  Fast beam collinear laser spectroscopy is the established method to
investigate nuclear ground state properties such as the spin, the
electromagnetic moments, and the charge radius of exotic nuclei. These are
extracted with high precision from atomic observables, i.e., the hyperfine
splitting and its the isotope shift, which becomes possible due to a large
reduction of the Doppler broadening by compressing the velocity width of the
ion beam through electrostatic acceleration. With the advancement of the
experimental methods and applied devices, e.g., to measure and stabilize the
laser frequency, the acceleration potential became the dominant systematic
uncertainty contribution. To overcome this, we present a custom-built
high-voltage divider, which was developed and tested at the German metrology
institute (PTB), and a feedback loop that enabled collinear laser spectroscopy
to be performed at a 100-kHz level. Furthermore, we describe the impact of
field penetration into the laser-ion-interaction region. This strongly affects
the determined isotope shifts and hyperfine splittings, if Doppler tuning is
applied, i.e., the ion beam energy is altered instead of scanning the laser
frequency. Using different laser frequencies that were referenced to a
frequency comb, the field penetration was extracted laser spectroscopically.
This allowed us to define an effective scanning potential to still apply the
faster and easier Doppler tuning without introducing systematic deviations.
