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

✍ Scribed by César Castilho

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 158 KB
Volume: 171
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.2000.3836

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✦ Synopsis

In this paper we study the motion of a charged particle on a Riemmanian 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 sufficient 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 S 1 -invariant magnetic fields on R 3 .

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