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Abstract

This PhD thesis presents the development of the setup and first measurements towards the determination of the g-factor of an electron bound in hydrogen- and lithium-like medium-heavy ions. Bound-state quantum electrodynamic calculations can be tested by high-precision g-factor measurements. The measurements are done in a triple Penning trap setup. During this PhD thesis highly charged ions up to ²⁸Si¹³⁺ are produced for the first time in a purpose-built electron-beam-ion-source/trap. To determine the g-factor the free cyclotron frequency and the Larmor frequency are required. The first one can be calculated from the ion’s three eigenfrequencies, which are measured in the so-called precision trap. Since the ion should not be lost during the measurements, the eigenfrequencies are measured non-destructively by coupling to a radiofrequency tank circuit. For the free cyclotron frequency a relative uncertainty of a few 10⁻⁹ has been achieved. To determine the Larmor frequency the electron’s spin direction in the magnetic field has to be known. The spin direction can be detected in the so-called analysis trap using the continuous Stern-Gerlach effect. Therefore a highly stable axial oscillation of the ion is required. To achieve this as well as high-precision measurements in the precision trap, both traps are characterized with regard to their electrical and magnetic properties during this theses.