Extreme field calculations for Penning ion traps and corresponding strong laser field scenarios

The extreme forces of highly charged ions and their trapping within high-precision experimental devices allow for challenging fundamental theories in yet unexplored territory. Here we focus on the theoretical side employing ab initio fully relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) methods to precisely calculate the bound-state energies of complex atoms and ions, as well as on presenting state-of-the-art high-precision g-factor calculations. In combination with similarly accurate experiments, one can competitively determine fundamental constants like the masses of the neutrino and the electron as well as setting new limits for physics beyond the standard model. Scenarios involving extreme laser pulses hold comparable potential but still require especially advances in the precision of the associated experiments.