  We study higher critical points of the variational functional associated with
a free boundary problem related to plasma confinement. Existence and regularity
of minimizers in elliptic free boundary problems have already been studied
extensively. But because the functionals are not smooth, standard variational
methods cannot be used directly to prove the existence of higher critical
points. Here we find a nontrivial critical point of mountain pass type and
prove many of the same estimates known for minimizers, including Lipschitz
continuity and nondegeneracy. We then show that the free boundary is smooth in
dimension 2 and prove partial regularity in higher dimensions.
