The Tritium-Helium-Trap (THe-Trap) is a Penning-trap mass spectrometer dedicated to measure the mass ratio of tritium and helium-3 with a relative precision of 10-11. To reach this precision, the properties of the Penning-trap must be understood very well. Geometrical deviations from the ideal case cause higher-order components in the electrostatic potential. Extended simulations have been carried out to investigate first the dependence of the simulation tool Comsol Multiphysics on the resolution chosen and then to quantify the higher-order terms. The simulations were successful and in good agreement with the experimental observations. It was also possible to simulate the image charge effect. The simulated image charge effect confirms the experimental value. Similar investigations were performed to estimate the influence of the experimental setup on the magnetic field. The influence of ferromagnetic materials was determined reliably. The final part of this thesis is the characterization of the external Penning-ion source. For this, a new Faraday cup was designed and implemented. The new device can measure an ion beam from the Penning-ion source and helps to improve their operating parameters
