Periodic dynamics in the relativistic regime of an electromagnetic field induced by a time-dependent wire. (English) Zbl 1519.34034
Summary: We consider the motion of a charged particle under the electromagnetic field generated by an electrically neutral infinite straight wire with a time-periodic oscillating (AC-DC) current. By using global continuation and topological degree, we identify a bi-parametric family of radially periodic motions. The proofs involve some delicate estimations of the induced electromagnetic field, which can be of independent interest.
MSC:
| 34C25 | Periodic solutions to ordinary differential equations |
| 37C60 | Nonautonomous smooth dynamical systems |
| 78A35 | Motion of charged particles |
| 47H11 | Degree theory for nonlinear operators |
Keywords:
Lorentz force equation; electromagnetic field; straight wire; oscillating current; radially periodic solution; global continuation; Bessel functionsReferences:
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