Laser spectroscopy methods for probing highly charged ions at GSI

We describe two opposite and partly complementary experimental approaches for performing high-precision laser spectroscopy of dipole-forbidden transitions in highly charged ions. We report on the wavelength determination of the ground state hyperfine transitions in hydrogen-like and lithium-like bismuth ions confined in the experimental storage ring at GSI. Direct comparison of the experimental results with theoretical predictions reveals an agreement of the specific hyperfine-structure splitting difference $Delta ^{prime }E$ within the 1- σ confidence interval of the experimental value. Additionally, we discuss an experimental strategy based on ion manipulation and cooling in a cylindrical open-endcap Penning trap to further increase the precision of the previous measurement. Trapping and laser cooling of external produced singly charged magnesium ions is demonstrated. This represents a first step towards sympathetic cooling of simultaneously confined ion species in order to perform laser spectroscopy measurements on highly charged ions nearly at rest. These measurements will offer new prospects in the field of laser-based tests of quantum electrodynamics in strong electric and magnetic fields.