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.
Recall that
the radial and axial Mathieu parameters are related by:
and that the secular frequencies are approximated by:
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]