The Motion of a Charged Particle on a Riemannian Surface Under a Non-Zero Magnetic Field

1999/08/06 by Cesar Castilho, Castilho, Cesar
Mathematics · Physics and Astronomy · #58F05 #58F22 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:58F05 #msc:58F22

paper · pdf · doi:10.48550/arxiv.math-ph/9908010

arxiv created 1999/08/06 · arxiv updated 2009/11/30

Abstract

In this paper we study the motion of a charged particle on a Riemannian surface under the influence of a positive magnetic field B. Using Moser's Twist Theorem and ideas from classical pertubation theory we find sufficient conditions to perpetually trap the motion of a particle with a sufficiently large charge in a neighborhood of a level set of the magnetic field. The conditions on the level set of the magnetic field that guarantee the trapping are local and hold near all non-degenerate critical local minima or maxima of B. Using symplectic reduction we apply the results of our work to certain S¹ - invariant magnetic fields on R³.

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