Laser cooling of a single trapped ion in a Paul trap is discussed theo
retically in the Lamb-Dicke limit, with full consideration of the time
dependence of the trapping potential. Resulting mean kinetic energies
are defined as time averages over one period of the micromotion and a
re compared with final temperatures expected from the laser cooling tr
eatment with harmonic traps. For laser-atom detunings close to the mic
romotion frequency the results differ significantly from those expecte
d for a harmonic trap potential. A physical interpretation is given an
d simple formulas are derived for the strong confinement case.