TY - JOUR

T1 - Remarkable charged particle dynamics near magnetic field null lines

AU - Neishtadt, Anatoly

AU - Artemyev, Anton

AU - Turaev, Dmitry

N1 - Funding Information:
This research was supported by EPSRC (Grant No. EP/P0260 01/1) and RSF (Grant No. 19-11-00280) to D.T. and the Leverhulme Trust (Grant No. RPG-2018-143) to A.N.
Publisher Copyright:
© 2019 Author(s).

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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 to 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 Painlevé II equation.

AB - 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 to 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 Painlevé II equation.

UR - http://www.scopus.com/inward/record.url?scp=85065724861&partnerID=8YFLogxK

U2 - 10.1063/1.5097838

DO - 10.1063/1.5097838

M3 - Article

AN - SCOPUS:85065724861

SN - 1054-1500

VL - 29

JO - Chaos

JF - Chaos

IS - 5

M1 - 051104

ER -