  In this paper we present numerical modeling results for endcap and linear ion
traps, used for experiments at the National Physical Laboratory in the UK and
Innsbruck University respectively. The secular frequencies for Strontium-88 and
Calcium-40 ions were calculated from ion trajectories, simulated using
boundary-element and finite-difference numerical methods. The results were
compared against experimental measurements. Both numerical methods showed high
accuracy with boundary-element method being more accurate. Such simulations can
be useful tools for designing new traps and trap arrays. They can also be used
for obtaining precise trapping parameters for desired ion control when no
analytical approach is possible as well as for investigating the ion heating
rates due to thermal electronic noise.
