to be caused by rapid release of magnetic energy stored in coronal magnetic fields. Recent studies of the linear phase of ideal MHD instabilities has shown that energy release is slow and weak, so it is therefore important to study the nonlinear phase to see if this provides a mechanism for significant energy release. In this paper we describe a Lagrangian numerical scheme for simulating nonlinear evolution of ideal MHD equilibria and apply it to an unstable finite Gold-Hoyle flux tube, line-tied to perfectly conducting endplates. The ensuing kink instability develops considerably faster than linear theory would predict, and eventually (over typically 100 Alfvén time scales) a new kinked equilibrium is attained, in which current sheets appear to be present. Little magnetic energy is lost in the ideal MHD phase, but resistive instabilities in the current sheets could lead to much more explosive energy release. Numerical studies of nonlinear interactions indicate that growth of the unstable kink mode is suppressed by the presence of other modes, which offers a possible explanation of the observed longevity of coronal loops