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Collinear laser spectroscopy has been performed on He-like C$^{4+}$ ionsextracted from an electron beam ion source (EBIS). In order to determine thetransition frequency with the highest-possible accuracy, the lineshape of thefluorescence response function was studied for pulsed and continuous ionextraction modes of the EBIS in order to optimize its symmetry and linewidth.We found that the best signal-to-noise ratio is obtained using the continuousbeam mode for ion extraction. Applying frequency-comb-referenced collinear andanticollinear laser spectroscopy, we achieved a measurement accuracy of betterthan 2\,MHz including statistical and systematic uncertainties. The origin andsize of systematic uncertainties, as well as further applications for otherisotopes and elements are discussed.

Collinear laser spectroscopy of highly charged ions produced with an electron beam ion source