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 sur face under the influence of a positive magnetic field B. Using Moser's Twis t Theorem and ideas from classical perturbation theory we find sufficient c onditions to perpetually trap the motion of a particle with a sufficient la rge charge in a neighborhood of a level set ui the magnetic field. The cond itions on the level set of the magnetic field that guarantee the trapping a re local and hold near all non-degenerate critical local minima or maxima o f B. Using symplectic reduction we apply the results of our work to certain S-1-invariant magnetic fields on R-3. (C) loot Academic Press.