The first thing to consider with regard to the simulation results is:
are they accurate? Because the equations of motion which govern
the ions' dynamics are nonlinear
, predicting long-term behavior is no simple
matter and assessing accuracy is not a straightforward question of whether
results agree with long-term predictions. Instead, accuracy is
gauged by comparing different algorithms, comparing different compilations
of the same algorithm, and monitoring values, such as energy and momentum,
which should be conserved.
Gear and Verlet algorithms were used to test simulations of the identical systems (i.e., identical initial conditions, temperature, number of ions, mass of ions, etc.). The results (temperature, energy, and final ion positions) of a four million time step simulation of ten ions in a Paul trap agreed to four significant figures. Likewise, the algorithms' results of a sixty-thousand time step simulation of ten ions in a Penning trap were identical to four significant figures.
Another test of the simulation was provided by comparing results generated by different compilations of the same code. The default compilation and the -fast compilation were compared for Gear and Verlet simulations of ten ions in a Penning trap, with identical results to four significant figures. Furthermore, the -fast compilation reduced CPU time by a factor of two to four.
A third test of the simulation's reliability was provided by monitoring energy and momentum. In a Penning trap, for which the potential energy is independent of time, total energy should remain constant. Figure 3 shows conservation of energy in a Penning trap. In a Paul trap, which has an oscillating potential term, energy fluctuates. However, the time average of kinetic, potential, and total energies should be relatively constant for simulations of particles which remain trapped (see Figure 4.).
In both Paul trap and Penning trap simulations, momentum was conserved.
The ions' velocities were initialized such that linear momentum was zero.
At the end of simulations, all components of linear momentum remained
less than .
