Contributions to fundamental physics and constants using Penning traps

In Penning traps charged particles are subject to a strong axial magnetic field and a weak electrostatic quadrupole field, which makes the particles moving with three independent frequencies. The quadrupole field can be generated either by using hyperboloidal or a set of cylindrical electrodes. A cyclotron frequency measurement gives access to an accurate value of the ion mass. This can be performed either by the determination of images currents in a ring electrode or by using a time-of-flight method after excitation of the ion motion. In 1970 Hans Dehmelt et al. measured the g-factors of a free electron and positron as well as their masses using a Penning trap. This lead to a shared Nobel Prize in Physics in 1989. These measurements were the overture to a large number of fundamental experiments. The experimental g-factor was compared to the value predicted by QED, which indirectly gives the fine structure constant alpha at an uncertainty of 4 ppb. The obvious question is to what extent the g-factor is changed when the electron is bound in a hydrogen-like ion. To obtain an answer a dedicated set of traps was constructed by the GSI-Mainz collaboration. Recently, a different way of calculating a was proposed. It is based on laser photon recoil experiments and may result in an even a more accurate value of alpha that is independent of QED. This alpha method requires very accurate mass values of the electron, the proton and Cs-133. Precise mass and g-factor measurements offer CPT-tests. Accurate mass values of H-3 and He-3, i.e. the Q-value of the H-3 decay, may enter in future experiments on the beta spectrum of H-3 searching for a finite rest mass of the electron antineutrino. The mass difference between Ge-76 and Se-76 is indispensable in the analysis of the data searching for the standard model violating neutrinoless double beta decay of Ge-76. Accurate masses of Si-28 and Au-197 are needed in efforts for a new definition of the kilogram based on atomic quantities.