  In this note, we exhibit a situation where a stationary state of Moffatt's
ideal magnetic relaxation problem is different than the corresponding
force-free $L^2$ energy minimizer of Woltjer's variational principle. Such
examples have been envisioned in Moffatt's seminal work on the subject and
involve divergence free vector fields supported on collections of essentially
linked magnetic tubes. Justification of Moffatt's examples requires the strong
convergence of a minimizing sequence. What is proven in the current note is
that there is a gap between the global minimum ({\em Woltjer's minimizer}) and
the minimum over the weak $L^2$ closure of the class of vector fields obtained
from a topologically non-trivial field by energy-decreasing diffeomorphisms. In
the context of Taylor's conjecture, our result shows that the Woltjer's
minimizer cannot be reached during the viscous MHD relaxation in the perfectly
conducting magneto-fluid if the initial field has a nontrivial topology. The
result also applies beyond Moffatt's relaxation to any other relaxation process
which evolves a divergence free field by means of energy-decreasing
diffeomorphisms, such processes were proposed by Vallis et.al and more recently
by Nishiyama.
