Motions of a charged particle in the electromagnetic field induced by a non-stationary current
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Elsevier
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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 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
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 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
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M.G. is partially supported by MINECO and ERDF project MTM2017-82348-C2-1-P. S.M. is partially supported by the University of Pisa project PRA 2020-82. This research is also part of S.M. activity within the UMI-DinAmicI community (www.dinamici.org) and the GNFM-INdAM, Italy.
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