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Remarkable charged particle dynamics near magnetic field null lines

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journal contribution
posted on 09.05.2019, 09:31 by Anatoly NeishtadtAnatoly Neishtadt, A.V. Artemyev, Dmitry Turaev
The study of charged-particle motion in electromagnetic fields is a rich source of problems, models, and new phenomena for nonlinear dynamics. The case of a strong magnetic field is well studied in the framework of a guiding center theory, which is based on conservation of an adiabatic invariant – the magnetic moment. This theory ceases to work near a line on which the magnetic field vanishes – the magnetic field null line. In this paper we show that the existence of these lines leads to remarkable phenomena which are new both for nonlinear dynamics in general and for the theory of charged-particle motion. We consider the planar motion of a charged particle in a strong stationary perpendicular magnetic field with a null line and a strong electric field. We show that particle dynamics switch between a slow guiding center motion and the fast traverse along a segment of the magnetic field null line. This segment is the same (in the principal approximation) for all particles with the same total energy. During the phase of a guiding center motion, the magnetic moment of particle’s Larmor rotation stays approximately constant, i.e., it is an adiabatic invariant. However, upon each traversing of the null-line, the magnetic moment changes in a random fashion, causing the particle choose a new trajectory of the guiding center motion. This results in a stationary distribution of the magnetic moment, which only depends on the particle’s total energy. The jumps in the adiabatic invariant are described by Painleve II equation.


EPSRC (grant EP/P026001/1, DT), RSF (grant 19-11-00280, DT) and the Leverhulme Trust (grant RPG-2018-143, AN).



  • Science


  • Mathematical Sciences

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NEISHTADT, A., ARTEMYEV, A.V. and TURAEV, D., 2019. Remarkable charged particle dynamics near magnetic field null lines. Chaos, 29 (5), 051104.


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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in NEISHTADT, A., ARTEMYEV, A.V. and TURAEV, D., 2019. Remarkable charged particle dynamics near magnetic field null lines. Chaos, 29 (5), 051104 and may be found at https://doi.org/10.1063/1.5097838.