PERIODIC MOTION OF ATOMS NEAR A CHARGED WIRE

We study the classical motion of an atom in the vicinity of an infinit e straight wire which carries an oscillating uniform charge. This syst em has been proposed as a mechanism for trapping cold neutral atoms. T he parameters of the problem are the magnitude Q and frequency of osci llation omega of the charge, the mass M and polarizability alpha of th e atom, and the angular momentum L of the atom about the wire. For ome ga not equal 0 and 2 alpha MQ(2) greater than, but close to, L(2) we p rove that the atom's radial motion is periodic (with period 2 pi/omega ), and that the atom moves in a helical path around the wire. For 2 al pha MQ(2) less than or equal to L(2) we prove that the atom must eithe r collide with the wire or else escape to infinity in the radial direc tion.