  We analyse the possibility of cooling ions with a single laser beam, due to
the coupling between the three components of their motion induced by the
Coulomb interaction. For this purpose, we numerically study the dynamics of ion
clouds of up to 140 particles, trapped in a linear quadrupole potential and
cooled with a laser beam propagating in the radial plane. We use Molecular
Dynamics simulations and model the laser cooling by a stochastic process. For
each component of the motion, we systematically study the dependence of the
temperature with the anisotropy of the trapping potential. Results obtained
using the full radio-frequency (rf) potential are compared to those of the
corresponding pseudo-potential. In the rf case, the rotation symmetry of the
potential has to be broken to keep ions inside the trap. Then, as for the
pseudo-potential case, we show that the efficiency of the Coulomb coupling to
thermalize the components of motion depends on the geometrical configuration of
the cloud. Coulomb coupling appears to be not efficient when the ions organise
as a line or a pancake and the three components of motion reach the same
temperature only if the cloud extends in three dimensions.
