  We investigate the existence of magnetohydrostatic equilibria for
topologically complex magnetic fields. The approach employed is to perform
ideal numerical relaxation experiments. We use a newly-developed Lagrangian
relaxation scheme that exactly preserves the magnetic field topology during the
relaxation. Our configurations include both twisted and sheared fields, of
which some fall into the category for which Parker (1972) predicted no
force-free equilibrium. The first class of field considered contains no
magnetic null points, and field lines connect between two perfectly conducting
plates. In these cases we observe only resolved current layers of finite
thickness. In further numerical experiments we confirm that magnetic null
points are loci of singular currents.
