  An atomic transition can be addressed by a single tooth of an optical
frequency comb if the excited state lifetime ($\tau$) is significantly longer
than the pulse repetition period ($T_\mathrm{r}$). In the crossover regime
between fully-resolved and unresolved comb teeth ($\tau \lessapprox
T_\mathrm{r}$), we observe Doppler cooling of a pre-cooled trapped atomic ion
by a single tooth of a frequency-doubled optical frequency comb. We find that
for initially hot ions, a multi-tooth effect gives rise to lasing of the ion's
harmonic motion in the trap, verified by acoustic injection locking. The gain
saturation of this phonon laser action leads to a comb of steady-state
oscillation amplitudes, allowing hot ions to be loaded directly into the trap
and laser cooled to crystallization despite the presence of hundreds of
blue-detuned teeth.
