The Motion of a Charged Particle on a Riemannian Surface Under a Non-Zero Magnetic Field
Mathematical Physics
2007-05-23 v1 math.MP
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 S^1 - invariant magnetic fields on R^3.
Keywords
Cite
@article{arxiv.math-ph/9908010,
title = {The Motion of a Charged Particle on a Riemannian Surface Under a Non-Zero Magnetic Field},
author = {Cesar Castilho},
journal= {arXiv preprint arXiv:math-ph/9908010},
year = {2007}
}