Motions of a charged particle in the electromagnetic field induced by a non-stationary current
| Autor: | Manuel J. Castillo Garzón, Stefano Marò |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Lyapunov function
Electromagnetic field Integrable system FOS: Physical sciences Dynamical Systems (math.DS) Lorentz force Maxwell's equations Non-steady current Periodic solutions of twist type Singular potentials Stability 01 natural sciences 010305 fluids & plasmas symbols.namesake 0103 physical sciences FOS: Mathematics Cylindrical coordinate system Mathematics - Dynamical Systems 010306 general physics Mathematical Physics Physics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Condensed Matter Physics Charged particle Classical mechanics Quasiperiodic function symbols |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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