The existence of a phase transition as a function of the Mathieu parameters
a,q was a point of dispute among various research groups.[4,21] As mentioned
in Sec. 
, Hoffnagle, et al., claimed ``reproducible''
order 
chaos transitions for 
and reproducible
chaos 
order transitions for 
. However, Blümel
claims that in region A, ``two-ion crystals are stable until the MI [Mathieu
Instability] is reached.''[4] For a=0, the Mathieu instability
occurs at approximately 
, significantly higher than the transition parameters set
forth by Hoffnagle, et al.
In order to test the stability of undamped
crystals as a function of the Mathieu parameters a and q, several crystals were
formed, allowed to equilibrate, then subjected--- in the absence of
damping--- to changes in the Mathieu parameter q.