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arXiv · 1711.05388

The Hamiltonian Dynamics of Magnetic Confinement in Toroidal Domains

Gabriel Martins
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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.

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BibTeXRIS

Gabriel Martins. 2017-11-15. The Hamiltonian Dynamics of Magnetic Confinement in Toroidal Domains. https://doi.org/10.2140/pjm.2020.304.613

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