Periodic dynamics in the relativistic regime of an electromagnetic field induced by a time-dependent wire

Abstract

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.