  This paper presents an analysis of the motion of an impurity ion in a
nanometer scale $^4$He cluster. Due to induction forces, ions are strongly
localized near the center of the cluster, with a root mean squared thermal
displacements of only a few \AA. The trapping potential is found to be nearly
harmonic, with a frequency of 2.3(1.0) GHz for a positive (negative) ion in a
He cluster of radius 5 nm. The anharmonicity is small and positive (energy
increases slightly faster than linear with quantum number). It is suggested
that by using frequency sweep microwave radiation, it should be possible to
drive the ion center of mass motion up to high quantum numbers, allowing the
study of the critical velocity as a function of cluster size.
