Finite deformation in ideal magnetohydrodynamics

Aims: In this paper we investigate the finite deformation of magnetic fields that can enable one to find complex analytical magnetohydrostatic (MHS) equilibria. These can be used as input to non-linear simulations. Methods: In order to find analytical equilibria, one normally has to consider simplifications or exploit a particular symmetry. Even with these measures, however, the desired equilibrium is often out of analytical reach. Here we describe a method that can work when traditional methods fail. It is based on the smooth deformation of simple magnetic fields into complex ones. Results: Examples are given, to demonstrate the method, that are of practical importance in coronal physics. This technique will prove useful in setting up the initial conditions of non-linear magnetohydrodynamic simulations.