On perturbations of magnetic field configurations

The behavior of stationary equilibrium solutions to the MHD equations possessing a well-defined symmetry to perturbations lacking that symmetry is explored. Two distinct situations of astrophysical interest are considered: solutions of the magnetostatic equations and of the magnetoconvection equations. The results show that in these cases changes in solution topology are not accessible to small-parameter (epsilon) expansions, so that such expansions do not describe the full range of behavior. In particular, finite-amplitude perturbations can lead to new stationary solutions possessing different symmetries from the initial solution.