Title: The Hamiltonian Dynamics of Magnetic Confinement in Toroidal Domains,
Abstract: We consider a class of magnetic fields defined over the interior of a
manifold $M$ which go to infinity at its boundary and whose direction near the
boundary of $M$ is controlled by a closed 1-form $\sigma_\infty \in
\Gamma(T^*\partial M)$. We are able to show that charged particles in the
interior of $M$ under the influence of such fields can only escape the manifold
through the zero locus of $\sigma_\infty$. In particular in the case where the
1-form is nowhere vanishing we conclude that the particles become confined to
its interior for all time.