Zeeman Spectroscopy in Penning Traps

Penning traps are the instruments of choice to determine the magnetic moments of long lived or stable charged particles. The virtual absence of collisions with background molecules when working in ultra-high vacuum, the small volume which the trapped particles occupy at low kinetic energies, and the extremely long observation and coherence times allow for very high precision in Zeeman spectroscopy. When applied to singly ionized multielectron atoms the experiments serve for tests of atomic structure calculations. The magnetic moments in few-electron systems such as hydrogen-or lithium-like highly charged ions can be calculated with remarkable precision in the frame of bound-state quantum electrodynamics. The results not only test corresponding calculations but also have impact on fundamental particle properties and fundamental constants. The chapter summarizes results obtained in recent years on various low- and highly charged systems.