Woltjer's variational principle, II: The case of unbounded domains
Peter M. Laurence, Marco Avellaneda · Geophysical & Astrophysical Fluid Dynamics · 1993
We show for a wide class of unbounded domains, that minimizing the magnetic energy subject to prescribed helicity or relative helicity, does not lead to non-trivial force-free fields. Instead, we show by an explicit construction that all minimizing sequences satisfying the helicity constraint, converge to a vacuum field.