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

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

1999-08-06

arxiv.org/abs/math-ph/9908010v1

Physics

Mathematical Physics

Scientific paper

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 S^1 - invariant magnetic fields on R^3.

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