Motions of a charged particle in the electromagnetic field induced by a non-stationary current

In this paper we study the non-relativistic dynamic of a charged particle in the electromagnetic field induced by a periodically time dependent current J along an infinitely long and infinitely thin straight wire. The motions are described by the Lorentz-Newton equation, in which the electromagnetic field is obtained by solving the Maxwell's equations with the current distribution (J) over right arrow as data. We prove that many features of the integrable time independent case are preserved. More precisely, introducing cylindrical coordinates, we prove the existence of (non-resonant) radially periodic motions that are also of twist type. In particular, these solutions are Lyapunov stable and accumulated by subharmonic and quasiperiodic motions. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the non-relativistic dynamics of a charged particle in a periodically time dependent electromagnetic field induced by a current along an infinitely long straight wire. The study shows the existence of radially periodic motions of twist type, which are Lyapunov stable and accumulated by subharmonic and quasiperiodic motions. Features of the integrable time independent case are preserved in this scenario.