The nonlinear MHD evolution of axisymmetric line-tied loops in the solar corona

The nonlinear evolution of the m = 0 sausage mode in coronal loops (Gold and Hoyle 1960 Mon. Not. R. Astron. Soc. 120 89) is investigated using numerical simulations. For the ideal line-tied case the growth rate of the linear phase of the instability is successfully reproduced, and it is found that the nonlinear development leads to the formation of a new equilibrium with an embedded, curved, current concentration ( not, however, a current sheet). This new equilibrium is not symmetric about the centre of the loop. For periodic boundary conditions a similar evolution is found, but with the final equilibrium being symmetric in which a straight, radial current concentration (possibly a current sheet) is embedded. In the line-tied resistive case the field lines reconnect, leading to the ejection of a plasmoid and relaxation to a (different) equilibrium.