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Violation of adiabaticity in magnetic billiards due to separatrix crossings

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posted on 2015-09-25, 14:57 authored by A.V. Artemyev, Anatoly NeishtadtAnatoly Neishtadt
We consider dynamics of magnetic billiards with curved boundaries and strong inhomogeneous magnetic field. We investigate a violation of adiabaticity of charged particle motion in this system. The destruction of adiabatic invariance is due to the change of type of the particle trajectory: particles can drift along the boundary reflecting from it or rotate around the magnetic field at some distance from the boundary without collisions with it. Trajectories of these two types are demarcated in the phase space by a separatrix. Crossings of the separatrix result in jumps of the adiabatic invariant. We derive an asymptotic formula for such a jump and demonstrate that an accumulation of these jumps leads to the destruction of the adiabatic invariance.


The work of A.V.A. was supported by the Russian Foundation for Basic Research (project 13-01-00251). The work of A.I.N. was supported by the Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools (project no. NSh-2964.2014.1).



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  • Mathematical Sciences

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ARTEMYEV, A.V. and NEISHTADT, A., 2015. Violation of adiabaticity in magnetic billiards due to separatrix crossings. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25, (083109).


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This work is made available according to the conditions of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/

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This paper was accepted for publication in the journal, Chaos: An Interdisciplinary Journal of Nonlinear Science and the definitive published version is available at:http://dx.doi.org/10.1063/1.4928473




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