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

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 sympletic reduction we apply the results of our work to certain S-invariant magnetic fields on R.