## 4 Comparison between Wire and Rod Traps
As a result, it was observed that in order to match the potential created by hyperbolic rods, the ideal rod trap needs a factor of 1.01, or about a 1% increase in the voltage; while the wire trap needs a voltage 5.4 times higher for the same. Thus, with a suitably higher voltage, it is possible to match the averaged potential. However, the ideal rod trap and wire traps exhibit maxima and minima over the azimuthal angle corresponding to the position of the rods/wires and the space in between them. These results are depicted in Figure 3b. The effective potential for the different trap configurations as a function of the azimuthal angle at three different radii (from the center of the trap) is shown. These radii are also marked in Figure 3a. At each of these radii, it can be seen that the amplitude of modulations in the wire trap exceeds those in the rod traps. Furthermore, these distortions become more prominent as one goes radially outwards in the case of a cylindrical rod/wire trap. As a consequence of these deviations, the minimum voltage for stable trapping of ions increases for a cylindrical rod trap, and is even further increased for a wire trap. In order to estimate the influence of the deviations from the ideal hyperbolic potential on the temperature of ions in the trap when they encounter a neutral collision partner, a Monte-Carlo buffer gas simulation for all three trap configurations was performed. The voltages used are the same as the ones previously used to match the potential landscape of a hyperbolic trap with 50 V rf amplitude. These simulated, matched voltages are used to calculate the electric field vectors, which are then loaded into a home-built script. Subsequently, the ion trajectories are calculated, and a classical, hard-sphere-based collision model is used to simulate the collisions with a buffer gas. For details on the Molecular Dynamics simulations, see Appendix B. In our case, we investigate the thermalization of OH\({}^{-}\) ions with a room-temperature helium buffer gas. The mean speed of the ions is obtained via the Molecular Dynamics (MD) simulations. The resultant energy distribution is demonstrated in Figure 4. The temperature of the ion ensemble \(T\) is calculated from the ions' mean speed (\(\bar{v}\)) as  
\[T=\frac{\pi m\bar{v}^{2}}{8k_{\mathrm{B}}}, \tag{3}\]  
where \(k_{\mathrm{B}}\) is the Boltzmann constant (We hereby use Equation (3) to define the notion of temperature, as well as in case of the emerging nonthermal distributions.). In all three cases, a temperature of 366 K was obtained, with the deviations between the traps being \(<1\) K. The insignificant deviation in the temperature between the different types of traps can be explained via the mean radial extension of ions in the trap which, in the simulations, is 0.24\(\cdot r_{0}\) (also depicted in Figure 3a). This means that the ions primarily explore the innermost region of the trap, and spend only a little time in the outer region of the trap, where the modulations in the effective potential are relatively higher. In Figure 4, the dashed black line represents an analytical Maxwell-Boltzmann distribution at 366 K [36]. Furthermore, it can be inferred that the ions energy distribution is not perfectly described by a Maxwell-Boltzmann distribution and exhibits a nonthermal behavior. The simulated temperature is significantly higher than the temperature of the buffer gas at 293 K. This effect is dependent on the multipole order and is well-investigated in previous works [37], amounting it to the collision of ions in the micromotion-dominated region of the rf trap. In view of the above results, it can be assumed that the main heating mechanism is the micromotion-dominated rf heating which causes the ions to gain additional energy when colliding in the rf field. In the case of thermalization of ions with a neutral buffer gas at room temperature, the deviations prevalent in the rod or wire trap from the ideal hyperbolic potential can be neglected.