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Abstract
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We consider a class of magnetic fields defined over the interior of a manifold
which
go to infinity at its boundary and whose direction near the boundary of
is controlled by
a closed 1-form
.
We are able to show that charged particles in the interior of
under
the influence of such fields can only escape the manifold through the zero locus of
. 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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Keywords
magnetic confinement, toroidal domains, completeness,
magnetic flow, manifolds with boundary
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Mathematical Subject Classification 2010
Primary: 53D25, 70H05, 78A35
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Milestones
Received: 28 August 2018
Revised: 7 January 2019
Accepted: 1 May 2019
Published: 12 February 2020
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