Periodic Motion of Atoms Near a Charged Wire

Abstract

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 ω of the charge, the mass M and polarizability α of the atom, and the angular momentum L of the atom about the wire. For ω ≠ 0 and 2αMQ ² greater than, but close to, L ², we prove that the atom's radial motion is periodic (with period 2π/ω), and that the atom moves in a helical path around the wire. For 2αMQ ² ≤ L ² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.