  In this paper we deal with the existence, regularity and Beltrami field
property of magnetic energy minimisers under a helicity constraint. We in
particular tackle the problem of characterising local as well as global
minimisers of the given minimisation problem. Further we generalise Arnold's
results concerning the problem of finding the minimum magnetic energy in an
orbit of the group of volume-preserving diffeomorphisms to the setting of
abstract manifolds with boundary.
