  We present a two particle model to explain the mechanism that stabilizes a
bunch of positively charged ions in an "ion trap resonator" [Pedersen etal,
Phys. Rev. Lett. 87 (2001) 055001]. The model decomposes the motion of the two
ions into two mappings for the free motion in different parts of the trap and
one for a compressing momentum kick. The ions' interaction is modelled by a
time delay, which then changes the balance between adjacent momentum kicks.
Through these mappings we identify the microscopic process that is responsible
for synchronization and give the conditions for that regime.
