Vol. 304, No. 2, 2020

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The Hamiltonian dynamics of magnetic confinement in toroidal domains

Gabriel Martins

Vol. 304 (2020), No. 2, 613–628

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 σ Γ(TM). 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 σ. 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.

magnetic confinement, toroidal domains, completeness, magnetic flow, manifolds with boundary
Mathematical Subject Classification 2010
Primary: 53D25, 70H05, 78A35
Received: 28 August 2018
Revised: 7 January 2019
Accepted: 1 May 2019
Published: 12 February 2020
Gabriel Martins
Department of Mathematics and Statistics
Sacramento State University
Sacramento, CA
United States