Can a local repulsive potential trap an electron?
N. Berglund, Alex Hansen, E. H. Hauge, J. Piasecki
Phys. Rev. Letters 77, 2149-2152 (1996)We study the classical dynamics of a charged particle in two dimensions, under the influence of a perpendicular magnetic and an in-plane electric field. We prove the surprising fact that there is a finite region in phase space that corresponds to the otherwise drifting particle being trapped by a local repulsive potential. Our result is a direct consequence of KAM-theory and, in particular, of Moser's theorem. We illustrate it by numerical phase portraits and by an analytic approximation to invariant curves.
Key words: billiards, KAM-theory, chaotic scattering, Lorentz model
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