Periodic Motion of Atoms Near a Charged Wire

We study the classical motion of an atom in the vicinity of an infinite straight wire which carries an oscillating uniform charge. This system has been proposed as a mechanism for trapping cold neutral atoms. The parameters of the problem are the magnitude Q and frequency of oscillation of the charge, the mass M and polarizability of the atom, and the angular momentum L of the atom about the wire. For 0 and 2MQ² greater than, but close to, L², we prove that the atom's radial motion is periodic (with period 2/), and that the atom moves in a helical path around the wire. For 2MQ² L² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.