Stability analysis of a charged particle subject to two non-stationary currents

We study the non relativistic motions of a charged particle in the electromagnetic field generated by two parallel electrically neutral vertical wires carrying time depends currents. Under quantitative conditions on the currents we prove the existence of a vertical strip of stable motions of the particle. The stable strip is contained in the plane of the two wires and the stability is understood in a stronger sense than the isoenergetic stability of Hamiltonian systems. Actually, also variations of the integral given by the linear momentum will be allowed.