  We have studied the dynamics of one and two laser-cooled trapped
$^{40}$Ca$^+$ ions by applying electric fields of different nature along the
axial direction of the trap, namely, driving the motion with a harmonic dipolar
field, or with white noise. These two types of driving induce distinct motional
states of the axial modes; a coherent oscillation with the dipolar field, or an
enhanced Brownian motion due to an additional contribution to the heating rate
from the electric noise. In both scenarios, the sensitivity of an isolated ion
and a laser-cooled two-ion crystal has been evaluated and compared. The
analysis and understanding of this dynamics is important towards the
implementation of a novel Penning-trap mass-spectroscopy technique based on
optical detection, aiming at improving precision and sensitivity.
