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Orientation of Two-Ion Crystals

In most cases, the orientation of a two-ion crystal in stability region A can be explained by a simple ``pseudopotential'' model which considers the relative strengths of the axial and radial secular potential wells.gif Recall that the radial and axial Mathieu parameters are related by:

and that the secular frequencies are approximated by:gif

Comparing the radial and axial secular frequencies leads to:

Thus, for , the radial secular frequency will be less than the axial secular frequency, implying a steeper time-averaged potential on the z-axis than on the radial axis. Consequently, the two-ion crystal will condense on the z=0 plane. For , the time-averaged radial potential is steeper than the time-averaged axial potential, and the two-ion crystal will lie on the z-axis.[4]


Wolfgang Christian
Fri May 12 10:36:01 EDT 1995