Nonlinear magnetohydrodynamic evolution of line-tied coronal loops

Simulations of the nonlinear evolution of the m = 1 kink mode in magnetic flux tubes with line-tying boundary conditions are presented, The initial structure of the flux tube is intended to model a solar coronal loop that either has evolved quasi-statically through sequences of equilibria with increasing twist due to the application of localized photospheric vortex flows or has emerged with a net current through the photosphere. It is well known that when the twist exceeds a critical value that depends on its radial profile and on the loop length, the loop becomes kink unstable, The nonlinear evolution of the instability is followed using a three-dimensional MHD code in cylindrical geometry, in different types of magnetic field configurations, with the common property that the current is confined within the same radius, so that the magnetic field is potential in the external regions. The differences reside in the net axial current carried by the structure, ranging from a vanishing current (corresponding to an outer axial potential field) to a high current (corresponding to an outer almost azimuthal potential field). It is shown that, during the nonlinear phase of the instability, loops develop current sheets and, consequently, their evolution becomes resistive with the occurrence of magnetic reconnection, The dependence of the topology of the currents at saturation on the initial magnetic structure, the details of the reconnection phenomenon, and the resistive dissipation mechanism are examined. Finally, the impact of the results on the understanding of coronal activity is discussed.