The Gamma Factory (GF) initiative aims at construction of a unique experimental tool exploiting resonant interaction of light with ultra-relativistic partially stripped ions (PSI) stored in circular accelerators at CERN. Resonant excitation of high-energy transitions of the ions is achieved through Doppler-boosting (by twice the Larmor factor; from hundred to several thousand times) of light energy. In order to efficiently excite the ions, and hence generate intense beams of scattered/fluorescent photons, a detailed knowledge of the ions energy structure and dynamics of optical pumping is required. Spectroscopic properties of PSI selected for the GF operation, as well as their optical pumping schemes are investigated. Two regimes of the light-ion interaction are identified, leading to different dynamics of the pumping process. The efficiency of the light-ion interaction as well as the number of photons emitted from a single ion bunch is estimated, both analytically and numerically, for three ions considered for the GF, i.e.~Li-like ${}^{208}_{phantom{0}82}$Pb$^{79+}$, Li-like ${}^{40}_{20}$Ca$^{17+}$, and H-like ${}^{208}_{phantom{0}82}$Pb$^{81+}$.
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