We study the motion of a charged particle under the action of a magnetic eld with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance r from the symmetry axis of the form 1+A|r|^{-gamma} as r oinfty, with A eq 0 and gamma>1. With perturbative-variational techniques, we can prove the existence of infinitely many trajectories whose projection on a plane orthogonal to the direction of the eld describe bounded curves given by the superposition of two motions: a rotation with constant angular speed at a unit distance about a point which moves along a circumference of large radius and with a slow angular speed, whose values are suitably related to each other. This problem has some interest also in the context of planar curves with prescribed curvature.

On the dynamics of a charged particle in magnetic fields with cylindrical symmetry

Caldiroli, Paolo;Cora, Gabriele
2019-01-01

Abstract

We study the motion of a charged particle under the action of a magnetic eld with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance r from the symmetry axis of the form 1+A|r|^{-gamma} as r oinfty, with A eq 0 and gamma>1. With perturbative-variational techniques, we can prove the existence of infinitely many trajectories whose projection on a plane orthogonal to the direction of the eld describe bounded curves given by the superposition of two motions: a rotation with constant angular speed at a unit distance about a point which moves along a circumference of large radius and with a slow angular speed, whose values are suitably related to each other. This problem has some interest also in the context of planar curves with prescribed curvature.
2019
267
3952
3976
https://arxiv.org/abs/1902.00513
Newton-Lorentz equation, magnetic field, motion of charged particles, curves in Euclidean plane, prescribed curvature
Caldiroli, Paolo; Cora, Gabriele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1700816
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