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.'' 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.