# THe-TRAP Project

## Simulations

To understand the experiment and the deviation from the ideal mathematical description better, various simulations are performed by the group. For this there are several tools available such as Matlab, Tosca Vector Fields Opera, SimIon and Comsol Multiphysics. In the following, a brief overview of already examined areas is given.

### Electrostatics

The hyperbolic electrodes of the Penning traps are different from the ideal shape due to manufacturing tolerances, the ability to transport ions through the end cap and the simple inability to make them infinitely large. In order to understand these (and other) effects on the fields in the trap in more detail, simulations were performed with Comsol Multiphysics. Comsol Multiphysics is a simulation tool that uses the finite element method for the simulation of different physical scenarios. For calculating the solution, a grid is placed on the defined geometry and the differential equation for each of the underlying problem is solved at the grid points. An advantage of Comsol Multiphysics is that it can use existing symmetries. Thus in most cases, the electrostatic simulation of THe-Trap can be considered as a rotationally symmetric problem. An example of the THe-Trap trap-geometry with a grid can be seen in Figure 7.1.

The simulated electric potential created with -90V at ring and -45V applied to the
correction electrodes is shown in Figure 7.2. These are typical values for the experiment,
because then the axial frequency of T^{+}, ^{3}He^{+} and ^{12}C^{4+} is close to the 4 MHz chosen
for the axial detection system.