  The holy grail of ion-neutral systems is reaching the s-wave scattering
regime. However, most of these systems have a fundamental lower collision
energy limit which is higher than this s-wave regime. This limit arises from
the time-dependant trapping potential of the ion, the Paul trap. In this work,
we studied both theoretically and experimentally, the way the Paul trap
parameters affect the energy distribution of an ion that is immersed in a bath
of ultra-cold atoms. Heating rates and energy distributions of the ion are
calculated for various trap parameters by a molecular dynamics (MD) simulation
that takes into account the attractive atom-ion potential. The deviation of the
energy distribution from a thermal one is discussed. Using the MD simulation,
the heating dynamics for different atom-ion combinations is also investigated.
In addition, we performed measurements of the heating rates of a ground-state
cooled $\ ^{88}$Sr$^+$ ion that is immersed in an ultra-cold cloud of $\
^{87}$Rb atoms, over a wide range of trap parameters, and compare our results
to the MD simulation. Both the simulation and the experiment reveal no
significant change in the heating for different parameters of the trap.
However, in the experiment a slightly higher global heating is observed,
relative to the simulation.
